math library (which is itself based on the math lib from FreeBSD).
-Erik
-/* mconf.h
- * <math.h>
- * ISO/IEC 9899:1999 -- Programming Languages C: 7.12 Mathematics
- * Derived from the Cephes Math Library Release 2.3
- * Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
- *
- *
- * DESCRIPTION:
- *
- * The file also includes a conditional assembly definition
- * for the type of computer arithmetic (IEEE, DEC, Motorola
- * IEEE, or UNKnown).
- *
- * For Digital Equipment PDP-11 and VAX computers, certain
- * IBM systems, and others that use numbers with a 56-bit
- * significand, the symbol DEC should be defined. In this
- * mode, most floating point constants are given as arrays
- * of octal integers to eliminate decimal to binary conversion
- * errors that might be introduced by the compiler.
- *
- * For little-endian computers, such as IBM PC, that follow the
- * IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE
- * Std 754-1985), the symbol IBMPC should be defined. These
- * numbers have 53-bit significands. In this mode, constants
- * are provided as arrays of hexadecimal 16 bit integers.
- *
- * Big-endian IEEE format is denoted MIEEE. On some RISC
- * systems such as Sun SPARC, double precision constants
- * must be stored on 8-byte address boundaries. Since integer
- * arrays may be aligned differently, the MIEEE configuration
- * may fail on such machines.
- *
- * To accommodate other types of computer arithmetic, all
- * constants are also provided in a normal decimal radix
- * which one can hope are correctly converted to a suitable
- * format by the available C language compiler. To invoke
- * this mode, define the symbol UNK.
- *
- * An important difference among these modes is a predefined
- * set of machine arithmetic constants for each. The numbers
- * MACHEP (the machine roundoff error), MAXNUM (largest number
- * represented), and several other parameters are preset by
- * the configuration symbol. Check the file const.c to
- * ensure that these values are correct for your computer.
- *
- * Configurations NANS, INFINITIES, MINUSZERO, and DENORMAL
- * may fail on many systems. Verify that they are supposed
- * to work on your computer.
+/* Declarations for math functions.
+ Copyright (C) 1991,92,93,95,96,97,98,99,2001 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, write to the Free
+ Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+ 02111-1307 USA. */
+
+/*
+ * ISO C99 Standard: 7.12 Mathematics <math.h>
*/
-
#ifndef _MATH_H
#define _MATH_H 1
#include <features.h>
-#include <bits/huge_val.h>
-
-/* Type of computer arithmetic */
-
-/* PDP-11, Pro350, VAX:
- */
-/* #define DEC 1 */
-
-/* Intel IEEE, low order words come first:
- */
-/* #define IBMPC 1 */
-
-/* Motorola IEEE, high order words come first
- * (Sun 680x0 workstation):
- */
-/* #define MIEEE 1 */
-
-/* UNKnown arithmetic, invokes coefficients given in
- * normal decimal format. Beware of range boundary
- * problems (MACHEP, MAXLOG, etc. in const.c) and
- * roundoff problems in pow.c:
- * (Sun SPARCstation)
- */
-#define UNK 1
+__BEGIN_DECLS
-/* Define if the `long double' type works. */
-#define HAVE_LONG_DOUBLE 1
-
-/* Define as the return type of signal handlers (int or void). */
-#define RETSIGTYPE void
-
-/* Define if you have the ANSI C header files. */
-#define STDC_HEADERS 1
-
-/* Define if your processor stores words with the most significant
- byte first (like Motorola and SPARC, unlike Intel and VAX). */
-/* #undef WORDS_BIGENDIAN */
-
-/* Define if floating point words are bigendian. */
-/* #undef FLOAT_WORDS_BIGENDIAN */
-
-/* The number of bytes in a int. */
-#define SIZEOF_INT 4
-
-/* Define if you have the <string.h> header file. */
-#define HAVE_STRING_H 1
-
-
-/* Define this `volatile' if your compiler thinks
- * that floating point arithmetic obeys the associative
- * and distributive laws. It will defeat some optimizations
- * (but probably not enough of them).
- *
- * #define VOLATILE volatile
- */
-#define VOLATILE
-
-/* For 12-byte long doubles on an i386, pad a 16-bit short 0
- * to the end of real constants initialized by integer arrays.
- *
- * #define XPD 0,
- *
- * Otherwise, the type is 10 bytes long and XPD should be
- * defined blank (e.g., Microsoft C).
- *
- * #define XPD
- */
-#define XPD 0,
-
-/* Define to support tiny denormal numbers, else undefine. */
-#define DENORMAL 1
-
-/* Define to ask for infinity support, else undefine. */
-#define INFINITIES 1
-
-/* Define to ask for support of numbers that are Not-a-Number,
- else undefine. This may automatically define INFINITIES in some files. */
-#define NANS 1
-
-/* Define to distinguish between -0.0 and +0.0. */
-#define MINUSZERO 1
-
-/* Define 1 for ANSI C atan2() function
- and ANSI prototypes for float arguments.
- See atan.c and clog.c. */
-#define ANSIC 1
-#define ANSIPROT 1
-
-
-/* Constant definitions for math error conditions */
-
-#define DOMAIN 1 /* argument domain error */
-#define SING 2 /* argument singularity */
-#define OVERFLOW 3 /* overflow range error */
-#define UNDERFLOW 4 /* underflow range error */
-#define TLOSS 5 /* total loss of precision */
-#define PLOSS 6 /* partial loss of precision */
-
-#define EDOM 33
-#define ERANGE 34
+/* Get machine-dependent HUGE_VAL value (returned on overflow).
+ On all IEEE754 machines, this is +Infinity. */
+#include <bits/huge_val.h>
-/* Complex numeral. */
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
-typedef struct
- {
- double r;
- double i;
- } cmplx;
+/* Get machine-dependent NAN value (returned for some domain errors). */
+#ifdef __USE_ISOC99
+# include <bits/nan.h>
#endif
+/* Get general and ISO C99 specific information. */
+#include <bits/mathdef.h>
-#ifdef __UCLIBC_HAS_LIBM_FLOAT__
-typedef struct
- {
- float r;
- float i;
- } cmplxf;
-#endif
-#ifdef __UCLIBC_HAS_LIBM_LONG_DOUBLE__
-/* Long double complex numeral. */
-typedef struct
- {
- long double r;
- long double i;
- } cmplxl;
-#endif
+/* The file <bits/mathcalls.h> contains the prototypes for all the
+ actual math functions. These macros are used for those prototypes,
+ so we can easily declare each function as both `name' and `__name',
+ and can declare the float versions `namef' and `__namef'. */
+#define __MATHCALL(function,suffix, args) \
+ __MATHDECL (_Mdouble_,function,suffix, args)
+#define __MATHDECL(type, function,suffix, args) \
+ __MATHDECL_1(type, function,suffix, args); \
+ __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
+#define __MATHCALLX(function,suffix, args, attrib) \
+ __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
+#define __MATHDECLX(type, function,suffix, args, attrib) \
+ __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
+ __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
+#define __MATHDECL_1(type, function,suffix, args) \
+ extern type __MATH_PRECNAME(function,suffix) args __THROW
+#define _Mdouble_ double
+#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
+#include <bits/mathcalls.h>
+#undef _Mdouble_
+#undef __MATH_PRECNAME
+
+#if defined __USE_MISC || defined __USE_ISOC99
-/* Variable for error reporting. See mtherr.c. */
-__BEGIN_DECLS
-extern int mtherr(char *name, int code);
-extern int merror;
-__END_DECLS
+/* Include the file of declarations again, this time using `float'
+ instead of `double' and appending f to each function name. */
-/* If you define UNK, then be sure to set BIGENDIAN properly. */
-#include <endian.h>
-#if __BYTE_ORDER == __BIG_ENDIAN
-# define BIGENDIAN 1
-#else /* __BYTE_ORDER == __LITTLE_ENDIAN */
-# define BIGENDIAN 0
+# ifndef _Mfloat_
+# define _Mfloat_ float
+# endif
+# define _Mdouble_ _Mfloat_
+# ifdef __STDC__
+# define __MATH_PRECNAME(name,r) name##f##r
+# else
+# define __MATH_PRECNAME(name,r) name/**/f/**/r
+# endif
+# include <bits/mathcalls.h>
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+
+# if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH
+/* Include the file of declarations again, this time using `long double'
+ instead of `double' and appending l to each function name. */
+
+# ifndef _Mlong_double_
+# define _Mlong_double_ long double
+# endif
+# define _Mdouble_ _Mlong_double_
+# ifdef __STDC__
+# define __MATH_PRECNAME(name,r) name##l##r
+# else
+# define __MATH_PRECNAME(name,r) name/**/l/**/r
+# endif
+# include <bits/mathcalls.h>
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+
+# endif /* __STDC__ || __GNUC__ */
+
+#endif /* Use misc or ISO C99. */
+#undef __MATHDECL_1
+#undef __MATHDECL
+#undef __MATHCALL
+
+
+#if defined __USE_MISC || defined __USE_XOPEN
+/* This variable is used by `gamma' and `lgamma'. */
+extern int signgam;
#endif
-
-#define __USE_ISOC9X
-/* Get general and ISO C 9X specific information. */
-#include <bits/mathdef.h>
-#undef INFINITY
-#undef DECIMAL_DIG
-#undef FP_ILOGB0
-#undef FP_ILOGBNAN
+/* ISO C99 defines some generic macros which work on any data type. */
+#if __USE_ISOC99
/* Get the architecture specific values describing the floating-point
evaluation. The following symbols will get defined:
};
/* Return number of classification appropriate for X. */
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
-# define fpclassify(x) \
- (sizeof (x) == sizeof (float) ? \
- __fpclassifyf (x) \
- : sizeof (x) == sizeof (double) ? \
- __fpclassify (x) : __fpclassifyl (x))
-#else
+# ifdef __NO_LONG_DOUBLE_MATH
# define fpclassify(x) \
(sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
-#endif
-
-__BEGIN_DECLS
+# else
+# define fpclassify(x) \
+ (sizeof (x) == sizeof (float) \
+ ? __fpclassifyf (x) \
+ : sizeof (x) == sizeof (double) \
+ ? __fpclassify (x) : __fpclassifyl (x))
+# endif
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
/* Return nonzero value if sign of X is negative. */
-extern int signbit(double x);
+# ifdef __NO_LONG_DOUBLE_MATH
+# define signbit(x) \
+ (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
+# else
+# define signbit(x) \
+ (sizeof (x) == sizeof (float) \
+ ? __signbitf (x) \
+ : sizeof (x) == sizeof (double) \
+ ? __signbit (x) : __signbitl (x))
+# endif
+
/* Return nonzero value if X is not +-Inf or NaN. */
-extern int isfinite(double x);
+# ifdef __NO_LONG_DOUBLE_MATH
+# define isfinite(x) \
+ (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
+# else
+# define isfinite(x) \
+ (sizeof (x) == sizeof (float) \
+ ? __finitef (x) \
+ : sizeof (x) == sizeof (double) \
+ ? __finite (x) : __finitel (x))
+# endif
+
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
# define isnormal(x) (fpclassify (x) == FP_NORMAL)
-/* Return nonzero value if X is a NaN */
-extern int isnan(double x);
-#define isinf(x) \
- (sizeof (x) == sizeof (float) ? \
- __isinff (x) \
- : sizeof (x) == sizeof (double) ? \
- __isinf (x) : __isinfl (x))
-#else
+
+/* Return nonzero value if X is a NaN. We could use `fpclassify' but
+ we already have this functions `__isnan' and it is faster. */
+# ifdef __NO_LONG_DOUBLE_MATH
+# define isnan(x) \
+ (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
+# else
+# define isnan(x) \
+ (sizeof (x) == sizeof (float) \
+ ? __isnanf (x) \
+ : sizeof (x) == sizeof (double) \
+ ? __isnan (x) : __isnanl (x))
+# endif
+
+/* Return nonzero value is X is positive or negative infinity. */
+# ifdef __NO_LONG_DOUBLE_MATH
# define isinf(x) \
(sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
+# else
+# define isinf(x) \
+ (sizeof (x) == sizeof (float) \
+ ? __isinff (x) \
+ : sizeof (x) == sizeof (double) \
+ ? __isinf (x) : __isinfl (x))
+# endif
+
+/* Bitmasks for the math_errhandling macro. */
+# define MATH_ERRNO 1 /* errno set by math functions. */
+# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
+
+#endif /* Use ISO C99. */
+
+#ifdef __USE_MISC
+/* Support for various different standard error handling behaviors. */
+typedef enum
+{
+ _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
+ _SVID_, /* According to System V, release 4. */
+ _XOPEN_, /* Nowadays also Unix98. */
+ _POSIX_,
+ _ISOC_ /* Actually this is ISO C99. */
+} _LIB_VERSION_TYPE;
+
+/* This variable can be changed at run-time to any of the values above to
+ affect floating point error handling behavior (it may also be necessary
+ to change the hardware FPU exception settings). */
+extern _LIB_VERSION_TYPE _LIB_VERSION;
#endif
-#ifdef __UCLIBC_HAS_LIBM_LONG_DOUBLE__
-/* Return nonzero value if sign of X is negative. */
-extern int signbitl(long double x);
-/* Return nonzero value if X is not +-Inf or NaN. */
-extern int isfinitel(long double x);
-/* Return nonzero value if X is a NaN */
-extern int isnanl(long double x);
-#endif
+#ifdef __USE_SVID
+/* In SVID error handling, `matherr' is called with this description
+ of the exceptional condition.
+
+ We have a problem when using C++ since `exception' is a reserved
+ name in C++. */
+# ifdef __cplusplus
+struct __exception
+# else
+struct exception
+# endif
+ {
+ int type;
+ char *name;
+ double arg1;
+ double arg2;
+ double retval;
+ };
+
+# ifdef __cplusplus
+extern int matherr (struct __exception *__exc) throw ();
+# else
+extern int matherr (struct exception *__exc);
+# endif
+
+# define X_TLOSS 1.41484755040568800000e+16
+
+/* Types of exceptions in the `type' field. */
+# define DOMAIN 1
+# define SING 2
+# define OVERFLOW 3
+# define UNDERFLOW 4
+# define TLOSS 5
+# define PLOSS 6
+
+/* SVID mode specifies returning this large value instead of infinity. */
+# define HUGE 3.40282347e+38F
+
+#else /* !SVID */
+
+# ifdef __USE_XOPEN
+/* X/Open wants another strange constant. */
+# define MAXFLOAT 3.40282347e+38F
+# endif
+
+#endif /* SVID */
/* Some useful constants. */
# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
#endif
+
+/* The above constants are not adequate for computation using `long double's.
+ Therefore we provide as an extension constants with similar names as a
+ GNU extension. Provide enough digits for the 128-bit IEEE quad. */
#ifdef __USE_GNU
-# define M_El M_E
-# define M_LOG2El M_LOG2E
-# define M_LOG10El M_LOG10E
-# define M_LN2l M_LN2
-# define M_LN10l M_LN10
-# define M_PIl M_PI
-# define M_PI_2l M_PI_2
-# define M_PI_4l M_PI_4
-# define M_1_PIl M_1_PI
-# define M_2_PIl M_2_PI
-# define M_2_SQRTPIl M_2_SQRTPI
-# define M_SQRT2l M_SQRT2
-# define M_SQRT1_2l M_SQRT1_2
+# define M_El 2.7182818284590452353602874713526625L /* e */
+# define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */
+# define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
+# define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
+# define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
+# define M_PIl 3.1415926535897932384626433832795029L /* pi */
+# define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
+# define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
+# define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
+# define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
+# define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
+# define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
+# define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
#endif
+/* When compiling in strict ISO C compatible mode we must not use the
+ inline functions since they, among other things, do not set the
+ `errno' variable correctly. */
+#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
+# define __NO_MATH_INLINES 1
+#endif
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
-/* 7.12.4 Trigonometric functions */
-extern double acos(double x);
-extern double asin(double x);
-extern double atan(double x);
-extern double atan2(double y, double x);
-extern double cos(double x);
-extern double sin(double x);
-extern double tan(double x);
-
-/* 7.12.5 Hyperbolic functions */
-extern double acosh(double x);
-extern double asinh(double x);
-extern double atanh(double x);
-extern double cosh(double x);
-extern double sinh(double x);
-extern double tanh(double x);
-
-/* 7.12.6 Exponential and logarithmic functions */
-extern double exp(double x);
-extern double exp2(double x);
-extern double expm1(double x);
-extern double frexp(double value, int *ex);
-extern int ilogb(double x);
-extern double ldexp(double x, int ex);
-extern double log(double x);
-extern double log10(double x);
-extern double log1p(double x);
-extern double log2(double x);
-extern double logb(double x);
-extern double modf(double value, double *iptr);
-extern double scalbn(double x, int n);
-extern double scalbln(double x, long int n);
-
-/* 7.12.7 Power and absolute-value functions */
-extern double fabs(double x);
-extern double hypot(double x, double y);
-extern double pow(double x, double y);
-extern double sqrt(double x);
-
-/* 7.12.8 Error and gamma functions */
-extern double erf(double x);
-extern double erfc(double x);
-extern double lgamma(double x);
-extern double tgamma(double x);
-
-/* 7.12.9 Nearest integer functions */
-extern double ceil(double x);
-extern double floor(double x);
-extern double nearbyint(double x);
-extern double rint(double x);
-extern long int lrint(double x);
-extern long long int llrint(double x);
-extern double round(double x);
-extern long int lround(double x);
-extern long long int llround(double x);
-extern double trunc(double x);
-
-/* 7.12.10 Remainder functions */
-extern double fmod(double x, double y);
-extern double remainder(double x, double y);
-extern double remquo(double x, double y, int *quo);
-
-/* 7.12.11 Manipulation functions */
-extern double copysign(double x, double y);
-extern double nan(const char *tagp);
-extern double nextafter(double x, double y);
-
-/* 7.12.12 Maximum, minimum, and positive difference functions */
-extern double fdim(double x, double y);
-extern double fmax(double x, double y);
-extern double fmin(double x, double y);
-
-/* 7.12.13 Floating multiply-add */
-extern double fma(double x, double y, double z);
-#endif
-
-#ifdef __UCLIBC_HAS_LIBM_FLOAT__
-/* 7.12.4 Trigonometric functions */
-extern float acosf(float x);
-extern float asinf(float x);
-extern float atanf(float x);
-extern float atan2f(float y, float x);
-extern float cosf(float x);
-extern float sinf(float x);
-extern float tanf(float x);
-
-/* 7.12.5 Hyperbolic functions */
-extern float acoshf(float x);
-extern float asinhf(float x);
-extern float atanhf(float x);
-extern float coshf(float x);
-extern float sinhf(float x);
-extern float tanhf(float x);
-
-/* 7.12.6 Exponential and logarithmic functions */
-extern float expf(float x);
-extern float exp2f(float x);
-extern float expm1f(float x);
-extern float frexpf(float value, int *ex);
-extern int ilogbf(float x);
-extern float ldexpf(float x, int ex);
-extern float logf(float x);
-extern float log10f(float x);
-extern float log1pf(float x);
-extern float log2f(float x);
-extern float logbf(float x);
-extern float modff(float value, float *iptr);
-extern float scalbnf(float x, int n);
-extern float scalblnf(float x, long int n);
-
-/* 7.12.7 Power and absolute-value functions */
-extern float fabsf(float x);
-extern float hypotf(float x, float y);
-extern float powf(float x, float y);
-extern float sqrtf(float x);
-
-/* 7.12.8 Error and gamma functions */
-extern float erff(float x);
-extern float erfcf(float x);
-extern float lgammaf(float x);
-extern float tgammaf(float x);
-
-/* 7.12.9 Nearest integer functions */
-extern float ceilf(float x);
-extern float floorf(float x);
-extern float nearbyintf(float x);
-extern float rintf(float x);
-extern long int lrintf(float x);
-extern long long int llrintf(float x);
-extern float roundf(float x);
-extern long int lroundf(float x);
-extern long long int llroundf(float x);
-extern float truncf(float x);
-
-/* 7.12.10 Remainder functions */
-extern float fmodf(float x, float y);
-extern float remainderf(float x, float y);
-extern float remquof(float x, float y, int *quo);
-
-/* 7.12.11 Manipulation functions */
-extern float copysignf(float x, float y);
-extern float nanf(const char *tagp);
-extern float nextafterf(float x, float y);
-
-/* 7.12.12 Maximum, minimum, and positive difference functions */
-extern float fdimf(float x, float y);
-extern float fmaxf(float x, float y);
-extern float fminf(float x, float y);
-
-/* 7.12.13 Floating multiply-add */
-extern float fmaf(float x, float y, float z);
-#endif
-
-#ifdef __UCLIBC_HAS_LIBM_LONG_DOUBLE__
-/* 7.12.4 Trigonometric functions */
-extern long double acosl(long double x);
-extern long double asinl(long double x);
-extern long double atanl(long double x);
-extern long double atan2l(long double y, long double x);
-extern long double cosl(long double x);
-extern long double sinl(long double x);
-extern long double tanl(long double x);
-
-/* 7.12.5 Hyperbolic functions */
-extern long double acoshl(long double x);
-extern long double asinhl(long double x);
-extern long double atanhl(long double x);
-extern long double coshl(long double x);
-extern long double sinhl(long double x);
-extern long double tanhl(long double x);
-
-/* 7.12.6 Exponential and logarithmic functions */
-extern long double expl(long double x);
-extern long double exp2l(long double x);
-extern long double expm1l(long double x);
-extern long double frexpl(long double value, int *ex);
-extern int ilogbl(long double x);
-extern long double ldexpl(long double x, int ex);
-extern long double logl(long double x);
-extern long double log10l(long double x);
-extern long double log1pl(long double x);
-extern long double log2l(long double x);
-extern long double logbl(long double x);
-extern long double modfl(long double value, long double *iptr);
-extern long double scalbnl(long double x, int n);
-extern long double scalblnl(long double x, long int n);
-
-/* 7.12.7 Power and absolute-value functions */
-extern long double fabsl(long double x);
-extern long double hypotl(long double x, long double y);
-extern long double powl(long double x, long double y);
-extern long double sqrtl(long double x);
-
-/* 7.12.8 Error and gamma functions */
-extern long double erfl(long double x);
-extern long double erfcl(long double x);
-extern long double lgammal(long double x);
-extern long double tgammal(long double x);
-
-/* 7.12.9 Nearest integer functions */
-extern long double ceill(long double x);
-extern long double floorl(long double x);
-extern long double nearbyintl(long double x);
-extern long double rintl(long double x);
-extern long int lrintl(long double x);
-extern long long int llrintl(long double x);
-extern long double roundl(long double x);
-extern long int lroundl(long double x);
-extern long long int llroundl(long double x);
-extern long double truncl(long double x);
-
-/* 7.12.10 Remainder functions */
-extern long double fmodl(long double x, long double y);
-extern long double remainderl(long double x, long double y);
-extern long double remquol(long double x, long double y, int *quo);
-
-/* 7.12.11 Manipulation functions */
-extern long double copysignl(long double x, long double y);
-extern long double nanl(const char *tagp);
-extern long double nextafterl(long double x, long double y);
-extern long double nexttowardl(long double x, long double y);
-
-/* 7.12.12 Maximum, minimum, and positive difference functions */
-extern long double fdiml(long double x, long double y);
-extern long double fmaxl(long double x, long double y);
-extern long double fminl(long double x, long double y);
-
-/* 7.12.13 Floating multiply-add */
-extern long double fmal(long double x, long double y, long double z);
+/* Get machine-dependent inline versions (if there are any). */
+#ifdef __USE_EXTERN_INLINES
+# include <bits/mathinline.h>
#endif
-/* 7.12.14 Comparison macros */
+
+#if __USE_ISOC99
+/* ISO C99 defines some macros to compare number while taking care
+ for unordered numbers. Since many FPUs provide special
+ instructions to support these operations and these tests are
+ defined in <bits/mathinline.h>, we define the generic macros at
+ this late point and only if they are not defined yet. */
+
+/* Return nonzero value if X is greater than Y. */
# ifndef isgreater
# define isgreater(x, y) \
(__extension__ \
fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
# endif
+#endif
+
__END_DECLS
+
#endif /* math.h */
LIBM=libm.a
LIBM_SHARED=libm.so
LIBM_SHARED_FULLNAME=libm-$(MAJOR_VERSION).$(MINOR_VERSION).so
+TARGET_CC= $(TOPDIR)extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+TARGET_CFLAGS+=-D_IEEE_LIBM -D_ISOC99_SOURCE -D_SVID_SOURCE
-DIRS=
-ifeq ($(strip $(HAS_LIBM_FLOAT)),true)
- DIRS+=float
+ifeq ($(strip $(DO_C89_ONLY)),true)
+CSRC = FIXME
+else
+CSRC = e_acos.c e_acosh.c e_asin.c e_atan2.c e_atanh.c e_cosh.c\
+ e_exp.c e_fmod.c e_gamma.c e_gamma_r.c e_hypot.c e_j0.c\
+ e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c e_log.c e_log10.c\
+ e_pow.c e_remainder.c e_rem_pio2.c e_scalb.c e_sinh.c\
+ e_sqrt.c k_cos.c k_rem_pio2.c k_sin.c k_standard.c k_tan.c\
+ s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c s_cos.c\
+ s_erf.c s_expm1.c s_fabs.c s_finite.c s_floor.c s_frexp.c\
+ s_ilogb.c s_ldexp.c s_lib_version.c s_log1p.c s_logb.c\
+ s_matherr.c s_modf.c s_nextafter.c s_rint.c s_scalbn.c\
+ s_signgam.c s_significand.c s_sin.c s_tan.c s_tanh.c\
+ w_acos.c w_acosh.c w_asin.c w_atan2.c w_atanh.c w_cabs.c\
+ w_cosh.c w_drem.c w_exp.c w_fmod.c w_gamma.c w_gamma_r.c\
+ w_hypot.c w_j0.c w_j1.c w_jn.c w_lgamma.c w_lgamma_r.c\
+ w_log.c w_log10.c w_pow.c w_remainder.c w_scalb.c w_sinh.c\
+ w_sqrt.c ceilfloor.c fpmacros.c frexpldexp.c logb.c rndint.c\
+ scalb.c sign.c
endif
-ifeq ($(strip $(HAS_LIBM_DOUBLE)),true)
- DIRS+=double
-endif
-ifeq ($(strip $(HAS_LIBM_LONG_DOUBLE)),true)
- DIRS+=ldouble
-endif
-ALL_SUBDIRS = float double ldouble
+COBJS=$(patsubst %.c,%.o, $(CSRC))
+OBJS=$(COBJS)
+
-all: $(LIBM)
-$(LIBM): subdirs
+all: $(OBJS) $(LIBM)
+
+$(LIBM): ar-target
@if [ -f $(LIBM) ] ; then \
install -d $(TOPDIR)lib; \
rm -f $(TOPDIR)lib/$(LIBM); \
install -m 644 $(LIBM) $(TOPDIR)lib; \
fi;
-tags:
- ctags -R
-
shared: all
if [ -f $(LIBM) ] ; then \
$(TARGET_CC) $(TARGET_LDFLAGS) -nostdlib -shared -o $(LIBM_SHARED_FULLNAME) \
(cd $(TOPDIR)lib; ln -sf $(LIBM_SHARED_FULLNAME) $(LIBM_SHARED).$(MAJOR_VERSION)); \
fi;
-subdirs: $(patsubst %, _dir_%, $(DIRS))
-subdirs_clean: $(patsubst %, _dirclean_%, $(ALL_SUBDIRS))
-
-$(patsubst %, _dir_%, $(DIRS)) : dummy
- $(MAKE) -C $(patsubst _dir_%, %, $@)
+ar-target: $(OBJS)
+ $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
-$(patsubst %, _dirclean_%, $(ALL_SUBDIRS)) : dummy
- $(MAKE) -C $(patsubst _dirclean_%, %, $@) clean
+$(COBJS): %.o : %.c
+ $(TARGET_CC) $(TARGET_CFLAGS) -c $< -o $@
+ $(STRIPTOOL) -x -R .note -R .comment $*.o
-clean: subdirs_clean
- rm -f *.[oa] *~ core $(LIBM_SHARED)* $(LIBM_SHARED_FULLNAME)*
+$(OBJ): Makefile
-.PHONY: dummy
+tags:
+ ctags -R
+clean:
+ rm -f *.[oa] *~ core $(LIBM_SHARED)* $(LIBM_SHARED_FULLNAME)*
-The actual routines included in this math library are derived almost
-exclusively from the Cephes Mathematical Library, which "is copyrighted by the
-author [and] may be used freely but ... comes with no support or guarantee"
+The routines included in this math library are derived from the
+math library for Apple's MacOS X/Darwin math library, which was
+itself swiped from FreeBSD. The original copyright information
+is as follows:
-It has been ported to fit into uClibc and generally behave
-by Erik Andersen <andersen@lineo.com>, <andersee@debian.org>
- 5 May, 2001
+ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
---------------------------------------------------
+ Developed at SunPro, a Sun Microsystems, Inc. business.
+ Permission to use, copy, modify, and distribute this
+ software is freely granted, provided that this notice
+ is preserved.
- Some software in this archive may be from the book _Methods and
-Programs for Mathematical Functions_ (Prentice-Hall, 1989) or
-from the Cephes Mathematical Library, a commercial product. In
-either event, it is copyrighted by the author. What you see here
-may be used freely but it comes with no support or guarantee.
+It has been ported to work with uClibc and generally behave
+by Erik Andersen <andersen@codepoet.org>
+ 22 May, 2001
- The two known misprints in the book are repaired here in the
-source listings for the gamma function and the incomplete beta
-integral.
-
-
- Stephen L. Moshier
- moshier@world.std.com
-
---------------------------------------------------
-
-19 November 1992
-
-ZIP archive constructed and index compiled.
-
-To reconstruct the original directory structure, use the -d switch:
-
- C:\CEPHES>pkunzip -d cephes
-
-This archive includes all the programs in the /netlib/cephes directory
-on research.att.com as of 17 Nov 92. The file "index" will tell you in
-what directory and file each function can be found. If there is
-something else mentioned in cephes.doc that you need, you can check
-research.att.com to see whether it has been added. Failing that, you
-can contact Stephen Moshier.
-
- Jim Van Zandt <jrv@mbunix.mitre.org>
--- /dev/null
+#if defined(__ppc__)
+/*******************************************************************************
+* *
+* File ceilfloor.c, *
+* Function ceil(x) and floor(x), *
+* Implementation of ceil and floor for the PowerPC. *
+* *
+* Copyright © 1991 Apple Computer, Inc. All rights reserved. *
+* *
+* Written by Ali Sazegari, started on November 1991, *
+* *
+* based on math.h, library code for Macintoshes with a 68881/68882 *
+* by Jim Thomas. *
+* *
+* W A R N I N G: This routine expects a 64 bit double model. *
+* *
+* December 03 1992: first rs6000 port. *
+* July 14 1993: comment changes and addition of #pragma fenv_access. *
+* May 06 1997: port of the ibm/taligent ceil and floor routines. *
+* April 11 2001: first port to os x using gcc. *
+* June 13 2001: replaced __setflm with in-line assembly *
+* *
+*******************************************************************************/
+
+#if !defined(__ppc__)
+#define asm(x)
+#endif
+
+static const double twoTo52 = 4503599627370496.0;
+static const unsigned long signMask = 0x80000000ul;
+
+typedef union
+ {
+ struct {
+#if defined(__BIG_ENDIAN__)
+ unsigned long int hi;
+ unsigned long int lo;
+#else
+ unsigned long int lo;
+ unsigned long int hi;
+#endif
+ } words;
+ double dbl;
+ } DblInHex;
+
+/*******************************************************************************
+* Functions needed for the computation. *
+*******************************************************************************/
+
+/*******************************************************************************
+* Ceil(x) returns the smallest integer not less than x. *
+*******************************************************************************/
+
+double ceil ( double x )
+ {
+ DblInHex xInHex,OldEnvironment;
+ register double y;
+ register unsigned long int xhi;
+ register int target;
+
+ xInHex.dbl = x;
+ xhi = xInHex.words.hi & 0x7fffffffUL; // xhi is the high half of |x|
+ target = ( xInHex.words.hi < signMask );
+
+ if ( xhi < 0x43300000ul )
+/*******************************************************************************
+* Is |x| < 2.0^52? *
+*******************************************************************************/
+ {
+ if ( xhi < 0x3ff00000ul )
+/*******************************************************************************
+* Is |x| < 1.0? *
+*******************************************************************************/
+ {
+ if ( ( xhi | xInHex.words.lo ) == 0ul ) // zero x is exact case
+ return ( x );
+ else
+ { // inexact case
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+ OldEnvironment.words.lo |= 0x02000000ul;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ if ( target )
+ return ( 1.0 );
+ else
+ return ( -0.0 );
+ }
+ }
+/*******************************************************************************
+* Is 1.0 < |x| < 2.0^52? *
+*******************************************************************************/
+ if ( target )
+ {
+ y = ( x + twoTo52 ) - twoTo52; // round at binary pt.
+ if ( y < x )
+ return ( y + 1.0 );
+ else
+ return ( y );
+ }
+
+ else
+ {
+ y = ( x - twoTo52 ) + twoTo52; // round at binary pt.
+ if ( y < x )
+ return ( y + 1.0 );
+ else
+ return ( y );
+ }
+ }
+/*******************************************************************************
+* |x| >= 2.0^52 or x is a NaN. *
+*******************************************************************************/
+ return ( x );
+ }
+
+/*******************************************************************************
+* Floor(x) returns the largest integer not greater than x. *
+*******************************************************************************/
+
+double floor ( double x )
+ {
+ DblInHex xInHex,OldEnvironment;
+ register double y;
+ register unsigned long int xhi;
+ register long int target;
+
+ xInHex.dbl = x;
+ xhi = xInHex.words.hi & 0x7fffffffUL; // xhi is the high half of |x|
+ target = ( xInHex.words.hi < signMask );
+
+ if ( xhi < 0x43300000ul )
+/*******************************************************************************
+* Is |x| < 2.0^52? *
+*******************************************************************************/
+ {
+ if ( xhi < 0x3ff00000ul )
+/*******************************************************************************
+* Is |x| < 1.0? *
+*******************************************************************************/
+ {
+ if ( ( xhi | xInHex.words.lo ) == 0ul ) // zero x is exact case
+ return ( x );
+ else
+ { // inexact case
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+ OldEnvironment.words.lo |= 0x02000000ul;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ if ( target )
+ return ( 0.0 );
+ else
+ return ( -1.0 );
+ }
+ }
+/*******************************************************************************
+* Is 1.0 < |x| < 2.0^52? *
+*******************************************************************************/
+ if ( target )
+ {
+ y = ( x + twoTo52 ) - twoTo52; // round at binary pt.
+ if ( y > x )
+ return ( y - 1.0 );
+ else
+ return ( y );
+ }
+
+ else
+ {
+ y = ( x - twoTo52 ) + twoTo52; // round at binary pt.
+ if ( y > x )
+ return ( y - 1.0 );
+ else
+ return ( y );
+ }
+ }
+/*******************************************************************************
+* |x| >= 2.0^52 or x is a NaN. *
+*******************************************************************************/
+ return ( x );
+ }
+#endif /* __ppc__ */
+++ /dev/null
-# Makefile for uClibc's math library
-# Copyright (C) 2001 by Lineo, inc.
-#
-# This math library is derived primarily from the Cephes Math Library,
-# copyright by Stephen L. Moshier <moshier@world.std.com>
-#
-# This program is free software; you can redistribute it and/or modify it under
-# the terms of the GNU Library General Public License as published by the Free
-# Software Foundation; either version 2 of the License, or (at your option) any
-# later version.
-#
-# This program is distributed in the hope that it will be useful, but WITHOUT
-# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
-# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
-# details.
-#
-# You should have received a copy of the GNU Library General Public License
-# along with this program; if not, write to the Free Software Foundation, Inc.,
-# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-#
-
-TOPDIR=../../
-include $(TOPDIR)Rules.mak
-
-LIBM=../libm.a
-TARGET_CC= $(TOPDIR)extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
-
-CSRC=acosh.c airy.c asin.c asinh.c atan.c atanh.c bdtr.c beta.c \
- btdtr.c cbrt.c chbevl.c chdtr.c clog.c cmplx.c const.c \
- cosh.c dawsn.c ei.c ellie.c ellik.c ellpe.c ellpj.c ellpk.c \
- exp.c exp10.c exp2.c expn.c fabs.c fac.c fdtr.c \
- fresnl.c gamma.c gdtr.c hyp2f1.c hyperg.c i0.c i1.c igami.c incbet.c \
- incbi.c igam.c isnan.c iv.c j0.c j1.c jn.c jv.c k0.c k1.c kn.c kolmogorov.c \
- log.c log2.c log10.c lrand.c nbdtr.c ndtr.c ndtri.c pdtr.c planck.c \
- polevl.c polmisc.c polylog.c polyn.c pow.c powi.c psi.c rgamma.c round.c \
- shichi.c sici.c sin.c sindg.c sinh.c spence.c stdtr.c struve.c \
- tan.c tandg.c tanh.c unity.c yn.c zeta.c zetac.c \
- sqrt.c floor.c setprec.c mtherr.c noncephes.c
-
-COBJS=$(patsubst %.c,%.o, $(CSRC))
-
-
-OBJS=$(COBJS)
-
-all: $(OBJS) $(LIBM)
-
-$(LIBM): ar-target
-
-ar-target: $(OBJS)
- $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
-
-$(COBJS): %.o : %.c
- $(TARGET_CC) $(TARGET_CFLAGS) -c $< -o $@
- $(STRIPTOOL) -x -R .note -R .comment $*.o
-
-$(OBJ): Makefile
-
-clean:
- rm -f *.[oa] *~ core
-
-
-
-#-----------------------------------------
-
-#all: libmd.a mtst dtestvec monot dcalc paranoia
-
-time-it: time-it.o
- $(TARGET_CC) -o time-it time-it.o
-
-time-it.o: time-it.c
- $(TARGET_CC) -O2 -c time-it.c
-
-dcalc: dcalc.o libmd.a
- $(TARGET_CC) -o dcalc dcalc.o libmd.a
-
-mtst: mtst.o libmd.a
- $(TARGET_CC) -v -o mtst mtst.o libmd.a
-
-mtst.o: mtst.c
- $(TARGET_CC) -O2 -Wall -c mtst.c
-
-dtestvec: dtestvec.o libmd.a
- $(TARGET_CC) -o dtestvec dtestvec.o libmd.a
-
-dtestvec.o: dtestvec.c
- $(TARGET_CC) -g -c dtestvec.c
-
-monot: monot.o libmd.a
- $(TARGET_CC) -o monot monot.o libmd.a
-
-monot.o: monot.c
- $(TARGET_CC) -g -c monot.c
-
-paranoia: paranoia.o setprec.o libmd.a
- $(TARGET_CC) -o paranoia paranoia.o setprec.o libmd.a
-
-paranoia.o: paranoia.c
- $(TARGET_CC) $(TARGET_CFLAGS) -Wno-implicit -c paranoia.c
-
-libmd.a: $(OBJS) $(INCS)
- $(AR) rv libmd.a $(OBJS)
-
-#clean:
-# rm -f *.o
-# rm -f mtst
-# rm -f paranoia
-# rm -f dcalc
-# rm -f dtestvec
-# rm -f monot
-# rm -f libmd.a
-# rm -f time-it
-# rm -f dtestvec
-
-
+++ /dev/null
-/* acosh.c
- *
- * Inverse hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acosh();
- *
- * y = acosh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a rational approximation
- *
- * sqrt(z) * P(z)/Q(z)
- *
- * where z = x-1, is used. Otherwise,
- *
- * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 1,3 30000 4.2e-17 1.1e-17
- * IEEE 1,3 30000 4.6e-16 8.7e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acosh domain |x| < 1 NAN
- *
- */
-\f
-/* airy.c
- *
- * Airy function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, ai, aip, bi, bip;
- * int airy();
- *
- * airy( x, _&ai, _&aip, _&bi, _&bip );
- *
- *
- *
- * DESCRIPTION:
- *
- * Solution of the differential equation
- *
- * y"(x) = xy.
- *
- * The function returns the two independent solutions Ai, Bi
- * and their first derivatives Ai'(x), Bi'(x).
- *
- * Evaluation is by power series summation for small x,
- * by rational minimax approximations for large x.
- *
- *
- *
- * ACCURACY:
- * Error criterion is absolute when function <= 1, relative
- * when function > 1, except * denotes relative error criterion.
- * For large negative x, the absolute error increases as x^1.5.
- * For large positive x, the relative error increases as x^1.5.
- *
- * Arithmetic domain function # trials peak rms
- * IEEE -10, 0 Ai 10000 1.6e-15 2.7e-16
- * IEEE 0, 10 Ai 10000 2.3e-14* 1.8e-15*
- * IEEE -10, 0 Ai' 10000 4.6e-15 7.6e-16
- * IEEE 0, 10 Ai' 10000 1.8e-14* 1.5e-15*
- * IEEE -10, 10 Bi 30000 4.2e-15 5.3e-16
- * IEEE -10, 10 Bi' 30000 4.9e-15 7.3e-16
- * DEC -10, 0 Ai 5000 1.7e-16 2.8e-17
- * DEC 0, 10 Ai 5000 2.1e-15* 1.7e-16*
- * DEC -10, 0 Ai' 5000 4.7e-16 7.8e-17
- * DEC 0, 10 Ai' 12000 1.8e-15* 1.5e-16*
- * DEC -10, 10 Bi 10000 5.5e-16 6.8e-17
- * DEC -10, 10 Bi' 7000 5.3e-16 8.7e-17
- *
- */
-\f
-/* asin.c
- *
- * Inverse circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, asin();
- *
- * y = asin( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
- *
- * A rational function of the form x + x**3 P(x**2)/Q(x**2)
- * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
- * transformed by the identity
- *
- * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1, 1 40000 2.6e-17 7.1e-18
- * IEEE -1, 1 10^6 1.9e-16 5.4e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 NAN
- *
- */
-\f/* acos()
- *
- * Inverse circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acos();
- *
- * y = acos( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between 0 and pi whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1, 1 50000 3.3e-17 8.2e-18
- * IEEE -1, 1 10^6 2.2e-16 6.5e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 NAN
- */
-\f
-/* asinh.c
- *
- * Inverse hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, asinh();
- *
- * y = asinh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic sine of argument.
- *
- * If |x| < 0.5, the function is approximated by a rational
- * form x + x**3 P(x)/Q(x). Otherwise,
- *
- * asinh(x) = log( x + sqrt(1 + x*x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -3,3 75000 4.6e-17 1.1e-17
- * IEEE -1,1 30000 3.7e-16 7.8e-17
- * IEEE 1,3 30000 2.5e-16 6.7e-17
- *
- */
-\f
-/* atan.c
- *
- * Inverse circular tangent
- * (arctangent)
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, atan();
- *
- * y = atan( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose tangent
- * is x.
- *
- * Range reduction is from three intervals into the interval
- * from zero to 0.66. The approximant uses a rational
- * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10, 10 50000 2.4e-17 8.3e-18
- * IEEE -10, 10 10^6 1.8e-16 5.0e-17
- *
- */
-\f/* atan2()
- *
- * Quadrant correct inverse circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, z, atan2();
- *
- * z = atan2( y, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle whose tangent is y/x.
- * Define compile time symbol ANSIC = 1 for ANSI standard,
- * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
- * 0 to 2PI, args (x,y).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 10^6 2.5e-16 6.9e-17
- * See atan.c.
- *
- */
-\f
-/* atanh.c
- *
- * Inverse hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, atanh();
- *
- * y = atanh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic tangent of argument in the range
- * MINLOG to MAXLOG.
- *
- * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
- * employed. Otherwise,
- * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1,1 50000 2.4e-17 6.4e-18
- * IEEE -1,1 30000 1.9e-16 5.2e-17
- *
- */
-\f
-/* bdtr.c
- *
- * Binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, bdtr();
- *
- * y = bdtr( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the Binomial
- * probability density:
- *
- * k
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p), with p between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between 0.001 and 1:
- * IEEE 0,100 100000 4.3e-15 2.6e-16
- * See also incbet.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtr domain k < 0 0.0
- * n < k
- * x < 0, x > 1
- */
-\f/* bdtrc()
- *
- * Complemented binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, bdtrc();
- *
- * y = bdtrc( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 through n of the Binomial
- * probability density:
- *
- * n
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between 0.001 and 1:
- * IEEE 0,100 100000 6.7e-15 8.2e-16
- * For p between 0 and .001:
- * IEEE 0,100 100000 1.5e-13 2.7e-15
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrc domain x<0, x>1, n<k 0.0
- */
-\f/* bdtri()
- *
- * Inverse binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, bdtri();
- *
- * p = bdtr( k, n, y );
- *
- * DESCRIPTION:
- *
- * Finds the event probability p such that the sum of the
- * terms 0 through k of the Binomial probability density
- * is equal to the given cumulative probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relation
- *
- * 1 - p = incbi( n-k, k+1, y ).
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between 0.001 and 1:
- * IEEE 0,100 100000 2.3e-14 6.4e-16
- * IEEE 0,10000 100000 6.6e-12 1.2e-13
- * For p between 10^-6 and 0.001:
- * IEEE 0,100 100000 2.0e-12 1.3e-14
- * IEEE 0,10000 100000 1.5e-12 3.2e-14
- * See also incbi.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtri domain k < 0, n <= k 0.0
- * x < 0, x > 1
- */
-\f
-/* beta.c
- *
- * Beta function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, y, beta();
- *
- * y = beta( a, b );
- *
- *
- *
- * DESCRIPTION:
- *
- * - -
- * | (a) | (b)
- * beta( a, b ) = -----------.
- * -
- * | (a+b)
- *
- * For large arguments the logarithm of the function is
- * evaluated using lgam(), then exponentiated.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 1700 7.7e-15 1.5e-15
- * IEEE 0,30 30000 8.1e-14 1.1e-14
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * beta overflow log(beta) > MAXLOG 0.0
- * a or b <0 integer 0.0
- *
- */
-\f
-/* btdtr.c
- *
- * Beta distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, btdtr();
- *
- * y = btdtr( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the beta density
- * function:
- *
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * P(x) = ---------- | t (1-t) dt
- * - - | |
- * | (a) | (b) -
- * 0
- *
- *
- * This function is identical to the incomplete beta
- * integral function incbet(a, b, x).
- *
- * The complemented function is
- *
- * 1 - P(1-x) = incbet( b, a, x );
- *
- *
- * ACCURACY:
- *
- * See incbet.c.
- *
- */
-\f
-/* cbrt.c
- *
- * Cube root
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cbrt();
- *
- * y = cbrt( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the cube root of the argument, which may be negative.
- *
- * Range reduction involves determining the power of 2 of
- * the argument. A polynomial of degree 2 applied to the
- * mantissa, and multiplication by the cube root of 1, 2, or 4
- * approximates the root to within about 0.1%. Then Newton's
- * iteration is used three times to converge to an accurate
- * result.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,10 200000 1.8e-17 6.2e-18
- * IEEE 0,1e308 30000 1.5e-16 5.0e-17
- *
- */
-\f
-/* chbevl.c
- *
- * Evaluate Chebyshev series
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * double x, y, coef[N], chebevl();
- *
- * y = chbevl( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the series
- *
- * N-1
- * - '
- * y = > coef[i] T (x/2)
- * - i
- * i=0
- *
- * of Chebyshev polynomials Ti at argument x/2.
- *
- * Coefficients are stored in reverse order, i.e. the zero
- * order term is last in the array. Note N is the number of
- * coefficients, not the order.
- *
- * If coefficients are for the interval a to b, x must
- * have been transformed to x -> 2(2x - b - a)/(b-a) before
- * entering the routine. This maps x from (a, b) to (-1, 1),
- * over which the Chebyshev polynomials are defined.
- *
- * If the coefficients are for the inverted interval, in
- * which (a, b) is mapped to (1/b, 1/a), the transformation
- * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
- * this becomes x -> 4a/x - 1.
- *
- *
- *
- * SPEED:
- *
- * Taking advantage of the recurrence properties of the
- * Chebyshev polynomials, the routine requires one more
- * addition per loop than evaluating a nested polynomial of
- * the same degree.
- *
- */
-\f
-/* chdtr.c
- *
- * Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double df, x, y, chdtr();
- *
- * y = chdtr( df, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the left hand tail (from 0 to x)
- * of the Chi square probability density function with
- * v degrees of freedom.
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtr domain x < 0 or v < 1 0.0
- */
-\f/* chdtrc()
- *
- * Complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, chdtrc();
- *
- * y = chdtrc( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the right hand tail (from x to
- * infinity) of the Chi square probability density function
- * with v degrees of freedom:
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrc domain x < 0 or v < 1 0.0
- */
-\f/* chdtri()
- *
- * Inverse of complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double df, x, y, chdtri();
- *
- * x = chdtri( df, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Chi-square argument x such that the integral
- * from x to infinity of the Chi-square density is equal
- * to the given cumulative probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * x/2 = igami( df/2, y );
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtri domain y < 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* clog.c
- *
- * Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clog();
- * cmplx z, w;
- *
- * clog( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns complex logarithm to the base e (2.718...) of
- * the complex argument x.
- *
- * If z = x + iy, r = sqrt( x**2 + y**2 ),
- * then
- * w = log(r) + i arctan(y/x).
- *
- * The arctangent ranges from -PI to +PI.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 7000 8.5e-17 1.9e-17
- * IEEE -10,+10 30000 5.0e-15 1.1e-16
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
- * absolute error 1.0e-16.
- */
-\f
-/* cexp()
- *
- * Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexp();
- * cmplx z, w;
- *
- * cexp( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the exponential of the complex argument z
- * into the complex result w.
- *
- * If
- * z = x + iy,
- * r = exp(x),
- *
- * then
- *
- * w = r cos y + i r sin y.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8700 3.7e-17 1.1e-17
- * IEEE -10,+10 30000 3.0e-16 8.7e-17
- *
- */
-\f/* csin()
- *
- * Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csin();
- * cmplx z, w;
- *
- * csin( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = sin x cosh y + i cos x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 5.3e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- * Also tested by csin(casin(z)) = z.
- *
- */
-\f/* ccos()
- *
- * Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccos();
- * cmplx z, w;
- *
- * ccos( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = cos x cosh y - i sin x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 4.5e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- */
-\f/* ctan()
- *
- * Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctan();
- * cmplx z, w;
- *
- * ctan( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x + i sinh 2y
- * w = --------------------.
- * cos 2x + cosh 2y
- *
- * On the real axis the denominator is zero at odd multiples
- * of PI/2. The denominator is evaluated by its Taylor
- * series near these points.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 7.1e-17 1.6e-17
- * IEEE -10,+10 30000 7.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
- */
-\f/* ccot()
- *
- * Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccot();
- * cmplx z, w;
- *
- * ccot( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x - i sinh 2y
- * w = --------------------.
- * cosh 2y - cos 2x
- *
- * On the real axis, the denominator has zeros at even
- * multiples of PI/2. Near these points it is evaluated
- * by a Taylor series.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 3000 6.5e-17 1.6e-17
- * IEEE -10,+10 30000 9.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 + i0.
- */
-\f/* casin()
- *
- * Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casin();
- * cmplx z, w;
- *
- * casin( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- * 2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 10100 2.1e-15 3.4e-16
- * IEEE -10,+10 30000 2.2e-14 2.7e-15
- * Larger relative error can be observed for z near zero.
- * Also tested by csin(casin(z)) = z.
- */
-\f
-\f/* cacos()
- *
- * Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacos();
- * cmplx z, w;
- *
- * cacos( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z = PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 1.6e-15 2.8e-16
- * IEEE -10,+10 30000 1.8e-14 2.2e-15
- */
-\f/* catan()
- *
- * Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catan();
- * cmplx z, w;
- *
- * catan( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- * 1 ( 2x )
- * Re w = - arctan(-----------) + k PI
- * 2 ( 2 2)
- * (1 - x - y )
- *
- * ( 2 2)
- * 1 (x + (y+1) )
- * Im w = - log(------------)
- * 4 ( 2 2)
- * (x + (y-1) )
- *
- * Where k is an arbitrary integer.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5900 1.3e-16 7.8e-18
- * IEEE -10,+10 30000 2.3e-15 8.5e-17
- * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
- * had peak relative error 1.5e-16, rms relative error
- * 2.9e-17. See also clog().
- */
-\f
-/* cmplx.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * double r; real part
- * double i; imaginary part
- * }cmplx;
- *
- * cmplx *a, *b, *c;
- *
- * cadd( a, b, c ); c = b + a
- * csub( a, b, c ); c = b - a
- * cmul( a, b, c ); c = b * a
- * cdiv( a, b, c ); c = b / a
- * cneg( c ); c = -c
- * cmov( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
- * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * DEC cadd 10000 1.4e-17 3.4e-18
- * IEEE cadd 100000 1.1e-16 2.7e-17
- * DEC csub 10000 1.4e-17 4.5e-18
- * IEEE csub 100000 1.1e-16 3.4e-17
- * DEC cmul 3000 2.3e-17 8.7e-18
- * IEEE cmul 100000 2.1e-16 6.9e-17
- * DEC cdiv 18000 4.9e-17 1.3e-17
- * IEEE cdiv 100000 3.7e-16 1.1e-16
- */
-\f
-/* cabs()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * double cabs();
- * cmplx z;
- * double a;
- *
- * a = cabs( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -30,+30 30000 3.2e-17 9.2e-18
- * IEEE -10,+10 100000 2.7e-16 6.9e-17
- */
-\f/* csqrt()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrt();
- * cmplx z, w;
- *
- * csqrt( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The root chosen
- * is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 25000 3.2e-17 9.6e-18
- * IEEE -10,+10 100000 3.2e-16 7.7e-17
- *
- * 2
- * Also tested by csqrt( z ) = z, and tested by arguments
- * close to the real axis.
- */
-\f
-/* const.c
- *
- * Globally declared constants
- *
- *
- *
- * SYNOPSIS:
- *
- * extern double nameofconstant;
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * This file contains a number of mathematical constants and
- * also some needed size parameters of the computer arithmetic.
- * The values are supplied as arrays of hexadecimal integers
- * for IEEE arithmetic; arrays of octal constants for DEC
- * arithmetic; and in a normal decimal scientific notation for
- * other machines. The particular notation used is determined
- * by a symbol (DEC, IBMPC, or UNK) defined in the include file
- * math.h.
- *
- * The default size parameters are as follows.
- *
- * For DEC and UNK modes:
- * MACHEP = 1.38777878078144567553E-17 2**-56
- * MAXLOG = 8.8029691931113054295988E1 log(2**127)
- * MINLOG = -8.872283911167299960540E1 log(2**-128)
- * MAXNUM = 1.701411834604692317316873e38 2**127
- *
- * For IEEE arithmetic (IBMPC):
- * MACHEP = 1.11022302462515654042E-16 2**-53
- * MAXLOG = 7.09782712893383996843E2 log(2**1024)
- * MINLOG = -7.08396418532264106224E2 log(2**-1022)
- * MAXNUM = 1.7976931348623158E308 2**1024
- *
- * The global symbols for mathematical constants are
- * PI = 3.14159265358979323846 pi
- * PIO2 = 1.57079632679489661923 pi/2
- * PIO4 = 7.85398163397448309616E-1 pi/4
- * SQRT2 = 1.41421356237309504880 sqrt(2)
- * SQRTH = 7.07106781186547524401E-1 sqrt(2)/2
- * LOG2E = 1.4426950408889634073599 1/log(2)
- * SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi )
- * LOGE2 = 6.93147180559945309417E-1 log(2)
- * LOGSQ2 = 3.46573590279972654709E-1 log(2)/2
- * THPIO4 = 2.35619449019234492885 3*pi/4
- * TWOOPI = 6.36619772367581343075535E-1 2/pi
- *
- * These lists are subject to change.
- */
-\f
-/* cosh.c
- *
- * Hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cosh();
- *
- * y = cosh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic cosine of argument in the range MINLOG to
- * MAXLOG.
- *
- * cosh(x) = ( exp(x) + exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +- 88 50000 4.0e-17 7.7e-18
- * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cosh overflow |x| > MAXLOG MAXNUM
- *
- *
- */
-\f
-/* cpmul.c
- *
- * Multiply two polynomials with complex coefficients
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct
- * {
- * double r;
- * double i;
- * }cmplx;
- *
- * cmplx a[], b[], c[];
- * int da, db, dc;
- *
- * cpmul( a, da, b, db, c, &dc );
- *
- *
- *
- * DESCRIPTION:
- *
- * The two argument polynomials are multiplied together, and
- * their product is placed in c.
- *
- * Each polynomial is represented by its coefficients stored
- * as an array of complex number structures (see the typedef).
- * The degree of a is da, which must be passed to the routine
- * as an argument; similarly the degree db of b is an argument.
- * Array a has da + 1 elements and array b has db + 1 elements.
- * Array c must have storage allocated for at least da + db + 1
- * elements. The value da + db is returned in dc; this is
- * the degree of the product polynomial.
- *
- * Polynomial coefficients are stored in ascending order; i.e.,
- * a(x) = a[0]*x**0 + a[1]*x**1 + ... + a[da]*x**da.
- *
- *
- * If desired, c may be the same as either a or b, in which
- * case the input argument array is replaced by the product
- * array (but only up to terms of degree da + db).
- *
- */
-\f
-/* dawsn.c
- *
- * Dawson's Integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, dawsn();
- *
- * y = dawsn( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- * x
- * -
- * 2 | | 2
- * dawsn(x) = exp( -x ) | exp( t ) dt
- * | |
- * -
- * 0
- *
- * Three different rational approximations are employed, for
- * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10 10000 6.9e-16 1.0e-16
- * DEC 0,10 6000 7.4e-17 1.4e-17
- *
- *
- */
-\f
-/* drand.c
- *
- * Pseudorandom number generator
- *
- *
- *
- * SYNOPSIS:
- *
- * double y, drand();
- *
- * drand( &y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Yields a random number 1.0 <= y < 2.0.
- *
- * The three-generator congruential algorithm by Brian
- * Wichmann and David Hill (BYTE magazine, March, 1987,
- * pp 127-8) is used. The period, given by them, is
- * 6953607871644.
- *
- * Versions invoked by the different arithmetic compile
- * time options DEC, IBMPC, and MIEEE, produce
- * approximately the same sequences, differing only in the
- * least significant bits of the numbers. The UNK option
- * implements the algorithm as recommended in the BYTE
- * article. It may be used on all computers. However,
- * the low order bits of a double precision number may
- * not be adequately random, and may vary due to arithmetic
- * implementation details on different computers.
- *
- * The other compile options generate an additional random
- * integer that overwrites the low order bits of the double
- * precision number. This reduces the period by a factor of
- * two but tends to overcome the problems mentioned.
- *
- */
-\f
-/* eigens.c
- *
- * Eigenvalues and eigenvectors of a real symmetric matrix
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double A[n*(n+1)/2], EV[n*n], E[n];
- * void eigens( A, EV, E, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * The algorithm is due to J. vonNeumann.
- *
- * A[] is a symmetric matrix stored in lower triangular form.
- * That is, A[ row, column ] = A[ (row*row+row)/2 + column ]
- * or equivalently with row and column interchanged. The
- * indices row and column run from 0 through n-1.
- *
- * EV[] is the output matrix of eigenvectors stored columnwise.
- * That is, the elements of each eigenvector appear in sequential
- * memory order. The jth element of the ith eigenvector is
- * EV[ n*i+j ] = EV[i][j].
- *
- * E[] is the output matrix of eigenvalues. The ith element
- * of E corresponds to the ith eigenvector (the ith row of EV).
- *
- * On output, the matrix A will have been diagonalized and its
- * orginal contents are destroyed.
- *
- * ACCURACY:
- *
- * The error is controlled by an internal parameter called RANGE
- * which is set to 1e-10. After diagonalization, the
- * off-diagonal elements of A will have been reduced by
- * this factor.
- *
- * ERROR MESSAGES:
- *
- * None.
- *
- */
-\f
-/* ellie.c
- *
- * Incomplete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double phi, m, y, ellie();
- *
- * y = ellie( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * phi
- * -
- * | |
- * | 2
- * E(phi_\m) = | sqrt( 1 - m sin t ) dt
- * |
- * | |
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random arguments with phi in [-10, 10] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,2 2000 1.9e-16 3.4e-17
- * IEEE -10,10 150000 3.3e-15 1.4e-16
- *
- *
- */
-\f
-/* ellik.c
- *
- * Incomplete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double phi, m, y, ellik();
- *
- * y = ellik( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * phi
- * -
- * | |
- * | dt
- * F(phi_\m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points with m in [0, 1] and phi as indicated.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 200000 7.4e-16 1.0e-16
- *
- *
- */
-\f
-/* ellpe.c
- *
- * Complete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double m1, y, ellpe();
- *
- * y = ellpe( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * pi/2
- * -
- * | | 2
- * E(m) = | sqrt( 1 - m sin t ) dt
- * | |
- * -
- * 0
- *
- * Where m = 1 - m1, using the approximation
- *
- * P(x) - x log x Q(x).
- *
- * Though there are no singularities, the argument m1 is used
- * rather than m for compatibility with ellpk().
- *
- * E(1) = 1; E(0) = pi/2.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 1 13000 3.1e-17 9.4e-18
- * IEEE 0, 1 10000 2.1e-16 7.3e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpe domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpj.c
- *
- * Jacobian Elliptic Functions
- *
- *
- *
- * SYNOPSIS:
- *
- * double u, m, sn, cn, dn, phi;
- * int ellpj();
- *
- * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
- * and dn(u|m) of parameter m between 0 and 1, and real
- * argument u.
- *
- * These functions are periodic, with quarter-period on the
- * real axis equal to the complete elliptic integral
- * ellpk(1.0-m).
- *
- * Relation to incomplete elliptic integral:
- * If u = ellik(phi,m), then sn(u|m) = sin(phi),
- * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
- *
- * Computation is by means of the arithmetic-geometric mean
- * algorithm, except when m is within 1e-9 of 0 or 1. In the
- * latter case with m close to 1, the approximation applies
- * only for phi < pi/2.
- *
- * ACCURACY:
- *
- * Tested at random points with u between 0 and 10, m between
- * 0 and 1.
- *
- * Absolute error (* = relative error):
- * arithmetic function # trials peak rms
- * DEC sn 1800 4.5e-16 8.7e-17
- * IEEE phi 10000 9.2e-16* 1.4e-16*
- * IEEE sn 50000 4.1e-15 4.6e-16
- * IEEE cn 40000 3.6e-15 4.4e-16
- * IEEE dn 10000 1.3e-12 1.8e-14
- *
- * Peak error observed in consistency check using addition
- * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
- * the above relation to the incomplete elliptic integral.
- * Accuracy deteriorates when u is large.
- *
- */
-\f
-/* ellpk.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double m1, y, ellpk();
- *
- * y = ellpk( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * pi/2
- * -
- * | |
- * | dt
- * K(m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * where m = 1 - m1, using the approximation
- *
- * P(x) - log x Q(x).
- *
- * The argument m1 is used rather than m so that the logarithmic
- * singularity at m = 1 will be shifted to the origin; this
- * preserves maximum accuracy.
- *
- * K(0) = pi/2.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,1 16000 3.5e-17 1.1e-17
- * IEEE 0,1 30000 2.5e-16 6.8e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpk domain x<0, x>1 0.0
- *
- */
-\f
-/* euclid.c
- *
- * Rational arithmetic routines
- *
- *
- *
- * SYNOPSIS:
- *
- *
- * typedef struct
- * {
- * double n; numerator
- * double d; denominator
- * }fract;
- *
- * radd( a, b, c ) c = b + a
- * rsub( a, b, c ) c = b - a
- * rmul( a, b, c ) c = b * a
- * rdiv( a, b, c ) c = b / a
- * euclid( &n, &d ) Reduce n/d to lowest terms,
- * return greatest common divisor.
- *
- * Arguments of the routines are pointers to the structures.
- * The double precision numbers are assumed, without checking,
- * to be integer valued. Overflow conditions are reported.
- */
- \f
-/* exp.c
- *
- * Exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, exp();
- *
- * y = exp( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns e (2.71828...) raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- *
- * x k f
- * e = 2 e.
- *
- * A Pade' form 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- * of degree 2/3 is used to approximate exp(f) in the basic
- * interval [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +- 88 50000 2.8e-17 7.0e-18
- * IEEE +- 708 40000 2.0e-16 5.6e-17
- *
- *
- * Error amplification in the exponential function can be
- * a serious matter. The error propagation involves
- * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
- * which shows that a 1 lsb error in representing X produces
- * a relative error of X times 1 lsb in the function.
- * While the routine gives an accurate result for arguments
- * that are exactly represented by a double precision
- * computer number, the result contains amplified roundoff
- * error for large arguments not exactly represented.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < MINLOG 0.0
- * exp overflow x > MAXLOG INFINITY
- *
- */
-\f
-/* exp10.c
- *
- * Base 10 exponential function
- * (Common antilogarithm)
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, exp10();
- *
- * y = exp10( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 10 raised to the x power.
- *
- * Range reduction is accomplished by expressing the argument
- * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
- * The Pade' form
- *
- * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- *
- * is used to approximate 10**f.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -307,+307 30000 2.2e-16 5.5e-17
- * Test result from an earlier version (2.1):
- * DEC -38,+38 70000 3.1e-17 7.0e-18
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp10 underflow x < -MAXL10 0.0
- * exp10 overflow x > MAXL10 MAXNUM
- *
- * DEC arithmetic: MAXL10 = 38.230809449325611792.
- * IEEE arithmetic: MAXL10 = 308.2547155599167.
- *
- */
-\f
-/* exp2.c
- *
- * Base 2 exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, exp2();
- *
- * y = exp2( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 2 raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- * x k f
- * 2 = 2 2.
- *
- * A Pade' form
- *
- * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
- *
- * approximates 2**x in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1022,+1024 30000 1.8e-16 5.4e-17
- *
- *
- * See exp.c for comments on error amplification.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < -MAXL2 0.0
- * exp overflow x > MAXL2 MAXNUM
- *
- * For DEC arithmetic, MAXL2 = 127.
- * For IEEE arithmetic, MAXL2 = 1024.
- */
-\f
-/* expn.c
- *
- * Exponential integral En
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double x, y, expn();
- *
- * y = expn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the exponential integral
- *
- * inf.
- * -
- * | | -xt
- * | e
- * E (x) = | ---- dt.
- * n | n
- * | | t
- * -
- * 1
- *
- *
- * Both n and x must be nonnegative.
- *
- * The routine employs either a power series, a continued
- * fraction, or an asymptotic formula depending on the
- * relative values of n and x.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 5000 2.0e-16 4.6e-17
- * IEEE 0, 30 10000 1.7e-15 3.6e-16
- *
- */
-\f
-/* fabs.c
- *
- * Absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y;
- *
- * y = fabs( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the absolute value of the argument.
- *
- */
-\f
-/* fac.c
- *
- * Factorial function
- *
- *
- *
- * SYNOPSIS:
- *
- * double y, fac();
- * int i;
- *
- * y = fac( i );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns factorial of i = 1 * 2 * 3 * ... * i.
- * fac(0) = 1.0.
- *
- * Due to machine arithmetic bounds the largest value of
- * i accepted is 33 in DEC arithmetic or 170 in IEEE
- * arithmetic. Greater values, or negative ones,
- * produce an error message and return MAXNUM.
- *
- *
- *
- * ACCURACY:
- *
- * For i < 34 the values are simply tabulated, and have
- * full machine accuracy. If i > 55, fac(i) = gamma(i+1);
- * see gamma.c.
- *
- * Relative error:
- * arithmetic domain peak
- * IEEE 0, 170 1.4e-15
- * DEC 0, 33 1.4e-17
- *
- */
-\f
-/* fdtr.c
- *
- * F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * double x, y, fdtr();
- *
- * y = fdtr( df1, df2, x );
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density). This is the density
- * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
- * variables having Chi square distributions with df1
- * and df2 degrees of freedom, respectively.
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
- *
- *
- * The arguments a and b are greater than zero, and x is
- * nonnegative.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x).
- *
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 0,100 100000 9.8e-15 1.7e-15
- * IEEE 1,5 0,100 100000 6.5e-15 3.5e-16
- * IEEE 0,1 1,10000 100000 2.2e-11 3.3e-12
- * IEEE 1,5 1,10000 100000 1.1e-11 1.7e-13
- * See also incbet.c.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtr domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrc()
- *
- * Complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * double x, y, fdtrc();
- *
- * y = fdtrc( df1, df2, x );
- *
- * DESCRIPTION:
- *
- * Returns the area from x to infinity under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density).
- *
- *
- * inf.
- * -
- * 1 | | a-1 b-1
- * 1-P(x) = ------ | t (1-t) dt
- * B(a,b) | |
- * -
- * x
- *
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
- *
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) in the indicated intervals.
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 1,100 100000 3.7e-14 5.9e-16
- * IEEE 1,5 1,100 100000 8.0e-15 1.6e-15
- * IEEE 0,1 1,10000 100000 1.8e-11 3.5e-13
- * IEEE 1,5 1,10000 100000 2.0e-11 3.0e-12
- * See also incbet.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrc domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtri()
- *
- * Inverse of complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * double x, p, fdtri();
- *
- * x = fdtri( df1, df2, p );
- *
- * DESCRIPTION:
- *
- * Finds the F density argument x such that the integral
- * from x to infinity of the F density is equal to the
- * given probability p.
- *
- * This is accomplished using the inverse beta integral
- * function and the relations
- *
- * z = incbi( df2/2, df1/2, p )
- * x = df2 (1-z) / (df1 z).
- *
- * Note: the following relations hold for the inverse of
- * the uncomplemented F distribution:
- *
- * z = incbi( df1/2, df2/2, p )
- * x = df2 z / (df1 (1-z)).
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between .001 and 1:
- * IEEE 1,100 100000 8.3e-15 4.7e-16
- * IEEE 1,10000 100000 2.1e-11 1.4e-13
- * For p between 10^-6 and 10^-3:
- * IEEE 1,100 50000 1.3e-12 8.4e-15
- * IEEE 1,10000 50000 3.0e-12 4.8e-14
- * See also fdtrc.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtri domain p <= 0 or p > 1 0.0
- * v < 1
- *
- */
-\f
-/* fftr.c
- *
- * FFT of Real Valued Sequence
- *
- *
- *
- * SYNOPSIS:
- *
- * double x[], sine[];
- * int m;
- *
- * fftr( x, m, sine );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the (complex valued) discrete Fourier transform of
- * the real valued sequence x[]. The input sequence x[] contains
- * n = 2**m samples. The program fills array sine[k] with
- * n/4 + 1 values of sin( 2 PI k / n ).
- *
- * Data format for complex valued output is real part followed
- * by imaginary part. The output is developed in the input
- * array x[].
- *
- * The algorithm takes advantage of the fact that the FFT of an
- * n point real sequence can be obtained from an n/2 point
- * complex FFT.
- *
- * A radix 2 FFT algorithm is used.
- *
- * Execution time on an LSI-11/23 with floating point chip
- * is 1.0 sec for n = 256.
- *
- *
- *
- * REFERENCE:
- *
- * E. Oran Brigham, The Fast Fourier Transform;
- * Prentice-Hall, Inc., 1974
- *
- */
-\f
-/* ceil()
- * floor()
- * frexp()
- * ldexp()
- * signbit()
- * isnan()
- * isfinite()
- *
- * Floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * double ceil(), floor(), frexp(), ldexp();
- * int signbit(), isnan(), isfinite();
- * double x, y;
- * int expnt, n;
- *
- * y = floor(x);
- * y = ceil(x);
- * y = frexp( x, &expnt );
- * y = ldexp( x, n );
- * n = signbit(x);
- * n = isnan(x);
- * n = isfinite(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * All four routines return a double precision floating point
- * result.
- *
- * floor() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * ceil() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * frexp() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * ldexp() multiplies x by 2**n.
- *
- * signbit(x) returns 1 if the sign bit of x is 1, else 0.
- *
- * These functions are part of the standard C run time library
- * for many but not all C compilers. The ones supplied are
- * written in C for either DEC or IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-/* fresnl.c
- *
- * Fresnel integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, S, C;
- * void fresnl();
- *
- * fresnl( x, _&S, _&C );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the Fresnel integrals
- *
- * x
- * -
- * | |
- * C(x) = | cos(pi/2 t**2) dt,
- * | |
- * -
- * 0
- *
- * x
- * -
- * | |
- * S(x) = | sin(pi/2 t**2) dt.
- * | |
- * -
- * 0
- *
- *
- * The integrals are evaluated by a power series for x < 1.
- * For x >= 1 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
- * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
- *
- *
- *
- * ACCURACY:
- *
- * Relative error.
- *
- * Arithmetic function domain # trials peak rms
- * IEEE S(x) 0, 10 10000 2.0e-15 3.2e-16
- * IEEE C(x) 0, 10 10000 1.8e-15 3.3e-16
- * DEC S(x) 0, 10 6000 2.2e-16 3.9e-17
- * DEC C(x) 0, 10 5000 2.3e-16 3.9e-17
- */
-\f
-/* gamma.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, gamma();
- * extern int sgngam;
- *
- * y = gamma( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
- *
- * Arguments |x| <= 34 are reduced by recurrence and the function
- * approximated by a rational function of degree 6/7 in the
- * interval (2,3). Large arguments are handled by Stirling's
- * formula. Large negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -34, 34 10000 1.3e-16 2.5e-17
- * IEEE -170,-33 20000 2.3e-15 3.3e-16
- * IEEE -33, 33 20000 9.4e-16 2.2e-16
- * IEEE 33, 171.6 20000 2.3e-15 3.2e-16
- *
- * Error for arguments outside the test range will be larger
- * owing to error amplification by the exponential function.
- *
- */\f
-/* lgam()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, lgam();
- * extern int sgngam;
- *
- * y = lgam( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
- *
- * For arguments greater than 13, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula using a polynomial approximation of
- * degree 4. Arguments between -33 and +33 are reduced by
- * recurrence to the interval [2,3] of a rational approximation.
- * The cosecant reflection formula is employed for arguments
- * less than -33.
- *
- * Arguments greater than MAXLGM return MAXNUM and an error
- * message. MAXLGM = 2.035093e36 for DEC
- * arithmetic or 2.556348e305 for IEEE arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- *
- * arithmetic domain # trials peak rms
- * DEC 0, 3 7000 5.2e-17 1.3e-17
- * DEC 2.718, 2.035e36 5000 3.9e-17 9.9e-18
- * IEEE 0, 3 28000 5.4e-16 1.1e-16
- * IEEE 2.718, 2.556e305 40000 3.5e-16 8.3e-17
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- *
- * The following test used the relative error criterion, though
- * at certain points the relative error could be much higher than
- * indicated.
- * IEEE -200, -4 10000 4.8e-16 1.3e-16
- *
- */
-\f
-/* gdtr.c
- *
- * Gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, gdtr();
- *
- * y = gdtr( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from zero to x of the gamma probability
- * density function:
- *
- *
- * x
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * 0
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igam( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtr domain x < 0 0.0
- *
- */
-\f/* gdtrc.c
- *
- * Complemented gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, gdtrc();
- *
- * y = gdtrc( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from x to infinity of the gamma
- * probability density function:
- *
- *
- * inf.
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * x
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igamc( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrc domain x < 0 0.0
- *
- */
-\f
-/*
-C
-C ..................................................................
-C
-C SUBROUTINE GELS
-C
-C PURPOSE
-C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
-C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
-C IS ASSUMED TO BE STORED COLUMNWISE.
-C
-C USAGE
-C CALL GELS(R,A,M,N,EPS,IER,AUX)
-C
-C DESCRIPTION OF PARAMETERS
-C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
-C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
-C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
-C M BY M COEFFICIENT MATRIX. (DESTROYED)
-C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
-C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
-C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
-C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
-C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
-C IER=0 - NO ERROR,
-C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
-C PIVOT ELEMENT AT ANY ELIMINATION STEP
-C EQUAL TO 0,
-C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
-C CANCE INDICATED AT ELIMINATION STEP K+1,
-C WHERE PIVOT ELEMENT WAS LESS THAN OR
-C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
-C ABSOLUTELY GREATEST MAIN DIAGONAL
-C ELEMENT OF MATRIX A.
-C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
-C
-C REMARKS
-C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
-C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
-C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
-C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
-C TOO.
-C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
-C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
-C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
-C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
-C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
-C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
-C GIVEN IN CASE M=1.
-C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
-C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
-C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
-C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
-C
-C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
-C NONE
-C
-C METHOD
-C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
-C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
-C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
-C
-C ..................................................................
-C
-*/
-\f
-/* hyp2f1.c
- *
- * Gauss hypergeometric function F
- * 2 1
- *
- *
- * SYNOPSIS:
- *
- * double a, b, c, x, y, hyp2f1();
- *
- * y = hyp2f1( a, b, c, x );
- *
- *
- * DESCRIPTION:
- *
- *
- * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
- * 2 1
- *
- * inf.
- * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
- * = 1 + > ----------------------------- x .
- * - c(c+1)...(c+k) (k+1)!
- * k = 0
- *
- * Cases addressed are
- * Tests and escapes for negative integer a, b, or c
- * Linear transformation if c - a or c - b negative integer
- * Special case c = a or c = b
- * Linear transformation for x near +1
- * Transformation for x < -0.5
- * Psi function expansion if x > 0.5 and c - a - b integer
- * Conditionally, a recurrence on c to make c-a-b > 0
- *
- * |x| > 1 is rejected.
- *
- * The parameters a, b, c are considered to be integer
- * valued if they are within 1.0e-14 of the nearest integer
- * (1.0e-13 for IEEE arithmetic).
- *
- * ACCURACY:
- *
- *
- * Relative error (-1 < x < 1):
- * arithmetic domain # trials peak rms
- * IEEE -1,7 230000 1.2e-11 5.2e-14
- *
- * Several special cases also tested with a, b, c in
- * the range -7 to 7.
- *
- * ERROR MESSAGES:
- *
- * A "partial loss of precision" message is printed if
- * the internally estimated relative error exceeds 1^-12.
- * A "singularity" message is printed on overflow or
- * in cases not addressed (such as x < -1).
- */
-\f
-/* hyperg.c
- *
- * Confluent hypergeometric function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, hyperg();
- *
- * y = hyperg( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the confluent hypergeometric function
- *
- * 1 2
- * a x a(a+1) x
- * F ( a,b;x ) = 1 + ---- + --------- + ...
- * 1 1 b 1! b(b+1) 2!
- *
- * Many higher transcendental functions are special cases of
- * this power series.
- *
- * As is evident from the formula, b must not be a negative
- * integer or zero unless a is an integer with 0 >= a > b.
- *
- * The routine attempts both a direct summation of the series
- * and an asymptotic expansion. In each case error due to
- * roundoff, cancellation, and nonconvergence is estimated.
- * The result with smaller estimated error is returned.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (a, b, x), all three variables
- * ranging from 0 to 30.
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 2000 1.2e-15 1.3e-16
- * IEEE 0,30 30000 1.8e-14 1.1e-15
- *
- * Larger errors can be observed when b is near a negative
- * integer or zero. Certain combinations of arguments yield
- * serious cancellation error in the power series summation
- * and also are not in the region of near convergence of the
- * asymptotic series. An error message is printed if the
- * self-estimated relative error is greater than 1.0e-12.
- *
- */
-\f
-/* i0.c
- *
- * Modified Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i0();
- *
- * y = i0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order zero of the
- * argument.
- *
- * The function is defined as i0(x) = j0( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 6000 8.2e-17 1.9e-17
- * IEEE 0,30 30000 5.8e-16 1.4e-16
- *
- */
-\f/* i0e.c
- *
- * Modified Bessel function of order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i0e();
- *
- * y = i0e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order zero of the argument.
- *
- * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 5.4e-16 1.2e-16
- * See i0().
- *
- */
-\f
-/* i1.c
- *
- * Modified Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i1();
- *
- * y = i1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order one of the
- * argument.
- *
- * The function is defined as i1(x) = -i j1( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 3400 1.2e-16 2.3e-17
- * IEEE 0, 30 30000 1.9e-15 2.1e-16
- *
- *
- */
-\f/* i1e.c
- *
- * Modified Bessel function of order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i1e();
- *
- * y = i1e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order one of the argument.
- *
- * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 2.0e-15 2.0e-16
- * See i1().
- *
- */
-\f
-/* igam.c
- *
- * Incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, y, igam();
- *
- * y = igam( a, x );
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 200000 3.6e-14 2.9e-15
- * IEEE 0,100 300000 9.9e-14 1.5e-14
- */
-\f/* igamc()
- *
- * Complemented incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, y, igamc();
- *
- * y = igamc( a, x );
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- * ACCURACY:
- *
- * Tested at random a, x.
- * a x Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
- * IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
- */
-\f
-/* igami()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, p, igami();
- *
- * x = igami( a, p );
- *
- * DESCRIPTION:
- *
- * Given p, the function finds x such that
- *
- * igamc( a, x ) = p.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(p) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - p = 0.
- *
- * ACCURACY:
- *
- * Tested at random a, p in the intervals indicated.
- *
- * a p Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15
- * IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15
- * IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14
- */
-\f
-/* incbet.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, incbet();
- *
- * y = incbet( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion
- * or, when b*x is small, by a power series.
- *
- * ACCURACY:
- *
- * Tested at uniformly distributed random points (a,b,x) with a and b
- * in "domain" and x between 0 and 1.
- * Relative error
- * arithmetic domain # trials peak rms
- * IEEE 0,5 10000 6.9e-15 4.5e-16
- * IEEE 0,85 250000 2.2e-13 1.7e-14
- * IEEE 0,1000 30000 5.3e-12 6.3e-13
- * IEEE 0,10000 250000 9.3e-11 7.1e-12
- * IEEE 0,100000 10000 8.7e-10 4.8e-11
- * Outputs smaller than the IEEE gradual underflow threshold
- * were excluded from these statistics.
- *
- * ERROR MESSAGES:
- * message condition value returned
- * incbet domain x<0, x>1 0.0
- * incbet underflow 0.0
- */
-\f
-/* incbi()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, incbi();
- *
- * x = incbi( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y .
- *
- * The routine performs interval halving or Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 .5,10000 50000 5.8e-12 1.3e-13
- * IEEE 0,1 .25,100 100000 1.8e-13 3.9e-15
- * IEEE 0,1 0,5 50000 1.1e-12 5.5e-15
- * VAX 0,1 .5,100 25000 3.5e-14 1.1e-15
- * With a and b constrained to half-integer or integer values:
- * IEEE 0,1 .5,10000 50000 5.8e-12 1.1e-13
- * IEEE 0,1 .5,100 100000 1.7e-14 7.9e-16
- * With a = .5, b constrained to half-integer or integer values:
- * IEEE 0,1 .5,10000 10000 8.3e-11 1.0e-11
- */
-\f
-/* iv.c
- *
- * Modified Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, iv();
- *
- * y = iv( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order v of the
- * argument. If x is negative, v must be integer valued.
- *
- * The function is defined as Iv(x) = Jv( ix ). It is
- * here computed in terms of the confluent hypergeometric
- * function, according to the formula
- *
- * v -x
- * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
- *
- * If v is a negative integer, then v is replaced by -v.
- *
- *
- * ACCURACY:
- *
- * Tested at random points (v, x), with v between 0 and
- * 30, x between 0 and 28.
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 2000 3.1e-15 5.4e-16
- * IEEE 0,30 10000 1.7e-14 2.7e-15
- *
- * Accuracy is diminished if v is near a negative integer.
- *
- * See also hyperg.c.
- *
- */
-\f
-/* j0.c
- *
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j0();
- *
- * y = j0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval the following rational
- * approximation is used:
- *
- *
- * 2 2
- * (w - r ) (w - r ) P (w) / Q (w)
- * 1 2 3 8
- *
- * 2
- * where w = x and the two r's are zeros of the function.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.4e-17 6.3e-18
- * IEEE 0, 30 60000 4.2e-16 1.1e-16
- *
- */
-\f/* y0.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y0();
- *
- * y = y0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
- * Thus a call to j0() is required.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * DEC 0, 30 9400 7.0e-17 7.9e-18
- * IEEE 0, 30 30000 1.3e-15 1.6e-16
- *
- */
-\f
-/* j1.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j1();
- *
- * y = j1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 24 term Chebyshev
- * expansion is used. In the second, the asymptotic
- * trigonometric representation is employed using two
- * rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.0e-17 1.1e-17
- * IEEE 0, 30 30000 2.6e-16 1.1e-16
- *
- *
- */
-\f/* y1.c
- *
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 25 term Chebyshev
- * expansion is used, and a call to j1() is required.
- * In the second, the asymptotic trigonometric representation
- * is employed using two rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 8.6e-17 1.3e-17
- * IEEE 0, 30 30000 1.0e-15 1.3e-16
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-\f
-/* jn.c
- *
- * Bessel function of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double x, y, jn();
- *
- * y = jn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The ratio of jn(x) to j0(x) is computed by backward
- * recurrence. First the ratio jn/jn-1 is found by a
- * continued fraction expansion. Then the recurrence
- * relating successive orders is applied until j0 or j1 is
- * reached.
- *
- * If n = 0 or 1 the routine for j0 or j1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic range # trials peak rms
- * DEC 0, 30 5500 6.9e-17 9.3e-18
- * IEEE 0, 30 5000 4.4e-16 7.9e-17
- *
- *
- * Not suitable for large n or x. Use jv() instead.
- *
- */
-\f
-/* jv.c
- *
- * Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, jv();
- *
- * y = jv( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order v of the argument,
- * where v is real. Negative x is allowed if v is an integer.
- *
- * Several expansions are included: the ascending power
- * series, the Hankel expansion, and two transitional
- * expansions for large v. If v is not too large, it
- * is reduced by recurrence to a region of best accuracy.
- * The transitional expansions give 12D accuracy for v > 500.
- *
- *
- *
- * ACCURACY:
- * Results for integer v are indicated by *, where x and v
- * both vary from -125 to +125. Otherwise,
- * x ranges from 0 to 125, v ranges as indicated by "domain."
- * Error criterion is absolute, except relative when |jv()| > 1.
- *
- * arithmetic v domain x domain # trials peak rms
- * IEEE 0,125 0,125 100000 4.6e-15 2.2e-16
- * IEEE -125,0 0,125 40000 5.4e-11 3.7e-13
- * IEEE 0,500 0,500 20000 4.4e-15 4.0e-16
- * Integer v:
- * IEEE -125,125 -125,125 50000 3.5e-15* 1.9e-16*
- *
- */
-\f
-/* k0.c
- *
- * Modified Bessel function, third kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k0();
- *
- * y = k0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order zero of the argument.
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at 2000 random points between 0 and 8. Peak absolute
- * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 3100 1.3e-16 2.1e-17
- * IEEE 0, 30 30000 1.2e-15 1.6e-16
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * K0 domain x <= 0 MAXNUM
- *
- */
-\f/* k0e()
- *
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k0e();
- *
- * y = k0e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.4e-15 1.4e-16
- * See k0().
- *
- */
-\f
-/* k1.c
- *
- * Modified Bessel function, third kind, order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k1();
- *
- * y = k1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the modified Bessel function of the third kind
- * of order one of the argument.
- *
- * The range is partitioned into the two intervals [0,2] and
- * (2, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 3300 8.9e-17 2.2e-17
- * IEEE 0, 30 30000 1.2e-15 1.6e-16
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * k1 domain x <= 0 MAXNUM
- *
- */
-\f/* k1e.c
- *
- * Modified Bessel function, third kind, order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k1e();
- *
- * y = k1e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order one of the argument:
- *
- * k1e(x) = exp(x) * k1(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-16 1.2e-16
- * See k1().
- *
- */
-\f
-/* kn.c
- *
- * Modified Bessel function, third kind, integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, kn();
- * int n;
- *
- * y = kn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order n of the argument.
- *
- * The range is partitioned into the two intervals [0,9.55] and
- * (9.55, infinity). An ascending power series is used in the
- * low range, and an asymptotic expansion in the high range.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 3000 1.3e-9 5.8e-11
- * IEEE 0,30 90000 1.8e-8 3.0e-10
- *
- * Error is high only near the crossover point x = 9.55
- * between the two expansions used.
- */
-\f
-
-/* Re Kolmogorov statistics, here is Birnbaum and Tingey's formula for the
- distribution of D+, the maximum of all positive deviations between a
- theoretical distribution function P(x) and an empirical one Sn(x)
- from n samples.
-
- +
- D = sup [ P(x) - Sn(x) ]
- n -inf < x < inf
-
-
- [n(1-e)]
- + - v-1 n-v
- Pr{D > e} = > C e (e + v/n) (1 - e - v/n)
- n - n v
- v=0
- [n(1-e)] is the largest integer not exceeding n(1-e).
- nCv is the number of combinations of n things taken v at a time.
-
- Exact Smirnov statistic, for one-sided test:
-double
-smirnov (n, e)
- int n;
- double e;
-
- Kolmogorov's limiting distribution of two-sided test, returns
- probability that sqrt(n) * max deviation > y,
- or that max deviation > y/sqrt(n).
- The approximation is useful for the tail of the distribution
- when n is large.
-double
-kolmogorov (y)
- double y;
-
-
- Functional inverse of Smirnov distribution
- finds e such that smirnov(n,e) = p.
-double
-smirnovi (n, p)
- int n;
- double p;
-
- Functional inverse of Kolmogorov statistic for two-sided test.
- Finds y such that kolmogorov(y) = p.
- If e = smirnovi (n,p), then kolmogi(2 * p) / sqrt(n) should
- be close to e.
-double
-kolmogi (p)
- double p;
- */
-\f
-/* Levnsn.c */
-/* Levinson-Durbin LPC
- *
- * | R0 R1 R2 ... RN-1 | | A1 | | -R1 |
- * | R1 R0 R1 ... RN-2 | | A2 | | -R2 |
- * | R2 R1 R0 ... RN-3 | | A3 | = | -R3 |
- * | ... | | ...| | ... |
- * | RN-1 RN-2... R0 | | AN | | -RN |
- *
- * Ref: John Makhoul, "Linear Prediction, A Tutorial Review"
- * Proc. IEEE Vol. 63, PP 561-580 April, 1975.
- *
- * R is the input autocorrelation function. R0 is the zero lag
- * term. A is the output array of predictor coefficients. Note
- * that a filter impulse response has a coefficient of 1.0 preceding
- * A1. E is an array of mean square error for each prediction order
- * 1 to N. REFL is an output array of the reflection coefficients.
- */
-\f
-/* log.c
- *
- * Natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, log();
- *
- * y = log( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 150000 1.44e-16 5.06e-17
- * IEEE +-MAXNUM 30000 1.20e-16 4.78e-17
- * DEC 0, 10 170000 1.8e-17 6.3e-18
- *
- * In the tests over the interval [+-MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [0, MAXLOG].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITY
- * log domain: x < 0; returns NAN
- */
-\f
-/* log10.c
- *
- * Common logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, log10();
- *
- * y = log10( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns logarithm to the base 10 of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. The logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 1.5e-16 5.0e-17
- * IEEE 0, MAXNUM 30000 1.4e-16 4.8e-17
- * DEC 1, MAXNUM 50000 2.5e-17 6.0e-18
- *
- * In the tests over the interval [1, MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [0, MAXLOG].
- *
- * ERROR MESSAGES:
- *
- * log10 singularity: x = 0; returns -INFINITY
- * log10 domain: x < 0; returns NAN
- */
-\f
-/* log2.c
- *
- * Base 2 logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, log2();
- *
- * y = log2( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 2 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the base e
- * logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 2.0e-16 5.5e-17
- * IEEE exp(+-700) 40000 1.3e-16 4.6e-17
- *
- * In the tests over the interval [exp(+-700)], the logarithms
- * of the random arguments were uniformly distributed.
- *
- * ERROR MESSAGES:
- *
- * log2 singularity: x = 0; returns -INFINITY
- * log2 domain: x < 0; returns NAN
- */
-\f
-/* lrand.c
- *
- * Pseudorandom number generator
- *
- *
- *
- * SYNOPSIS:
- *
- * long y, drand();
- *
- * drand( &y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Yields a long integer random number.
- *
- * The three-generator congruential algorithm by Brian
- * Wichmann and David Hill (BYTE magazine, March, 1987,
- * pp 127-8) is used. The period, given by them, is
- * 6953607871644.
- *
- *
- */
-\f
-/* lsqrt.c
- *
- * Integer square root
- *
- *
- *
- * SYNOPSIS:
- *
- * long x, y;
- * long lsqrt();
- *
- * y = lsqrt( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns a long integer square root of the long integer
- * argument. The computation is by binary long division.
- *
- * The largest possible result is lsqrt(2,147,483,647)
- * = 46341.
- *
- * If x < 0, the square root of |x| is returned, and an
- * error message is printed.
- *
- *
- * ACCURACY:
- *
- * An extra, roundoff, bit is computed; hence the result
- * is the nearest integer to the actual square root.
- * NOTE: only DEC arithmetic is currently supported.
- *
- */
-\f
-/* minv.c
- *
- * Matrix inversion
- *
- *
- *
- * SYNOPSIS:
- *
- * int n, errcod;
- * double A[n*n], X[n*n];
- * double B[n];
- * int IPS[n];
- * int minv();
- *
- * errcod = minv( A, X, n, B, IPS );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the inverse of the n by n matrix A. The result goes
- * to X. B and IPS are scratch pad arrays of length n.
- * The contents of matrix A are destroyed.
- *
- * The routine returns nonzero on error; error messages are printed
- * by subroutine simq().
- *
- */
-\f
-/* mmmpy.c
- *
- * Matrix multiply
- *
- *
- *
- * SYNOPSIS:
- *
- * int r, c;
- * double A[r*c], B[c*r], Y[r*r];
- *
- * mmmpy( r, c, A, B, Y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Y = A B
- * c-1
- * --
- * Y[i][j] = > A[i][k] B[k][j]
- * --
- * k=0
- *
- * Multiplies an r (rows) by c (columns) matrix A on the left
- * by a c (rows) by r (columns) matrix B on the right
- * to produce an r by r matrix Y.
- *
- *
- */
-\f
-/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * int mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file math.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * math.h
- *
- */
-\f
-/* mtransp.c
- *
- * Matrix transpose
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double A[n*n], T[n*n];
- *
- * mtransp( n, A, T );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * T[r][c] = A[c][r]
- *
- *
- * Transposes the n by n square matrix A and puts the result in T.
- * The output, T, may occupy the same storage as A.
- *
- *
- *
- */
-\f
-/* mvmpy.c
- *
- * Matrix times vector
- *
- *
- *
- * SYNOPSIS:
- *
- * int r, c;
- * double A[r*c], V[c], Y[r];
- *
- * mvmpy( r, c, A, V, Y );
- *
- *
- *
- * DESCRIPTION:
- *
- * c-1
- * --
- * Y[j] = > A[j][k] V[k] , j = 1, ..., r
- * --
- * k=0
- *
- * Multiplies the r (rows) by c (columns) matrix A on the left
- * by column vector V of dimension c on the right
- * to produce a (column) vector Y output of dimension r.
- *
- *
- *
- *
- */
-\f
-/* nbdtr.c
- *
- * Negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtr();
- *
- * y = nbdtr( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the negative
- * binomial distribution:
- *
- * k
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * In a sequence of Bernoulli trials, this is the probability
- * that k or fewer failures precede the nth success.
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p), with p between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 100000 1.7e-13 8.8e-15
- * See also incbet.c.
- *
- */
-\f/* nbdtrc.c
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtrc();
- *
- * y = nbdtrc( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p), with p between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 100000 1.7e-13 8.8e-15
- * See also incbet.c.
- */
-\f
-/* nbdtrc
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtrc();
- *
- * y = nbdtrc( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * See incbet.c.
- */
-\f/* nbdtri
- *
- * Functional inverse of negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtri();
- *
- * p = nbdtri( k, n, y );
- *
- * DESCRIPTION:
- *
- * Finds the argument p such that nbdtr(k,n,p) is equal to y.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,y), with y between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 100000 1.5e-14 8.5e-16
- * See also incbi.c.
- */
-\f
-/* ndtr.c
- *
- * Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, ndtr();
- *
- * y = ndtr( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the Gaussian probability density
- * function, integrated from minus infinity to x:
- *
- * x
- * -
- * 1 | | 2
- * ndtr(x) = --------- | exp( - t /2 ) dt
- * sqrt(2pi) | |
- * -
- * -inf.
- *
- * = ( 1 + erf(z) ) / 2
- * = erfc(z) / 2
- *
- * where z = x/sqrt(2). Computation is via the functions
- * erf and erfc.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -13,0 8000 2.1e-15 4.8e-16
- * IEEE -13,0 30000 3.4e-14 6.7e-15
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfc underflow x > 37.519379347 0.0
- *
- */
-\f/* erf.c
- *
- * Error function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, erf();
- *
- * y = erf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The integral is
- *
- * x
- * -
- * 2 | | 2
- * erf(x) = -------- | exp( - t ) dt.
- * sqrt(pi) | |
- * -
- * 0
- *
- * The magnitude of x is limited to 9.231948545 for DEC
- * arithmetic; 1 or -1 is returned outside this range.
- *
- * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
- * erf(x) = 1 - erfc(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,1 14000 4.7e-17 1.5e-17
- * IEEE 0,1 30000 3.7e-16 1.0e-16
- *
- */
-\f/* erfc.c
- *
- * Complementary error function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, erfc();
- *
- * y = erfc( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * 1 - erf(x) =
- *
- * inf.
- * -
- * 2 | | 2
- * erfc(x) = -------- | exp( - t ) dt
- * sqrt(pi) | |
- * -
- * x
- *
- *
- * For small x, erfc(x) = 1 - erf(x); otherwise rational
- * approximations are computed.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 9.2319 12000 5.1e-16 1.2e-16
- * IEEE 0,26.6417 30000 5.7e-14 1.5e-14
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfc underflow x > 9.231948545 (DEC) 0.0
- *
- *
- */
-\f
-/* ndtri.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, ndtri();
- *
- * x = ndtri( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2.0 * log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
- * There are two rational functions P/Q, one for 0 < y < exp(-32)
- * and the other for y up to exp(-2). For larger arguments,
- * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0.125, 1 5500 9.5e-17 2.1e-17
- * DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
- * IEEE 0.125, 1 20000 7.2e-16 1.3e-16
- * IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtri domain x <= 0 -MAXNUM
- * ndtri domain x >= 1 MAXNUM
- *
- */
-\f
-/* pdtr.c
- *
- * Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * double m, y, pdtr();
- *
- * y = pdtr( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the first k terms of the Poisson
- * distribution:
- *
- * k j
- * -- -m m
- * > e --
- * -- j!
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the relation
- *
- * y = pdtr( k, m ) = igamc( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- */
-\f/* pdtrc()
- *
- * Complemented poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * double m, y, pdtrc();
- *
- * y = pdtrc( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the Poisson
- * distribution:
- *
- * inf. j
- * -- -m m
- * > e --
- * -- j!
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the formula
- *
- * y = pdtrc( k, m ) = igam( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam.c.
- *
- */
-\f/* pdtri()
- *
- * Inverse Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * double m, y, pdtr();
- *
- * m = pdtri( k, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Poisson variable x such that the integral
- * from 0 to x of the Poisson density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * m = igami( k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pdtri domain y < 0 or y >= 1 0.0
- * k < 0
- *
- */
-\f
-/* polevl.c
- * p1evl.c
- *
- * Evaluate polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * double x, y, coef[N+1], polevl[];
- *
- * y = polevl( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates polynomial of degree N:
- *
- * 2 N
- * y = C + C x + C x +...+ C x
- * 0 1 2 N
- *
- * Coefficients are stored in reverse order:
- *
- * coef[0] = C , ..., coef[N] = C .
- * N 0
- *
- * The function p1evl() assumes that coef[N] = 1.0 and is
- * omitted from the array. Its calling arguments are
- * otherwise the same as polevl().
- *
- *
- * SPEED:
- *
- * In the interest of speed, there are no checks for out
- * of bounds arithmetic. This routine is used by most of
- * the functions in the library. Depending on available
- * equipment features, the user may wish to rewrite the
- * program in microcode or assembly language.
- *
- */
-\f
-/* polmisc.c
- * Square root, sine, cosine, and arctangent of polynomial.
- * See polyn.c for data structures and discussion.
- */
-\f
-/* polrt.c
- *
- * Find roots of a polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct
- * {
- * double r;
- * double i;
- * }cmplx;
- *
- * double xcof[], cof[];
- * int m;
- * cmplx root[];
- *
- * polrt( xcof, cof, m, root )
- *
- *
- *
- * DESCRIPTION:
- *
- * Iterative determination of the roots of a polynomial of
- * degree m whose coefficient vector is xcof[]. The
- * coefficients are arranged in ascending order; i.e., the
- * coefficient of x**m is xcof[m].
- *
- * The array cof[] is working storage the same size as xcof[].
- * root[] is the output array containing the complex roots.
- *
- *
- * ACCURACY:
- *
- * Termination depends on evaluation of the polynomial at
- * the trial values of the roots. The values of multiple roots
- * or of roots that are nearly equal may have poor relative
- * accuracy after the first root in the neighborhood has been
- * found.
- *
- */
-\f
-/* polyn.c
- * polyr.c
- * Arithmetic operations on polynomials
- *
- * In the following descriptions a, b, c are polynomials of degree
- * na, nb, nc respectively. The degree of a polynomial cannot
- * exceed a run-time value MAXPOL. An operation that attempts
- * to use or generate a polynomial of higher degree may produce a
- * result that suffers truncation at degree MAXPOL. The value of
- * MAXPOL is set by calling the function
- *
- * polini( maxpol );
- *
- * where maxpol is the desired maximum degree. This must be
- * done prior to calling any of the other functions in this module.
- * Memory for internal temporary polynomial storage is allocated
- * by polini().
- *
- * Each polynomial is represented by an array containing its
- * coefficients, together with a separately declared integer equal
- * to the degree of the polynomial. The coefficients appear in
- * ascending order; that is,
- *
- * 2 na
- * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
- *
- *
- *
- * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
- * polprt( a, na, D ); Print the coefficients of a to D digits.
- * polclr( a, na ); Set a identically equal to zero, up to a[na].
- * polmov( a, na, b ); Set b = a.
- * poladd( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
- * polsub( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
- * polmul( a, na, b, nb, c ); c = b * a, nc = na+nb
- *
- *
- * Division:
- *
- * i = poldiv( a, na, b, nb, c ); c = b / a, nc = MAXPOL
- *
- * returns i = the degree of the first nonzero coefficient of a.
- * The computed quotient c must be divided by x^i. An error message
- * is printed if a is identically zero.
- *
- *
- * Change of variables:
- * If a and b are polynomials, and t = a(x), then
- * c(t) = b(a(x))
- * is a polynomial found by substituting a(x) for t. The
- * subroutine call for this is
- *
- * polsbt( a, na, b, nb, c );
- *
- *
- * Notes:
- * poldiv() is an integer routine; poleva() is double.
- * Any of the arguments a, b, c may refer to the same array.
- *
- */
-\f
-/* pow.c
- *
- * Power function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, z, pow();
- *
- * z = pow( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/16 and pseudo extended precision arithmetic to
- * obtain an extra three bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -26,26 30000 4.2e-16 7.7e-17
- * DEC -26,26 60000 4.8e-17 9.1e-18
- * 1/26 < x < 26, with log(x) uniformly distributed.
- * -26 < y < 26, y uniformly distributed.
- * IEEE 0,8700 30000 1.5e-14 2.1e-15
- * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pow overflow x**y > MAXNUM INFINITY
- * pow underflow x**y < 1/MAXNUM 0.0
- * pow domain x<0 and y noninteger 0.0
- *
- */
-\f
-/* powi.c
- *
- * Real raised to integer power
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, powi();
- * int n;
- *
- * y = powi( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns argument x raised to the nth power.
- * The routine efficiently decomposes n as a sum of powers of
- * two. The desired power is a product of two-to-the-kth
- * powers of x. Thus to compute the 32767 power of x requires
- * 28 multiplications instead of 32767 multiplications.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic x domain n domain # trials peak rms
- * DEC .04,26 -26,26 100000 2.7e-16 4.3e-17
- * IEEE .04,26 -26,26 50000 2.0e-15 3.8e-16
- * IEEE 1,2 -1022,1023 50000 8.6e-14 1.6e-14
- *
- * Returns MAXNUM on overflow, zero on underflow.
- *
- */
-\f
-/* psi.c
- *
- * Psi (digamma) function
- *
- *
- * SYNOPSIS:
- *
- * double x, y, psi();
- *
- * y = psi( x );
- *
- *
- * DESCRIPTION:
- *
- * d -
- * psi(x) = -- ln | (x)
- * dx
- *
- * is the logarithmic derivative of the gamma function.
- * For integer x,
- * n-1
- * -
- * psi(n) = -EUL + > 1/k.
- * -
- * k=1
- *
- * This formula is used for 0 < n <= 10. If x is negative, it
- * is transformed to a positive argument by the reflection
- * formula psi(1-x) = psi(x) + pi cot(pi x).
- * For general positive x, the argument is made greater than 10
- * using the recurrence psi(x+1) = psi(x) + 1/x.
- * Then the following asymptotic expansion is applied:
- *
- * inf. B
- * - 2k
- * psi(x) = log(x) - 1/2x - > -------
- * - 2k
- * k=1 2k x
- *
- * where the B2k are Bernoulli numbers.
- *
- * ACCURACY:
- * Relative error (except absolute when |psi| < 1):
- * arithmetic domain # trials peak rms
- * DEC 0,30 2500 1.7e-16 2.0e-17
- * IEEE 0,30 30000 1.3e-15 1.4e-16
- * IEEE -30,0 40000 1.5e-15 2.2e-16
- *
- * ERROR MESSAGES:
- * message condition value returned
- * psi singularity x integer <=0 MAXNUM
- */
-\f
-/* revers.c
- *
- * Reversion of power series
- *
- *
- *
- * SYNOPSIS:
- *
- * extern int MAXPOL;
- * int n;
- * double x[n+1], y[n+1];
- *
- * polini(n);
- * revers( y, x, n );
- *
- * Note, polini() initializes the polynomial arithmetic subroutines;
- * see polyn.c.
- *
- *
- * DESCRIPTION:
- *
- * If
- *
- * inf
- * - i
- * y(x) = > a x
- * - i
- * i=1
- *
- * then
- *
- * inf
- * - j
- * x(y) = > A y ,
- * - j
- * j=1
- *
- * where
- * 1
- * A = ---
- * 1 a
- * 1
- *
- * etc. The coefficients of x(y) are found by expanding
- *
- * inf inf
- * - - i
- * x(y) = > A > a x
- * - j - i
- * j=1 i=1
- *
- * and setting each coefficient of x , higher than the first,
- * to zero.
- *
- *
- *
- * RESTRICTIONS:
- *
- * y[0] must be zero, and y[1] must be nonzero.
- *
- */
-\f
-/* rgamma.c
- *
- * Reciprocal gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, rgamma();
- *
- * y = rgamma( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns one divided by the gamma function of the argument.
- *
- * The function is approximated by a Chebyshev expansion in
- * the interval [0,1]. Range reduction is by recurrence
- * for arguments between -34.034 and +34.84425627277176174.
- * 1/MAXNUM is returned for positive arguments outside this
- * range. For arguments less than -34.034 the cosecant
- * reflection formula is applied; lograrithms are employed
- * to avoid unnecessary overflow.
- *
- * The reciprocal gamma function has no singularities,
- * but overflow and underflow may occur for large arguments.
- * These conditions return either MAXNUM or 1/MAXNUM with
- * appropriate sign.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -30,+30 4000 1.2e-16 1.8e-17
- * IEEE -30,+30 30000 1.1e-15 2.0e-16
- * For arguments less than -34.034 the peak error is on the
- * order of 5e-15 (DEC), excepting overflow or underflow.
- */
-\f
-/* round.c
- *
- * Round double to nearest or even integer valued double
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, round();
- *
- * y = round(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the nearest integer to x as a double precision
- * floating point result. If x ends in 0.5 exactly, the
- * nearest even integer is chosen.
- *
- *
- *
- * ACCURACY:
- *
- * If x is greater than 1/(2*MACHEP), its closest machine
- * representation is already an integer, so rounding does
- * not change it.
- */
-\f
-/* shichi.c
- *
- * Hyperbolic sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, Chi, Shi, shichi();
- *
- * shichi( x, &Chi, &Shi );
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integrals
- *
- * x
- * -
- * | | cosh t - 1
- * Chi(x) = eul + ln x + | ----------- dt,
- * | | t
- * -
- * 0
- *
- * x
- * -
- * | | sinh t
- * Shi(x) = | ------ dt
- * | | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are evaluated by power series for x < 8
- * and by Chebyshev expansions for x between 8 and 88.
- * For large x, both functions approach exp(x)/2x.
- * Arguments greater than 88 in magnitude return MAXNUM.
- *
- *
- * ACCURACY:
- *
- * Test interval 0 to 88.
- * Relative error:
- * arithmetic function # trials peak rms
- * DEC Shi 3000 9.1e-17
- * IEEE Shi 30000 6.9e-16 1.6e-16
- * Absolute error, except relative when |Chi| > 1:
- * DEC Chi 2500 9.3e-17
- * IEEE Chi 30000 8.4e-16 1.4e-16
- */
-\f
-/* sici.c
- *
- * Sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, Ci, Si, sici();
- *
- * sici( x, &Si, &Ci );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the integrals
- *
- * x
- * -
- * | cos t - 1
- * Ci(x) = eul + ln x + | --------- dt,
- * | t
- * -
- * 0
- * x
- * -
- * | sin t
- * Si(x) = | ----- dt
- * | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are approximated by rational functions.
- * For x > 8 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * Ci(x) = f(x) sin(x) - g(x) cos(x)
- * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
- *
- *
- * ACCURACY:
- * Test interval = [0,50].
- * Absolute error, except relative when > 1:
- * arithmetic function # trials peak rms
- * IEEE Si 30000 4.4e-16 7.3e-17
- * IEEE Ci 30000 6.9e-16 5.1e-17
- * DEC Si 5000 4.4e-17 9.0e-18
- * DEC Ci 5300 7.9e-17 5.2e-18
- */
-\f
-/* simpsn.c */
- * Numerical integration of function tabulated
- * at equally spaced arguments
- */
-\f
-/* simq.c
- *
- * Solution of simultaneous linear equations AX = B
- * by Gaussian elimination with partial pivoting
- *
- *
- *
- * SYNOPSIS:
- *
- * double A[n*n], B[n], X[n];
- * int n, flag;
- * int IPS[];
- * int simq();
- *
- * ercode = simq( A, B, X, n, flag, IPS );
- *
- *
- *
- * DESCRIPTION:
- *
- * B, X, IPS are vectors of length n.
- * A is an n x n matrix (i.e., a vector of length n*n),
- * stored row-wise: that is, A(i,j) = A[ij],
- * where ij = i*n + j, which is the transpose of the normal
- * column-wise storage.
- *
- * The contents of matrix A are destroyed.
- *
- * Set flag=0 to solve.
- * Set flag=-1 to do a new back substitution for different B vector
- * using the same A matrix previously reduced when flag=0.
- *
- * The routine returns nonzero on error; messages are printed.
- *
- *
- * ACCURACY:
- *
- * Depends on the conditioning (range of eigenvalues) of matrix A.
- *
- *
- * REFERENCE:
- *
- * Computer Solution of Linear Algebraic Systems,
- * by George E. Forsythe and Cleve B. Moler; Prentice-Hall, 1967.
- *
- */
-\f
-/* sin.c
- *
- * Circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sin();
- *
- * y = sin( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 Q(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 10 150000 3.0e-17 7.8e-18
- * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 1.073741824e9 0.0
- *
- * Partial loss of accuracy begins to occur at x = 2**30
- * = 1.074e9. The loss is not gradual, but jumps suddenly to
- * about 1 part in 10e7. Results may be meaningless for
- * x > 2**49 = 5.6e14. The routine as implemented flags a
- * TLOSS error for x > 2**30 and returns 0.0.
- */
-\f/* cos.c
- *
- * Circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cos();
- *
- * y = cos( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 Q(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
- * DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
- */
-\f
-/* sincos.c
- *
- * Circular sine and cosine of argument in degrees
- * Table lookup and interpolation algorithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, sine, cosine, flg, sincos();
- *
- * sincos( x, &sine, &cosine, flg );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns both the sine and the cosine of the argument x.
- * Several different compile time options and minimax
- * approximations are supplied to permit tailoring the
- * tradeoff between computation speed and accuracy.
- *
- * Since range reduction is time consuming, the reduction
- * of x modulo 360 degrees is also made optional.
- *
- * sin(i) is internally tabulated for 0 <= i <= 90 degrees.
- * Approximation polynomials, ranging from linear interpolation
- * to cubics in (x-i)**2, compute the sine and cosine
- * of the residual x-i which is between -0.5 and +0.5 degree.
- * In the case of the high accuracy options, the residual
- * and the tabulated values are combined using the trigonometry
- * formulas for sin(A+B) and cos(A+B).
- *
- * Compile time options are supplied for 5, 11, or 17 decimal
- * relative accuracy (ACC5, ACC11, ACC17 respectively).
- * A subroutine flag argument "flg" chooses betwen this
- * accuracy and table lookup only (peak absolute error
- * = 0.0087).
- *
- * If the argument flg = 1, then the tabulated value is
- * returned for the nearest whole number of degrees. The
- * approximation polynomials are not computed. At
- * x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087.
- *
- * An intermediate speed and precision can be obtained using
- * the compile time option LINTERP and flg = 1. This yields
- * a linear interpolation using a slope estimated from the sine
- * or cosine at the nearest integer argument. The peak absolute
- * error with this option is 3.8e-5. Relative error at small
- * angles is about 1e-5.
- *
- * If flg = 0, then the approximation polynomials are computed
- * and applied.
- *
- *
- *
- * SPEED:
- *
- * Relative speed comparisons follow for 6MHz IBM AT clone
- * and Microsoft C version 4.0. These figures include
- * software overhead of do loop and function calls.
- * Since system hardware and software vary widely, the
- * numbers should be taken as representative only.
- *
- * flg=0 flg=0 flg=1 flg=1
- * ACC11 ACC5 LINTERP Lookup only
- * In-line 8087 (/FPi)
- * sin(), cos() 1.0 1.0 1.0 1.0
- *
- * In-line 8087 (/FPi)
- * sincos() 1.1 1.4 1.9 3.0
- *
- * Software (/FPa)
- * sin(), cos() 0.19 0.19 0.19 0.19
- *
- * Software (/FPa)
- * sincos() 0.39 0.50 0.73 1.7
- *
- *
- *
- * ACCURACY:
- *
- * The accurate approximations are designed with a relative error
- * criterion. The absolute error is greatest at x = 0.5 degree.
- * It decreases from a local maximum at i+0.5 degrees to full
- * machine precision at each integer i degrees. With the
- * ACC5 option, the relative error of 6.3e-6 is equivalent to
- * an absolute angular error of 0.01 arc second in the argument
- * at x = i+0.5 degrees. For small angles < 0.5 deg, the ACC5
- * accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute
- * error decreases in proportion to the argument. This is true
- * for both the sine and cosine approximations, since the latter
- * is for the function 1 - cos(x).
- *
- * If absolute error is of most concern, use the compile time
- * option ABSERR to obtain an absolute error of 2.7e-8 for ACC5
- * precision. This is about half the absolute error of the
- * relative precision option. In this case the relative error
- * for small angles will increase to 9.5e-6 -- a reasonable
- * tradeoff.
- */
-\f
-/* sindg.c
- *
- * Circular sine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sindg();
- *
- * y = sindg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 P(x**2).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +-1000 3100 3.3e-17 9.0e-18
- * IEEE +-1000 30000 2.3e-16 5.6e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sindg total loss x > 8.0e14 (DEC) 0.0
- * x > 1.0e14 (IEEE)
- *
- */
-\f/* cosdg.c
- *
- * Circular cosine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cosdg();
- *
- * y = cosdg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 P(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +-1000 3400 3.5e-17 9.1e-18
- * IEEE +-1000 30000 2.1e-16 5.7e-17
- * See also sin().
- *
- */
-\f
-/* sinh.c
- *
- * Hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sinh();
- *
- * y = sinh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic sine of argument in the range MINLOG to
- * MAXLOG.
- *
- * The range is partitioned into two segments. If |x| <= 1, a
- * rational function of the form x + x**3 P(x)/Q(x) is employed.
- * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +- 88 50000 4.0e-17 7.7e-18
- * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
- *
- */
-\f
-/* spence.c
- *
- * Dilogarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, spence();
- *
- * y = spence( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral
- *
- * x
- * -
- * | | log t
- * spence(x) = - | ----- dt
- * | | t - 1
- * -
- * 1
- *
- * for x >= 0. A rational approximation gives the integral in
- * the interval (0.5, 1.5). Transformation formulas for 1/x
- * and 1-x are employed outside the basic expansion range.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,4 30000 3.9e-15 5.4e-16
- * DEC 0,4 3000 2.5e-16 4.5e-17
- *
- *
- */
-\f
-/* sqrt.c
- *
- * Square root
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sqrt();
- *
- * y = sqrt( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the square root of x.
- *
- * Range reduction involves isolating the power of two of the
- * argument and using a polynomial approximation to obtain
- * a rough value for the square root. Then Heron's iteration
- * is used three times to converge to an accurate value.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 10 60000 2.1e-17 7.9e-18
- * IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sqrt domain x < 0 0.0
- *
- */
-\f
-/* stdtr.c
- *
- * Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double t, stdtr();
- * short k;
- *
- * y = stdtr( k, t );
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral from minus infinity to t of the Student
- * t distribution with integer k > 0 degrees of freedom:
- *
- * t
- * -
- * | |
- * - | 2 -(k+1)/2
- * | ( (k+1)/2 ) | ( x )
- * ---------------------- | ( 1 + --- ) dx
- * - | ( k )
- * sqrt( k pi ) | ( k/2 ) |
- * | |
- * -
- * -inf.
- *
- * Relation to incomplete beta integral:
- *
- * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
- * where
- * z = k/(k + t**2).
- *
- * For t < -2, this is the method of computation. For higher t,
- * a direct method is derived from integration by parts.
- * Since the function is symmetric about t=0, the area under the
- * right tail of the density is found by calling the function
- * with -t instead of t.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 25. The "domain" refers to t.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -100,-2 50000 5.9e-15 1.4e-15
- * IEEE -2,100 500000 2.7e-15 4.9e-17
- */
-\f
-/* stdtri.c
- *
- * Functional inverse of Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double p, t, stdtri();
- * int k;
- *
- * t = stdtri( k, p );
- *
- *
- * DESCRIPTION:
- *
- * Given probability p, finds the argument t such that stdtr(k,t)
- * is equal to p.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 100. The "domain" refers to p:
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE .001,.999 25000 5.7e-15 8.0e-16
- * IEEE 10^-6,.001 25000 2.0e-12 2.9e-14
- */
-\f
-/* struve.c
- *
- * Struve function
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, struve();
- *
- * y = struve( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the Struve function Hv(x) of order v, argument x.
- * Negative x is rejected unless v is an integer.
- *
- * This module also contains the hypergeometric functions 1F2
- * and 3F0 and a routine for the Bessel function Yv(x) with
- * noninteger v.
- *
- *
- *
- * ACCURACY:
- *
- * Not accurately characterized, but spot checked against tables.
- *
- */
-\f
-/* tan.c
- *
- * Circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, tan();
- *
- * y = tan( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +-1.07e9 44000 4.1e-17 1.0e-17
- * IEEE +-1.07e9 30000 2.9e-16 8.1e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tan total loss x > 1.073741824e9 0.0
- *
- */
-\f/* cot.c
- *
- * Circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cot();
- *
- * y = cot( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-1.07e9 30000 2.9e-16 8.2e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 1.073741824e9 0.0
- * cot singularity x = 0 INFINITY
- *
- */
-\f
-/* tandg.c
- *
- * Circular tangent of argument in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, tandg();
- *
- * y = tandg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the argument x in degrees.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,10 8000 3.4e-17 1.2e-17
- * IEEE 0,10 30000 3.2e-16 8.4e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tandg total loss x > 8.0e14 (DEC) 0.0
- * x > 1.0e14 (IEEE)
- * tandg singularity x = 180 k + 90 MAXNUM
- */
-\f/* cotdg.c
- *
- * Circular cotangent of argument in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cotdg();
- *
- * y = cotdg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the argument x in degrees.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cotdg total loss x > 8.0e14 (DEC) 0.0
- * x > 1.0e14 (IEEE)
- * cotdg singularity x = 180 k MAXNUM
- */
-\f
-/* tanh.c
- *
- * Hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, tanh();
- *
- * y = tanh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic tangent of argument in the range MINLOG to
- * MAXLOG.
- *
- * A rational function is used for |x| < 0.625. The form
- * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
- * Otherwise,
- * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -2,2 50000 3.3e-17 6.4e-18
- * IEEE -2,2 30000 2.5e-16 5.8e-17
- *
- */
-\f
-/* unity.c
- *
- * Relative error approximations for function arguments near
- * unity.
- *
- * log1p(x) = log(1+x)
- * expm1(x) = exp(x) - 1
- * cosm1(x) = cos(x) - 1
- *
- */
-\f
-/* yn.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, yn();
- * int n;
- *
- * y = yn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0() and y1().
- *
- * If n = 0 or 1 the routine for y0 or y1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative
- * when y > 1:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 2200 2.9e-16 5.3e-17
- * IEEE 0, 30 30000 3.4e-15 4.3e-16
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * yn singularity x = 0 MAXNUM
- * yn overflow MAXNUM
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
-\f
-/* zeta.c
- *
- * Riemann zeta function of two arguments
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, q, y, zeta();
- *
- * y = zeta( x, q );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=0
- *
- * where x > 1 and q is not a negative integer or zero.
- * The Euler-Maclaurin summation formula is used to obtain
- * the expansion
- *
- * n
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=1
- *
- * 1-x inf. B x(x+1)...(x+2j)
- * (n+q) 1 - 2j
- * + --------- - ------- + > --------------------
- * x-1 x - x+2j+1
- * 2(n+q) j=1 (2j)! (n+q)
- *
- * where the B2j are Bernoulli numbers. Note that (see zetac.c)
- * zeta(x,1) = zetac(x) + 1.
- *
- *
- *
- * ACCURACY:
- *
- *
- *
- * REFERENCE:
- *
- * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
- * Series, and Products, p. 1073; Academic Press, 1980.
- *
- */
-\f
- /* zetac.c
- *
- * Riemann zeta function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, zetac();
- *
- * y = zetac( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zetac(x) = > k , x > 1,
- * -
- * k=2
- *
- * is related to the Riemann zeta function by
- *
- * Riemann zeta(x) = zetac(x) + 1.
- *
- * Extension of the function definition for x < 1 is implemented.
- * Zero is returned for x > log2(MAXNUM).
- *
- * An overflow error may occur for large negative x, due to the
- * gamma function in the reflection formula.
- *
- * ACCURACY:
- *
- * Tabulated values have full machine accuracy.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,50 10000 9.8e-16 1.3e-16
- * DEC 1,50 2000 1.1e-16 1.9e-17
- *
- *
- */
+++ /dev/null
-/* acos()
- *
- * Inverse circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acos();
- *
- * y = acos( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between 0 and pi whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1, 1 50000 3.3e-17 8.2e-18
- * IEEE -1, 1 10^6 2.2e-16 6.5e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 NAN
- */
-
-#define __USE_BSD
-#include <math.h>
-
-double acos(double x)
-{
- if (x < -0.5) {
- return (M_PI - 2.0 * asin( sqrt((1+x)/2) ));
- }
- if (x > 0.5) {
- return (2.0 * asin( sqrt((1-x)/2) ));
- }
-
- return(M_PI_2 - asin(x));
-}
+++ /dev/null
-/* acosh.c
- *
- * Inverse hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acosh();
- *
- * y = acosh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a rational approximation
- *
- * sqrt(z) * P(z)/Q(z)
- *
- * where z = x-1, is used. Otherwise,
- *
- * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 1,3 30000 4.2e-17 1.1e-17
- * IEEE 1,3 30000 4.6e-16 8.7e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acosh domain |x| < 1 NAN
- *
- */
-\f
-/* acosh.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
- 1.18801130533544501356E2,
- 3.94726656571334401102E3,
- 3.43989375926195455866E4,
- 1.08102874834699867335E5,
- 1.10855947270161294369E5
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 1.86145380837903397292E2,
- 4.15352677227719831579E3,
- 2.97683430363289370382E4,
- 8.29725251988426222434E4,
- 7.83869920495893927727E4
-};
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0041755,0115055,0144002,0146444,
-0043166,0132103,0155150,0150302,
-0044006,0057360,0003021,0162753,
-0044323,0021557,0175225,0056253,
-0044330,0101771,0040046,0006636
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0042072,0022467,0126670,0041232,
-0043201,0146066,0152142,0034015,
-0043750,0110257,0121165,0026100,
-0044242,0007103,0034667,0033173,
-0044231,0014576,0175573,0017472
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x59a4,0xb900,0xb345,0x405d,
-0x1a18,0x7b4d,0xd688,0x40ae,
-0x3cbd,0x00c2,0xcbde,0x40e0,
-0xab95,0xff52,0x646d,0x40fa,
-0xc1b4,0x2804,0x107f,0x40fb
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x0853,0xf5b7,0x44a6,0x4067,
-0x4702,0xda8c,0x3986,0x40b0,
-0xa588,0xf44e,0x1215,0x40dd,
-0xe6cf,0x6736,0x41c8,0x40f4,
-0x63e7,0xdf6f,0x232f,0x40f3
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x405d,0xb345,0xb900,0x59a4,
-0x40ae,0xd688,0x7b4d,0x1a18,
-0x40e0,0xcbde,0x00c2,0x3cbd,
-0x40fa,0x646d,0xff52,0xab95,
-0x40fb,0x107f,0x2804,0xc1b4
-};
-static unsigned short Q[] = {
-0x4067,0x44a6,0xf5b7,0x0853,
-0x40b0,0x3986,0xda8c,0x4702,
-0x40dd,0x1215,0xf44e,0xa588,
-0x40f4,0x41c8,0x6736,0xe6cf,
-0x40f3,0x232f,0xdf6f,0x63e7,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-extern double sqrt ( double );
-#else
-double log(), sqrt(), polevl(), p1evl();
-#endif
-extern double LOGE2, INFINITY, NAN;
-
-double acosh(x)
-double x;
-{
-double a, z;
-
-if( x < 1.0 )
- {
- mtherr( "acosh", DOMAIN );
- return(NAN);
- }
-
-if( x > 1.0e8 )
- {
-#ifdef INFINITIES
- if( x == INFINITY )
- return( INFINITY );
-#endif
- return( log(x) + LOGE2 );
- }
-
-z = x - 1.0;
-
-if( z < 0.5 )
- {
- a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
- return( a );
- }
-
-a = sqrt( z*(x+1.0) );
-return( log(x + a) );
-}
+++ /dev/null
-/* airy.c
- *
- * Airy function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, ai, aip, bi, bip;
- * int airy();
- *
- * airy( x, _&ai, _&aip, _&bi, _&bip );
- *
- *
- *
- * DESCRIPTION:
- *
- * Solution of the differential equation
- *
- * y"(x) = xy.
- *
- * The function returns the two independent solutions Ai, Bi
- * and their first derivatives Ai'(x), Bi'(x).
- *
- * Evaluation is by power series summation for small x,
- * by rational minimax approximations for large x.
- *
- *
- *
- * ACCURACY:
- * Error criterion is absolute when function <= 1, relative
- * when function > 1, except * denotes relative error criterion.
- * For large negative x, the absolute error increases as x^1.5.
- * For large positive x, the relative error increases as x^1.5.
- *
- * Arithmetic domain function # trials peak rms
- * IEEE -10, 0 Ai 10000 1.6e-15 2.7e-16
- * IEEE 0, 10 Ai 10000 2.3e-14* 1.8e-15*
- * IEEE -10, 0 Ai' 10000 4.6e-15 7.6e-16
- * IEEE 0, 10 Ai' 10000 1.8e-14* 1.5e-15*
- * IEEE -10, 10 Bi 30000 4.2e-15 5.3e-16
- * IEEE -10, 10 Bi' 30000 4.9e-15 7.3e-16
- * DEC -10, 0 Ai 5000 1.7e-16 2.8e-17
- * DEC 0, 10 Ai 5000 2.1e-15* 1.7e-16*
- * DEC -10, 0 Ai' 5000 4.7e-16 7.8e-17
- * DEC 0, 10 Ai' 12000 1.8e-15* 1.5e-16*
- * DEC -10, 10 Bi 10000 5.5e-16 6.8e-17
- * DEC -10, 10 Bi' 7000 5.3e-16 8.7e-17
- *
- */
-\f/* airy.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-static double c1 = 0.35502805388781723926;
-static double c2 = 0.258819403792806798405;
-static double sqrt3 = 1.732050807568877293527;
-static double sqpii = 5.64189583547756286948E-1;
-extern double PI;
-
-extern double MAXNUM, MACHEP;
-#ifdef UNK
-#define MAXAIRY 25.77
-#endif
-#ifdef DEC
-#define MAXAIRY 25.77
-#endif
-#ifdef IBMPC
-#define MAXAIRY 103.892
-#endif
-#ifdef MIEEE
-#define MAXAIRY 103.892
-#endif
-
-
-#ifdef UNK
-static double AN[8] = {
- 3.46538101525629032477E-1,
- 1.20075952739645805542E1,
- 7.62796053615234516538E1,
- 1.68089224934630576269E2,
- 1.59756391350164413639E2,
- 7.05360906840444183113E1,
- 1.40264691163389668864E1,
- 9.99999999999999995305E-1,
-};
-static double AD[8] = {
- 5.67594532638770212846E-1,
- 1.47562562584847203173E1,
- 8.45138970141474626562E1,
- 1.77318088145400459522E2,
- 1.64234692871529701831E2,
- 7.14778400825575695274E1,
- 1.40959135607834029598E1,
- 1.00000000000000000470E0,
-};
-#endif
-#ifdef DEC
-static unsigned short AN[32] = {
-0037661,0066561,0024675,0131301,
-0041100,0017434,0034324,0101466,
-0041630,0107450,0067427,0007430,
-0042050,0013327,0071000,0034737,
-0042037,0140642,0156417,0167366,
-0041615,0011172,0075147,0051165,
-0041140,0066152,0160520,0075146,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short AD[32] = {
-0040021,0046740,0011422,0064606,
-0041154,0014640,0024631,0062450,
-0041651,0003435,0101152,0106401,
-0042061,0050556,0034605,0136602,
-0042044,0036024,0152377,0151414,
-0041616,0172247,0072216,0115374,
-0041141,0104334,0124154,0166007,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short AN[32] = {
-0xb658,0x2537,0x2dae,0x3fd6,
-0x9067,0x871a,0x03e3,0x4028,
-0xe1e3,0x0de2,0x11e5,0x4053,
-0x073c,0xee40,0x02da,0x4065,
-0xfddf,0x5ba1,0xf834,0x4063,
-0xea4f,0x4f4c,0xa24f,0x4051,
-0x0f4d,0x5c2a,0x0d8d,0x402c,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short AD[32] = {
-0x4d31,0x0262,0x29bc,0x3fe2,
-0x2ca5,0x0533,0x8334,0x402d,
-0x51a0,0xb04d,0x20e3,0x4055,
-0xb7b0,0xc730,0x2a2d,0x4066,
-0xfa61,0x9a9f,0x8782,0x4064,
-0xd35f,0xee91,0xde94,0x4051,
-0x9d81,0x950d,0x311b,0x402c,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short AN[32] = {
-0x3fd6,0x2dae,0x2537,0xb658,
-0x4028,0x03e3,0x871a,0x9067,
-0x4053,0x11e5,0x0de2,0xe1e3,
-0x4065,0x02da,0xee40,0x073c,
-0x4063,0xf834,0x5ba1,0xfddf,
-0x4051,0xa24f,0x4f4c,0xea4f,
-0x402c,0x0d8d,0x5c2a,0x0f4d,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short AD[32] = {
-0x3fe2,0x29bc,0x0262,0x4d31,
-0x402d,0x8334,0x0533,0x2ca5,
-0x4055,0x20e3,0xb04d,0x51a0,
-0x4066,0x2a2d,0xc730,0xb7b0,
-0x4064,0x8782,0x9a9f,0xfa61,
-0x4051,0xde94,0xee91,0xd35f,
-0x402c,0x311b,0x950d,0x9d81,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef UNK
-static double APN[8] = {
- 6.13759184814035759225E-1,
- 1.47454670787755323881E1,
- 8.20584123476060982430E1,
- 1.71184781360976385540E2,
- 1.59317847137141783523E2,
- 6.99778599330103016170E1,
- 1.39470856980481566958E1,
- 1.00000000000000000550E0,
-};
-static double APD[8] = {
- 3.34203677749736953049E-1,
- 1.11810297306158156705E1,
- 7.11727352147859965283E1,
- 1.58778084372838313640E2,
- 1.53206427475809220834E2,
- 6.86752304592780337944E1,
- 1.38498634758259442477E1,
- 9.99999999999999994502E-1,
-};
-#endif
-#ifdef DEC
-static unsigned short APN[32] = {
-0040035,0017522,0065145,0054755,
-0041153,0166556,0161471,0057174,
-0041644,0016750,0034445,0046462,
-0042053,0027515,0152316,0046717,
-0042037,0050536,0067023,0023264,
-0041613,0172252,0007240,0131055,
-0041137,0023503,0052472,0002305,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short APD[32] = {
-0037653,0016276,0112106,0126625,
-0041062,0162577,0067111,0111761,
-0041616,0054160,0140004,0137455,
-0042036,0143460,0104626,0157206,
-0042031,0032330,0067131,0114260,
-0041611,0054667,0147207,0134564,
-0041135,0114412,0070653,0146015,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short APN[32] = {
-0xab3e,0x4d4c,0xa3ea,0x3fe3,
-0x2bcf,0xdc67,0x7dad,0x402d,
-0xa9a6,0x0724,0x83bd,0x4054,
-0xc9ba,0xba99,0x65e9,0x4065,
-0x64d7,0xcdc2,0xea2b,0x4063,
-0x1646,0x41d4,0x7e95,0x4051,
-0x4099,0x6aa7,0xe4e8,0x402b,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short APD[32] = {
-0xd5b3,0xd288,0x6397,0x3fd5,
-0x327e,0xedc9,0x5caf,0x4026,
-0x97e6,0x1800,0xcb0e,0x4051,
-0xdbd1,0x1132,0xd8e6,0x4063,
-0x3316,0x0dcb,0x269b,0x4063,
-0xf72f,0xf9d0,0x2b36,0x4051,
-0x7982,0x4e35,0xb321,0x402b,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short APN[32] = {
-0x3fe3,0xa3ea,0x4d4c,0xab3e,
-0x402d,0x7dad,0xdc67,0x2bcf,
-0x4054,0x83bd,0x0724,0xa9a6,
-0x4065,0x65e9,0xba99,0xc9ba,
-0x4063,0xea2b,0xcdc2,0x64d7,
-0x4051,0x7e95,0x41d4,0x1646,
-0x402b,0xe4e8,0x6aa7,0x4099,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short APD[32] = {
-0x3fd5,0x6397,0xd288,0xd5b3,
-0x4026,0x5caf,0xedc9,0x327e,
-0x4051,0xcb0e,0x1800,0x97e6,
-0x4063,0xd8e6,0x1132,0xdbd1,
-0x4063,0x269b,0x0dcb,0x3316,
-0x4051,0x2b36,0xf9d0,0xf72f,
-0x402b,0xb321,0x4e35,0x7982,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef UNK
-static double BN16[5] = {
--2.53240795869364152689E-1,
- 5.75285167332467384228E-1,
--3.29907036873225371650E-1,
- 6.44404068948199951727E-2,
--3.82519546641336734394E-3,
-};
-static double BD16[5] = {
-/* 1.00000000000000000000E0,*/
--7.15685095054035237902E0,
- 1.06039580715664694291E1,
--5.23246636471251500874E0,
- 9.57395864378383833152E-1,
--5.50828147163549611107E-2,
-};
-#endif
-#ifdef DEC
-static unsigned short BN16[20] = {
-0137601,0124307,0010213,0035210,
-0040023,0042743,0101621,0016031,
-0137650,0164623,0036056,0074511,
-0037203,0174525,0000473,0142474,
-0136172,0130041,0066726,0064324,
-};
-static unsigned short BD16[20] = {
-/*0040200,0000000,0000000,0000000,*/
-0140745,0002354,0044335,0055276,
-0041051,0124717,0170130,0104013,
-0140647,0070135,0046473,0103501,
-0040165,0013745,0033324,0127766,
-0137141,0117204,0076164,0033107,
-};
-#endif
-#ifdef IBMPC
-static unsigned short BN16[20] = {
-0x6751,0xe211,0x3518,0xbfd0,
-0x2383,0x7072,0x68bc,0x3fe2,
-0xcf29,0x6785,0x1d32,0xbfd5,
-0x78a8,0xa027,0x7f2a,0x3fb0,
-0xcd1b,0x2dba,0x5604,0xbf6f,
-};
-static unsigned short BD16[20] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xab58,0x891b,0xa09d,0xc01c,
-0x1101,0xfe0b,0x3539,0x4025,
-0x70e8,0xa9a7,0xee0b,0xc014,
-0x95ff,0xa6da,0xa2fc,0x3fee,
-0x86c9,0x8f8e,0x33d0,0xbfac,
-};
-#endif
-#ifdef MIEEE
-static unsigned short BN16[20] = {
-0xbfd0,0x3518,0xe211,0x6751,
-0x3fe2,0x68bc,0x7072,0x2383,
-0xbfd5,0x1d32,0x6785,0xcf29,
-0x3fb0,0x7f2a,0xa027,0x78a8,
-0xbf6f,0x5604,0x2dba,0xcd1b,
-};
-static unsigned short BD16[20] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc01c,0xa09d,0x891b,0xab58,
-0x4025,0x3539,0xfe0b,0x1101,
-0xc014,0xee0b,0xa9a7,0x70e8,
-0x3fee,0xa2fc,0xa6da,0x95ff,
-0xbfac,0x33d0,0x8f8e,0x86c9,
-};
-#endif
-
-#ifdef UNK
-static double BPPN[5] = {
- 4.65461162774651610328E-1,
--1.08992173800493920734E0,
- 6.38800117371827987759E-1,
--1.26844349553102907034E-1,
- 7.62487844342109852105E-3,
-};
-static double BPPD[5] = {
-/* 1.00000000000000000000E0,*/
--8.70622787633159124240E0,
- 1.38993162704553213172E1,
--7.14116144616431159572E0,
- 1.34008595960680518666E0,
--7.84273211323341930448E-2,
-};
-#endif
-#ifdef DEC
-static unsigned short BPPN[20] = {
-0037756,0050354,0167531,0135731,
-0140213,0101216,0032767,0020375,
-0040043,0104147,0106312,0177632,
-0137401,0161574,0032015,0043714,
-0036371,0155035,0143165,0142262,
-};
-static unsigned short BPPD[20] = {
-/*0040200,0000000,0000000,0000000,*/
-0141013,0046265,0115005,0161053,
-0041136,0061631,0072445,0156131,
-0140744,0102145,0001127,0065304,
-0040253,0103757,0146453,0102513,
-0137240,0117200,0155402,0113500,
-};
-#endif
-#ifdef IBMPC
-static unsigned short BPPN[20] = {
-0x377b,0x9deb,0xca1d,0x3fdd,
-0xe420,0xc6be,0x7051,0xbff1,
-0x5ff3,0xf199,0x710c,0x3fe4,
-0xa8fa,0x8681,0x3c6f,0xbfc0,
-0xb896,0xb8ce,0x3b43,0x3f7f,
-};
-static unsigned short BPPD[20] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xbc45,0xb340,0x6996,0xc021,
-0xbb8b,0x2ea4,0xcc73,0x402b,
-0xed59,0xa04a,0x908c,0xc01c,
-0x70a9,0xf9a5,0x70fd,0x3ff5,
-0x52e8,0x1b60,0x13d0,0xbfb4,
-};
-#endif
-#ifdef MIEEE
-static unsigned short BPPN[20] = {
-0x3fdd,0xca1d,0x9deb,0x377b,
-0xbff1,0x7051,0xc6be,0xe420,
-0x3fe4,0x710c,0xf199,0x5ff3,
-0xbfc0,0x3c6f,0x8681,0xa8fa,
-0x3f7f,0x3b43,0xb8ce,0xb896,
-};
-static unsigned short BPPD[20] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc021,0x6996,0xb340,0xbc45,
-0x402b,0xcc73,0x2ea4,0xbb8b,
-0xc01c,0x908c,0xa04a,0xed59,
-0x3ff5,0x70fd,0xf9a5,0x70a9,
-0xbfb4,0x13d0,0x1b60,0x52e8,
-};
-#endif
-
-#ifdef UNK
-static double AFN[9] = {
--1.31696323418331795333E-1,
--6.26456544431912369773E-1,
--6.93158036036933542233E-1,
--2.79779981545119124951E-1,
--4.91900132609500318020E-2,
--4.06265923594885404393E-3,
--1.59276496239262096340E-4,
--2.77649108155232920844E-6,
--1.67787698489114633780E-8,
-};
-static double AFD[9] = {
-/* 1.00000000000000000000E0,*/
- 1.33560420706553243746E1,
- 3.26825032795224613948E1,
- 2.67367040941499554804E1,
- 9.18707402907259625840E0,
- 1.47529146771666414581E0,
- 1.15687173795188044134E-1,
- 4.40291641615211203805E-3,
- 7.54720348287414296618E-5,
- 4.51850092970580378464E-7,
-};
-#endif
-#ifdef DEC
-static unsigned short AFN[36] = {
-0137406,0155546,0124127,0033732,
-0140040,0057564,0141263,0041222,
-0140061,0071316,0013674,0175754,
-0137617,0037522,0056637,0120130,
-0137111,0075567,0121755,0166122,
-0136205,0020016,0043317,0002201,
-0135047,0001565,0075130,0002334,
-0133472,0051700,0165021,0131551,
-0131620,0020347,0132165,0013215,
-};
-static unsigned short AFD[36] = {
-/*0040200,0000000,0000000,0000000,*/
-0041125,0131131,0025627,0067623,
-0041402,0135342,0021703,0154315,
-0041325,0162305,0016671,0120175,
-0041022,0177101,0053114,0141632,
-0040274,0153131,0147364,0114306,
-0037354,0166545,0120042,0150530,
-0036220,0043127,0000727,0130273,
-0034636,0043275,0075667,0034733,
-0032762,0112715,0146250,0142474,
-};
-#endif
-#ifdef IBMPC
-static unsigned short AFN[36] = {
-0xe6fb,0xd50a,0xdb6c,0xbfc0,
-0x6852,0x9856,0x0bee,0xbfe4,
-0x9f7d,0xc2f7,0x2e59,0xbfe6,
-0xf40b,0x4bb3,0xe7ea,0xbfd1,
-0xbd8a,0xf47d,0x2f6e,0xbfa9,
-0xe090,0xc8d9,0xa401,0xbf70,
-0x009c,0xaf4b,0xe06e,0xbf24,
-0x366d,0x1d42,0x4a78,0xbec7,
-0xa2d2,0xf68e,0x041c,0xbe52,
-};
-static unsigned short AFD[36] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xedf2,0x2572,0xb64b,0x402a,
-0x7b1a,0x4478,0x575c,0x4040,
-0x3410,0xa3b7,0xbc98,0x403a,
-0x9873,0x2ac9,0x5fc8,0x4022,
-0x9319,0x39de,0x9acb,0x3ff7,
-0x5a2b,0xb404,0x9dac,0x3fbd,
-0xf617,0xe03a,0x08ca,0x3f72,
-0xe73b,0xaf76,0xc8d7,0x3f13,
-0x18a7,0xb995,0x52b9,0x3e9e,
-};
-#endif
-#ifdef MIEEE
-static unsigned short AFN[36] = {
-0xbfc0,0xdb6c,0xd50a,0xe6fb,
-0xbfe4,0x0bee,0x9856,0x6852,
-0xbfe6,0x2e59,0xc2f7,0x9f7d,
-0xbfd1,0xe7ea,0x4bb3,0xf40b,
-0xbfa9,0x2f6e,0xf47d,0xbd8a,
-0xbf70,0xa401,0xc8d9,0xe090,
-0xbf24,0xe06e,0xaf4b,0x009c,
-0xbec7,0x4a78,0x1d42,0x366d,
-0xbe52,0x041c,0xf68e,0xa2d2,
-};
-static unsigned short AFD[36] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x402a,0xb64b,0x2572,0xedf2,
-0x4040,0x575c,0x4478,0x7b1a,
-0x403a,0xbc98,0xa3b7,0x3410,
-0x4022,0x5fc8,0x2ac9,0x9873,
-0x3ff7,0x9acb,0x39de,0x9319,
-0x3fbd,0x9dac,0xb404,0x5a2b,
-0x3f72,0x08ca,0xe03a,0xf617,
-0x3f13,0xc8d7,0xaf76,0xe73b,
-0x3e9e,0x52b9,0xb995,0x18a7,
-};
-#endif
-
-#ifdef UNK
-static double AGN[11] = {
- 1.97339932091685679179E-2,
- 3.91103029615688277255E-1,
- 1.06579897599595591108E0,
- 9.39169229816650230044E-1,
- 3.51465656105547619242E-1,
- 6.33888919628925490927E-2,
- 5.85804113048388458567E-3,
- 2.82851600836737019778E-4,
- 6.98793669997260967291E-6,
- 8.11789239554389293311E-8,
- 3.41551784765923618484E-10,
-};
-static double AGD[10] = {
-/* 1.00000000000000000000E0,*/
- 9.30892908077441974853E0,
- 1.98352928718312140417E1,
- 1.55646628932864612953E1,
- 5.47686069422975497931E0,
- 9.54293611618961883998E-1,
- 8.64580826352392193095E-2,
- 4.12656523824222607191E-3,
- 1.01259085116509135510E-4,
- 1.17166733214413521882E-6,
- 4.91834570062930015649E-9,
-};
-#endif
-#ifdef DEC
-static unsigned short AGN[44] = {
-0036641,0124456,0167175,0157354,
-0037710,0037250,0001441,0136671,
-0040210,0066031,0150401,0123532,
-0040160,0066545,0003570,0153133,
-0037663,0171516,0072507,0170345,
-0037201,0151011,0007510,0045702,
-0036277,0172317,0104572,0101030,
-0035224,0045663,0000160,0136422,
-0033752,0074753,0047702,0135160,
-0032256,0052225,0156550,0107103,
-0030273,0142443,0166277,0071720,
-};
-static unsigned short AGD[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0041024,0170537,0117253,0055003,
-0041236,0127256,0003570,0143240,
-0041171,0004333,0172476,0160645,
-0040657,0041161,0055716,0157161,
-0040164,0046226,0006257,0063431,
-0037261,0010357,0065445,0047563,
-0036207,0034043,0057434,0116732,
-0034724,0055416,0130035,0026377,
-0033235,0041056,0154071,0023502,
-0031250,0177071,0167254,0047242,
-};
-#endif
-#ifdef IBMPC
-static unsigned short AGN[44] = {
-0xbbde,0xddcf,0x3525,0x3f94,
-0x37b7,0x0064,0x07d5,0x3fd9,
-0x34eb,0x3a20,0x0d83,0x3ff1,
-0x1acb,0xa0ef,0x0dac,0x3fee,
-0xfe1d,0xcea8,0x7e69,0x3fd6,
-0x0978,0x21e9,0x3a41,0x3fb0,
-0x5043,0xf12f,0xfe99,0x3f77,
-0x17a2,0x600e,0x8976,0x3f32,
-0x574e,0x69f8,0x4f3d,0x3edd,
-0x11c8,0xbbad,0xca92,0x3e75,
-0xee7a,0x7d97,0x78a4,0x3df7,
-};
-static unsigned short AGD[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x6b40,0xf3d5,0x9e2b,0x4022,
-0x18d4,0xc0ef,0xd5d5,0x4033,
-0xdc35,0x7ea7,0x211b,0x402f,
-0xdbce,0x2b79,0xe84e,0x4015,
-0xece3,0xc195,0x8992,0x3fee,
-0xa9ee,0xed64,0x221d,0x3fb6,
-0x93bb,0x6be3,0xe704,0x3f70,
-0xa5a0,0xd603,0x8b61,0x3f1a,
-0x24e8,0xdb07,0xa845,0x3eb3,
-0x89d4,0x3dd5,0x1fc7,0x3e35,
-};
-#endif
-#ifdef MIEEE
-static unsigned short AGN[44] = {
-0x3f94,0x3525,0xddcf,0xbbde,
-0x3fd9,0x07d5,0x0064,0x37b7,
-0x3ff1,0x0d83,0x3a20,0x34eb,
-0x3fee,0x0dac,0xa0ef,0x1acb,
-0x3fd6,0x7e69,0xcea8,0xfe1d,
-0x3fb0,0x3a41,0x21e9,0x0978,
-0x3f77,0xfe99,0xf12f,0x5043,
-0x3f32,0x8976,0x600e,0x17a2,
-0x3edd,0x4f3d,0x69f8,0x574e,
-0x3e75,0xca92,0xbbad,0x11c8,
-0x3df7,0x78a4,0x7d97,0xee7a,
-};
-static unsigned short AGD[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4022,0x9e2b,0xf3d5,0x6b40,
-0x4033,0xd5d5,0xc0ef,0x18d4,
-0x402f,0x211b,0x7ea7,0xdc35,
-0x4015,0xe84e,0x2b79,0xdbce,
-0x3fee,0x8992,0xc195,0xece3,
-0x3fb6,0x221d,0xed64,0xa9ee,
-0x3f70,0xe704,0x6be3,0x93bb,
-0x3f1a,0x8b61,0xd603,0xa5a0,
-0x3eb3,0xa845,0xdb07,0x24e8,
-0x3e35,0x1fc7,0x3dd5,0x89d4,
-};
-#endif
-
-#ifdef UNK
-static double APFN[9] = {
- 1.85365624022535566142E-1,
- 8.86712188052584095637E-1,
- 9.87391981747398547272E-1,
- 4.01241082318003734092E-1,
- 7.10304926289631174579E-2,
- 5.90618657995661810071E-3,
- 2.33051409401776799569E-4,
- 4.08718778289035454598E-6,
- 2.48379932900442457853E-8,
-};
-static double APFD[9] = {
-/* 1.00000000000000000000E0,*/
- 1.47345854687502542552E1,
- 3.75423933435489594466E1,
- 3.14657751203046424330E1,
- 1.09969125207298778536E1,
- 1.78885054766999417817E0,
- 1.41733275753662636873E-1,
- 5.44066067017226003627E-3,
- 9.39421290654511171663E-5,
- 5.65978713036027009243E-7,
-};
-#endif
-#ifdef DEC
-static unsigned short APFN[36] = {
-0037475,0150174,0071752,0166651,
-0040142,0177621,0164246,0101757,
-0040174,0142670,0106760,0006573,
-0037715,0067570,0116274,0022404,
-0037221,0074157,0053341,0117207,
-0036301,0104257,0015075,0004777,
-0035164,0057502,0164034,0001313,
-0033611,0022254,0176000,0112565,
-0031725,0055523,0025153,0166057,
-};
-static unsigned short APFD[36] = {
-/*0040200,0000000,0000000,0000000,*/
-0041153,0140334,0130506,0061402,
-0041426,0025551,0024440,0070611,
-0041373,0134750,0047147,0176702,
-0041057,0171532,0105430,0017674,
-0040344,0174416,0001726,0047754,
-0037421,0021207,0020167,0136264,
-0036262,0043621,0151321,0124324,
-0034705,0001313,0163733,0016407,
-0033027,0166702,0150440,0170561,
-};
-#endif
-#ifdef IBMPC
-static unsigned short APFN[36] = {
-0x5db5,0x8e7d,0xba0f,0x3fc7,
-0xd07e,0x3d14,0x5ff2,0x3fec,
-0x01af,0x11be,0x98b7,0x3fef,
-0x84a1,0x1397,0xadef,0x3fd9,
-0x33d1,0xeadc,0x2f0d,0x3fb2,
-0xa140,0xe347,0x3115,0x3f78,
-0x8059,0x5d03,0x8be8,0x3f2e,
-0x12af,0x9f80,0x2495,0x3ed1,
-0x7d86,0x654d,0xab6a,0x3e5a,
-};
-static unsigned short APFD[36] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xcc60,0x9628,0x781b,0x402d,
-0x0e31,0x2524,0xc56d,0x4042,
-0xffb8,0x09cc,0x773d,0x403f,
-0x03f7,0x5163,0xfe6b,0x4025,
-0xc9fd,0xc07a,0x9f21,0x3ffc,
-0xf796,0xe40e,0x2450,0x3fc2,
-0x351a,0x3a5a,0x48f2,0x3f76,
-0x63a1,0x7cfb,0xa059,0x3f18,
-0x1e2e,0x5a24,0xfdb8,0x3ea2,
-};
-#endif
-#ifdef MIEEE
-static unsigned short APFN[36] = {
-0x3fc7,0xba0f,0x8e7d,0x5db5,
-0x3fec,0x5ff2,0x3d14,0xd07e,
-0x3fef,0x98b7,0x11be,0x01af,
-0x3fd9,0xadef,0x1397,0x84a1,
-0x3fb2,0x2f0d,0xeadc,0x33d1,
-0x3f78,0x3115,0xe347,0xa140,
-0x3f2e,0x8be8,0x5d03,0x8059,
-0x3ed1,0x2495,0x9f80,0x12af,
-0x3e5a,0xab6a,0x654d,0x7d86,
-};
-static unsigned short APFD[36] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x402d,0x781b,0x9628,0xcc60,
-0x4042,0xc56d,0x2524,0x0e31,
-0x403f,0x773d,0x09cc,0xffb8,
-0x4025,0xfe6b,0x5163,0x03f7,
-0x3ffc,0x9f21,0xc07a,0xc9fd,
-0x3fc2,0x2450,0xe40e,0xf796,
-0x3f76,0x48f2,0x3a5a,0x351a,
-0x3f18,0xa059,0x7cfb,0x63a1,
-0x3ea2,0xfdb8,0x5a24,0x1e2e,
-};
-#endif
-
-#ifdef UNK
-static double APGN[11] = {
--3.55615429033082288335E-2,
--6.37311518129435504426E-1,
--1.70856738884312371053E0,
--1.50221872117316635393E0,
--5.63606665822102676611E-1,
--1.02101031120216891789E-1,
--9.48396695961445269093E-3,
--4.60325307486780994357E-4,
--1.14300836484517375919E-5,
--1.33415518685547420648E-7,
--5.63803833958893494476E-10,
-};
-static double APGD[11] = {
-/* 1.00000000000000000000E0,*/
- 9.85865801696130355144E0,
- 2.16401867356585941885E1,
- 1.73130776389749389525E1,
- 6.17872175280828766327E0,
- 1.08848694396321495475E0,
- 9.95005543440888479402E-2,
- 4.78468199683886610842E-3,
- 1.18159633322838625562E-4,
- 1.37480673554219441465E-6,
- 5.79912514929147598821E-9,
-};
-#endif
-#ifdef DEC
-static unsigned short APGN[44] = {
-0137021,0124372,0176075,0075331,
-0140043,0023330,0177672,0161655,
-0140332,0131126,0010413,0171112,
-0140300,0044263,0175560,0054070,
-0140020,0044206,0142603,0073324,
-0137321,0015130,0066144,0144033,
-0136433,0061243,0175542,0103373,
-0135361,0053721,0020441,0053203,
-0134077,0141725,0160277,0130612,
-0132417,0040372,0100363,0060200,
-0130432,0175052,0171064,0034147,
-};
-static unsigned short APGD[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0041035,0136420,0030124,0140220,
-0041255,0017432,0034447,0162256,
-0041212,0100456,0154544,0006321,
-0040705,0134026,0127154,0123414,
-0040213,0051612,0044470,0172607,
-0037313,0143362,0053273,0157051,
-0036234,0144322,0054536,0007264,
-0034767,0146170,0054265,0170342,
-0033270,0102777,0167362,0073631,
-0031307,0040644,0167103,0021763,
-};
-#endif
-#ifdef IBMPC
-static unsigned short APGN[44] = {
-0xaf5b,0x5f87,0x351f,0xbfa2,
-0x5c76,0x1ff7,0x64db,0xbfe4,
-0x7e49,0xc221,0x564a,0xbffb,
-0x0b07,0x7f6e,0x0916,0xbff8,
-0x6edb,0xd8b0,0x0910,0xbfe2,
-0x9903,0x0d8c,0x234b,0xbfba,
-0x50df,0x7f6c,0x6c54,0xbf83,
-0x2ad0,0x2424,0x2afa,0xbf3e,
-0xf631,0xbc17,0xf87a,0xbee7,
-0x6c10,0x501e,0xe81f,0xbe81,
-0x870d,0x5e46,0x5f45,0xbe03,
-};
-static unsigned short APGD[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x9812,0x060a,0xb7a2,0x4023,
-0xfc96,0x4724,0xa3e3,0x4035,
-0x819a,0xdb2c,0x5025,0x4031,
-0x94e2,0xd5cd,0xb702,0x4018,
-0x1eb1,0x4927,0x6a71,0x3ff1,
-0x7bc5,0x4ad7,0x78de,0x3fb9,
-0xc1d7,0x4b2b,0x991a,0x3f73,
-0xbe1c,0x0b16,0xf98f,0x3f1e,
-0x4ef3,0xfdde,0x10bf,0x3eb7,
-0x647e,0x9dc8,0xe834,0x3e38,
-};
-#endif
-#ifdef MIEEE
-static unsigned short APGN[44] = {
-0xbfa2,0x351f,0x5f87,0xaf5b,
-0xbfe4,0x64db,0x1ff7,0x5c76,
-0xbffb,0x564a,0xc221,0x7e49,
-0xbff8,0x0916,0x7f6e,0x0b07,
-0xbfe2,0x0910,0xd8b0,0x6edb,
-0xbfba,0x234b,0x0d8c,0x9903,
-0xbf83,0x6c54,0x7f6c,0x50df,
-0xbf3e,0x2afa,0x2424,0x2ad0,
-0xbee7,0xf87a,0xbc17,0xf631,
-0xbe81,0xe81f,0x501e,0x6c10,
-0xbe03,0x5f45,0x5e46,0x870d,
-};
-static unsigned short APGD[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4023,0xb7a2,0x060a,0x9812,
-0x4035,0xa3e3,0x4724,0xfc96,
-0x4031,0x5025,0xdb2c,0x819a,
-0x4018,0xb702,0xd5cd,0x94e2,
-0x3ff1,0x6a71,0x4927,0x1eb1,
-0x3fb9,0x78de,0x4ad7,0x7bc5,
-0x3f73,0x991a,0x4b2b,0xc1d7,
-0x3f1e,0xf98f,0x0b16,0xbe1c,
-0x3eb7,0x10bf,0xfdde,0x4ef3,
-0x3e38,0xe834,0x9dc8,0x647e,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double exp ( double );
-extern double sqrt ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double sin ( double );
-extern double cos ( double );
-#else
-double fabs(), exp(), sqrt();
-double polevl(), p1evl(), sin(), cos();
-#endif
-
-int airy( x, ai, aip, bi, bip )
-double x, *ai, *aip, *bi, *bip;
-{
-double z, zz, t, f, g, uf, ug, k, zeta, theta;
-int domflg;
-
-domflg = 0;
-if( x > MAXAIRY )
- {
- *ai = 0;
- *aip = 0;
- *bi = MAXNUM;
- *bip = MAXNUM;
- return(-1);
- }
-
-if( x < -2.09 )
- {
- domflg = 15;
- t = sqrt(-x);
- zeta = -2.0 * x * t / 3.0;
- t = sqrt(t);
- k = sqpii / t;
- z = 1.0/zeta;
- zz = z * z;
- uf = 1.0 + zz * polevl( zz, AFN, 8 ) / p1evl( zz, AFD, 9 );
- ug = z * polevl( zz, AGN, 10 ) / p1evl( zz, AGD, 10 );
- theta = zeta + 0.25 * PI;
- f = sin( theta );
- g = cos( theta );
- *ai = k * (f * uf - g * ug);
- *bi = k * (g * uf + f * ug);
- uf = 1.0 + zz * polevl( zz, APFN, 8 ) / p1evl( zz, APFD, 9 );
- ug = z * polevl( zz, APGN, 10 ) / p1evl( zz, APGD, 10 );
- k = sqpii * t;
- *aip = -k * (g * uf + f * ug);
- *bip = k * (f * uf - g * ug);
- return(0);
- }
-
-if( x >= 2.09 ) /* cbrt(9) */
- {
- domflg = 5;
- t = sqrt(x);
- zeta = 2.0 * x * t / 3.0;
- g = exp( zeta );
- t = sqrt(t);
- k = 2.0 * t * g;
- z = 1.0/zeta;
- f = polevl( z, AN, 7 ) / polevl( z, AD, 7 );
- *ai = sqpii * f / k;
- k = -0.5 * sqpii * t / g;
- f = polevl( z, APN, 7 ) / polevl( z, APD, 7 );
- *aip = f * k;
-
- if( x > 8.3203353 ) /* zeta > 16 */
- {
- f = z * polevl( z, BN16, 4 ) / p1evl( z, BD16, 5 );
- k = sqpii * g;
- *bi = k * (1.0 + f) / t;
- f = z * polevl( z, BPPN, 4 ) / p1evl( z, BPPD, 5 );
- *bip = k * t * (1.0 + f);
- return(0);
- }
- }
-
-f = 1.0;
-g = x;
-t = 1.0;
-uf = 1.0;
-ug = x;
-k = 1.0;
-z = x * x * x;
-while( t > MACHEP )
- {
- uf *= z;
- k += 1.0;
- uf /=k;
- ug *= z;
- k += 1.0;
- ug /=k;
- uf /=k;
- f += uf;
- k += 1.0;
- ug /=k;
- g += ug;
- t = fabs(uf/f);
- }
-uf = c1 * f;
-ug = c2 * g;
-if( (domflg & 1) == 0 )
- *ai = uf - ug;
-if( (domflg & 2) == 0 )
- *bi = sqrt3 * (uf + ug);
-
-/* the deriviative of ai */
-k = 4.0;
-uf = x * x/2.0;
-ug = z/3.0;
-f = uf;
-g = 1.0 + ug;
-uf /= 3.0;
-t = 1.0;
-
-while( t > MACHEP )
- {
- uf *= z;
- ug /=k;
- k += 1.0;
- ug *= z;
- uf /=k;
- f += uf;
- k += 1.0;
- ug /=k;
- uf /=k;
- g += ug;
- k += 1.0;
- t = fabs(ug/g);
- }
-
-uf = c1 * f;
-ug = c2 * g;
-if( (domflg & 4) == 0 )
- *aip = uf - ug;
-if( (domflg & 8) == 0 )
- *bip = sqrt3 * (uf + ug);
-return(0);
-}
+++ /dev/null
-/* arcdot.c
- *
- * Angle between two vectors
- *
- *
- *
- *
- * SYNOPSIS:
- *
- * double p[3], q[3], arcdot();
- *
- * y = arcdot( p, q );
- *
- *
- *
- * DESCRIPTION:
- *
- * For two vectors p, q, the angle A between them is given by
- *
- * p.q / (|p| |q|) = cos A .
- *
- * where "." represents inner product, "|x|" the length of vector x.
- * If the angle is small, an expression in sin A is preferred.
- * Set r = q - p. Then
- *
- * p.q = p.p + p.r ,
- *
- * |p|^2 = p.p ,
- *
- * |q|^2 = p.p + 2 p.r + r.r ,
- *
- * p.p^2 + 2 p.p p.r + p.r^2
- * cos^2 A = ----------------------------
- * p.p (p.p + 2 p.r + r.r)
- *
- * p.p + 2 p.r + p.r^2 / p.p
- * = --------------------------- ,
- * p.p + 2 p.r + r.r
- *
- * sin^2 A = 1 - cos^2 A
- *
- * r.r - p.r^2 / p.p
- * = --------------------
- * p.p + 2 p.r + r.r
- *
- * = (r.r - p.r^2 / p.p) / q.q .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 10^6 1.7e-16 4.2e-17
- *
- */
-\f
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double acos ( double );
-extern double asin ( double );
-extern double atan ( double );
-#else
-double sqrt(), acos(), asin(), atan();
-#endif
-extern double PI;
-
-double arcdot(p,q)
-double p[], q[];
-{
-double pp, pr, qq, rr, rt, pt, qt, pq;
-int i;
-
-pq = 0.0;
-qq = 0.0;
-pp = 0.0;
-pr = 0.0;
-rr = 0.0;
-for (i=0; i<3; i++)
- {
- pt = p[i];
- qt = q[i];
- pq += pt * qt;
- qq += qt * qt;
- pp += pt * pt;
- rt = qt - pt;
- pr += pt * rt;
- rr += rt * rt;
- }
-if (rr == 0.0 || pp == 0.0 || qq == 0.0)
- return 0.0;
-rt = (rr - (pr * pr) / pp) / qq;
-if (rt <= 0.75)
- {
- rt = sqrt(rt);
- qt = asin(rt);
- if (pq < 0.0)
- qt = PI - qt;
- }
-else
- {
- pt = pq / sqrt(pp*qq);
- qt = acos(pt);
- }
-return qt;
-}
+++ /dev/null
-/* asin.c
- *
- * Inverse circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, asin();
- *
- * y = asin( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
- *
- * A rational function of the form x + x**3 P(x**2)/Q(x**2)
- * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
- * transformed by the identity
- *
- * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1, 1 40000 2.6e-17 7.1e-18
- * IEEE -1, 1 10^6 1.9e-16 5.4e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 NAN
- *
- */
-\f/* acos()
- *
- * Inverse circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acos();
- *
- * y = acos( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between 0 and pi whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1, 1 50000 3.3e-17 8.2e-18
- * IEEE -1, 1 10^6 2.2e-16 6.5e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 NAN
- */
-\f
-/* asin.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* arcsin(x) = x + x^3 P(x^2)/Q(x^2)
- 0 <= x <= 0.625
- Peak relative error = 1.2e-18 */
-#if UNK
-static double P[6] = {
- 4.253011369004428248960E-3,
--6.019598008014123785661E-1,
- 5.444622390564711410273E0,
--1.626247967210700244449E1,
- 1.956261983317594739197E1,
--8.198089802484824371615E0,
-};
-static double Q[5] = {
-/* 1.000000000000000000000E0, */
--1.474091372988853791896E1,
- 7.049610280856842141659E1,
--1.471791292232726029859E2,
- 1.395105614657485689735E2,
--4.918853881490881290097E1,
-};
-#endif
-#if DEC
-static short P[24] = {
-0036213,0056330,0057244,0053234,
-0140032,0015011,0114762,0160255,
-0040656,0035130,0136121,0067313,
-0141202,0014616,0170474,0101731,
-0041234,0100076,0151674,0111310,
-0141003,0025540,0033165,0077246,
-};
-static short Q[20] = {
-/* 0040200,0000000,0000000,0000000, */
-0141153,0155310,0055360,0072530,
-0041614,0177001,0027764,0101237,
-0142023,0026733,0064653,0133266,
-0042013,0101264,0023775,0176351,
-0141504,0140420,0050660,0036543,
-};
-#endif
-#if IBMPC
-static short P[24] = {
-0x8ad3,0x0bd4,0x6b9b,0x3f71,
-0x5c16,0x333e,0x4341,0xbfe3,
-0x2dd9,0x178a,0xc74b,0x4015,
-0x907b,0xde27,0x4331,0xc030,
-0x9259,0xda77,0x9007,0x4033,
-0xafd5,0x06ce,0x656c,0xc020,
-};
-static short Q[20] = {
-/* 0x0000,0x0000,0x0000,0x3ff0, */
-0x0eab,0x0b5e,0x7b59,0xc02d,
-0x9054,0x25fe,0x9fc0,0x4051,
-0x76d7,0x6d35,0x65bb,0xc062,
-0xbf9d,0x84ff,0x7056,0x4061,
-0x07ac,0x0a36,0x9822,0xc048,
-};
-#endif
-#if MIEEE
-static short P[24] = {
-0x3f71,0x6b9b,0x0bd4,0x8ad3,
-0xbfe3,0x4341,0x333e,0x5c16,
-0x4015,0xc74b,0x178a,0x2dd9,
-0xc030,0x4331,0xde27,0x907b,
-0x4033,0x9007,0xda77,0x9259,
-0xc020,0x656c,0x06ce,0xafd5,
-};
-static short Q[20] = {
-/* 0x3ff0,0x0000,0x0000,0x0000, */
-0xc02d,0x7b59,0x0b5e,0x0eab,
-0x4051,0x9fc0,0x25fe,0x9054,
-0xc062,0x65bb,0x6d35,0x76d7,
-0x4061,0x7056,0x84ff,0xbf9d,
-0xc048,0x9822,0x0a36,0x07ac,
-};
-#endif
-
-/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
- 0 <= x <= 0.5
- Peak relative error = 4.2e-18 */
-#if UNK
-static double R[5] = {
- 2.967721961301243206100E-3,
--5.634242780008963776856E-1,
- 6.968710824104713396794E0,
--2.556901049652824852289E1,
- 2.853665548261061424989E1,
-};
-static double S[4] = {
-/* 1.000000000000000000000E0, */
--2.194779531642920639778E1,
- 1.470656354026814941758E2,
--3.838770957603691357202E2,
- 3.424398657913078477438E2,
-};
-#endif
-#if DEC
-static short R[20] = {
-0036102,0077034,0142164,0174103,
-0140020,0036222,0147711,0044173,
-0040736,0177655,0153631,0171523,
-0141314,0106525,0060015,0055474,
-0041344,0045422,0003630,0040344,
-};
-static short S[16] = {
-/* 0040200,0000000,0000000,0000000, */
-0141257,0112425,0132772,0166136,
-0042023,0010315,0075523,0175020,
-0142277,0170104,0126203,0017563,
-0042253,0034115,0102662,0022757,
-};
-#endif
-#if IBMPC
-static short R[20] = {
-0x9f08,0x988e,0x4fc3,0x3f68,
-0x290f,0x59f9,0x0792,0xbfe2,
-0x3e6a,0xbaf3,0xdff5,0x401b,
-0xab68,0xac01,0x91aa,0xc039,
-0x081d,0x40f3,0x8962,0x403c,
-};
-static short S[16] = {
-/* 0x0000,0x0000,0x0000,0x3ff0, */
-0x5d8c,0xb6bf,0xf2a2,0xc035,
-0x7f42,0xaf6a,0x6219,0x4062,
-0x63ee,0x9590,0xfe08,0xc077,
-0x44be,0xb0b6,0x6709,0x4075,
-};
-#endif
-#if MIEEE
-static short R[20] = {
-0x3f68,0x4fc3,0x988e,0x9f08,
-0xbfe2,0x0792,0x59f9,0x290f,
-0x401b,0xdff5,0xbaf3,0x3e6a,
-0xc039,0x91aa,0xac01,0xab68,
-0x403c,0x8962,0x40f3,0x081d,
-};
-static short S[16] = {
-/* 0x3ff0,0x0000,0x0000,0x0000, */
-0xc035,0xf2a2,0xb6bf,0x5d8c,
-0x4062,0x6219,0xaf6a,0x7f42,
-0xc077,0xfe08,0x9590,0x63ee,
-0x4075,0x6709,0xb0b6,0x44be,
-};
-#endif
-
-/* pi/2 = PIO2 + MOREBITS. */
-#ifdef DEC
-#define MOREBITS 5.721188726109831840122E-18
-#else
-#define MOREBITS 6.123233995736765886130E-17
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double sqrt ( double );
-double asin ( double );
-#else
-double sqrt(), polevl(), p1evl();
-double asin();
-#endif
-extern double PIO2, PIO4, NAN;
-
-double asin(x)
-double x;
-{
-double a, p, z, zz;
-short sign;
-
-if( x > 0 )
- {
- sign = 1;
- a = x;
- }
-else
- {
- sign = -1;
- a = -x;
- }
-
-if( a > 1.0 )
- {
- mtherr( "asin", DOMAIN );
- return( NAN );
- }
-
-if( a > 0.625 )
- {
- /* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x)) */
- zz = 1.0 - a;
- p = zz * polevl( zz, R, 4)/p1evl( zz, S, 4);
- zz = sqrt(zz+zz);
- z = PIO4 - zz;
- zz = zz * p - MOREBITS;
- z = z - zz;
- z = z + PIO4;
- }
-else
- {
- if( a < 1.0e-8 )
- {
- return(x);
- }
- zz = a * a;
- z = zz * polevl( zz, P, 5)/p1evl( zz, Q, 5);
- z = a * z + a;
- }
-if( sign < 0 )
- z = -z;
-return(z);
-}
-
-
-
-double acos(x)
-double x;
-{
-double z;
-
-if( (x < -1.0) || (x > 1.0) )
- {
- mtherr( "acos", DOMAIN );
- return( NAN );
- }
-if( x > 0.5 )
- {
- return( 2.0 * asin( sqrt(0.5 - 0.5*x) ) );
- }
-z = PIO4 - asin(x);
-z = z + MOREBITS;
-z = z + PIO4;
-return( z );
-}
+++ /dev/null
-/* asinh.c
- *
- * Inverse hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, asinh();
- *
- * y = asinh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic sine of argument.
- *
- * If |x| < 0.5, the function is approximated by a rational
- * form x + x**3 P(x)/Q(x). Otherwise,
- *
- * asinh(x) = log( x + sqrt(1 + x*x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -3,3 75000 4.6e-17 1.1e-17
- * IEEE -1,1 30000 3.7e-16 7.8e-17
- * IEEE 1,3 30000 2.5e-16 6.7e-17
- *
- */
-\f
-/* asinh.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
--4.33231683752342103572E-3,
--5.91750212056387121207E-1,
--4.37390226194356683570E0,
--9.09030533308377316566E0,
--5.56682227230859640450E0
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 1.28757002067426453537E1,
- 4.86042483805291788324E1,
- 6.95722521337257608734E1,
- 3.34009336338516356383E1
-};
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0136215,0173033,0110410,0105475,
-0140027,0076361,0020056,0164520,
-0140613,0173401,0160136,0053142,
-0141021,0070744,0000503,0176261,
-0140662,0021550,0073106,0133351
-};
-static unsigned short Q[] = {
-/* 0040200,0000000,0000000,0000000,*/
-0041116,0001336,0034120,0173054,
-0041502,0065300,0013144,0021231,
-0041613,0022376,0035516,0153063,
-0041405,0115216,0054265,0004557
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x1168,0x7221,0xbec3,0xbf71,
-0xdd2a,0x2405,0xef9e,0xbfe2,
-0xcacc,0x3c0b,0x7ee0,0xc011,
-0x7f96,0x8028,0x2e3c,0xc022,
-0xd6dd,0x0ec8,0x446d,0xc016
-};
-static unsigned short Q[] = {
-/* 0x0000,0x0000,0x0000,0x3ff0,*/
-0x1ec5,0xc70a,0xc05b,0x4029,
-0x8453,0x02cc,0x4d58,0x4048,
-0xdac6,0xc769,0x649f,0x4051,
-0xa12e,0xcb16,0xb351,0x4040
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0xbf71,0xbec3,0x7221,0x1168,
-0xbfe2,0xef9e,0x2405,0xdd2a,
-0xc011,0x7ee0,0x3c0b,0xcacc,
-0xc022,0x2e3c,0x8028,0x7f96,
-0xc016,0x446d,0x0ec8,0xd6dd
-};
-static unsigned short Q[] = {
-0x4029,0xc05b,0xc70a,0x1ec5,
-0x4048,0x4d58,0x02cc,0x8453,
-0x4051,0x649f,0xc769,0xdac6,
-0x4040,0xb351,0xcb16,0xa12e
-};
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double sqrt ( double );
-extern double log ( double );
-#else
-double log(), sqrt(), polevl(), p1evl();
-#endif
-extern double LOGE2, INFINITY;
-
-double asinh(xx)
-double xx;
-{
-double a, z, x;
-int sign;
-
-#ifdef MINUSZERO
-if( xx == 0.0 )
- return(xx);
-#endif
-if( xx < 0.0 )
- {
- sign = -1;
- x = -xx;
- }
-else
- {
- sign = 1;
- x = xx;
- }
-
-if( x > 1.0e8 )
- {
-#ifdef INFINITIES
- if( x == INFINITY )
- return(xx);
-#endif
- return( sign * (log(x) + LOGE2) );
- }
-
-z = x * x;
-if( x < 0.5 )
- {
- a = ( polevl(z, P, 4)/p1evl(z, Q, 4) ) * z;
- a = a * x + x;
- if( sign < 0 )
- a = -a;
- return(a);
- }
-
-a = sqrt( z + 1.0 );
-return( sign * log(x + a) );
-}
+++ /dev/null
-/* atan.c
- *
- * Inverse circular tangent
- * (arctangent)
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, atan();
- *
- * y = atan( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose tangent
- * is x.
- *
- * Range reduction is from three intervals into the interval
- * from zero to 0.66. The approximant uses a rational
- * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10, 10 50000 2.4e-17 8.3e-18
- * IEEE -10, 10 10^6 1.8e-16 5.0e-17
- *
- */
-\f/* atan2()
- *
- * Quadrant correct inverse circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, z, atan2();
- *
- * z = atan2( y, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle whose tangent is y/x.
- * Define compile time symbol ANSIC = 1 for ANSI standard,
- * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
- * 0 to 2PI, args (x,y).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 10^6 2.5e-16 6.9e-17
- * See atan.c.
- *
- */
-\f
-/* atan.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-/* arctan(x) = x + x^3 P(x^2)/Q(x^2)
- 0 <= x <= 0.66
- Peak relative error = 2.6e-18 */
-#ifdef UNK
-static double P[5] = {
--8.750608600031904122785E-1,
--1.615753718733365076637E1,
--7.500855792314704667340E1,
--1.228866684490136173410E2,
--6.485021904942025371773E1,
-};
-static double Q[5] = {
-/* 1.000000000000000000000E0, */
- 2.485846490142306297962E1,
- 1.650270098316988542046E2,
- 4.328810604912902668951E2,
- 4.853903996359136964868E2,
- 1.945506571482613964425E2,
-};
-
-/* tan( 3*pi/8 ) */
-static double T3P8 = 2.41421356237309504880;
-#endif
-
-#ifdef DEC
-static short P[20] = {
-0140140,0001775,0007671,0026242,
-0141201,0041242,0155534,0001715,
-0141626,0002141,0132100,0011625,
-0141765,0142771,0064055,0150453,
-0141601,0131517,0164507,0062164,
-};
-static short Q[20] = {
-/* 0040200,0000000,0000000,0000000, */
-0041306,0157042,0154243,0000742,
-0042045,0003352,0016707,0150452,
-0042330,0070306,0113425,0170730,
-0042362,0130770,0116602,0047520,
-0042102,0106367,0156753,0013541,
-};
-
-/* tan( 3*pi/8 ) = 2.41421356237309504880 */
-static unsigned short T3P8A[] = {040432,0101171,0114774,0167462,};
-#define T3P8 *(double *)T3P8A
-#endif
-
-#ifdef IBMPC
-static short P[20] = {
-0x2594,0xa1f7,0x007f,0xbfec,
-0x807a,0x5b6b,0x2854,0xc030,
-0x0273,0x3688,0xc08c,0xc052,
-0xba25,0x2d05,0xb8bf,0xc05e,
-0xec8e,0xfd28,0x3669,0xc050,
-};
-static short Q[20] = {
-/* 0x0000,0x0000,0x0000,0x3ff0, */
-0x603c,0x5b14,0xdbc4,0x4038,
-0xfa25,0x43b8,0xa0dd,0x4064,
-0xbe3b,0xd2e2,0x0e18,0x407b,
-0x49ea,0x13b0,0x563f,0x407e,
-0x62ec,0xfbbd,0x519e,0x4068,
-};
-
-/* tan( 3*pi/8 ) = 2.41421356237309504880 */
-static unsigned short T3P8A[] = {0x9de6,0x333f,0x504f,0x4003};
-#define T3P8 *(double *)T3P8A
-#endif
-
-#ifdef MIEEE
-static short P[20] = {
-0xbfec,0x007f,0xa1f7,0x2594,
-0xc030,0x2854,0x5b6b,0x807a,
-0xc052,0xc08c,0x3688,0x0273,
-0xc05e,0xb8bf,0x2d05,0xba25,
-0xc050,0x3669,0xfd28,0xec8e,
-};
-static short Q[20] = {
-/* 0x3ff0,0x0000,0x0000,0x0000, */
-0x4038,0xdbc4,0x5b14,0x603c,
-0x4064,0xa0dd,0x43b8,0xfa25,
-0x407b,0x0e18,0xd2e2,0xbe3b,
-0x407e,0x563f,0x13b0,0x49ea,
-0x4068,0x519e,0xfbbd,0x62ec,
-};
-
-/* tan( 3*pi/8 ) = 2.41421356237309504880 */
-static unsigned short T3P8A[] = {
-0x4003,0x504f,0x333f,0x9de6
-};
-#define T3P8 *(double *)T3P8A
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double atan ( double );
-extern double fabs ( double );
-extern int signbit ( double );
-extern int isnan ( double );
-#else
-double polevl(), p1evl(), atan(), fabs();
-//int signbit(), isnan();
-#endif
-extern double PI, PIO2, PIO4, INFINITY, NEGZERO, MAXNUM;
-
-/* pi/2 = PIO2 + MOREBITS. */
-#ifdef DEC
-#define MOREBITS 5.721188726109831840122E-18
-#else
-#define MOREBITS 6.123233995736765886130E-17
-#endif
-
-
-double atan(x)
-double x;
-{
-double y, z;
-short sign, flag;
-
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-#ifdef INFINITIES
-if(x == INFINITY)
- return(PIO2);
-if(x == -INFINITY)
- return(-PIO2);
-#endif
-/* make argument positive and save the sign */
-sign = 1;
-if( x < 0.0 )
- {
- sign = -1;
- x = -x;
- }
-/* range reduction */
-flag = 0;
-if( x > T3P8 )
- {
- y = PIO2;
- flag = 1;
- x = -( 1.0/x );
- }
-else if( x <= 0.66 )
- {
- y = 0.0;
- }
-else
- {
- y = PIO4;
- flag = 2;
- x = (x-1.0)/(x+1.0);
- }
-z = x * x;
-z = z * polevl( z, P, 4 ) / p1evl( z, Q, 5 );
-z = x * z + x;
-if( flag == 2 )
- z += 0.5 * MOREBITS;
-else if( flag == 1 )
- z += MOREBITS;
-y = y + z;
-if( sign < 0 )
- y = -y;
-return(y);
-}
-\f
-/* atan2 */
-
-#ifdef ANSIC
-double atan2( y, x )
-#else
-double atan2( x, y )
-#endif
-double x, y;
-{
-double z, w;
-short code;
-
-code = 0;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-if( isnan(y) )
- return(y);
-#endif
-#ifdef MINUSZERO
-if( y == 0.0 )
- {
- if( signbit(y) )
- {
- if( x > 0.0 )
- z = y;
- else if( x < 0.0 )
- z = -PI;
- else
- {
- if( signbit(x) )
- z = -PI;
- else
- z = y;
- }
- }
- else /* y is +0 */
- {
- if( x == 0.0 )
- {
- if( signbit(x) )
- z = PI;
- else
- z = 0.0;
- }
- else if( x > 0.0 )
- z = 0.0;
- else
- z = PI;
- }
- return z;
- }
-if( x == 0.0 )
- {
- if( y > 0.0 )
- z = PIO2;
- else
- z = -PIO2;
- return z;
- }
-#endif /* MINUSZERO */
-#ifdef INFINITIES
-if( x == INFINITY )
- {
- if( y == INFINITY )
- z = 0.25 * PI;
- else if( y == -INFINITY )
- z = -0.25 * PI;
- else if( y < 0.0 )
- z = NEGZERO;
- else
- z = 0.0;
- return z;
- }
-if( x == -INFINITY )
- {
- if( y == INFINITY )
- z = 0.75 * PI;
- else if( y <= -INFINITY )
- z = -0.75 * PI;
- else if( y >= 0.0 )
- z = PI;
- else
- z = -PI;
- return z;
- }
-if( y == INFINITY )
- return( PIO2 );
-if( y == -INFINITY )
- return( -PIO2 );
-#endif
-
-if( x < 0.0 )
- code = 2;
-if( y < 0.0 )
- code |= 1;
-
-#ifdef INFINITIES
-if( x == 0.0 )
-#else
-if( fabs(x) <= (fabs(y) / MAXNUM) )
-#endif
- {
- if( code & 1 )
- {
-#if ANSIC
- return( -PIO2 );
-#else
- return( 3.0*PIO2 );
-#endif
- }
- if( y == 0.0 )
- return( 0.0 );
- return( PIO2 );
- }
-
-if( y == 0.0 )
- {
- if( code & 2 )
- return( PI );
- return( 0.0 );
- }
-
-
-switch( code )
- {
-#if ANSIC
- default:
- case 0:
- case 1: w = 0.0; break;
- case 2: w = PI; break;
- case 3: w = -PI; break;
-#else
- default:
- case 0: w = 0.0; break;
- case 1: w = 2.0 * PI; break;
- case 2:
- case 3: w = PI; break;
-#endif
- }
-
-z = w + atan( y/x );
-#ifdef MINUSZERO
-if( z == 0.0 && y < 0 )
- z = NEGZERO;
-#endif
-return( z );
-}
+++ /dev/null
-/* atanh.c
- *
- * Inverse hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, atanh();
- *
- * y = atanh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic tangent of argument in the range
- * MINLOG to MAXLOG.
- *
- * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
- * employed. Otherwise,
- * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -1,1 50000 2.4e-17 6.4e-18
- * IEEE -1,1 30000 1.9e-16 5.2e-17
- *
- */
-\f
-/* atanh.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
--8.54074331929669305196E-1,
- 1.20426861384072379242E1,
--4.61252884198732692637E1,
- 6.54566728676544377376E1,
--3.09092539379866942570E1
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
--1.95638849376911654834E1,
- 1.08938092147140262656E2,
--2.49839401325893582852E2,
- 2.52006675691344555838E2,
--9.27277618139601130017E1
-};
-#endif
-#ifdef DEC
-static unsigned short P[] = {
-0140132,0122235,0105775,0130300,
-0041100,0127327,0124407,0034722,
-0141470,0100113,0115607,0130535,
-0041602,0164721,0003257,0013673,
-0141367,0043046,0166673,0045750
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0141234,0101326,0015460,0134564,
-0041731,0160115,0116451,0032045,
-0142171,0153343,0000532,0167226,
-0042174,0000665,0077604,0000310,
-0141671,0072235,0031114,0074377
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0xb618,0xb17f,0x5493,0xbfeb,
-0xe73a,0xf520,0x15da,0x4028,
-0xf62c,0x7370,0x1009,0xc047,
-0xe2f7,0x20d5,0x5d3a,0x4050,
-0x697d,0xddb7,0xe8c4,0xc03e
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x172f,0xc366,0x905a,0xc033,
-0x2685,0xb3a5,0x3c09,0x405b,
-0x5dd3,0x602b,0x3adc,0xc06f,
-0x8019,0xaff0,0x8036,0x406f,
-0x8f20,0xa649,0x2e93,0xc057
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0xbfeb,0x5493,0xb17f,0xb618,
-0x4028,0x15da,0xf520,0xe73a,
-0xc047,0x1009,0x7370,0xf62c,
-0x4050,0x5d3a,0x20d5,0xe2f7,
-0xc03e,0xe8c4,0xddb7,0x697d
-};
-static unsigned short Q[] = {
-0xc033,0x905a,0xc366,0x172f,
-0x405b,0x3c09,0xb3a5,0x2685,
-0xc06f,0x3adc,0x602b,0x5dd3,
-0x406f,0x8036,0xaff0,0x8019,
-0xc057,0x2e93,0xa649,0x8f20
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double log ( double x );
-extern double polevl ( double x, void *P, int N );
-extern double p1evl ( double x, void *P, int N );
-#else
-double fabs(), log(), polevl(), p1evl();
-#endif
-extern double INFINITY, NAN;
-
-double atanh(x)
-double x;
-{
-double s, z;
-
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-z = fabs(x);
-if( z >= 1.0 )
- {
- if( x == 1.0 )
- return( INFINITY );
- if( x == -1.0 )
- return( -INFINITY );
- mtherr( "atanh", DOMAIN );
- return( NAN );
- }
-
-if( z < 1.0e-7 )
- return(x);
-
-if( z < 0.5 )
- {
- z = x * x;
- s = x + x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
- return(s);
- }
-
-return( 0.5 * log((1.0+x)/(1.0-x)) );
-}
+++ /dev/null
-/* bdtr.c
- *
- * Binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, bdtr();
- *
- * y = bdtr( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the Binomial
- * probability density:
- *
- * k
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p), with p between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between 0.001 and 1:
- * IEEE 0,100 100000 4.3e-15 2.6e-16
- * See also incbet.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtr domain k < 0 0.0
- * n < k
- * x < 0, x > 1
- */
-\f/* bdtrc()
- *
- * Complemented binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, bdtrc();
- *
- * y = bdtrc( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 through n of the Binomial
- * probability density:
- *
- * n
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between 0.001 and 1:
- * IEEE 0,100 100000 6.7e-15 8.2e-16
- * For p between 0 and .001:
- * IEEE 0,100 100000 1.5e-13 2.7e-15
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrc domain x<0, x>1, n<k 0.0
- */
-\f/* bdtri()
- *
- * Inverse binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, bdtri();
- *
- * p = bdtr( k, n, y );
- *
- * DESCRIPTION:
- *
- * Finds the event probability p such that the sum of the
- * terms 0 through k of the Binomial probability density
- * is equal to the given cumulative probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relation
- *
- * 1 - p = incbi( n-k, k+1, y ).
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between 0.001 and 1:
- * IEEE 0,100 100000 2.3e-14 6.4e-16
- * IEEE 0,10000 100000 6.6e-12 1.2e-13
- * For p between 10^-6 and 0.001:
- * IEEE 0,100 100000 2.0e-12 1.3e-14
- * IEEE 0,10000 100000 1.5e-12 3.2e-14
- * See also incbi.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtri domain k < 0, n <= k 0.0
- * x < 0, x > 1
- */
-\f
-/* bdtr() */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double incbet ( double, double, double );
-extern double incbi ( double, double, double );
-extern double pow ( double, double );
-extern double log1p ( double );
-extern double expm1 ( double );
-#else
-double incbet(), incbi(), pow(), log1p(), expm1();
-#endif
-
-double bdtrc( k, n, p )
-int k, n;
-double p;
-{
-double dk, dn;
-
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- return( 1.0 );
-
-if( n < k )
- {
-domerr:
- mtherr( "bdtrc", DOMAIN );
- return( 0.0 );
- }
-
-if( k == n )
- return( 0.0 );
-dn = n - k;
-if( k == 0 )
- {
- if( p < .01 )
- dk = -expm1( dn * log1p(-p) );
- else
- dk = 1.0 - pow( 1.0-p, dn );
- }
-else
- {
- dk = k + 1;
- dk = incbet( dk, dn, p );
- }
-return( dk );
-}
-
-
-
-double bdtr( k, n, p )
-int k, n;
-double p;
-{
-double dk, dn;
-
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( (k < 0) || (n < k) )
- {
-domerr:
- mtherr( "bdtr", DOMAIN );
- return( 0.0 );
- }
-
-if( k == n )
- return( 1.0 );
-
-dn = n - k;
-if( k == 0 )
- {
- dk = pow( 1.0-p, dn );
- }
-else
- {
- dk = k + 1;
- dk = incbet( dn, dk, 1.0 - p );
- }
-return( dk );
-}
-
-
-double bdtri( k, n, y )
-int k, n;
-double y;
-{
-double dk, dn, p;
-
-if( (y < 0.0) || (y > 1.0) )
- goto domerr;
-if( (k < 0) || (n <= k) )
- {
-domerr:
- mtherr( "bdtri", DOMAIN );
- return( 0.0 );
- }
-
-dn = n - k;
-if( k == 0 )
- {
- if( y > 0.8 )
- p = -expm1( log1p(y-1.0) / dn );
- else
- p = 1.0 - pow( y, 1.0/dn );
- }
-else
- {
- dk = k + 1;
- p = incbet( dn, dk, 0.5 );
- if( p > 0.5 )
- p = incbi( dk, dn, 1.0-y );
- else
- p = 1.0 - incbi( dn, dk, y );
- }
-return( p );
-}
+++ /dev/null
-/* This program computes the Bernoulli numbers.
- * See radd.c for rational arithmetic.
- */
-
-typedef struct{
- double n;
- double d;
- }fract;
-
-#define PD 44
-fract x[PD+1] = {0.0};
-fract p[PD+1] = {0.0};
-#include <math.h>
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double log10 ( double );
-#else
-double fabs(), log10();
-#endif
-extern double MACHEP;
-
-main()
-{
-int nx, np, nu;
-int i, j, k, n, sign;
-fract r, s, t;
-
-
-for(i=0; i<=PD; i++ )
- {
- x[i].n = 0.0;
- x[i].d = 1.0;
- p[i].n = 0.0;
- p[i].d = 1.0;
- }
-p[0].n = 1.0;
-p[0].d = 1.0;
-p[1].n = 1.0;
-p[1].d = 1.0;
-np = 1;
-x[0].n = 1.0;
-x[0].d = 1.0;
-
-for( n=1; n<PD-2; n++ )
-{
-
-/* Create line of Pascal's triangle */
-/* multiply p = u * p */
-for( k=0; k<=np; k++ )
- {
- radd( &p[np-k+1], &p[np-k], &p[np-k+1] );
- }
-np += 1;
-
-/* B0 + nC1 B1 + ... + nCn-1 Bn-1 = 0 */
-s.n = 0.0;
-s.d = 1.0;
-
-for( i=0; i<n; i++ )
- {
- rmul( &p[i], &x[i], &t );
- radd( &s, &t, &s );
- }
-
-
-rdiv( &p[n], &s, &x[n] ); /* x[n] = -s/p[n] */
-x[n].n = -x[n].n;
-nx += 1;
-printf( "%2d %.15e / %.15e\n", n, x[n].n, x[n].d );
-}
-
-
-}
-
+++ /dev/null
-/* beta.c
- *
- * Beta function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, y, beta();
- *
- * y = beta( a, b );
- *
- *
- *
- * DESCRIPTION:
- *
- * - -
- * | (a) | (b)
- * beta( a, b ) = -----------.
- * -
- * | (a+b)
- *
- * For large arguments the logarithm of the function is
- * evaluated using lgam(), then exponentiated.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 1700 7.7e-15 1.5e-15
- * IEEE 0,30 30000 8.1e-14 1.1e-14
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * beta overflow log(beta) > MAXLOG 0.0
- * a or b <0 integer 0.0
- *
- */
-\f
-/* beta.c */
-
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef UNK
-#define MAXGAM 34.84425627277176174
-#endif
-#ifdef DEC
-#define MAXGAM 34.84425627277176174
-#endif
-#ifdef IBMPC
-#define MAXGAM 171.624376956302725
-#endif
-#ifdef MIEEE
-#define MAXGAM 171.624376956302725
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double gamma ( double );
-extern double lgam ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double floor ( double );
-#else
-double fabs(), gamma(), lgam(), exp(), log(), floor();
-#endif
-extern double MAXLOG, MAXNUM;
-extern int sgngam;
-
-double beta( a, b )
-double a, b;
-{
-double y;
-int sign;
-
-sign = 1;
-
-if( a <= 0.0 )
- {
- if( a == floor(a) )
- goto over;
- }
-if( b <= 0.0 )
- {
- if( b == floor(b) )
- goto over;
- }
-
-
-y = a + b;
-if( fabs(y) > MAXGAM )
- {
- y = lgam(y);
- sign *= sgngam; /* keep track of the sign */
- y = lgam(b) - y;
- sign *= sgngam;
- y = lgam(a) + y;
- sign *= sgngam;
- if( y > MAXLOG )
- {
-over:
- mtherr( "beta", OVERFLOW );
- return( sign * MAXNUM );
- }
- return( sign * exp(y) );
- }
-
-y = gamma(y);
-if( y == 0.0 )
- goto over;
-
-if( a > b )
- {
- y = gamma(a)/y;
- y *= gamma(b);
- }
-else
- {
- y = gamma(b)/y;
- y *= gamma(a);
- }
-
-return(y);
-}
-
-
-
-/* Natural log of |beta|. Return the sign of beta in sgngam. */
-
-double lbeta( a, b )
-double a, b;
-{
-double y;
-int sign;
-
-sign = 1;
-
-if( a <= 0.0 )
- {
- if( a == floor(a) )
- goto over;
- }
-if( b <= 0.0 )
- {
- if( b == floor(b) )
- goto over;
- }
-
-
-y = a + b;
-if( fabs(y) > MAXGAM )
- {
- y = lgam(y);
- sign *= sgngam; /* keep track of the sign */
- y = lgam(b) - y;
- sign *= sgngam;
- y = lgam(a) + y;
- sign *= sgngam;
- sgngam = sign;
- return( y );
- }
-
-y = gamma(y);
-if( y == 0.0 )
- {
-over:
- mtherr( "lbeta", OVERFLOW );
- return( sign * MAXNUM );
- }
-
-if( a > b )
- {
- y = gamma(a)/y;
- y *= gamma(b);
- }
-else
- {
- y = gamma(b)/y;
- y *= gamma(a);
- }
-
-if( y < 0 )
- {
- sgngam = -1;
- y = -y;
- }
-else
- sgngam = 1;
-
-return( log(y) );
-}
+++ /dev/null
-
-/* btdtr.c
- *
- * Beta distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, btdtr();
- *
- * y = btdtr( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the beta density
- * function:
- *
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * P(x) = ---------- | t (1-t) dt
- * - - | |
- * | (a) | (b) -
- * 0
- *
- *
- * This function is identical to the incomplete beta
- * integral function incbet(a, b, x).
- *
- * The complemented function is
- *
- * 1 - P(1-x) = incbet( b, a, x );
- *
- *
- * ACCURACY:
- *
- * See incbet.c.
- *
- */
-\f
-/* btdtr() */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-#include <math.h>
-#ifdef ANSIPROT
-extern double incbet ( double, double, double );
-#else
-double incbet();
-#endif
-
-double btdtr( a, b, x )
-double a, b, x;
-{
-
-return( incbet( a, b, x ) );
-}
+++ /dev/null
-/* cbrt.c
- *
- * Cube root
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cbrt();
- *
- * y = cbrt( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the cube root of the argument, which may be negative.
- *
- * Range reduction involves determining the power of 2 of
- * the argument. A polynomial of degree 2 applied to the
- * mantissa, and multiplication by the cube root of 1, 2, or 4
- * approximates the root to within about 0.1%. Then Newton's
- * iteration is used three times to converge to an accurate
- * result.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,10 200000 1.8e-17 6.2e-18
- * IEEE 0,1e308 30000 1.5e-16 5.0e-17
- *
- */
-\f/* cbrt.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1991, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-static double CBRT2 = 1.2599210498948731647672;
-static double CBRT4 = 1.5874010519681994747517;
-static double CBRT2I = 0.79370052598409973737585;
-static double CBRT4I = 0.62996052494743658238361;
-
-#ifdef ANSIPROT
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double frexp(), ldexp();
-int isnan(), isfinite();
-#endif
-
-double cbrt(x)
-double x;
-{
-int e, rem, sign;
-double z;
-
-#ifdef NANS
-if( isnan(x) )
- return x;
-#endif
-#ifdef INFINITIES
-if( !isfinite(x) )
- return x;
-#endif
-if( x == 0 )
- return( x );
-if( x > 0 )
- sign = 1;
-else
- {
- sign = -1;
- x = -x;
- }
-
-z = x;
-/* extract power of 2, leaving
- * mantissa between 0.5 and 1
- */
-x = frexp( x, &e );
-
-/* Approximate cube root of number between .5 and 1,
- * peak relative error = 9.2e-6
- */
-x = (((-1.3466110473359520655053e-1 * x
- + 5.4664601366395524503440e-1) * x
- - 9.5438224771509446525043e-1) * x
- + 1.1399983354717293273738e0 ) * x
- + 4.0238979564544752126924e-1;
-
-/* exponent divided by 3 */
-if( e >= 0 )
- {
- rem = e;
- e /= 3;
- rem -= 3*e;
- if( rem == 1 )
- x *= CBRT2;
- else if( rem == 2 )
- x *= CBRT4;
- }
-
-
-/* argument less than 1 */
-
-else
- {
- e = -e;
- rem = e;
- e /= 3;
- rem -= 3*e;
- if( rem == 1 )
- x *= CBRT2I;
- else if( rem == 2 )
- x *= CBRT4I;
- e = -e;
- }
-
-/* multiply by power of 2 */
-x = ldexp( x, e );
-
-/* Newton iteration */
-x -= ( x - (z/(x*x)) )*0.33333333333333333333;
-#ifdef DEC
-x -= ( x - (z/(x*x)) )/3.0;
-#else
-x -= ( x - (z/(x*x)) )*0.33333333333333333333;
-#endif
-
-if( sign < 0 )
- x = -x;
-return(x);
-}
+++ /dev/null
-/* chbevl.c
- *
- * Evaluate Chebyshev series
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * double x, y, coef[N], chebevl();
- *
- * y = chbevl( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the series
- *
- * N-1
- * - '
- * y = > coef[i] T (x/2)
- * - i
- * i=0
- *
- * of Chebyshev polynomials Ti at argument x/2.
- *
- * Coefficients are stored in reverse order, i.e. the zero
- * order term is last in the array. Note N is the number of
- * coefficients, not the order.
- *
- * If coefficients are for the interval a to b, x must
- * have been transformed to x -> 2(2x - b - a)/(b-a) before
- * entering the routine. This maps x from (a, b) to (-1, 1),
- * over which the Chebyshev polynomials are defined.
- *
- * If the coefficients are for the inverted interval, in
- * which (a, b) is mapped to (1/b, 1/a), the transformation
- * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
- * this becomes x -> 4a/x - 1.
- *
- *
- *
- * SPEED:
- *
- * Taking advantage of the recurrence properties of the
- * Chebyshev polynomials, the routine requires one more
- * addition per loop than evaluating a nested polynomial of
- * the same degree.
- *
- */
-\f/* chbevl.c */
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1985, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-double chbevl( x, array, n )
-double x;
-double array[];
-int n;
-{
-double b0, b1, b2, *p;
-int i;
-
-p = array;
-b0 = *p++;
-b1 = 0.0;
-i = n - 1;
-
-do
- {
- b2 = b1;
- b1 = b0;
- b0 = x * b1 - b2 + *p++;
- }
-while( --i );
-
-return( 0.5*(b0-b2) );
-}
+++ /dev/null
-/* chdtr.c
- *
- * Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double df, x, y, chdtr();
- *
- * y = chdtr( df, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the left hand tail (from 0 to x)
- * of the Chi square probability density function with
- * v degrees of freedom.
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtr domain x < 0 or v < 1 0.0
- */
-\f/* chdtrc()
- *
- * Complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, chdtrc();
- *
- * y = chdtrc( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the right hand tail (from x to
- * infinity) of the Chi square probability density function
- * with v degrees of freedom:
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrc domain x < 0 or v < 1 0.0
- */
-\f/* chdtri()
- *
- * Inverse of complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double df, x, y, chdtri();
- *
- * x = chdtri( df, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Chi-square argument x such that the integral
- * from x to infinity of the Chi-square density is equal
- * to the given cumulative probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * x/2 = igami( df/2, y );
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtri domain y < 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* chdtr() */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double igamc ( double, double );
-extern double igam ( double, double );
-extern double igami ( double, double );
-#else
-double igamc(), igam(), igami();
-#endif
-
-double chdtrc(df,x)
-double df, x;
-{
-
-if( (x < 0.0) || (df < 1.0) )
- {
- mtherr( "chdtrc", DOMAIN );
- return(0.0);
- }
-return( igamc( df/2.0, x/2.0 ) );
-}
-
-
-
-double chdtr(df,x)
-double df, x;
-{
-
-if( (x < 0.0) || (df < 1.0) )
- {
- mtherr( "chdtr", DOMAIN );
- return(0.0);
- }
-return( igam( df/2.0, x/2.0 ) );
-}
-
-
-
-double chdtri( df, y )
-double df, y;
-{
-double x;
-
-if( (y < 0.0) || (y > 1.0) || (df < 1.0) )
- {
- mtherr( "chdtri", DOMAIN );
- return(0.0);
- }
-
-x = igami( 0.5 * df, y );
-return( 2.0 * x );
-}
+++ /dev/null
-/* cheby.c
- *
- * Program to calculate coefficients of the Chebyshev polynomial
- * expansion of a given input function. The algorithm computes
- * the discrete Fourier cosine transform of the function evaluated
- * at unevenly spaced points. Library routine chbevl.c uses the
- * coefficients to calculate an approximate value of the original
- * function.
- * -- S. L. Moshier
- */
-
-extern double PI; /* 3.14159... */
-extern double PIO2;
-double cosi[33] = {0.0,}; /* cosine array for Fourier transform */
-double func[65] = {0.0,}; /* values of the function */
-double cos(), log(), exp(), sqrt();
-
-main()
-{
-double c, r, s, t, x, y, z, temp;
-double low, high, dtemp;
-long n;
-int i, ii, j, n2, k, rr, invflg;
-short *p;
-char st[40];
-
-low = 0.0; /* low end of approximation interval */
-high = 1.0; /* high end */
-invflg = 0; /* set to 1 if inverted interval, else zero */
-/* Note: inverted interval goes from 1/high to 1/low */
-z = 0.0;
-n = 64; /* will find 64 coefficients */
- /* but use only those greater than roundoff error */
-n2 = n/2;
-t = n;
-t = PI/t;
-
-/* calculate array of cosines */
-puts("calculating cosines");
-s = 1.0;
-cosi[0] = 1.0;
-i = 1;
-while( i < 32 )
- {
- y = cos( s * t );
- cosi[i] = y;
- s += 1.0;
- ++i;
- }
-cosi[32] = 0.0;
-\f
-/* cheby.c 2 */
-
-/* calculate function at special values of the argument */
-puts("calculating function values");
-x = low;
-y = high;
-if( invflg && (low != 0.0) )
- { /* inverted interval */
- temp = 1.0/x;
- x = 1.0/y;
- y = temp;
- }
-r = (x + y)/2.0;
-printf( "center %.15E ", r);
-s = (y - x)/2.0;
-printf( "width %.15E\n", s);
-i = 0;
-while( i < 65 )
- {
- if( i < n2 )
- c = cosi[i];
- else
- c = -cosi[64-i];
- temp = r + s * c;
-/* if inverted interval, compute function(1/x) */
- if( invflg && (temp != 0.0) )
- temp = 1.0/temp;
-
- printf( "%.15E ", temp );
-
-/* insert call to function routine here: */
-/**********************************/
-
- if( temp == 0.0 )
- y = 1.0;
- else
- y = exp( temp * log(2.0) );
-
-/**********************************/
- func[i] = y;
- printf( "%.15E\n", y );
- ++i;
- }
-\f
-/* cheby.c 3 */
-
-puts( "calculating Chebyshev coefficients");
-rr = 0;
-while( rr < 65 )
- {
- z = func[0]/2.0;
- j = 1;
- while( j < 65 )
- {
- k = (rr * j)/n2;
- i = rr * j - n2 * k;
- k &= 3;
- if( k == 0 )
- c = cosi[i];
- if( k == 1 )
- {
- i = 32-i;
- c = -cosi[i];
- if( i == 32 )
- c = -c;
- }
- if( k == 2 )
- {
- c = -cosi[i];
- }
- if( k == 3 )
- {
- i = 32-i;
- c = cosi[i];
- }
- if( i != 32)
- {
- temp = func[j];
- temp = c * temp;
- z += temp;
- }
- ++j;
- }
-
- if( i != 32 )
- {
- temp /= 2.0;
- z = z - temp;
- }
- z *= 2.0;
- temp = n;
- z /= temp;
- dtemp = z;
- ++rr;
- sprintf( st, "/* %.16E */", dtemp );
- puts( st );
- }
-}
+++ /dev/null
-/* clog.c
- *
- * Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clog();
- * cmplx z, w;
- *
- * clog( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns complex logarithm to the base e (2.718...) of
- * the complex argument x.
- *
- * If z = x + iy, r = sqrt( x**2 + y**2 ),
- * then
- * w = log(r) + i arctan(y/x).
- *
- * The arctangent ranges from -PI to +PI.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 7000 8.5e-17 1.9e-17
- * IEEE -10,+10 30000 5.0e-15 1.1e-16
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
- * absolute error 1.0e-16.
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-#include <math.h>
-#ifdef ANSIPROT
-static void cchsh ( double x, double *c, double *s );
-static double redupi ( double x );
-static double ctans ( cmplx *z );
-/* These are supposed to be in some standard place. */
-double fabs (double);
-double sqrt (double);
-double pow (double, double);
-double log (double);
-double exp (double);
-double atan2 (double, double);
-double cosh (double);
-double sinh (double);
-double asin (double);
-double sin (double);
-double cos (double);
-double cabs (cmplx *);
-void cadd ( cmplx *, cmplx *, cmplx * );
-void cmul ( cmplx *, cmplx *, cmplx * );
-void csqrt ( cmplx *, cmplx * );
-static void cchsh ( double, double *, double * );
-static double redupi ( double );
-static double ctans ( cmplx * );
-void clog ( cmplx *, cmplx * );
-void casin ( cmplx *, cmplx * );
-void cacos ( cmplx *, cmplx * );
-void catan ( cmplx *, cmplx * );
-#else
-static void cchsh();
-static double redupi();
-static double ctans();
-double cabs(), fabs(), sqrt(), pow();
-double log(), exp(), atan2(), cosh(), sinh();
-double asin(), sin(), cos();
-void cadd(), cmul(), csqrt();
-void clog(), casin(), cacos(), catan();
-#endif
-
-
-extern double MAXNUM, MACHEP, PI, PIO2;
-
-void clog( z, w )
-register cmplx *z, *w;
-{
-double p, rr;
-
-/*rr = sqrt( z->r * z->r + z->i * z->i );*/
-rr = cabs(z);
-p = log(rr);
-#if ANSIC
-rr = atan2( z->i, z->r );
-#else
-rr = atan2( z->r, z->i );
-if( rr > PI )
- rr -= PI + PI;
-#endif
-w->i = rr;
-w->r = p;
-}
-\f/* cexp()
- *
- * Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexp();
- * cmplx z, w;
- *
- * cexp( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the exponential of the complex argument z
- * into the complex result w.
- *
- * If
- * z = x + iy,
- * r = exp(x),
- *
- * then
- *
- * w = r cos y + i r sin y.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8700 3.7e-17 1.1e-17
- * IEEE -10,+10 30000 3.0e-16 8.7e-17
- *
- */
-\f
-void cexp( z, w )
-register cmplx *z, *w;
-{
-double r;
-
-r = exp( z->r );
-w->r = r * cos( z->i );
-w->i = r * sin( z->i );
-}
-\f/* csin()
- *
- * Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csin();
- * cmplx z, w;
- *
- * csin( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = sin x cosh y + i cos x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 5.3e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- * Also tested by csin(casin(z)) = z.
- *
- */
-\f
-void csin( z, w )
-register cmplx *z, *w;
-{
-double ch, sh;
-
-cchsh( z->i, &ch, &sh );
-w->r = sin( z->r ) * ch;
-w->i = cos( z->r ) * sh;
-}
-
-
-
-/* calculate cosh and sinh */
-
-static void cchsh( x, c, s )
-double x, *c, *s;
-{
-double e, ei;
-
-if( fabs(x) <= 0.5 )
- {
- *c = cosh(x);
- *s = sinh(x);
- }
-else
- {
- e = exp(x);
- ei = 0.5/e;
- e = 0.5 * e;
- *s = e - ei;
- *c = e + ei;
- }
-}
-
-\f/* ccos()
- *
- * Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccos();
- * cmplx z, w;
- *
- * ccos( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = cos x cosh y - i sin x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 4.5e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- */
-\f
-void ccos( z, w )
-register cmplx *z, *w;
-{
-double ch, sh;
-
-cchsh( z->i, &ch, &sh );
-w->r = cos( z->r ) * ch;
-w->i = -sin( z->r ) * sh;
-}
-\f/* ctan()
- *
- * Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctan();
- * cmplx z, w;
- *
- * ctan( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x + i sinh 2y
- * w = --------------------.
- * cos 2x + cosh 2y
- *
- * On the real axis the denominator is zero at odd multiples
- * of PI/2. The denominator is evaluated by its Taylor
- * series near these points.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 7.1e-17 1.6e-17
- * IEEE -10,+10 30000 7.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
- */
-\f
-void ctan( z, w )
-register cmplx *z, *w;
-{
-double d;
-
-d = cos( 2.0 * z->r ) + cosh( 2.0 * z->i );
-
-if( fabs(d) < 0.25 )
- d = ctans(z);
-
-if( d == 0.0 )
- {
- mtherr( "ctan", OVERFLOW );
- w->r = MAXNUM;
- w->i = MAXNUM;
- return;
- }
-
-w->r = sin( 2.0 * z->r ) / d;
-w->i = sinh( 2.0 * z->i ) / d;
-}
-\f/* ccot()
- *
- * Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccot();
- * cmplx z, w;
- *
- * ccot( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x - i sinh 2y
- * w = --------------------.
- * cosh 2y - cos 2x
- *
- * On the real axis, the denominator has zeros at even
- * multiples of PI/2. Near these points it is evaluated
- * by a Taylor series.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 3000 6.5e-17 1.6e-17
- * IEEE -10,+10 30000 9.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 + i0.
- */
-\f
-void ccot( z, w )
-register cmplx *z, *w;
-{
-double d;
-
-d = cosh(2.0 * z->i) - cos(2.0 * z->r);
-
-if( fabs(d) < 0.25 )
- d = ctans(z);
-
-if( d == 0.0 )
- {
- mtherr( "ccot", OVERFLOW );
- w->r = MAXNUM;
- w->i = MAXNUM;
- return;
- }
-
-w->r = sin( 2.0 * z->r ) / d;
-w->i = -sinh( 2.0 * z->i ) / d;
-}
-\f
-/* Program to subtract nearest integer multiple of PI */
-/* extended precision value of PI: */
-#ifdef UNK
-static double DP1 = 3.14159265160560607910E0;
-static double DP2 = 1.98418714791870343106E-9;
-static double DP3 = 1.14423774522196636802E-17;
-#endif
-
-#ifdef DEC
-static unsigned short P1[] = {0040511,0007732,0120000,0000000,};
-static unsigned short P2[] = {0031010,0055060,0100000,0000000,};
-static unsigned short P3[] = {0022123,0011431,0105056,0001560,};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef IBMPC
-static unsigned short P1[] = {0x0000,0x5400,0x21fb,0x4009};
-static unsigned short P2[] = {0x0000,0x1000,0x0b46,0x3e21};
-static unsigned short P3[] = {0xc06e,0x3145,0x6263,0x3c6a};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef MIEEE
-static unsigned short P1[] = {
-0x4009,0x21fb,0x5400,0x0000
-};
-static unsigned short P2[] = {
-0x3e21,0x0b46,0x1000,0x0000
-};
-static unsigned short P3[] = {
-0x3c6a,0x6263,0x3145,0xc06e
-};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-static double redupi(x)
-double x;
-{
-double t;
-long i;
-
-t = x/PI;
-if( t >= 0.0 )
- t += 0.5;
-else
- t -= 0.5;
-
-i = t; /* the multiple */
-t = i;
-t = ((x - t * DP1) - t * DP2) - t * DP3;
-return(t);
-}
-\f
-/* Taylor series expansion for cosh(2y) - cos(2x) */
-
-static double ctans(z)
-cmplx *z;
-{
-double f, x, x2, y, y2, rn, t;
-double d;
-
-x = fabs( 2.0 * z->r );
-y = fabs( 2.0 * z->i );
-
-x = redupi(x);
-
-x = x * x;
-y = y * y;
-x2 = 1.0;
-y2 = 1.0;
-f = 1.0;
-rn = 0.0;
-d = 0.0;
-do
- {
- rn += 1.0;
- f *= rn;
- rn += 1.0;
- f *= rn;
- x2 *= x;
- y2 *= y;
- t = y2 + x2;
- t /= f;
- d += t;
-
- rn += 1.0;
- f *= rn;
- rn += 1.0;
- f *= rn;
- x2 *= x;
- y2 *= y;
- t = y2 - x2;
- t /= f;
- d += t;
- }
-while( fabs(t/d) > MACHEP );
-return(d);
-}
-\f/* casin()
- *
- * Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casin();
- * cmplx z, w;
- *
- * casin( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- * 2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 10100 2.1e-15 3.4e-16
- * IEEE -10,+10 30000 2.2e-14 2.7e-15
- * Larger relative error can be observed for z near zero.
- * Also tested by csin(casin(z)) = z.
- */
-\f
-void casin( z, w )
-cmplx *z, *w;
-{
-static cmplx ca, ct, zz, z2;
-double x, y;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0 )
- {
- if( fabs(x) > 1.0 )
- {
- w->r = PIO2;
- w->i = 0.0;
- mtherr( "casin", DOMAIN );
- }
- else
- {
- w->r = asin(x);
- w->i = 0.0;
- }
- return;
- }
-
-/* Power series expansion */
-/*
-b = cabs(z);
-if( b < 0.125 )
-{
-z2.r = (x - y) * (x + y);
-z2.i = 2.0 * x * y;
-
-cn = 1.0;
-n = 1.0;
-ca.r = x;
-ca.i = y;
-sum.r = x;
-sum.i = y;
-do
- {
- ct.r = z2.r * ca.r - z2.i * ca.i;
- ct.i = z2.r * ca.i + z2.i * ca.r;
- ca.r = ct.r;
- ca.i = ct.i;
-
- cn *= n;
- n += 1.0;
- cn /= n;
- n += 1.0;
- b = cn/n;
-
- ct.r *= b;
- ct.i *= b;
- sum.r += ct.r;
- sum.i += ct.i;
- b = fabs(ct.r) + fabs(ct.i);
- }
-while( b > MACHEP );
-w->r = sum.r;
-w->i = sum.i;
-return;
-}
-*/
-
-
-ca.r = x;
-ca.i = y;
-
-ct.r = -ca.i; /* iz */
-ct.i = ca.r;
-
- /* sqrt( 1 - z*z) */
-/* cmul( &ca, &ca, &zz ) */
-zz.r = (ca.r - ca.i) * (ca.r + ca.i); /*x * x - y * y */
-zz.i = 2.0 * ca.r * ca.i;
-
-zz.r = 1.0 - zz.r;
-zz.i = -zz.i;
-csqrt( &zz, &z2 );
-
-cadd( &z2, &ct, &zz );
-clog( &zz, &zz );
-w->r = zz.i; /* mult by 1/i = -i */
-w->i = -zz.r;
-return;
-}
-\f/* cacos()
- *
- * Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacos();
- * cmplx z, w;
- *
- * cacos( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z = PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 1.6e-15 2.8e-16
- * IEEE -10,+10 30000 1.8e-14 2.2e-15
- */
-\f
-void cacos( z, w )
-cmplx *z, *w;
-{
-
-casin( z, w );
-w->r = PIO2 - w->r;
-w->i = -w->i;
-}
-\f/* catan()
- *
- * Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catan();
- * cmplx z, w;
- *
- * catan( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- * 1 ( 2x )
- * Re w = - arctan(-----------) + k PI
- * 2 ( 2 2)
- * (1 - x - y )
- *
- * ( 2 2)
- * 1 (x + (y+1) )
- * Im w = - log(------------)
- * 4 ( 2 2)
- * (x + (y-1) )
- *
- * Where k is an arbitrary integer.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5900 1.3e-16 7.8e-18
- * IEEE -10,+10 30000 2.3e-15 8.5e-17
- * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
- * had peak relative error 1.5e-16, rms relative error
- * 2.9e-17. See also clog().
- */
-\f
-void catan( z, w )
-cmplx *z, *w;
-{
-double a, t, x, x2, y;
-
-x = z->r;
-y = z->i;
-
-if( (x == 0.0) && (y > 1.0) )
- goto ovrf;
-
-x2 = x * x;
-a = 1.0 - x2 - (y * y);
-if( a == 0.0 )
- goto ovrf;
-
-#if ANSIC
-t = atan2( 2.0 * x, a )/2.0;
-#else
-t = atan2( a, 2.0 * x )/2.0;
-#endif
-w->r = redupi( t );
-
-t = y - 1.0;
-a = x2 + (t * t);
-if( a == 0.0 )
- goto ovrf;
-
-t = y + 1.0;
-a = (x2 + (t * t))/a;
-w->i = log(a)/4.0;
-return;
-
-ovrf:
-mtherr( "catan", OVERFLOW );
-w->r = MAXNUM;
-w->i = MAXNUM;
-}
-
-
-/* csinh
- *
- * Complex hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csinh();
- * cmplx z, w;
- *
- * csinh( &z, &w );
- *
- *
- * DESCRIPTION:
- *
- * csinh z = (cexp(z) - cexp(-z))/2
- * = sinh x * cos y + i cosh x * sin y .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 3.1e-16 8.2e-17
- *
- */
-
-void
-csinh (z, w)
- cmplx *z, *w;
-{
- double x, y;
-
- x = z->r;
- y = z->i;
- w->r = sinh (x) * cos (y);
- w->i = cosh (x) * sin (y);
-}
-
-
-/* casinh
- *
- * Complex inverse hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casinh();
- * cmplx z, w;
- *
- * casinh (&z, &w);
- *
- *
- *
- * DESCRIPTION:
- *
- * casinh z = -i casin iz .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.8e-14 2.6e-15
- *
- */
-
-void
-casinh (z, w)
- cmplx *z, *w;
-{
- cmplx u;
-
- u.r = 0.0;
- u.i = 1.0;
- cmul( z, &u, &u );
- casin( &u, w );
- u.r = 0.0;
- u.i = -1.0;
- cmul( &u, w, w );
-}
-
-/* ccosh
- *
- * Complex hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccosh();
- * cmplx z, w;
- *
- * ccosh (&z, &w);
- *
- *
- *
- * DESCRIPTION:
- *
- * ccosh(z) = cosh x cos y + i sinh x sin y .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 2.9e-16 8.1e-17
- *
- */
-
-void
-ccosh (z, w)
- cmplx *z, *w;
-{
- double x, y;
-
- x = z->r;
- y = z->i;
- w->r = cosh (x) * cos (y);
- w->i = sinh (x) * sin (y);
-}
-
-
-/* cacosh
- *
- * Complex inverse hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacosh();
- * cmplx z, w;
- *
- * cacosh (&z, &w);
- *
- *
- *
- * DESCRIPTION:
- *
- * acosh z = i acos z .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.6e-14 2.1e-15
- *
- */
-
-void
-cacosh (z, w)
- cmplx *z, *w;
-{
- cmplx u;
-
- cacos( z, w );
- u.r = 0.0;
- u.i = 1.0;
- cmul( &u, w, w );
-}
-
-
-/* ctanh
- *
- * Complex hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctanh();
- * cmplx z, w;
- *
- * ctanh (&z, &w);
- *
- *
- *
- * DESCRIPTION:
- *
- * tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.7e-14 2.4e-16
- *
- */
-
-/* 5.253E-02,1.550E+00 1.643E+01,6.553E+00 1.729E-14 21355 */
-
-void
-ctanh (z, w)
- cmplx *z, *w;
-{
- double x, y, d;
-
- x = z->r;
- y = z->i;
- d = cosh (2.0 * x) + cos (2.0 * y);
- w->r = sinh (2.0 * x) / d;
- w->i = sin (2.0 * y) / d;
- return;
-}
-
-
-/* catanh
- *
- * Complex inverse hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catanh();
- * cmplx z, w;
- *
- * catanh (&z, &w);
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse tanh, equal to -i catan (iz);
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 2.3e-16 6.2e-17
- *
- */
-
-void
-catanh (z, w)
- cmplx *z, *w;
-{
- cmplx u;
-
- u.r = 0.0;
- u.i = 1.0;
- cmul (z, &u, &u); /* i z */
- catan (&u, w);
- u.r = 0.0;
- u.i = -1.0;
- cmul (&u, w, w); /* -i catan iz */
- return;
-}
-
-
-/* cpow
- *
- * Complex power function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cpow();
- * cmplx a, z, w;
- *
- * cpow (&a, &z, &w);
- *
- *
- *
- * DESCRIPTION:
- *
- * Raises complex A to the complex Zth power.
- * Definition is per AMS55 # 4.2.8,
- * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 9.4e-15 1.5e-15
- *
- */
-
-
-void
-cpow (a, z, w)
- cmplx *a, *z, *w;
-{
- double x, y, r, theta, absa, arga;
-
- x = z->r;
- y = z->i;
- absa = cabs (a);
- if (absa == 0.0)
- {
- w->r = 0.0;
- w->i = 0.0;
- return;
- }
- arga = atan2 (a->i, a->r);
- r = pow (absa, x);
- theta = x * arga;
- if (y != 0.0)
- {
- r = r * exp (-y * arga);
- theta = theta + y * log (absa);
- }
- w->r = r * cos (theta);
- w->i = r * sin (theta);
- return;
-}
+++ /dev/null
-/* cmplx.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * double r; real part
- * double i; imaginary part
- * }cmplx;
- *
- * cmplx *a, *b, *c;
- *
- * cadd( a, b, c ); c = b + a
- * csub( a, b, c ); c = b - a
- * cmul( a, b, c ); c = b * a
- * cdiv( a, b, c ); c = b / a
- * cneg( c ); c = -c
- * cmov( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
-\f * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * DEC cadd 10000 1.4e-17 3.4e-18
- * IEEE cadd 100000 1.1e-16 2.7e-17
- * DEC csub 10000 1.4e-17 4.5e-18
- * IEEE csub 100000 1.1e-16 3.4e-17
- * DEC cmul 3000 2.3e-17 8.7e-18
- * IEEE cmul 100000 2.1e-16 6.9e-17
- * DEC cdiv 18000 4.9e-17 1.3e-17
- * IEEE cdiv 100000 3.7e-16 1.1e-16
- */
-\f/* cmplx.c
- * complex number arithmetic
- */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double cabs ( cmplx * );
-extern double sqrt ( double );
-extern double atan2 ( double, double );
-extern double cos ( double );
-extern double sin ( double );
-extern double sqrt ( double );
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-int isnan ( double );
-void cdiv ( cmplx *, cmplx *, cmplx * );
-void cadd ( cmplx *, cmplx *, cmplx * );
-#else
-double fabs(), cabs(), sqrt(), atan2(), cos(), sin();
-double sqrt(), frexp(), ldexp();
-int isnan();
-void cdiv(), cadd();
-#endif
-
-extern double MAXNUM, MACHEP, PI, PIO2, INFINITY, NAN;
-/*
-typedef struct
- {
- double r;
- double i;
- }cmplx;
-*/
-cmplx czero = {0.0, 0.0};
-extern cmplx czero;
-cmplx cone = {1.0, 0.0};
-extern cmplx cone;
-
-/* c = b + a */
-
-void cadd( a, b, c )
-register cmplx *a, *b;
-cmplx *c;
-{
-
-c->r = b->r + a->r;
-c->i = b->i + a->i;
-}
-
-
-/* c = b - a */
-
-void csub( a, b, c )
-register cmplx *a, *b;
-cmplx *c;
-{
-
-c->r = b->r - a->r;
-c->i = b->i - a->i;
-}
-
-/* c = b * a */
-
-void cmul( a, b, c )
-register cmplx *a, *b;
-cmplx *c;
-{
-double y;
-
-y = b->r * a->r - b->i * a->i;
-c->i = b->r * a->i + b->i * a->r;
-c->r = y;
-}
-
-
-
-/* c = b / a */
-
-void cdiv( a, b, c )
-register cmplx *a, *b;
-cmplx *c;
-{
-double y, p, q, w;
-
-
-y = a->r * a->r + a->i * a->i;
-p = b->r * a->r + b->i * a->i;
-q = b->i * a->r - b->r * a->i;
-
-if( y < 1.0 )
- {
- w = MAXNUM * y;
- if( (fabs(p) > w) || (fabs(q) > w) || (y == 0.0) )
- {
- c->r = MAXNUM;
- c->i = MAXNUM;
- mtherr( "cdiv", OVERFLOW );
- return;
- }
- }
-c->r = p/y;
-c->i = q/y;
-}
-
-
-/* b = a
- Caution, a `short' is assumed to be 16 bits wide. */
-
-void cmov( a, b )
-void *a, *b;
-{
-register short *pa, *pb;
-int i;
-
-pa = (short *) a;
-pb = (short *) b;
-i = 8;
-do
- *pb++ = *pa++;
-while( --i );
-}
-
-
-void cneg( a )
-register cmplx *a;
-{
-
-a->r = -a->r;
-a->i = -a->i;
-}
-
-/* cabs()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * double cabs();
- * cmplx z;
- * double a;
- *
- * a = cabs( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -30,+30 30000 3.2e-17 9.2e-18
- * IEEE -10,+10 100000 2.7e-16 6.9e-17
- */
-\f
-
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/*
-typedef struct
- {
- double r;
- double i;
- }cmplx;
-*/
-
-#ifdef UNK
-#define PREC 27
-#define MAXEXP 1024
-#define MINEXP -1077
-#endif
-#ifdef DEC
-#define PREC 29
-#define MAXEXP 128
-#define MINEXP -128
-#endif
-#ifdef IBMPC
-#define PREC 27
-#define MAXEXP 1024
-#define MINEXP -1077
-#endif
-#ifdef MIEEE
-#define PREC 27
-#define MAXEXP 1024
-#define MINEXP -1077
-#endif
-
-
-double cabs( z )
-register cmplx *z;
-{
-double x, y, b, re, im;
-int ex, ey, e;
-
-#ifdef INFINITIES
-/* Note, cabs(INFINITY,NAN) = INFINITY. */
-if( z->r == INFINITY || z->i == INFINITY
- || z->r == -INFINITY || z->i == -INFINITY )
- return( INFINITY );
-#endif
-
-#ifdef NANS
-if( isnan(z->r) )
- return(z->r);
-if( isnan(z->i) )
- return(z->i);
-#endif
-
-re = fabs( z->r );
-im = fabs( z->i );
-
-if( re == 0.0 )
- return( im );
-if( im == 0.0 )
- return( re );
-
-/* Get the exponents of the numbers */
-x = frexp( re, &ex );
-y = frexp( im, &ey );
-
-/* Check if one number is tiny compared to the other */
-e = ex - ey;
-if( e > PREC )
- return( re );
-if( e < -PREC )
- return( im );
-
-/* Find approximate exponent e of the geometric mean. */
-e = (ex + ey) >> 1;
-
-/* Rescale so mean is about 1 */
-x = ldexp( re, -e );
-y = ldexp( im, -e );
-
-/* Hypotenuse of the right triangle */
-b = sqrt( x * x + y * y );
-
-/* Compute the exponent of the answer. */
-y = frexp( b, &ey );
-ey = e + ey;
-
-/* Check it for overflow and underflow. */
-if( ey > MAXEXP )
- {
- mtherr( "cabs", OVERFLOW );
- return( INFINITY );
- }
-if( ey < MINEXP )
- return(0.0);
-
-/* Undo the scaling */
-b = ldexp( b, e );
-return( b );
-}
-\f/* csqrt()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrt();
- * cmplx z, w;
- *
- * csqrt( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The root chosen
- * is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 25000 3.2e-17 9.6e-18
- * IEEE -10,+10 100000 3.2e-16 7.7e-17
- *
- * 2
- * Also tested by csqrt( z ) = z, and tested by arguments
- * close to the real axis.
- */
-\f
-
-void csqrt( z, w )
-cmplx *z, *w;
-{
-cmplx q, s;
-double x, y, r, t;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0 )
- {
- if( x < 0.0 )
- {
- w->r = 0.0;
- w->i = sqrt(-x);
- return;
- }
- else
- {
- w->r = sqrt(x);
- w->i = 0.0;
- return;
- }
- }
-
-
-if( x == 0.0 )
- {
- r = fabs(y);
- r = sqrt(0.5*r);
- if( y > 0 )
- w->r = r;
- else
- w->r = -r;
- w->i = r;
- return;
- }
-
-/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
- * The relative error in the first term is approximately y^2/12x^2 .
- */
-if( (fabs(y) < 2.e-4 * fabs(x))
- && (x > 0) )
- {
- t = 0.25*y*(y/x);
- }
-else
- {
- r = cabs(z);
- t = 0.5*(r - x);
- }
-
-r = sqrt(t);
-q.i = r;
-q.r = y/(2.0*r);
-/* Heron iteration in complex arithmetic */
-cdiv( &q, z, &s );
-cadd( &q, &s, w );
-w->r *= 0.5;
-w->i *= 0.5;
-}
-
-
-double hypot( x, y )
-double x, y;
-{
-cmplx z;
-
-z.r = x;
-z.i = y;
-return( cabs(&z) );
-}
+++ /dev/null
-/* Program to calculate the inductance of a coil
- *
- * Reference: E. Jahnke and F. Emde, _Tables of Functions_,
- * 4th edition, Dover, 1945, pp 86-89.
- */
-
-double sin(), cos(), atan(), ellpe(), ellpk();
-
-double d;
-double l;
-double N;
-
-/* double PI = 3.14159265358979323846; */
-extern double PI;
-
-main()
-{
-double a, f, tana, sina, K, E, m, L, t;
-
-printf( "Self inductance of circular solenoidal coil\n" );
-
-loop:
-getnum( "diameter in centimeters", &d );
-if( d < 0.0 )
- exit(0); /* escape gracefully */
-getnum( "length in centimeters", &l );
-if( d < 0.0 )
- exit(0);
-getnum( "total number of turns", &N );
-if( d < 0.0 )
- exit(0);
-tana = d/l; /* form factor */
-a = atan( tana );
-sina = sin(a); /* modulus of the elliptic functions (k) */
-m = cos(a); /* subroutine argument = 1 - k^2 */
-m = m * m;
-K = ellpk(m);
-E = ellpe(m);
-tana = tana * tana; /* square of tan(a) */
-
-f = ((K + (tana - 1.0) * E)/sina - tana)/3.0;
-L = 4.e-9 * PI * N * N * d * f;
-printf( "L = %.4e Henries\n", L );
-goto loop;
-}
-
-
-/* Get value entered on keyboard
- */
-getnum( str, pd )
-char *str;
-double *pd;
-{
-char s[40];
-
-printf( "%s (%.10e) ? ", str, *pd );
-gets(s);
-if( s[0] != '\0' )
- {
- sscanf( s, "%lf", pd );
- printf( "%.10e\n", *pd );
- }
-}
+++ /dev/null
-/* const.c
- *
- * Globally declared constants
- *
- *
- *
- * SYNOPSIS:
- *
- * extern double nameofconstant;
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * This file contains a number of mathematical constants and
- * also some needed size parameters of the computer arithmetic.
- * The values are supplied as arrays of hexadecimal integers
- * for IEEE arithmetic; arrays of octal constants for DEC
- * arithmetic; and in a normal decimal scientific notation for
- * other machines. The particular notation used is determined
- * by a symbol (DEC, IBMPC, or UNK) defined in the include file
- * math.h.
- *
- * The default size parameters are as follows.
- *
- * For DEC and UNK modes:
- * MACHEP = 1.38777878078144567553E-17 2**-56
- * MAXLOG = 8.8029691931113054295988E1 log(2**127)
- * MINLOG = -8.872283911167299960540E1 log(2**-128)
- * MAXNUM = 1.701411834604692317316873e38 2**127
- *
- * For IEEE arithmetic (IBMPC):
- * MACHEP = 1.11022302462515654042E-16 2**-53
- * MAXLOG = 7.09782712893383996843E2 log(2**1024)
- * MINLOG = -7.08396418532264106224E2 log(2**-1022)
- * MAXNUM = 1.7976931348623158E308 2**1024
- *
- * The global symbols for mathematical constants are
- * PI = 3.14159265358979323846 pi
- * PIO2 = 1.57079632679489661923 pi/2
- * PIO4 = 7.85398163397448309616E-1 pi/4
- * SQRT2 = 1.41421356237309504880 sqrt(2)
- * SQRTH = 7.07106781186547524401E-1 sqrt(2)/2
- * LOG2E = 1.4426950408889634073599 1/log(2)
- * SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi )
- * LOGE2 = 6.93147180559945309417E-1 log(2)
- * LOGSQ2 = 3.46573590279972654709E-1 log(2)/2
- * THPIO4 = 2.35619449019234492885 3*pi/4
- * TWOOPI = 6.36619772367581343075535E-1 2/pi
- *
- * These lists are subject to change.
- */
-\f
-/* const.c */
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-#if 1
-double MACHEP = 1.11022302462515654042E-16; /* 2**-53 */
-#else
-double MACHEP = 1.38777878078144567553E-17; /* 2**-56 */
-#endif
-double UFLOWTHRESH = 2.22507385850720138309E-308; /* 2**-1022 */
-#ifdef DENORMAL
-double MAXLOG = 7.09782712893383996732E2; /* log(MAXNUM) */
-/* double MINLOG = -7.44440071921381262314E2; */ /* log(2**-1074) */
-double MINLOG = -7.451332191019412076235E2; /* log(2**-1075) */
-#else
-double MAXLOG = 7.08396418532264106224E2; /* log 2**1022 */
-double MINLOG = -7.08396418532264106224E2; /* log 2**-1022 */
-#endif
-double MAXNUM = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
-double PI = 3.14159265358979323846; /* pi */
-double PIO2 = 1.57079632679489661923; /* pi/2 */
-double PIO4 = 7.85398163397448309616E-1; /* pi/4 */
-double SQRT2 = 1.41421356237309504880; /* sqrt(2) */
-double SQRTH = 7.07106781186547524401E-1; /* sqrt(2)/2 */
-double LOG2E = 1.4426950408889634073599; /* 1/log(2) */
-double SQ2OPI = 7.9788456080286535587989E-1; /* sqrt( 2/pi ) */
-double LOGE2 = 6.93147180559945309417E-1; /* log(2) */
-double LOGSQ2 = 3.46573590279972654709E-1; /* log(2)/2 */
-double THPIO4 = 2.35619449019234492885; /* 3*pi/4 */
-double TWOOPI = 6.36619772367581343075535E-1; /* 2/pi */
-#ifdef INFINITIES
-double INFINITY = 1.0/0.0; /* 99e999; */
-#else
-double INFINITY = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
-#endif
-#ifdef NANS
-double NAN = 1.0/0.0 - 1.0/0.0;
-#else
-double NAN = 0.0;
-#endif
-#ifdef MINUSZERO
-double NEGZERO = -0.0;
-#else
-double NEGZERO = 0.0;
-#endif
-#endif
-
-#ifdef IBMPC
- /* 2**-53 = 1.11022302462515654042E-16 */
-unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
-unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
-#ifdef DENORMAL
- /* log(MAXNUM) = 7.09782712893383996732224E2 */
-unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
- /* log(2**-1074) = - -7.44440071921381262314E2 */
-/*unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
-unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
-#else
- /* log(2**1022) = 7.08396418532264106224E2 */
-unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
- /* log(2**-1022) = - 7.08396418532264106224E2 */
-unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
-#endif
- /* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
-unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
-unsigned short PI[4] = {0x2d18,0x5444,0x21fb,0x4009};
-unsigned short PIO2[4] = {0x2d18,0x5444,0x21fb,0x3ff9};
-unsigned short PIO4[4] = {0x2d18,0x5444,0x21fb,0x3fe9};
-unsigned short SQRT2[4] = {0x3bcd,0x667f,0xa09e,0x3ff6};
-unsigned short SQRTH[4] = {0x3bcd,0x667f,0xa09e,0x3fe6};
-unsigned short LOG2E[4] = {0x82fe,0x652b,0x1547,0x3ff7};
-unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
-unsigned short LOGE2[4] = {0x39ef,0xfefa,0x2e42,0x3fe6};
-unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
-unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
-unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
-#ifdef INFINITIES
-unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
-#else
-unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
-#endif
-#ifdef NANS
-unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
-#else
-unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
-#endif
-#ifdef MINUSZERO
-unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
-#else
-unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
-#endif
-#endif
-
-#ifdef MIEEE
- /* 2**-53 = 1.11022302462515654042E-16 */
-unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
-unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
-#ifdef DENORMAL
- /* log(2**1024) = 7.09782712893383996843E2 */
-unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
- /* log(2**-1074) = - -7.44440071921381262314E2 */
-/* unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
-unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
-#else
- /* log(2**1022) = 7.08396418532264106224E2 */
-unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
- /* log(2**-1022) = - 7.08396418532264106224E2 */
-unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
-#endif
- /* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
-unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
-unsigned short PI[4] = {0x4009,0x21fb,0x5444,0x2d18};
-unsigned short PIO2[4] = {0x3ff9,0x21fb,0x5444,0x2d18};
-unsigned short PIO4[4] = {0x3fe9,0x21fb,0x5444,0x2d18};
-unsigned short SQRT2[4] = {0x3ff6,0xa09e,0x667f,0x3bcd};
-unsigned short SQRTH[4] = {0x3fe6,0xa09e,0x667f,0x3bcd};
-unsigned short LOG2E[4] = {0x3ff7,0x1547,0x652b,0x82fe};
-unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
-unsigned short LOGE2[4] = {0x3fe6,0x2e42,0xfefa,0x39ef};
-unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
-unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
-unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
-#ifdef INFINITIES
-unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
-#else
-unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
-#endif
-#ifdef NANS
-unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
-#else
-unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
-#endif
-#ifdef MINUSZERO
-unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
-#else
-unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
-#endif
-#endif
-
-#ifdef DEC
- /* 2**-56 = 1.38777878078144567553E-17 */
-unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
-unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
- /* log 2**127 = 88.029691931113054295988 */
-unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
- /* log 2**-128 = -88.72283911167299960540 */
-unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
- /* 2**127 = 1.701411834604692317316873e38 */
-unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
-unsigned short PI[4] = {040511,007732,0121041,064302,};
-unsigned short PIO2[4] = {040311,007732,0121041,064302,};
-unsigned short PIO4[4] = {040111,007732,0121041,064302,};
-unsigned short SQRT2[4] = {040265,002363,031771,0157145,};
-unsigned short SQRTH[4] = {040065,002363,031771,0157144,};
-unsigned short LOG2E[4] = {040270,0125073,024534,013761,};
-unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
-unsigned short LOGE2[4] = {040061,071027,0173721,0147572,};
-unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
-unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
-unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
-/* Approximate infinity by MAXNUM. */
-unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
-unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
-#ifdef MINUSZERO
-unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
-#else
-unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
-#endif
-#endif
-
-#ifndef UNK
-extern unsigned short MACHEP[];
-extern unsigned short UFLOWTHRESH[];
-extern unsigned short MAXLOG[];
-extern unsigned short UNDLOG[];
-extern unsigned short MINLOG[];
-extern unsigned short MAXNUM[];
-extern unsigned short PI[];
-extern unsigned short PIO2[];
-extern unsigned short PIO4[];
-extern unsigned short SQRT2[];
-extern unsigned short SQRTH[];
-extern unsigned short LOG2E[];
-extern unsigned short SQ2OPI[];
-extern unsigned short LOGE2[];
-extern unsigned short LOGSQ2[];
-extern unsigned short THPIO4[];
-extern unsigned short TWOOPI[];
-extern unsigned short INFINITY[];
-extern unsigned short NAN[];
-extern unsigned short NEGZERO[];
-#endif
+++ /dev/null
-/* cosh.c
- *
- * Hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cosh();
- *
- * y = cosh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic cosine of argument in the range MINLOG to
- * MAXLOG.
- *
- * cosh(x) = ( exp(x) + exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +- 88 50000 4.0e-17 7.7e-18
- * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cosh overflow |x| > MAXLOG MAXNUM
- *
- *
- */
-\f
-/* cosh.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1985, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double exp ( double );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double exp();
-int isnan(), isfinite();
-#endif
-extern double MAXLOG, INFINITY, LOGE2;
-
-double cosh(x)
-double x;
-{
-double y;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-if( x < 0 )
- x = -x;
-if( x > (MAXLOG + LOGE2) )
- {
- mtherr( "cosh", OVERFLOW );
- return( INFINITY );
- }
-if( x >= (MAXLOG - LOGE2) )
- {
- y = exp(0.5 * x);
- y = (0.5 * y) * y;
- return(y);
- }
-y = exp(x);
-y = 0.5 * (y + 1.0 / y);
-return( y );
-}
+++ /dev/null
-/* cpmul.c
- *
- * Multiply two polynomials with complex coefficients
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct
- * {
- * double r;
- * double i;
- * }cmplx;
- *
- * cmplx a[], b[], c[];
- * int da, db, dc;
- *
- * cpmul( a, da, b, db, c, &dc );
- *
- *
- *
- * DESCRIPTION:
- *
- * The two argument polynomials are multiplied together, and
- * their product is placed in c.
- *
- * Each polynomial is represented by its coefficients stored
- * as an array of complex number structures (see the typedef).
- * The degree of a is da, which must be passed to the routine
- * as an argument; similarly the degree db of b is an argument.
- * Array a has da + 1 elements and array b has db + 1 elements.
- * Array c must have storage allocated for at least da + db + 1
- * elements. The value da + db is returned in dc; this is
- * the degree of the product polynomial.
- *
- * Polynomial coefficients are stored in ascending order; i.e.,
- * a(x) = a[0]*x**0 + a[1]*x**1 + ... + a[da]*x**da.
- *
- *
- * If desired, c may be the same as either a or b, in which
- * case the input argument array is replaced by the product
- * array (but only up to terms of degree da + db).
- *
- */
-\f
-/* cpmul */
-
-typedef struct
- {
- double r;
- double i;
- }cmplx;
-
-int cpmul( a, da, b, db, c, dc )
-cmplx *a, *b, *c;
-int da, db;
-int *dc;
-{
-int i, j, k;
-cmplx y;
-register cmplx *pa, *pb, *pc;
-
-if( da > db ) /* Know which polynomial has higher degree */
- {
- i = da; /* Swapping is OK because args are on the stack */
- da = db;
- db = i;
- pa = a;
- a = b;
- b = pa;
- }
-
-k = da + db;
-*dc = k; /* Output the degree of the product */
-pc = &c[db+1];
-for( i=db+1; i<=k; i++ ) /* Clear high order terms of output */
- {
- pc->r = 0;
- pc->i = 0;
- pc++;
- }
-/* To permit replacement of input, work backward from highest degree */
-pb = &b[db];
-for( j=0; j<=db; j++ )
- {
- pa = &a[da];
- pc = &c[k-j];
- for( i=0; i<da; i++ )
- {
- y.r = pa->r * pb->r - pa->i * pb->i; /* cmpx multiply */
- y.i = pa->r * pb->i + pa->i * pb->r;
- pc->r += y.r; /* accumulate partial product */
- pc->i += y.i;
- pa--;
- pc--;
- }
- y.r = pa->r * pb->r - pa->i * pb->i; /* replace last term, */
- y.i = pa->r * pb->i + pa->i * pb->r; /* ...do not accumulate */
- pc->r = y.r;
- pc->i = y.i;
- pb--;
- }
- return 0;
-}
+++ /dev/null
-/* dawsn.c
- *
- * Dawson's Integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, dawsn();
- *
- * y = dawsn( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- * x
- * -
- * 2 | | 2
- * dawsn(x) = exp( -x ) | exp( t ) dt
- * | |
- * -
- * 0
- *
- * Three different rational approximations are employed, for
- * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10 10000 6.9e-16 1.0e-16
- * DEC 0,10 6000 7.4e-17 1.4e-17
- *
- *
- */
-\f
-/* dawsn.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-/* Dawson's integral, interval 0 to 3.25 */
-#ifdef UNK
-static double AN[10] = {
- 1.13681498971755972054E-11,
- 8.49262267667473811108E-10,
- 1.94434204175553054283E-8,
- 9.53151741254484363489E-7,
- 3.07828309874913200438E-6,
- 3.52513368520288738649E-4,
--8.50149846724410912031E-4,
- 4.22618223005546594270E-2,
--9.17480371773452345351E-2,
- 9.99999999999999994612E-1,
-};
-static double AD[11] = {
- 2.40372073066762605484E-11,
- 1.48864681368493396752E-9,
- 5.21265281010541664570E-8,
- 1.27258478273186970203E-6,
- 2.32490249820789513991E-5,
- 3.25524741826057911661E-4,
- 3.48805814657162590916E-3,
- 2.79448531198828973716E-2,
- 1.58874241960120565368E-1,
- 5.74918629489320327824E-1,
- 1.00000000000000000539E0,
-};
-#endif
-#ifdef DEC
-static unsigned short AN[40] = {
-0027107,0176630,0075752,0107612,
-0030551,0070604,0166707,0127727,
-0031647,0002210,0117120,0056376,
-0033177,0156026,0141275,0140627,
-0033516,0112200,0037035,0165515,
-0035270,0150613,0016423,0105634,
-0135536,0156227,0023515,0044413,
-0037055,0015273,0105147,0064025,
-0137273,0163145,0014460,0166465,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short AD[44] = {
-0027323,0067372,0115566,0131320,
-0030714,0114432,0074206,0006637,
-0032137,0160671,0044203,0026344,
-0033252,0146656,0020247,0100231,
-0034303,0003346,0123260,0022433,
-0035252,0125460,0173041,0155415,
-0036144,0113747,0125203,0124617,
-0036744,0166232,0143671,0133670,
-0037442,0127755,0162625,0000100,
-0040023,0026736,0003604,0106265,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short AN[40] = {
-0x51f1,0x0f7d,0xffb3,0x3da8,
-0xf5fb,0x9db8,0x2e30,0x3e0d,
-0x0ba0,0x13ca,0xe091,0x3e54,
-0xb833,0xd857,0xfb82,0x3eaf,
-0xbd6a,0x07c3,0xd290,0x3ec9,
-0x7174,0x63a2,0x1a31,0x3f37,
-0xa921,0xe4e9,0xdb92,0xbf4b,
-0xed03,0x714c,0xa357,0x3fa5,
-0x1da7,0xa326,0x7ccc,0xbfb7,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short AD[44] = {
-0xd65a,0x536e,0x6ddf,0x3dba,
-0xc1b4,0x4f10,0x9323,0x3e19,
-0x659c,0x2910,0xfc37,0x3e6b,
-0xf013,0xc414,0x59b5,0x3eb5,
-0x04a3,0xd4d6,0x60dc,0x3ef8,
-0x3b62,0x1ec4,0x5566,0x3f35,
-0x7532,0xf550,0x92fc,0x3f6c,
-0x36f7,0x58f7,0x9d93,0x3f9c,
-0xa008,0xbcb2,0x55fd,0x3fc4,
-0x9197,0xc0f0,0x65bb,0x3fe2,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short AN[40] = {
-0x3da8,0xffb3,0x0f7d,0x51f1,
-0x3e0d,0x2e30,0x9db8,0xf5fb,
-0x3e54,0xe091,0x13ca,0x0ba0,
-0x3eaf,0xfb82,0xd857,0xb833,
-0x3ec9,0xd290,0x07c3,0xbd6a,
-0x3f37,0x1a31,0x63a2,0x7174,
-0xbf4b,0xdb92,0xe4e9,0xa921,
-0x3fa5,0xa357,0x714c,0xed03,
-0xbfb7,0x7ccc,0xa326,0x1da7,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short AD[44] = {
-0x3dba,0x6ddf,0x536e,0xd65a,
-0x3e19,0x9323,0x4f10,0xc1b4,
-0x3e6b,0xfc37,0x2910,0x659c,
-0x3eb5,0x59b5,0xc414,0xf013,
-0x3ef8,0x60dc,0xd4d6,0x04a3,
-0x3f35,0x5566,0x1ec4,0x3b62,
-0x3f6c,0x92fc,0xf550,0x7532,
-0x3f9c,0x9d93,0x58f7,0x36f7,
-0x3fc4,0x55fd,0xbcb2,0xa008,
-0x3fe2,0x65bb,0xc0f0,0x9197,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-/* interval 3.25 to 6.25 */
-#ifdef UNK
-static double BN[11] = {
- 5.08955156417900903354E-1,
--2.44754418142697847934E-1,
- 9.41512335303534411857E-2,
--2.18711255142039025206E-2,
- 3.66207612329569181322E-3,
--4.23209114460388756528E-4,
- 3.59641304793896631888E-5,
--2.14640351719968974225E-6,
- 9.10010780076391431042E-8,
--2.40274520828250956942E-9,
- 3.59233385440928410398E-11,
-};
-static double BD[10] = {
-/* 1.00000000000000000000E0,*/
--6.31839869873368190192E-1,
- 2.36706788228248691528E-1,
--5.31806367003223277662E-2,
- 8.48041718586295374409E-3,
--9.47996768486665330168E-4,
- 7.81025592944552338085E-5,
--4.55875153252442634831E-6,
- 1.89100358111421846170E-7,
--4.91324691331920606875E-9,
- 7.18466403235734541950E-11,
-};
-#endif
-#ifdef DEC
-static unsigned short BN[44] = {
-0040002,0045342,0113762,0004360,
-0137572,0120346,0172745,0144046,
-0037300,0151134,0123440,0117047,
-0136663,0025423,0014755,0046026,
-0036157,0177561,0027535,0046744,
-0135335,0161052,0071243,0146535,
-0034426,0154060,0164506,0135625,
-0133420,0005356,0100017,0151334,
-0032303,0066137,0024013,0046212,
-0131045,0016612,0066270,0047574,
-0027435,0177025,0060625,0116363,
-};
-static unsigned short BD[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0140041,0140101,0174552,0037073,
-0037562,0061503,0124271,0160756,
-0137131,0151760,0073210,0110534,
-0036412,0170562,0117017,0155377,
-0135570,0101374,0074056,0037276,
-0034643,0145376,0001516,0060636,
-0133630,0173540,0121344,0155231,
-0032513,0005602,0134516,0007144,
-0131250,0150540,0075747,0105341,
-0027635,0177020,0012465,0125402,
-};
-#endif
-#ifdef IBMPC
-static unsigned short BN[44] = {
-0x411e,0x52fe,0x495c,0x3fe0,
-0xb905,0xdebc,0x541c,0xbfcf,
-0x13c5,0x94e4,0x1a4b,0x3fb8,
-0xa983,0x633d,0x6562,0xbf96,
-0xa9bd,0x25eb,0xffee,0x3f6d,
-0x79ac,0x4e54,0xbc45,0xbf3b,
-0xd773,0x1d28,0xdb06,0x3f02,
-0xfa5b,0xd001,0x015d,0xbec2,
-0x6991,0xe501,0x6d8b,0x3e78,
-0x09f0,0x4d97,0xa3b1,0xbe24,
-0xb39e,0xac32,0xbfc2,0x3dc3,
-};
-static unsigned short BD[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x47c7,0x3f2d,0x3808,0xbfe4,
-0x3c3e,0x7517,0x4c68,0x3fce,
-0x122b,0x0ed1,0x3a7e,0xbfab,
-0xfb60,0x53c1,0x5e2e,0x3f81,
-0xc7d8,0x8f05,0x105f,0xbf4f,
-0xcc34,0xc069,0x795f,0x3f14,
-0x9b53,0x145c,0x1eec,0xbed3,
-0xc1cd,0x5729,0x6170,0x3e89,
-0xf15c,0x0f7c,0x1a2c,0xbe35,
-0xb560,0x02a6,0xbfc2,0x3dd3,
-};
-#endif
-#ifdef MIEEE
-static unsigned short BN[44] = {
-0x3fe0,0x495c,0x52fe,0x411e,
-0xbfcf,0x541c,0xdebc,0xb905,
-0x3fb8,0x1a4b,0x94e4,0x13c5,
-0xbf96,0x6562,0x633d,0xa983,
-0x3f6d,0xffee,0x25eb,0xa9bd,
-0xbf3b,0xbc45,0x4e54,0x79ac,
-0x3f02,0xdb06,0x1d28,0xd773,
-0xbec2,0x015d,0xd001,0xfa5b,
-0x3e78,0x6d8b,0xe501,0x6991,
-0xbe24,0xa3b1,0x4d97,0x09f0,
-0x3dc3,0xbfc2,0xac32,0xb39e,
-};
-static unsigned short BD[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xbfe4,0x3808,0x3f2d,0x47c7,
-0x3fce,0x4c68,0x7517,0x3c3e,
-0xbfab,0x3a7e,0x0ed1,0x122b,
-0x3f81,0x5e2e,0x53c1,0xfb60,
-0xbf4f,0x105f,0x8f05,0xc7d8,
-0x3f14,0x795f,0xc069,0xcc34,
-0xbed3,0x1eec,0x145c,0x9b53,
-0x3e89,0x6170,0x5729,0xc1cd,
-0xbe35,0x1a2c,0x0f7c,0xf15c,
-0x3dd3,0xbfc2,0x02a6,0xb560,
-};
-#endif
-
-/* 6.25 to infinity */
-#ifdef UNK
-static double CN[5] = {
--5.90592860534773254987E-1,
- 6.29235242724368800674E-1,
--1.72858975380388136411E-1,
- 1.64837047825189632310E-2,
--4.86827613020462700845E-4,
-};
-static double CD[5] = {
-/* 1.00000000000000000000E0,*/
--2.69820057197544900361E0,
- 1.73270799045947845857E0,
--3.93708582281939493482E-1,
- 3.44278924041233391079E-2,
--9.73655226040941223894E-4,
-};
-#endif
-#ifdef DEC
-static unsigned short CN[20] = {
-0140027,0030427,0176477,0074402,
-0040041,0012617,0112375,0162657,
-0137461,0000761,0074120,0135160,
-0036607,0004325,0117246,0115525,
-0135377,0036345,0064750,0047732,
-};
-static unsigned short CD[20] = {
-/*0040200,0000000,0000000,0000000,*/
-0140454,0127521,0071653,0133415,
-0040335,0144540,0016105,0045241,
-0137711,0112053,0155034,0062237,
-0037015,0002102,0177442,0074546,
-0135577,0036345,0064750,0052152,
-};
-#endif
-#ifdef IBMPC
-static unsigned short CN[20] = {
-0xef20,0xffa7,0xe622,0xbfe2,
-0xbcb6,0xf29f,0x22b1,0x3fe4,
-0x174e,0x2f0a,0x203e,0xbfc6,
-0xd36b,0xb3d4,0xe11a,0x3f90,
-0x09fb,0xad3d,0xe79c,0xbf3f,
-};
-static unsigned short CD[20] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x76e2,0x2e75,0x95ea,0xc005,
-0xa954,0x0388,0xb92c,0x3ffb,
-0x8c94,0x7b43,0x3285,0xbfd9,
-0x4f2d,0x5fe4,0xa088,0x3fa1,
-0x0a8d,0xad3d,0xe79c,0xbf4f,
-};
-#endif
-#ifdef MIEEE
-static unsigned short CN[20] = {
-0xbfe2,0xe622,0xffa7,0xef20,
-0x3fe4,0x22b1,0xf29f,0xbcb6,
-0xbfc6,0x203e,0x2f0a,0x174e,
-0x3f90,0xe11a,0xb3d4,0xd36b,
-0xbf3f,0xe79c,0xad3d,0x09fb,
-};
-static unsigned short CD[20] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc005,0x95ea,0x2e75,0x76e2,
-0x3ffb,0xb92c,0x0388,0xa954,
-0xbfd9,0x3285,0x7b43,0x8c94,
-0x3fa1,0xa088,0x5fe4,0x4f2d,
-0xbf4f,0xe79c,0xad3d,0x0a8d,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double chbevl(), sqrt(), fabs(), polevl(), p1evl();
-#endif
-extern double PI, MACHEP;
-
-double dawsn( xx )
-double xx;
-{
-double x, y;
-int sign;
-
-
-sign = 1;
-if( xx < 0.0 )
- {
- sign = -1;
- xx = -xx;
- }
-
-if( xx < 3.25 )
-{
-x = xx*xx;
-y = xx * polevl( x, AN, 9 )/polevl( x, AD, 10 );
-return( sign * y );
-}
-
-
-x = 1.0/(xx*xx);
-
-if( xx < 6.25 )
- {
- y = 1.0/xx + x * polevl( x, BN, 10) / (p1evl( x, BD, 10) * xx);
- return( sign * 0.5 * y );
- }
-
-
-if( xx > 1.0e9 )
- return( (sign * 0.5)/xx );
-
-/* 6.25 to infinity */
-y = 1.0/xx + x * polevl( x, CN, 4) / (p1evl( x, CD, 5) * xx);
-return( sign * 0.5 * y );
-}
+++ /dev/null
-/* calc.c */
-/* Keyboard command interpreter */
-/* by Stephen L. Moshier */
-
-
-/* length of command line: */
-#define LINLEN 128
-
-#define XON 0x11
-#define XOFF 0x13
-
-#define SALONE 1
-#define DECPDP 0
-#define INTLOGIN 0
-#define INTHELP 1
-#ifndef TRUE
-#define TRUE 1
-#endif
-
-/* Initialize squirrel printf: */
-#define INIPRINTF 0
-
-#if DECPDP
-#define TRUE 1
-#endif
-
-#include <stdio.h>
-#include <string.h>
-
-static char idterp[] = {
-"\n\nSteve Moshier's command interpreter V1.3\n"};
-#define ISLOWER(c) ((c >= 'a') && (c <= 'z'))
-#define ISUPPER(c) ((c >= 'A') && (c <= 'Z'))
-#define ISALPHA(c) (ISLOWER(c) || ISUPPER(c))
-#define ISDIGIT(c) ((c >= '0') && (c <= '9'))
-#define ISATF(c) (((c >= 'a')&&(c <= 'f')) || ((c >= 'A')&&(c <= 'F')))
-#define ISXDIGIT(c) (ISDIGIT(c) || ISATF(c))
-#define ISOCTAL(c) ((c >= '0') && (c < '8'))
-#define ISALNUM(c) (ISALPHA(c) || (ISDIGIT(c))
-FILE *fopen();
-
-#include "dcalc.h"
-/* #include "ehead.h" */
-#include <math.h>
-/* int strlen(), strcmp(); */
-int system();
-
-/* space for working precision numbers */
-static double vs[22];
-
-/* the symbol table of temporary variables: */
-
-#define NTEMP 4
-struct varent temp[NTEMP] = {
-{"T", OPR | TEMP, &vs[14]},
-{"T", OPR | TEMP, &vs[15]},
-{"T", OPR | TEMP, &vs[16]},
-{"\0", OPR | TEMP, &vs[17]}
-};
-\f
-/* the symbol table of operators */
-/* EOL is interpreted on null, newline, or ; */
-struct symbol oprtbl[] = {
-{"BOL", OPR | BOL, 0},
-{"EOL", OPR | EOL, 0},
-{"-", OPR | UMINUS, 8},
-/*"~", OPR | COMP, 8,*/
-{",", OPR | EOE, 1},
-{"=", OPR | EQU, 2},
-/*"|", OPR | LOR, 3,*/
-/*"^", OPR | LXOR, 4,*/
-/*"&", OPR | LAND, 5,*/
-{"+", OPR | PLUS, 6},
-{"-", OPR | MINUS, 6},
-{"*", OPR | MULT, 7},
-{"/", OPR | DIV, 7},
-/*"%", OPR | MOD, 7,*/
-{"(", OPR | LPAREN, 11},
-{")", OPR | RPAREN, 11},
-{"\0", ILLEG, 0}
-};
-
-#define NOPR 8
-
-/* the symbol table of indirect variables: */
-extern double PI;
-struct varent indtbl[] = {
-{"t", VAR | IND, &vs[21]},
-{"u", VAR | IND, &vs[20]},
-{"v", VAR | IND, &vs[19]},
-{"w", VAR | IND, &vs[18]},
-{"x", VAR | IND, &vs[10]},
-{"y", VAR | IND, &vs[11]},
-{"z", VAR | IND, &vs[12]},
-{"pi", VAR | IND, &PI},
-{"\0", ILLEG, 0}
-};
-\f
-/* the symbol table of constants: */
-
-#define NCONST 10
-struct varent contbl[NCONST] = {
-{"C",CONST,&vs[0]},
-{"C",CONST,&vs[1]},
-{"C",CONST,&vs[2]},
-{"C",CONST,&vs[3]},
-{"C",CONST,&vs[4]},
-{"C",CONST,&vs[5]},
-{"C",CONST,&vs[6]},
-{"C",CONST,&vs[7]},
-{"C",CONST,&vs[8]},
-{"\0",CONST,&vs[9]}
-};
-
-/* the symbol table of string variables: */
-
-static char strngs[160] = {0};
-
-#define NSTRNG 5
-struct strent strtbl[NSTRNG] = {
-{0, VAR | STRING, 0},
-{0, VAR | STRING, 0},
-{0, VAR | STRING, 0},
-{0, VAR | STRING, 0},
-{"\0",ILLEG,0},
-};
-\f
-
-/* Help messages */
-#if INTHELP
-static char *intmsg[] = {
-"?",
-"Unkown symbol",
-"Expression ends in illegal operator",
-"Precede ( by operator",
-")( is illegal",
-"Unmatched )",
-"Missing )",
-"Illegal left hand side",
-"Missing symbol",
-"Must assign to a variable",
-"Divide by zero",
-"Missing symbol",
-"Missing operator",
-"Precede quantity by operator",
-"Quantity preceded by )",
-"Function syntax",
-"Too many function args",
-"No more temps",
-"Arg list"
-};
-#endif
-
-#ifdef ANSIPROT
-double floor ( double );
-int dprec ( void );
-#else
-double floor();
-int dprec();
-#endif
-/* the symbol table of functions: */
-#if SALONE
-#ifdef ANSIPROT
-extern double floor ( double );
-extern double log ( double );
-extern double pow ( double, double );
-extern double sqrt ( double );
-extern double tanh ( double );
-extern double exp ( double );
-extern double fabs ( double );
-extern double hypot ( double, double );
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern double incbet ( double, double, double );
-extern double incbi ( double, double, double );
-extern double sin ( double );
-extern double cos ( double );
-extern double atan ( double );
-extern double atan2 ( double, double );
-extern double gamma ( double );
-extern double lgam ( double );
-double zfrexp ( double );
-double zldexp ( double, double );
-double makenan ( double );
-double makeinfinity ( double );
-double hex ( double );
-double hexinput ( double, double );
-double cmdh ( void );
-double cmdhlp ( void );
-double init ( void );
-double cmddm ( void );
-double cmdtm ( void );
-double cmdem ( double );
-double take ( char * );
-double mxit ( void );
-double bits ( double );
-double csys ( char * );
-double cmddig ( double );
-double prhlst ( void * );
-double abmac ( void );
-double ifrac ( double );
-double xcmpl ( double, double );
-void exit ( int );
-#else
-void exit();
-double hex(), hexinput(), cmdh(), cmdhlp(), init();
-double cmddm(), cmdtm(), cmdem();
-double take(), mxit(), bits(), csys();
-double cmddig(), prhlst(), abmac();
-double ifrac(), xcmpl();
-double floor(), log(), pow(), sqrt(), tanh(), exp(), fabs(), hypot();
-double frexp(), zfrexp(), ldexp(), zldexp(), makenan(), makeinfinity();
-double incbet(), incbi(), sin(), cos(), atan(), atan2(), gamma(), lgam();
-#define GLIBC2 0
-#if GLIBC2
-double lgamma();
-#endif
-#endif /* not ANSIPROT */
-struct funent funtbl[] = {
-{"h", OPR | FUNC, cmdh},
-{"help", OPR | FUNC, cmdhlp},
-{"hex", OPR | FUNC, hex},
-{"hexinput", OPR | FUNC, hexinput},
-/*"view", OPR | FUNC, view,*/
-{"exp", OPR | FUNC, exp},
-{"floor", OPR | FUNC, floor},
-{"log", OPR | FUNC, log},
-{"pow", OPR | FUNC, pow},
-{"sqrt", OPR | FUNC, sqrt},
-{"tanh", OPR | FUNC, tanh},
-{"sin", OPR | FUNC, sin},
-{"cos", OPR | FUNC, cos},
-{"atan", OPR | FUNC, atan},
-{"atantwo", OPR | FUNC, atan2},
-{"tanh", OPR | FUNC, tanh},
-{"gamma", OPR | FUNC, gamma},
-#if GLIBC2
-{"lgamma", OPR | FUNC, lgamma},
-#else
-{"lgam", OPR | FUNC, lgam},
-#endif
-{"incbet", OPR | FUNC, incbet},
-{"incbi", OPR | FUNC, incbi},
-{"fabs", OPR | FUNC, fabs},
-{"hypot", OPR | FUNC, hypot},
-{"ldexp", OPR | FUNC, zldexp},
-{"frexp", OPR | FUNC, zfrexp},
-{"nan", OPR | FUNC, makenan},
-{"infinity", OPR | FUNC, makeinfinity},
-{"ifrac", OPR | FUNC, ifrac},
-{"cmp", OPR | FUNC, xcmpl},
-{"bits", OPR | FUNC, bits},
-{"digits", OPR | FUNC, cmddig},
-{"dm", OPR | FUNC, cmddm},
-{"tm", OPR | FUNC, cmdtm},
-{"em", OPR | FUNC, cmdem},
-{"take", OPR | FUNC | COMMAN, take},
-{"system", OPR | FUNC | COMMAN, csys},
-{"exit", OPR | FUNC, mxit},
-/*
-"remain", OPR | FUNC, eremain,
-*/
-{"\0", OPR | FUNC, 0}
-};
-
-/* the symbol table of key words */
-struct funent keytbl[] = {
-{"\0", ILLEG, 0}
-};
-#endif
-
-void zgets();
-
-/* Number of decimals to display */
-#define DEFDIS 70
-static int ndigits = DEFDIS;
-
-/* Menu stack */
-struct funent *menstk[5] = {&funtbl[0], NULL, NULL, NULL, NULL};
-int menptr = 0;
-
-/* Take file stack */
-FILE *takstk[10] = {0};
-int takptr = -1;
-
-/* size of the expression scan list: */
-#define NSCAN 20
-
-/* previous token, saved for syntax checking: */
-struct symbol *lastok = 0;
-
-/* variables used by parser: */
-static char str[128] = {0};
-int uposs = 0; /* possible unary operator */
-static double qnc;
-char lc[40] = { '\n' }; /* ASCII string of token symbol */
-static char line[LINLEN] = { '\n','\0' }; /* input command line */
-static char maclin[LINLEN] = { '\n','\0' }; /* macro command */
-char *interl = line; /* pointer into line */
-extern char *interl;
-static int maccnt = 0; /* number of times to execute macro command */
-static int comptr = 0; /* comma stack pointer */
-static double comstk[5]; /* comma argument stack */
-static int narptr = 0; /* pointer to number of args */
-static int narstk[5] = {0}; /* stack of number of function args */
-\f
-/* main() */
-
-/* Entire program starts here */
-
-int main()
-{
-
-/* the scan table: */
-
-/* array of pointers to symbols which have been parsed: */
-struct symbol *ascsym[NSCAN];
-
-/* current place in ascsym: */
-register struct symbol **as;
-
-/* array of attributes of operators parsed: */
-int ascopr[NSCAN];
-
-/* current place in ascopr: */
-register int *ao;
-
-#if LARGEMEM
-/* array of precedence levels of operators: */
-long asclev[NSCAN];
-/* current place in asclev: */
-long *al;
-long symval; /* value of symbol just parsed */
-#else
-int asclev[NSCAN];
-int *al;
-int symval;
-#endif
-
-double acc; /* the accumulator, for arithmetic */
-int accflg; /* flags accumulator in use */
-double val; /* value to be combined into accumulator */
-register struct symbol *psym; /* pointer to symbol just parsed */
-struct varent *pvar; /* pointer to an indirect variable symbol */
-struct funent *pfun; /* pointer to a function symbol */
-struct strent *pstr; /* pointer to a string symbol */
-int att; /* attributes of symbol just parsed */
-int i; /* counter */
-int offset; /* parenthesis level */
-int lhsflg; /* kluge to detect illegal assignments */
-struct symbol *parser(); /* parser returns pointer to symbol */
-int errcod; /* for syntax error printout */
-\f
-
-/* Perform general initialization */
-
-init();
-
-menstk[0] = &funtbl[0];
-menptr = 0;
-cmdhlp(); /* print out list of symbols */
-\f
-
-/* Return here to get next command line to execute */
-getcmd:
-
-/* initialize registers and mutable symbols */
-
-accflg = 0; /* Accumulator not in use */
-acc = 0.0; /* Clear the accumulator */
-offset = 0; /* Parenthesis level zero */
-comptr = 0; /* Start of comma stack */
-narptr = -1; /* Start of function arg counter stack */
-
-psym = (struct symbol *)&contbl[0];
-for( i=0; i<NCONST; i++ )
- {
- psym->attrib = CONST; /* clearing the busy bit */
- ++psym;
- }
-psym = (struct symbol *)&temp[0];
-for( i=0; i<NTEMP; i++ )
- {
- psym->attrib = VAR | TEMP; /* clearing the busy bit */
- ++psym;
- }
-
-pstr = &strtbl[0];
-for( i=0; i<NSTRNG; i++ )
- {
- pstr->spel = &strngs[ 40*i ];
- pstr->attrib = STRING | VAR;
- pstr->string = &strngs[ 40*i ];
- ++pstr;
- }
-
-/* List of scanned symbols is empty: */
-as = &ascsym[0];
-*as = 0;
---as;
-/* First item in scan list is Beginning of Line operator */
-ao = &ascopr[0];
-*ao = oprtbl[0].attrib & 0xf; /* BOL */
-/* value of first item: */
-al = &asclev[0];
-*al = oprtbl[0].sym;
-
-lhsflg = 0; /* illegal left hand side flag */
-psym = &oprtbl[0]; /* pointer to current token */
-\f
-/* get next token from input string */
-
-gettok:
-lastok = psym; /* last token = current token */
-psym = parser(); /* get a new current token */
-/*printf( "%s attrib %7o value %7o\n", psym->spel, psym->attrib & 0xffff,
- psym->sym );*/
-
-/* Examine attributes of the symbol returned by the parser */
-att = psym->attrib;
-if( att == ILLEG )
- {
- errcod = 1;
- goto synerr;
- }
-
-/* Push functions onto scan list without analyzing further */
-if( att & FUNC )
- {
- /* A command is a function whose argument is
- * a pointer to the rest of the input line.
- * A second argument is also passed: the address
- * of the last token parsed.
- */
- if( att & COMMAN )
- {
- pfun = (struct funent *)psym;
- ( *(pfun->fun))( interl, lastok );
- abmac(); /* scrub the input line */
- goto getcmd; /* and ask for more input */
- }
- ++narptr; /* offset to number of args */
- narstk[narptr] = 0;
- i = lastok->attrib & 0xffff; /* attrib=short, i=int */
- if( ((i & OPR) == 0)
- || (i == (OPR | RPAREN))
- || (i == (OPR | FUNC)) )
- {
- errcod = 15;
- goto synerr;
- }
-
- ++lhsflg;
- ++as;
- *as = psym;
- ++ao;
- *ao = FUNC;
- ++al;
- *al = offset + UMINUS;
- goto gettok;
- }
-
-/* deal with operators */
-if( att & OPR )
- {
- att &= 0xf;
- /* expression cannot end with an operator other than
- * (, ), BOL, or a function
- */
- if( (att == RPAREN) || (att == EOL) || (att == EOE))
- {
- i = lastok->attrib & 0xffff; /* attrib=short, i=int */
- if( (i & OPR)
- && (i != (OPR | RPAREN))
- && (i != (OPR | LPAREN))
- && (i != (OPR | FUNC))
- && (i != (OPR | BOL)) )
- {
- errcod = 2;
- goto synerr;
- }
- }
- ++lhsflg; /* any operator but ( and = is not a legal lhs */
-\f
-/* operator processing, continued */
-
- switch( att )
- {
- case EOE:
- lhsflg = 0;
- break;
- case LPAREN:
- /* ( must be preceded by an operator of some sort. */
- if( ((lastok->attrib & OPR) == 0) )
- {
- errcod = 3;
- goto synerr;
- }
- /* also, a preceding ) is illegal */
- if( (unsigned short )lastok->attrib == (OPR|RPAREN))
- {
- errcod = 4;
- goto synerr;
- }
- /* Begin looking for illegal left hand sides: */
- lhsflg = 0;
- offset += RPAREN; /* new parenthesis level */
- goto gettok;
- case RPAREN:
- offset -= RPAREN; /* parenthesis level */
- if( offset < 0 )
- {
- errcod = 5; /* parenthesis error */
- goto synerr;
- }
- goto gettok;
- case EOL:
- if( offset != 0 )
- {
- errcod = 6; /* parenthesis error */
- goto synerr;
- }
- break;
- case EQU:
- if( --lhsflg ) /* was incremented before switch{} */
- {
- errcod = 7;
- goto synerr;
- }
- case UMINUS:
- case COMP:
- goto pshopr; /* evaluate right to left */
- default: ;
- }
-\f
-
-/* evaluate expression whenever precedence is not increasing */
-
-symval = psym->sym + offset;
-
-while( symval <= *al )
- {
- /* if just starting, must fill accumulator with last
- * thing on the line
- */
- if( (accflg == 0) && (as >= ascsym) && (((*as)->attrib & FUNC) == 0 ))
- {
- pvar = (struct varent *)*as;
-/*
- if( pvar->attrib & STRING )
- strcpy( (char *)&acc, (char *)pvar->value );
- else
-*/
- acc = *pvar->value;
- --as;
- accflg = 1;
- }
-
-/* handle beginning of line type cases, where the symbol
- * list ascsym[] may be empty.
- */
- switch( *ao )
- {
- case BOL:
- printf( "%.16e\n", acc );
-#if 0
-#if NE == 6
- e64toasc( &acc, str, 100 );
-#else
- e113toasc( &acc, str, 100 );
-#endif
-#endif
- printf( "%s\n", str );
- goto getcmd; /* all finished */
- case UMINUS:
- acc = -acc;
- goto nochg;
-/*
- case COMP:
- acc = ~acc;
- goto nochg;
-*/
- default: ;
- }
-/* Now it is illegal for symbol list to be empty,
- * because we are going to need a symbol below.
- */
- if( as < &ascsym[0] )
- {
- errcod = 8;
- goto synerr;
- }
-/* get attributes and value of current symbol */
- att = (*as)->attrib;
- pvar = (struct varent *)*as;
- if( att & FUNC )
- val = 0.0;
- else
- {
-/*
- if( att & STRING )
- strcpy( (char *)&val, (char *)pvar->value );
- else
-*/
- val = *pvar->value;
- }
-
-/* Expression evaluation, continued. */
-
- switch( *ao )
- {
- case FUNC:
- pfun = (struct funent *)*as;
- /* Call the function with appropriate number of args */
- i = narstk[ narptr ];
- --narptr;
- switch(i)
- {
- case 0:
- acc = ( *(pfun->fun) )(acc);
- break;
- case 1:
- acc = ( *(pfun->fun) )(acc, comstk[comptr-1]);
- break;
- case 2:
- acc = ( *(pfun->fun) )(acc, comstk[comptr-2],
- comstk[comptr-1]);
- break;
- case 3:
- acc = ( *(pfun->fun) )(acc, comstk[comptr-3],
- comstk[comptr-2], comstk[comptr-1]);
- break;
- default:
- errcod = 16;
- goto synerr;
- }
- comptr -= i;
- accflg = 1; /* in case at end of line */
- break;
- case EQU:
- if( ( att & TEMP) || ((att & VAR) == 0) || (att & STRING) )
- {
- errcod = 9;
- goto synerr; /* can only assign to a variable */
- }
- pvar = (struct varent *)*as;
- *pvar->value = acc;
- break;
- case PLUS:
- acc = acc + val; break;
- case MINUS:
- acc = val - acc; break;
- case MULT:
- acc = acc * val; break;
- case DIV:
- if( acc == 0.0 )
- {
-/*
-divzer:
-*/
- errcod = 10;
- goto synerr;
- }
- acc = val / acc; break;
-/*
- case MOD:
- if( acc == 0 )
- goto divzer;
- acc = val % acc; break;
- case LOR:
- acc |= val; break;
- case LXOR:
- acc ^= val; break;
- case LAND:
- acc &= val; break;
-*/
- case EOE:
- if( narptr < 0 )
- {
- errcod = 18;
- goto synerr;
- }
- narstk[narptr] += 1;
- comstk[comptr++] = acc;
-/* printf( "\ncomptr: %d narptr: %d %d\n", comptr, narptr, acc );*/
- acc = val;
- break;
- }
-\f
-
-/* expression evaluation, continued */
-
-/* Pop evaluated tokens from scan list: */
- /* make temporary variable not busy */
- if( att & TEMP )
- (*as)->attrib &= ~BUSY;
- if( as < &ascsym[0] ) /* can this happen? */
- {
- errcod = 11;
- goto synerr;
- }
- --as;
-nochg:
- --ao;
- --al;
- if( ao < &ascopr[0] ) /* can this happen? */
- {
- errcod = 12;
- goto synerr;
- }
-/* If precedence level will now increase, then */
-/* save accumulator in a temporary location */
- if( symval > *al )
- {
- /* find a free temp location */
- pvar = &temp[0];
- for( i=0; i<NTEMP; i++ )
- {
- if( (pvar->attrib & BUSY) == 0)
- goto temfnd;
- ++pvar;
- }
- errcod = 17;
- printf( "no more temps\n" );
- pvar = &temp[0];
- goto synerr;
-
- temfnd:
- pvar->attrib |= BUSY;
- *pvar->value = acc;
- /*printf( "temp %d\n", acc );*/
- accflg = 0;
- ++as; /* push the temp onto the scan list */
- *as = (struct symbol *)pvar;
- }
- } /* End of evaluation loop */
-\f
-
-/* Push operator onto scan list when precedence increases */
-
-pshopr:
- ++ao;
- *ao = psym->attrib & 0xf;
- ++al;
- *al = psym->sym + offset;
- goto gettok;
- } /* end of OPR processing */
-
-
-/* Token was not an operator. Push symbol onto scan list. */
-if( (lastok->attrib & OPR) == 0 )
- {
- errcod = 13;
- goto synerr; /* quantities must be preceded by an operator */
- }
-if( (unsigned short )lastok->attrib == (OPR | RPAREN) ) /* ...but not by ) */
- {
- errcod = 14;
- goto synerr;
- }
-++as;
-*as = psym;
-goto gettok;
-
-synerr:
-
-#if INTHELP
-printf( "%s ", intmsg[errcod] );
-#endif
-printf( " error %d\n", errcod );
-abmac(); /* flush the command line */
-goto getcmd;
-} /* end of program */
-\f
-/* parser() */
-
-/* Get token from input string and identify it. */
-
-
-static char number[128];
-
-struct symbol *parser( )
-{
-register struct symbol *psym;
-register char *pline;
-struct varent *pvar;
-struct strent *pstr;
-char *cp, *plc, *pn;
-long lnc;
-int i;
-double tem;
-
-/* reference for old Whitesmiths compiler: */
-/*
- *extern FILE *stdout;
- */
-
-pline = interl; /* get current location in command string */
-
-
-/* If at beginning of string, must ask for more input */
-if( pline == line )
- {
-
- if( maccnt > 0 )
- {
- --maccnt;
- cp = maclin;
- plc = pline;
- while( (*plc++ = *cp++) != 0 )
- ;
- goto mstart;
- }
- if( takptr < 0 )
- { /* no take file active: prompt keyboard input */
- printf("* ");
- }
-/* Various ways of typing in a command line. */
-
-/*
- * Old Whitesmiths call to print "*" immediately
- * use RT11 .GTLIN to get command string
- * from command file or terminal
- */
-
-/*
- * fflush(stdout);
- * gtlin(line);
- */
-
-
- zgets( line, TRUE ); /* keyboard input for other systems: */
-\f
-
-mstart:
- uposs = 1; /* unary operators possible at start of line */
- }
-
-ignore:
-/* Skip over spaces */
-while( *pline == ' ' )
- ++pline;
-
-/* unary minus after operator */
-if( uposs && (*pline == '-') )
- {
- psym = &oprtbl[2]; /* UMINUS */
- ++pline;
- goto pdon3;
- }
- /* COMP */
-/*
-if( uposs && (*pline == '~') )
- {
- psym = &oprtbl[3];
- ++pline;
- goto pdon3;
- }
-*/
-if( uposs && (*pline == '+') ) /* ignore leading plus sign */
- {
- ++pline;
- goto ignore;
- }
-
-/* end of null terminated input */
-if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
- {
- pline = line;
- goto endlin;
- }
-if( *pline == ';' )
- {
- ++pline;
-endlin:
- psym = &oprtbl[1]; /* EOL */
- goto pdon2;
- }
-
-\f
-/* parser() */
-
-
-/* Test for numeric input */
-if( (ISDIGIT(*pline)) || (*pline == '.') )
- {
- lnc = 0; /* initialize numeric input to zero */
- qnc = 0.0;
- if( *pline == '0' )
- { /* leading "0" may mean octal or hex radix */
- ++pline;
- if( *pline == '.' )
- goto decimal; /* 0.ddd */
- /* leading "0x" means hexadecimal radix */
- if( (*pline == 'x') || (*pline == 'X') )
- {
- ++pline;
- while( ISXDIGIT(*pline) )
- {
- i = *pline++ & 0xff;
- if( i >= 'a' )
- i -= 047;
- if( i >= 'A' )
- i -= 07;
- i -= 060;
- lnc = (lnc << 4) + i;
- qnc = lnc;
- }
- goto numdon;
- }
- else
- {
- while( ISOCTAL( *pline ) )
- {
- i = ((*pline++) & 0xff) - 060;
- lnc = (lnc << 3) + i;
- qnc = lnc;
- }
- goto numdon;
- }
- }
- else
- {
- /* no leading "0" means decimal radix */
-/******/
-decimal:
- pn = number;
- while( (ISDIGIT(*pline)) || (*pline == '.') )
- *pn++ = *pline++;
-/* get possible exponent field */
- if( (*pline == 'e') || (*pline == 'E') )
- *pn++ = *pline++;
- else
- goto numcvt;
- if( (*pline == '-') || (*pline == '+') )
- *pn++ = *pline++;
- while( ISDIGIT(*pline) )
- *pn++ = *pline++;
-numcvt:
- *pn++ = ' ';
- *pn++ = 0;
-#if 0
-#if NE == 6
- asctoe64( number, &qnc );
-#else
- asctoe113( number, &qnc );
-#endif
-#endif
- sscanf( number, "%le", &qnc );
- }
-/* output the number */
-numdon:
- /* search the symbol table of constants */
- pvar = &contbl[0];
- for( i=0; i<NCONST; i++ )
- {
- if( (pvar->attrib & BUSY) == 0 )
- goto confnd;
- tem = *pvar->value;
- if( tem == qnc )
- {
- psym = (struct symbol *)pvar;
- goto pdon2;
- }
- ++pvar;
- }
- printf( "no room for constant\n" );
- psym = (struct symbol *)&contbl[0];
- goto pdon2;
-
-confnd:
- pvar->spel= contbl[0].spel;
- pvar->attrib = CONST | BUSY;
- *pvar->value = qnc;
- psym = (struct symbol *)pvar;
- goto pdon2;
- }
-
-/* check for operators */
-psym = &oprtbl[3];
-for( i=0; i<NOPR; i++ )
- {
- if( *pline == *(psym->spel) )
- goto pdon1;
- ++psym;
- }
-\f
-/* if quoted, it is a string variable */
-if( *pline == '"' )
- {
- /* find an empty slot for the string */
- pstr = strtbl; /* string table */
- for( i=0; i<NSTRNG-1; i++ )
- {
- if( (pstr->attrib & BUSY) == 0 )
- goto fndstr;
- ++pstr;
- }
- printf( "No room for string\n" );
- pstr->attrib |= ILLEG;
- psym = (struct symbol *)pstr;
- goto pdon0;
-
-fndstr:
- pstr->attrib |= BUSY;
- plc = pstr->string;
- ++pline;
- for( i=0; i<39; i++ )
- {
- *plc++ = *pline;
- if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
- {
-illstr:
- pstr = &strtbl[NSTRNG-1];
- pstr->attrib |= ILLEG;
- printf( "Missing string terminator\n" );
- psym = (struct symbol *)pstr;
- goto pdon0;
- }
- if( *pline++ == '"' )
- goto finstr;
- }
-
- goto illstr; /* no terminator found */
-
-finstr:
- --plc;
- *plc = '\0';
- psym = (struct symbol *)pstr;
- goto pdon2;
- }
-/* If none of the above, search function and symbol tables: */
-
-/* copy character string to array lc[] */
-plc = &lc[0];
-while( ISALPHA(*pline) )
- {
- /* convert to lower case characters */
- if( ISUPPER( *pline ) )
- *pline += 040;
- *plc++ = *pline++;
- }
-*plc = 0; /* Null terminate the output string */
-\f
-/* parser() */
-
-psym = (struct symbol *)menstk[menptr]; /* function table */
-plc = &lc[0];
-cp = psym->spel;
-do
- {
- if( strcmp( plc, cp ) == 0 )
- goto pdon3; /* following unary minus is possible */
- ++psym;
- cp = psym->spel;
- }
-while( *cp != '\0' );
-
-psym = (struct symbol *)&indtbl[0]; /* indirect symbol table */
-plc = &lc[0];
-cp = psym->spel;
-do
- {
- if( strcmp( plc, cp ) == 0 )
- goto pdon2;
- ++psym;
- cp = psym->spel;
- }
-while( *cp != '\0' );
-
-pdon0:
-pline = line; /* scrub line if illegal symbol */
-goto pdon2;
-
-pdon1:
-++pline;
-if( (psym->attrib & 0xf) == RPAREN )
-pdon2: uposs = 0;
-else
-pdon3: uposs = 1;
-
-interl = pline;
-return( psym );
-} /* end of parser */
-\f
-/* exit from current menu */
-
-double cmdex()
-{
-
-if( menptr == 0 )
- {
- printf( "Main menu is active.\n" );
- }
-else
- --menptr;
-
-cmdh();
-return(0.0);
-}
-
-\f
-/* gets() */
-
-void zgets( gline, echo )
-char *gline;
-int echo;
-{
-register char *pline;
-register int i;
-
-
-scrub:
-pline = gline;
-getsl:
- if( (pline - gline) >= LINLEN )
- {
- printf( "\nLine too long\n *" );
- goto scrub;
- }
- if( takptr < 0 )
- { /* get character from keyboard */
-/*
-if DECPDP
- gtlin( gline );
- return(0);
-else
-*/
- *pline = getchar();
-/*endif*/
- }
- else
- { /* get a character from take file */
- i = fgetc( takstk[takptr] );
- if( i == -1 )
- { /* end of take file */
- if( takptr >= 0 )
- { /* close file and bump take stack */
- fclose( takstk[takptr] );
- takptr -= 1;
- }
- if( takptr < 0 ) /* no more take files: */
- printf( "*" ); /* prompt keyboard input */
- goto scrub; /* start a new input line */
- }
- *pline = i;
- }
-
- *pline &= 0x7f;
- /* xon or xoff characters need filtering out. */
- if ( *pline == XON || *pline == XOFF )
- goto getsl;
-
- /* control U or control C */
- if( (*pline == 025) || (*pline == 03) )
- {
- printf( "\n" );
- goto scrub;
- }
-
- /* Backspace or rubout */
- if( (*pline == 010) || (*pline == 0177) )
- {
- pline -= 1;
- if( pline >= gline )
- {
- if ( echo )
- printf( "\010\040\010" );
- goto getsl;
- }
- else
- goto scrub;
- }
- if ( echo )
- printf( "%c", *pline );
- if( (*pline != '\n') && (*pline != '\r') )
- {
- ++pline;
- goto getsl;
- }
- *pline = 0;
- if ( echo )
- printf( "%c", '\n' ); /* \r already echoed */
-}
-\f
-
-/* help function */
-double cmdhlp()
-{
-
-printf( "%s", idterp );
-printf( "\nFunctions:\n" );
-prhlst( &funtbl[0] );
-printf( "\nVariables:\n" );
-prhlst( &indtbl[0] );
-printf( "\nOperators:\n" );
-prhlst( &oprtbl[2] );
-printf("\n");
-return(0.0);
-}
-
-
-double cmdh()
-{
-
-prhlst( menstk[menptr] );
-printf( "\n" );
-return(0.0);
-}
-
-/* print keyword spellings */
-
-double prhlst(vps)
-void *vps;
-{
-register int j, k;
-int m;
-register struct symbol *ps = vps;
-
-j = 0;
-while( *(ps->spel) != '\0' )
- {
- k = strlen( ps->spel ) - 1;
-/* size of a tab field is 2**3 chars */
- m = ((k >> 3) + 1) << 3;
- j += m;
- if( j > 72 )
- {
- printf( "\n" );
- j = m;
- }
- printf( "%s\t", ps->spel );
- ++ps;
- }
-return(0.0);
-}
-
-
-#if SALONE
-double init()
-{
-/* Set coprocessor to double precision. */
-dprec();
-return 0.0;
-}
-#endif
-\f
-
-/* macro commands */
-
-/* define macro */
-double cmddm()
-{
-
-zgets( maclin, TRUE );
-return(0.0);
-}
-
-/* type (i.e., display) macro */
-double cmdtm()
-{
-
-printf( "%s\n", maclin );
-return 0.0;
-}
-
-/* execute macro # times */
-double cmdem( arg )
-double arg;
-{
-double f;
-long n;
-
-f = floor(arg);
-n = f;
-if( n <= 0 )
- n = 1;
-maccnt = n;
-return(0.0);
-}
-\f
-
-/* open a take file */
-
-double take( fname )
-char *fname;
-{
-FILE *f;
-
-while( *fname == ' ' )
- fname += 1;
-f = fopen( fname, "r" );
-
-if( f == 0 )
- {
- printf( "Can't open take file %s\n", fname );
- takptr = -1; /* terminate all take file input */
- return 0.0;
- }
-takptr += 1;
-takstk[ takptr ] = f;
-printf( "Running %s\n", fname );
-return(0.0);
-}
-
-
-/* abort macro execution */
-double abmac()
-{
-
-maccnt = 0;
-interl = line;
-return(0.0);
-}
-
-
-/* display integer part in hex, octal, and decimal
- */
-double hex(qx)
-double qx;
-{
-double f;
-long z;
-
-f = floor(qx);
-z = f;
-printf( "0%lo 0x%lx %ld.\n", z, z, z );
-return(qx);
-}
-
-#define NASC 16
-
-double bits( x )
-double x;
-{
-union
- {
- double d;
- short i[4];
- } du;
-union
- {
- float f;
- short i[2];
- } df;
-int i;
-
-du.d = x;
-printf( "double: " );
-for( i=0; i<4; i++ )
- printf( "0x%04x,", du.i[i] & 0xffff );
-printf( "\n" );
-
-df.f = (float) x;
-printf( "float: " );
-for( i=0; i<2; i++ )
- printf( "0x%04x,", df.i[i] & 0xffff );
-printf( "\n" );
-return(x);
-}
-
-
-/* Exit to monitor. */
-double mxit()
-{
-
-exit(0);
-return(0.0);
-}
-
-
-double cmddig( x )
-double x;
-{
-double f;
-long lx;
-
-f = floor(x);
-lx = f;
-ndigits = lx;
-if( ndigits <= 0 )
- ndigits = DEFDIS;
-return(f);
-}
-
-
-double csys(x)
-char *x;
-{
-
-system( x+1 );
-cmdh();
-return(0.0);
-}
-
-
-double ifrac(x)
-double x;
-{
-unsigned long lx;
-long double y, z;
-
-z = floor(x);
-lx = z;
-y = x - z;
-printf( " int = %lx\n", lx );
-return(y);
-}
-
-double xcmpl(x,y)
-double x,y;
-{
-double ans;
-
-ans = -2.0;
-if( x == y )
- {
- printf( "x == y " );
- ans = 0.0;
- }
-if( x < y )
- {
- printf( "x < y" );
- ans = -1.0;
- }
-if( x > y )
- {
- printf( "x > y" );
- ans = 1.0;
- }
-return( ans );
-}
-
-extern double INFINITY, NAN;
-
-double makenan(x)
-double x;
-{
-return(NAN);
-}
-
-double makeinfinity(x)
-double x;
-{
-return(INFINITY);
-}
-
-double zfrexp(x)
-double x;
-{
-double y;
-int e;
-y = frexp(x, &e);
-printf("exponent = %d, significand = ", e );
-return(y);
-}
-
-double zldexp(x,e)
-double x, e;
-{
-double y;
-int i;
-
-i = e;
-y = ldexp(x,i);
-return(y);
-}
-
-double hexinput(a, b)
-double a,b;
-{
-union
- {
- double d;
- unsigned short i[4];
- } u;
-unsigned long l;
-
-#ifdef IBMPC
-l = a;
-u.i[3] = l >> 16;
-u.i[2] = l;
-l = b;
-u.i[1] = l >> 16;
-u.i[0] = l;
-#endif
-#ifdef DEC
-l = a;
-u.i[3] = l >> 16;
-u.i[2] = l;
-l = b;
-u.i[1] = l >> 16;
-u.i[0] = l;
-#endif
-#ifdef MIEEE
-l = a;
-u.i[0] = l >> 16;
-u.i[1] = l;
-l = b;
-u.i[2] = l >> 16;
-u.i[3] = l;
-#endif
-#ifdef UNK
-l = a;
-u.i[0] = l >> 16;
-u.i[1] = l;
-l = b;
-u.i[2] = l >> 16;
-u.i[3] = l;
-#endif
-return(u.d);
-}
+++ /dev/null
-/* calc.h
- * include file for calc.c
- */
-
-/* 32 bit memory addresses: */
-#define LARGEMEM 1
-
-/* data structure of symbol table */
-struct symbol
- {
- char *spel;
- short attrib;
-#if LARGEMEM
- long sym;
-#else
- short sym;
-#endif
- };
-
-struct funent
- {
- char *spel;
- short attrib;
- double (*fun )();
- };
-
-struct varent
- {
- char *spel;
- short attrib;
- double *value;
- };
-
-struct strent
- {
- char *spel;
- short attrib;
- char *string;
- };
-
-
-/* general symbol attributes: */
-#define OPR 0x8000
-#define VAR 0x4000
-#define CONST 0x2000
-#define FUNC 0x1000
-#define ILLEG 0x800
-#define BUSY 0x400
-#define TEMP 0x200
-#define STRING 0x100
-#define COMMAN 0x80
-#define IND 0x1
-
-/* attributes of operators (ordered by precedence): */
-#define BOL 1
-#define EOL 2
-/* end of expression (comma): */
-#define EOE 3
-#define EQU 4
-#define PLUS 5
-#define MINUS 6
-#define MULT 7
-#define DIV 8
-#define UMINUS 9
-#define LPAREN 10
-#define RPAREN 11
-#define COMP 12
-#define MOD 13
-#define LAND 14
-#define LOR 15
-#define LXOR 16
-
-
-extern struct funent funtbl[];
-/*extern struct symbol symtbl[];*/
-extern struct varent indtbl[];
-
+++ /dev/null
-
-/* Test vectors for math functions.
- See C9X section F.9. */
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1998, 2000 by Stephen L. Moshier
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-int isfinite (double);
-
-/* C9X spells lgam lgamma. */
-#define GLIBC2 0
-
-extern double PI;
-static double MPI, PIO2, MPIO2, PIO4, MPIO4, THPIO4, MTHPIO4;
-
-#if 0
-#define PI 3.141592653589793238463E0
-#define PIO2 1.570796326794896619231E0
-#define PIO4 7.853981633974483096157E-1
-#define THPIO4 2.35619449019234492884698
-#define SQRT2 1.414213562373095048802E0
-#define SQRTH 7.071067811865475244008E-1
-#define INF (1.0/0.0)
-#define MINF (-1.0/0.0)
-#endif
-
-extern double MACHEP, SQRTH, SQRT2;
-extern double NAN, INFINITY, NEGZERO;
-static double INF, MINF;
-static double ZERO, MZERO, HALF, MHALF, ONE, MONE, TWO, MTWO, THREE, MTHREE;
-/* #define NAN (1.0/0.0 - 1.0/0.0) */
-
-/* Functions of one variable. */
-double log (double);
-double exp ( double);
-double atan (double);
-double sin (double);
-double cos (double);
-double tan (double);
-double acos (double);
-double asin (double);
-double acosh (double);
-double asinh (double);
-double atanh (double);
-double sinh (double);
-double cosh (double);
-double tanh (double);
-double exp2 (double);
-double expm1 (double);
-double log10 (double);
-double log1p (double);
-double log2 (double);
-double fabs (double);
-double erf (double);
-double erfc (double);
-double gamma (double);
-double floor (double);
-double ceil (double);
-double cbrt (double);
-#if GLIBC2
-double lgamma (double);
-#else
-double lgam (double);
-#endif
-
-struct oneargument
- {
- char *name; /* Name of the function. */
- double (*func) (double);
- double *arg1;
- double *answer;
- int thresh; /* Error report threshold. */
- };
-
-struct oneargument test1[] =
-{
- {"atan", atan, &ONE, &PIO4, 0},
- {"sin", sin, &PIO2, &ONE, 0},
-#if 0
- {"cos", cos, &PIO4, &SQRTH, 0},
- {"sin", sin, 32767., 1.8750655394138942394239E-1, 0},
- {"cos", cos, 32767., 9.8226335176928229845654E-1, 0},
- {"tan", tan, 32767., 1.9089234430221485740826E-1, 0},
- {"sin", sin, 8388607., 9.9234509376961249835628E-1, 0},
- {"cos", cos, 8388607., -1.2349580912475928183718E-1, 0},
- {"tan", tan, 8388607., -8.0354556223613614748329E0, 0},
- /*
- {"sin", sin, 2147483647., -7.2491655514455639054829E-1, 0},
- {"cos", cos, 2147483647., -6.8883669187794383467976E-1, 0},
- {"tan", tan, 2147483647., 1.0523779637351339136698E0, 0},
- */
- {"cos", cos, &PIO2, 6.1232339957367574e-17, 1},
- {"sin", sin, &PIO4, &SQRTH, 1},
-#endif
- {"acos", acos, &NAN, &NAN, 0},
- {"acos", acos, &ONE, &ZERO, 0},
- {"acos", acos, &TWO, &NAN, 0},
- {"acos", acos, &MTWO, &NAN, 0},
- {"asin", asin, &NAN, &NAN, 0},
- {"asin", asin, &ZERO, &ZERO, 0},
- {"asin", asin, &MZERO, &MZERO, 0},
- {"asin", asin, &TWO, &NAN, 0},
- {"asin", asin, &MTWO, &NAN, 0},
- {"atan", atan, &NAN, &NAN, 0},
- {"atan", atan, &ZERO, &ZERO, 0},
- {"atan", atan, &MZERO, &MZERO, 0},
- {"atan", atan, &INF, &PIO2, 0},
- {"atan", atan, &MINF, &MPIO2, 0},
- {"cos", cos, &NAN, &NAN, 0},
- {"cos", cos, &ZERO, &ONE, 0},
- {"cos", cos, &MZERO, &ONE, 0},
- {"cos", cos, &INF, &NAN, 0},
- {"cos", cos, &MINF, &NAN, 0},
- {"sin", sin, &NAN, &NAN, 0},
- {"sin", sin, &MZERO, &MZERO, 0},
- {"sin", sin, &ZERO, &ZERO, 0},
- {"sin", sin, &INF, &NAN, 0},
- {"sin", sin, &MINF, &NAN, 0},
- {"tan", tan, &NAN, &NAN, 0},
- {"tan", tan, &ZERO, &ZERO, 0},
- {"tan", tan, &MZERO, &MZERO, 0},
- {"tan", tan, &INF, &NAN, 0},
- {"tan", tan, &MINF, &NAN, 0},
- {"acosh", acosh, &NAN, &NAN, 0},
- {"acosh", acosh, &ONE, &ZERO, 0},
- {"acosh", acosh, &INF, &INF, 0},
- {"acosh", acosh, &HALF, &NAN, 0},
- {"acosh", acosh, &MONE, &NAN, 0},
- {"asinh", asinh, &NAN, &NAN, 0},
- {"asinh", asinh, &ZERO, &ZERO, 0},
- {"asinh", asinh, &MZERO, &MZERO, 0},
- {"asinh", asinh, &INF, &INF, 0},
- {"asinh", asinh, &MINF, &MINF, 0},
- {"atanh", atanh, &NAN, &NAN, 0},
- {"atanh", atanh, &ZERO, &ZERO, 0},
- {"atanh", atanh, &MZERO, &MZERO, 0},
- {"atanh", atanh, &ONE, &INF, 0},
- {"atanh", atanh, &MONE, &MINF, 0},
- {"atanh", atanh, &TWO, &NAN, 0},
- {"atanh", atanh, &MTWO, &NAN, 0},
- {"cosh", cosh, &NAN, &NAN, 0},
- {"cosh", cosh, &ZERO, &ONE, 0},
- {"cosh", cosh, &MZERO, &ONE, 0},
- {"cosh", cosh, &INF, &INF, 0},
- {"cosh", cosh, &MINF, &INF, 0},
- {"sinh", sinh, &NAN, &NAN, 0},
- {"sinh", sinh, &ZERO, &ZERO, 0},
- {"sinh", sinh, &MZERO, &MZERO, 0},
- {"sinh", sinh, &INF, &INF, 0},
- {"sinh", sinh, &MINF, &MINF, 0},
- {"tanh", tanh, &NAN, &NAN, 0},
- {"tanh", tanh, &ZERO, &ZERO, 0},
- {"tanh", tanh, &MZERO, &MZERO, 0},
- {"tanh", tanh, &INF, &ONE, 0},
- {"tanh", tanh, &MINF, &MONE, 0},
- {"exp", exp, &NAN, &NAN, 0},
- {"exp", exp, &ZERO, &ONE, 0},
- {"exp", exp, &MZERO, &ONE, 0},
- {"exp", exp, &INF, &INF, 0},
- {"exp", exp, &MINF, &ZERO, 0},
-#if !GLIBC2
- {"exp2", exp2, &NAN, &NAN, 0},
- {"exp2", exp2, &ZERO, &ONE, 0},
- {"exp2", exp2, &MZERO, &ONE, 0},
- {"exp2", exp2, &INF, &INF, 0},
- {"exp2", exp2, &MINF, &ZERO, 0},
-#endif
- {"expm1", expm1, &NAN, &NAN, 0},
- {"expm1", expm1, &ZERO, &ZERO, 0},
- {"expm1", expm1, &MZERO, &MZERO, 0},
- {"expm1", expm1, &INF, &INF, 0},
- {"expm1", expm1, &MINF, &MONE, 0},
- {"log", log, &NAN, &NAN, 0},
- {"log", log, &ZERO, &MINF, 0},
- {"log", log, &MZERO, &MINF, 0},
- {"log", log, &ONE, &ZERO, 0},
- {"log", log, &MONE, &NAN, 0},
- {"log", log, &INF, &INF, 0},
- {"log10", log10, &NAN, &NAN, 0},
- {"log10", log10, &ZERO, &MINF, 0},
- {"log10", log10, &MZERO, &MINF, 0},
- {"log10", log10, &ONE, &ZERO, 0},
- {"log10", log10, &MONE, &NAN, 0},
- {"log10", log10, &INF, &INF, 0},
- {"log1p", log1p, &NAN, &NAN, 0},
- {"log1p", log1p, &ZERO, &ZERO, 0},
- {"log1p", log1p, &MZERO, &MZERO, 0},
- {"log1p", log1p, &MONE, &MINF, 0},
- {"log1p", log1p, &MTWO, &NAN, 0},
- {"log1p", log1p, &INF, &INF, 0},
-#if !GLIBC2
- {"log2", log2, &NAN, &NAN, 0},
- {"log2", log2, &ZERO, &MINF, 0},
- {"log2", log2, &MZERO, &MINF, 0},
- {"log2", log2, &MONE, &NAN, 0},
- {"log2", log2, &INF, &INF, 0},
-#endif
- /* {"fabs", fabs, NAN, NAN, 0}, */
- {"fabs", fabs, &ONE, &ONE, 0},
- {"fabs", fabs, &MONE, &ONE, 0},
- {"fabs", fabs, &ZERO, &ZERO, 0},
- {"fabs", fabs, &MZERO, &ZERO, 0},
- {"fabs", fabs, &INF, &INF, 0},
- {"fabs", fabs, &MINF, &INF, 0},
- {"cbrt", cbrt, &NAN, &NAN, 0},
- {"cbrt", cbrt, &ZERO, &ZERO, 0},
- {"cbrt", cbrt, &MZERO, &MZERO, 0},
- {"cbrt", cbrt, &INF, &INF, 0},
- {"cbrt", cbrt, &MINF, &MINF, 0},
- {"erf", erf, &NAN, &NAN, 0},
- {"erf", erf, &ZERO, &ZERO, 0},
- {"erf", erf, &MZERO, &MZERO, 0},
- {"erf", erf, &INF, &ONE, 0},
- {"erf", erf, &MINF, &MONE, 0},
- {"erfc", erfc, &NAN, &NAN, 0},
- {"erfc", erfc, &INF, &ZERO, 0},
- {"erfc", erfc, &MINF, &TWO, 0},
- {"gamma", gamma, &NAN, &NAN, 0},
- {"gamma", gamma, &INF, &INF, 0},
- {"gamma", gamma, &MONE, &NAN, 0},
- {"gamma", gamma, &ZERO, &NAN, 0},
- {"gamma", gamma, &MINF, &NAN, 0},
-#if GLIBC2
- {"lgamma", lgamma, &NAN, &NAN, 0},
- {"lgamma", lgamma, &INF, &INF, 0},
- {"lgamma", lgamma, &MONE, &INF, 0},
- {"lgamma", lgamma, &ZERO, &INF, 0},
- {"lgamma", lgamma, &MINF, &INF, 0},
-#else
- {"lgam", lgam, &NAN, &NAN, 0},
- {"lgam", lgam, &INF, &INF, 0},
- {"lgam", lgam, &MONE, &INF, 0},
- {"lgam", lgam, &ZERO, &INF, 0},
- {"lgam", lgam, &MINF, &INF, 0},
-#endif
- {"ceil", ceil, &NAN, &NAN, 0},
- {"ceil", ceil, &ZERO, &ZERO, 0},
- {"ceil", ceil, &MZERO, &MZERO, 0},
- {"ceil", ceil, &INF, &INF, 0},
- {"ceil", ceil, &MINF, &MINF, 0},
- {"floor", floor, &NAN, &NAN, 0},
- {"floor", floor, &ZERO, &ZERO, 0},
- {"floor", floor, &MZERO, &MZERO, 0},
- {"floor", floor, &INF, &INF, 0},
- {"floor", floor, &MINF, &MINF, 0},
- {"null", NULL, &ZERO, &ZERO, 0},
-};
-
-/* Functions of two variables. */
-double atan2 (double, double);
-double pow (double, double);
-
-struct twoarguments
- {
- char *name; /* Name of the function. */
- double (*func) (double, double);
- double *arg1;
- double *arg2;
- double *answer;
- int thresh;
- };
-
-struct twoarguments test2[] =
-{
- {"atan2", atan2, &ZERO, &ONE, &ZERO, 0},
- {"atan2", atan2, &MZERO, &ONE, &MZERO, 0},
- {"atan2", atan2, &ZERO, &ZERO, &ZERO, 0},
- {"atan2", atan2, &MZERO, &ZERO, &MZERO, 0},
- {"atan2", atan2, &ZERO, &MONE, &PI, 0},
- {"atan2", atan2, &MZERO, &MONE, &MPI, 0},
- {"atan2", atan2, &ZERO, &MZERO, &PI, 0},
- {"atan2", atan2, &MZERO, &MZERO, &MPI, 0},
- {"atan2", atan2, &ONE, &ZERO, &PIO2, 0},
- {"atan2", atan2, &ONE, &MZERO, &PIO2, 0},
- {"atan2", atan2, &MONE, &ZERO, &MPIO2, 0},
- {"atan2", atan2, &MONE, &MZERO, &MPIO2, 0},
- {"atan2", atan2, &ONE, &INF, &ZERO, 0},
- {"atan2", atan2, &MONE, &INF, &MZERO, 0},
- {"atan2", atan2, &INF, &ONE, &PIO2, 0},
- {"atan2", atan2, &INF, &MONE, &PIO2, 0},
- {"atan2", atan2, &MINF, &ONE, &MPIO2, 0},
- {"atan2", atan2, &MINF, &MONE, &MPIO2, 0},
- {"atan2", atan2, &ONE, &MINF, &PI, 0},
- {"atan2", atan2, &MONE, &MINF, &MPI, 0},
- {"atan2", atan2, &INF, &INF, &PIO4, 0},
- {"atan2", atan2, &MINF, &INF, &MPIO4, 0},
- {"atan2", atan2, &INF, &MINF, &THPIO4, 0},
- {"atan2", atan2, &MINF, &MINF, &MTHPIO4, 0},
- {"atan2", atan2, &ONE, &ONE, &PIO4, 0},
- {"atan2", atan2, &NAN, &ONE, &NAN, 0},
- {"atan2", atan2, &ONE, &NAN, &NAN, 0},
- {"atan2", atan2, &NAN, &NAN, &NAN, 0},
- {"pow", pow, &ONE, &ZERO, &ONE, 0},
- {"pow", pow, &ONE, &MZERO, &ONE, 0},
- {"pow", pow, &MONE, &ZERO, &ONE, 0},
- {"pow", pow, &MONE, &MZERO, &ONE, 0},
- {"pow", pow, &INF, &ZERO, &ONE, 0},
- {"pow", pow, &INF, &MZERO, &ONE, 0},
- {"pow", pow, &NAN, &ZERO, &ONE, 0},
- {"pow", pow, &NAN, &MZERO, &ONE, 0},
- {"pow", pow, &TWO, &INF, &INF, 0},
- {"pow", pow, &MTWO, &INF, &INF, 0},
- {"pow", pow, &HALF, &INF, &ZERO, 0},
- {"pow", pow, &MHALF, &INF, &ZERO, 0},
- {"pow", pow, &TWO, &MINF, &ZERO, 0},
- {"pow", pow, &MTWO, &MINF, &ZERO, 0},
- {"pow", pow, &HALF, &MINF, &INF, 0},
- {"pow", pow, &MHALF, &MINF, &INF, 0},
- {"pow", pow, &INF, &HALF, &INF, 0},
- {"pow", pow, &INF, &TWO, &INF, 0},
- {"pow", pow, &INF, &MHALF, &ZERO, 0},
- {"pow", pow, &INF, &MTWO, &ZERO, 0},
- {"pow", pow, &MINF, &THREE, &MINF, 0},
- {"pow", pow, &MINF, &TWO, &INF, 0},
- {"pow", pow, &MINF, &MTHREE, &MZERO, 0},
- {"pow", pow, &MINF, &MTWO, &ZERO, 0},
- {"pow", pow, &NAN, &ONE, &NAN, 0},
- {"pow", pow, &ONE, &NAN, &NAN, 0},
- {"pow", pow, &NAN, &NAN, &NAN, 0},
- {"pow", pow, &ONE, &INF, &NAN, 0},
- {"pow", pow, &MONE, &INF, &NAN, 0},
- {"pow", pow, &ONE, &MINF, &NAN, 0},
- {"pow", pow, &MONE, &MINF, &NAN, 0},
- {"pow", pow, &MTWO, &HALF, &NAN, 0},
- {"pow", pow, &ZERO, &MTHREE, &INF, 0},
- {"pow", pow, &MZERO, &MTHREE, &MINF, 0},
- {"pow", pow, &ZERO, &MHALF, &INF, 0},
- {"pow", pow, &MZERO, &MHALF, &INF, 0},
- {"pow", pow, &ZERO, &THREE, &ZERO, 0},
- {"pow", pow, &MZERO, &THREE, &MZERO, 0},
- {"pow", pow, &ZERO, &HALF, &ZERO, 0},
- {"pow", pow, &MZERO, &HALF, &ZERO, 0},
- {"null", NULL, &ZERO, &ZERO, &ZERO, 0},
-};
-
-/* Integer functions of one variable. */
-
-int isnan (double);
-int signbit (double);
-
-struct intans
- {
- char *name; /* Name of the function. */
- int (*func) (double);
- double *arg1;
- int ianswer;
- };
-
-struct intans test3[] =
-{
- {"isfinite", isfinite, &ZERO, 1},
- {"isfinite", isfinite, &INF, 0},
- {"isfinite", isfinite, &MINF, 0},
- {"isnan", isnan, &NAN, 1},
- {"isnan", isnan, &INF, 0},
- {"isnan", isnan, &ZERO, 0},
- {"isnan", isnan, &MZERO, 0},
- {"signbit", signbit, &MZERO, 1},
- {"signbit", signbit, &MONE, 1},
- {"signbit", signbit, &ZERO, 0},
- {"signbit", signbit, &ONE, 0},
- {"signbit", signbit, &MINF, 1},
- {"signbit", signbit, &INF, 0},
- {"null", NULL, &ZERO, 0},
-};
-
-static volatile double x1;
-static volatile double x2;
-static volatile double y;
-static volatile double answer;
-
-void
-pvec(x)
-double x;
-{
- union
- {
- double d;
- unsigned short s[4];
- } u;
- int i;
-
- u.d = x;
- for (i = 0; i < 4; i++)
- printf ("0x%04x ", u.s[i]);
- printf ("\n");
-}
-
-
-int
-main ()
-{
- int i, nerrors, k, ianswer, ntests;
- double (*fun1) (double);
- double (*fun2) (double, double);
- int (*fun3) (double);
- double e;
- union
- {
- double d;
- char c[8];
- } u, v;
-
- ZERO = 0.0;
- MZERO = NEGZERO;
- HALF = 0.5;
- MHALF = -HALF;
- ONE = 1.0;
- MONE = -ONE;
- TWO = 2.0;
- MTWO = -TWO;
- THREE = 3.0;
- MTHREE = -THREE;
- INF = INFINITY;
- MINF = -INFINITY;
- MPI = -PI;
- PIO2 = 0.5 * PI;
- MPIO2 = -PIO2;
- PIO4 = 0.5 * PIO2;
- MPIO4 = -PIO4;
- THPIO4 = 3.0 * PIO4;
- MTHPIO4 = -THPIO4;
-
- nerrors = 0;
- ntests = 0;
- i = 0;
- for (;;)
- {
- fun1 = test1[i].func;
- if (fun1 == NULL)
- break;
- x1 = *(test1[i].arg1);
- y = (*(fun1)) (x1);
- answer = *(test1[i].answer);
- if (test1[i].thresh == 0)
- {
- v.d = answer;
- u.d = y;
- if (memcmp(u.c, v.c, 8) != 0)
- {
- if( isnan(v.d) && isnan(u.d) )
- goto nxttest1;
- goto wrongone;
- }
- else
- goto nxttest1;
- }
- if (y != answer)
- {
- e = y - answer;
- if (answer != 0.0)
- e = e / answer;
- if (e < 0)
- e = -e;
- if (e > test1[i].thresh * MACHEP)
- {
-wrongone:
- printf ("%s (%.16e) = %.16e\n should be %.16e\n",
- test1[i].name, x1, y, answer);
- nerrors += 1;
- }
- }
-nxttest1:
- ntests += 1;
- i += 1;
- }
-
- i = 0;
- for (;;)
- {
- fun2 = test2[i].func;
- if (fun2 == NULL)
- break;
- x1 = *(test2[i].arg1);
- x2 = *(test2[i].arg2);
- y = (*(fun2)) (x1, x2);
- answer = *(test2[i].answer);
- if (test2[i].thresh == 0)
- {
- v.d = answer;
- u.d = y;
- if (memcmp(u.c, v.c, 8) != 0)
- {
- if( isnan(v.d) && isnan(u.d) )
- goto nxttest2;
-#if 0
- if( isnan(v.d) )
- pvec(v.d);
- if( isnan(u.d) )
- pvec(u.d);
-#endif
- goto wrongtwo;
- }
- else
- goto nxttest2;
- }
- if (y != answer)
- {
- e = y - answer;
- if (answer != 0.0)
- e = e / answer;
- if (e < 0)
- e = -e;
- if (e > test2[i].thresh * MACHEP)
- {
-wrongtwo:
- printf ("%s (%.16e, %.16e) = %.16e\n should be %.16e\n",
- test2[i].name, x1, x2, y, answer);
- nerrors += 1;
- }
- }
-nxttest2:
- ntests += 1;
- i += 1;
- }
-
-
- i = 0;
- for (;;)
- {
- fun3 = test3[i].func;
- if (fun3 == NULL)
- break;
- x1 = *(test3[i].arg1);
- k = (*(fun3)) (x1);
- ianswer = test3[i].ianswer;
- if (k != ianswer)
- {
- printf ("%s (%.16e) = %d\n should be. %d\n",
- test3[i].name, x1, k, ianswer);
- nerrors += 1;
- }
- ntests += 1;
- i += 1;
- }
-
- printf ("testvect: %d errors in %d tests\n", nerrors, ntests);
- exit (0);
-}
+++ /dev/null
-/* ei.c
- *
- * Exponential integral
- *
- *
- * SYNOPSIS:
- *
- * double x, y, ei();
- *
- * y = ei( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * x
- * - t
- * | | e
- * Ei(x) = -|- --- dt .
- * | | t
- * -
- * -inf
- *
- * Not defined for x <= 0.
- * See also expn.c.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 50000 8.6e-16 1.3e-16
- *
- */
-
-/*
-Cephes Math Library Release 2.8: May, 1999
-Copyright 1999 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double log ( double );
-extern double exp ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-extern double log(), exp(), polevl(), p1evl();
-#endif
-
-#define EUL 5.772156649015328606065e-1
-
-/* 0 < x <= 2
- Ei(x) - EUL - ln(x) = x A(x)/B(x)
- Theoretical peak relative error 9.73e-18 */
-#if UNK
-static double A[6] = {
--5.350447357812542947283E0,
- 2.185049168816613393830E2,
--4.176572384826693777058E3,
- 5.541176756393557601232E4,
--3.313381331178144034309E5,
- 1.592627163384945414220E6,
-};
-static double B[6] = {
- /* 1.000000000000000000000E0, */
--5.250547959112862969197E1,
- 1.259616186786790571525E3,
--1.756549581973534652631E4,
- 1.493062117002725991967E5,
--7.294949239640527645655E5,
- 1.592627163384945429726E6,
-};
-#endif
-#if DEC
-static short A[24] = {
-0140653,0033335,0060230,0144217,
-0042132,0100502,0035625,0167413,
-0143202,0102224,0037176,0175403,
-0044130,0071704,0077421,0170343,
-0144641,0144504,0041200,0045154,
-0045302,0064631,0047234,0142052,
-};
-static short B[24] = {
- /* 0040200,0000000,0000000,0000000, */
-0141522,0002634,0070442,0142614,
-0042635,0071667,0146532,0027705,
-0143611,0035375,0156025,0114015,
-0044421,0147215,0106177,0046330,
-0145062,0014556,0144216,0103725,
-0045302,0064631,0047234,0142052,
-};
-#endif
-#if IBMPC
-static short A[24] = {
-0x1912,0xac13,0x66db,0xc015,
-0xbde1,0x4772,0x5028,0x406b,
-0xdf60,0x87cf,0x5092,0xc0b0,
-0x3e1c,0x8fe2,0x0e78,0x40eb,
-0x094e,0x8850,0x3928,0xc114,
-0x9885,0x29d3,0x4d33,0x4138,
-};
-static short B[24] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0x58b1,0x8e24,0x40b3,0xc04a,
-0x45f9,0xf9ab,0xae76,0x4093,
-0xb302,0xbb82,0x275f,0xc0d1,
-0xe99b,0xb18f,0x39d1,0x4102,
-0xd0fb,0xd911,0x432d,0xc126,
-0x9885,0x29d3,0x4d33,0x4138,
-};
-#endif
-#if MIEEE
-static short A[24] = {
-0xc015,0x66db,0xac13,0x1912,
-0x406b,0x5028,0x4772,0xbde1,
-0xc0b0,0x5092,0x87cf,0xdf60,
-0x40eb,0x0e78,0x8fe2,0x3e1c,
-0xc114,0x3928,0x8850,0x094e,
-0x4138,0x4d33,0x29d3,0x9885,
-};
-static short B[24] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xc04a,0x40b3,0x8e24,0x58b1,
-0x4093,0xae76,0xf9ab,0x45f9,
-0xc0d1,0x275f,0xbb82,0xb302,
-0x4102,0x39d1,0xb18f,0xe99b,
-0xc126,0x432d,0xd911,0xd0fb,
-0x4138,0x4d33,0x29d3,0x9885,
-};
-#endif
-
-#if 0
-/* 0 < x <= 4
- Ei(x) - EUL - ln(x) = x A(x)/B(x)
- Theoretical peak relative error 4.75e-17 */
-#if UNK
-static double A[7] = {
--6.831869820732773831942E0,
- 2.920190530726774500309E2,
--1.195883839286649567993E4,
- 1.761045255472548975666E5,
--2.623034438354006526979E6,
- 1.472430336917880803157E7,
--8.205359388213261174960E7,
-};
-static double B[7] = {
- /* 1.000000000000000000000E0, */
--7.731946237840033971071E1,
- 2.751808700543578450827E3,
--5.829268609072186897994E4,
- 7.916610857961870631379E5,
--6.873926904825733094076E6,
- 3.523770183971164032710E7,
--8.205359388213260785363E7,
-};
-#endif
-#if DEC
-static short A[28] = {
-0140732,0117255,0072522,0071743,
-0042222,0001160,0052302,0002334,
-0143472,0155532,0101650,0155462,
-0044453,0175041,0121220,0172022,
-0145440,0014351,0140337,0157550,
-0046140,0126317,0057202,0100233,
-0146634,0100473,0036072,0067054,
-};
-static short B[28] = {
- /* 0040200,0000000,0000000,0000000, */
-0141632,0121620,0111247,0010115,
-0043053,0176360,0067773,0027324,
-0144143,0132257,0121644,0036204,
-0045101,0043321,0057553,0151231,
-0145721,0143215,0147505,0050610,
-0046406,0065721,0072675,0152744,
-0146634,0100473,0036072,0067052,
-};
-#endif
-#if IBMPC
-static short A[28] = {
-0x4e7c,0xaeaa,0x53d5,0xc01b,
-0x409b,0x0a98,0x404e,0x4072,
-0x1b66,0x5075,0x5b6b,0xc0c7,
-0x1e82,0x3452,0x7f44,0x4105,
-0xfbed,0x381b,0x031d,0xc144,
-0x5013,0xebd0,0x1599,0x416c,
-0x4dc5,0x6787,0x9027,0xc193,
-};
-static short B[28] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xe20a,0x1254,0x5472,0xc053,
-0x65db,0x0dff,0x7f9e,0x40a5,
-0x8791,0xf474,0x7695,0xc0ec,
-0x7a53,0x2bed,0x28da,0x4128,
-0xaa31,0xb9e8,0x38d1,0xc15a,
-0xbabd,0x2eb7,0xcd7a,0x4180,
-0x4dc5,0x6787,0x9027,0xc193,
-};
-#endif
-#if MIEEE
-static short A[28] = {
-0xc01b,0x53d5,0xaeaa,0x4e7c,
-0x4072,0x404e,0x0a98,0x409b,
-0xc0c7,0x5b6b,0x5075,0x1b66,
-0x4105,0x7f44,0x3452,0x1e82,
-0xc144,0x031d,0x381b,0xfbed,
-0x416c,0x1599,0xebd0,0x5013,
-0xc193,0x9027,0x6787,0x4dc5,
-};
-static short B[28] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xc053,0x5472,0x1254,0xe20a,
-0x40a5,0x7f9e,0x0dff,0x65db,
-0xc0ec,0x7695,0xf474,0x8791,
-0x4128,0x28da,0x2bed,0x7a53,
-0xc15a,0x38d1,0xb9e8,0xaa31,
-0x4180,0xcd7a,0x2eb7,0xbabd,
-0xc193,0x9027,0x6787,0x4dc5,
-};
-#endif
-#endif /* 0 */
-
-#if 0
-/* 0 < x <= 8
- Ei(x) - EUL - ln(x) = x A(x)/B(x)
- Theoretical peak relative error 2.14e-17 */
-
-#if UNK
-static double A[9] = {
--1.111230942210860450145E1,
- 3.688203982071386319616E2,
--4.924786153494029574350E4,
- 1.050677503345557903241E6,
--3.626713709916703688968E7,
- 4.353499908839918635414E8,
--6.454613717232006895409E9,
- 3.408243056457762907071E10,
--1.995466674647028468613E11,
-};
-static double B[9] = {
- /* 1.000000000000000000000E0, */
--1.356757648138514017969E2,
- 8.562181317107341736606E3,
--3.298257180413775117555E5,
- 8.543534058481435917210E6,
--1.542380618535140055068E8,
- 1.939251779195993632028E9,
--1.636096210465615015435E10,
- 8.396909743075306970605E10,
--1.995466674647028425886E11,
-};
-#endif
-#if DEC
-static short A[36] = {
-0141061,0146004,0173357,0151553,
-0042270,0064402,0147366,0126701,
-0144100,0057734,0106615,0144356,
-0045200,0040654,0003332,0004456,
-0146412,0054440,0043130,0140263,
-0047317,0113517,0033422,0065123,
-0150300,0056313,0065235,0131147,
-0050775,0167423,0146222,0075760,
-0151471,0153642,0003442,0147667,
-};
-static short B[36] = {
- /* 0040200,0000000,0000000,0000000, */
-0142007,0126376,0166077,0043600,
-0043405,0144271,0125461,0014364,
-0144641,0006066,0175061,0164463,
-0046002,0056456,0007370,0121657,
-0147023,0013706,0156647,0177115,
-0047747,0026504,0103144,0054507,
-0150563,0146036,0007051,0177135,
-0051234,0063625,0173266,0003111,
-0151471,0153642,0003442,0147666,
-};
-#endif
-#if IBMPC
-static short A[36] = {
-0xfa6d,0x9edd,0x3980,0xc026,
-0xd5b8,0x59de,0x0d20,0x4077,
-0xb91e,0x91b1,0x0bfb,0xc0e8,
-0x4126,0x80db,0x0835,0x4130,
-0x1816,0x08cb,0x4b24,0xc181,
-0x4d4a,0xe6e2,0xf2e9,0x41b9,
-0xb64d,0x6d53,0x0b99,0xc1f8,
-0x4f7e,0x7992,0xbde2,0x421f,
-0x59f7,0x40e4,0x3af4,0xc247,
-};
-static short B[36] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xe8f0,0xdd87,0xf59f,0xc060,
-0x231e,0x3566,0xb917,0x40c0,
-0x3d26,0xdf46,0x2186,0xc114,
-0x1476,0xc1df,0x4ba5,0x4160,
-0xffca,0xdbb4,0x62f8,0xc1a2,
-0x8b29,0x90cc,0xe5a8,0x41dc,
-0x3fcc,0xc1c5,0x7983,0xc20e,
-0xc0c9,0xbed6,0x8cf2,0x4233,
-0x59f7,0x40e4,0x3af4,0xc247,
-};
-#endif
-#if MIEEE
-static short A[36] = {
-0xc026,0x3980,0x9edd,0xfa6d,
-0x4077,0x0d20,0x59de,0xd5b8,
-0xc0e8,0x0bfb,0x91b1,0xb91e,
-0x4130,0x0835,0x80db,0x4126,
-0xc181,0x4b24,0x08cb,0x1816,
-0x41b9,0xf2e9,0xe6e2,0x4d4a,
-0xc1f8,0x0b99,0x6d53,0xb64d,
-0x421f,0xbde2,0x7992,0x4f7e,
-0xc247,0x3af4,0x40e4,0x59f7,
-};
-static short B[36] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xc060,0xf59f,0xdd87,0xe8f0,
-0x40c0,0xb917,0x3566,0x231e,
-0xc114,0x2186,0xdf46,0x3d26,
-0x4160,0x4ba5,0xc1df,0x1476,
-0xc1a2,0x62f8,0xdbb4,0xffca,
-0x41dc,0xe5a8,0x90cc,0x8b29,
-0xc20e,0x7983,0xc1c5,0x3fcc,
-0x4233,0x8cf2,0xbed6,0xc0c9,
-0xc247,0x3af4,0x40e4,0x59f7,
-};
-#endif
-#endif /* 0 */
-
-/* 8 <= x <= 20
- x exp(-x) Ei(x) - 1 = 1/x R(1/x)
- Theoretical peak absolute error = 1.07e-17 */
-#if UNK
-static double A2[10] = {
--2.106934601691916512584E0,
- 1.732733869664688041885E0,
--2.423619178935841904839E-1,
- 2.322724180937565842585E-2,
- 2.372880440493179832059E-4,
--8.343219561192552752335E-5,
- 1.363408795605250394881E-5,
--3.655412321999253963714E-7,
- 1.464941733975961318456E-8,
- 6.176407863710360207074E-10,
-};
-static double B2[9] = {
- /* 1.000000000000000000000E0, */
--2.298062239901678075778E-1,
- 1.105077041474037862347E-1,
--1.566542966630792353556E-2,
- 2.761106850817352773874E-3,
--2.089148012284048449115E-4,
- 1.708528938807675304186E-5,
--4.459311796356686423199E-7,
- 1.394634930353847498145E-8,
- 6.150865933977338354138E-10,
-};
-#endif
-#if DEC
-static short A2[40] = {
-0140406,0154004,0035104,0173336,
-0040335,0145071,0031560,0150165,
-0137570,0026670,0176230,0055040,
-0036676,0043416,0077122,0054476,
-0035170,0150206,0034407,0175571,
-0134656,0174121,0123231,0021751,
-0034144,0136766,0036746,0121115,
-0132704,0037632,0135077,0107300,
-0031573,0126321,0117076,0004314,
-0030451,0143233,0041352,0172464,
-};
-static short B2[36] = {
- /* 0040200,0000000,0000000,0000000, */
-0137553,0051122,0120721,0170437,
-0037342,0050734,0175047,0032132,
-0136600,0052311,0101406,0147050,
-0036064,0171657,0120001,0071165,
-0135133,0010043,0151244,0066340,
-0034217,0051141,0026115,0043305,
-0132757,0064120,0106341,0051217,
-0031557,0114261,0060663,0135017,
-0030451,0011337,0001344,0175542,
-};
-#endif
-#if IBMPC
-static short A2[40] = {
-0x9edc,0x8748,0xdb00,0xc000,
-0x1a0f,0x266e,0xb947,0x3ffb,
-0x0b44,0x1f93,0x05b7,0xbfcf,
-0x4b28,0xcfca,0xc8e1,0x3f97,
-0xff6f,0xc720,0x1a10,0x3f2f,
-0x247d,0x34d3,0xdf0a,0xbf15,
-0xd44a,0xc7bc,0x97be,0x3eec,
-0xf1d8,0x5747,0x87f3,0xbe98,
-0xc119,0x33c7,0x759a,0x3e4f,
-0x5ea6,0x685d,0x38d3,0x3e05,
-};
-static short B2[36] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0x3e24,0x543a,0x6a4a,0xbfcd,
-0xe68b,0x9f44,0x4a3b,0x3fbc,
-0xd9c5,0x3060,0x0a99,0xbf90,
-0x2e4f,0xf400,0x9e75,0x3f66,
-0x8d9c,0x7a54,0x6204,0xbf2b,
-0xa8d9,0x2589,0xea4c,0x3ef1,
-0x2a52,0x119c,0xed0a,0xbe9d,
-0x7742,0x2c36,0xf316,0x3e4d,
-0x9f6c,0xe05c,0x225b,0x3e05,
-};
-#endif
-#if MIEEE
-static short A2[40] = {
-0xc000,0xdb00,0x8748,0x9edc,
-0x3ffb,0xb947,0x266e,0x1a0f,
-0xbfcf,0x05b7,0x1f93,0x0b44,
-0x3f97,0xc8e1,0xcfca,0x4b28,
-0x3f2f,0x1a10,0xc720,0xff6f,
-0xbf15,0xdf0a,0x34d3,0x247d,
-0x3eec,0x97be,0xc7bc,0xd44a,
-0xbe98,0x87f3,0x5747,0xf1d8,
-0x3e4f,0x759a,0x33c7,0xc119,
-0x3e05,0x38d3,0x685d,0x5ea6,
-};
-static short B2[36] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xbfcd,0x6a4a,0x543a,0x3e24,
-0x3fbc,0x4a3b,0x9f44,0xe68b,
-0xbf90,0x0a99,0x3060,0xd9c5,
-0x3f66,0x9e75,0xf400,0x2e4f,
-0xbf2b,0x6204,0x7a54,0x8d9c,
-0x3ef1,0xea4c,0x2589,0xa8d9,
-0xbe9d,0xed0a,0x119c,0x2a52,
-0x3e4d,0xf316,0x2c36,0x7742,
-0x3e05,0x225b,0xe05c,0x9f6c,
-};
-#endif
-
-/* x > 20
- x exp(-x) Ei(x) - 1 = 1/x A3(1/x)/B3(1/x)
- Theoretical absolute error = 6.15e-17 */
-#if UNK
-static double A3[9] = {
--7.657847078286127362028E-1,
- 6.886192415566705051750E-1,
--2.132598113545206124553E-1,
- 3.346107552384193813594E-2,
--3.076541477344756050249E-3,
- 1.747119316454907477380E-4,
--6.103711682274170530369E-6,
- 1.218032765428652199087E-7,
--1.086076102793290233007E-9,
-};
-static double B3[9] = {
- /* 1.000000000000000000000E0, */
--1.888802868662308731041E0,
- 1.066691687211408896850E0,
--2.751915982306380647738E-1,
- 3.930852688233823569726E-2,
--3.414684558602365085394E-3,
- 1.866844370703555398195E-4,
--6.345146083130515357861E-6,
- 1.239754287483206878024E-7,
--1.086076102793126632978E-9,
-};
-#endif
-#if DEC
-static short A3[36] = {
-0140104,0005167,0071746,0115510,
-0040060,0044531,0140741,0154556,
-0137532,0060307,0126506,0071123,
-0037011,0007173,0010405,0127224,
-0136111,0117715,0003654,0175577,
-0035067,0031340,0102657,0147714,
-0133714,0147173,0167473,0136640,
-0032402,0144407,0115547,0060114,
-0130625,0042347,0156431,0113425,
-};
-static short B3[36] = {
- /* 0040200,0000000,0000000,0000000, */
-0140361,0142112,0155277,0067714,
-0040210,0104532,0065676,0074326,
-0137614,0162751,0142421,0131033,
-0037041,0000772,0053236,0002632,
-0136137,0144346,0100536,0153136,
-0035103,0140270,0152211,0166215,
-0133724,0164143,0145763,0021153,
-0032405,0017033,0035333,0025736,
-0130625,0042347,0156431,0077134,
-};
-#endif
-#if IBMPC
-static short A3[36] = {
-0xd369,0xee7c,0x814e,0xbfe8,
-0x3b2e,0x383c,0x092b,0x3fe6,
-0xce4a,0xf5a8,0x4c18,0xbfcb,
-0xb5d2,0x6220,0x21cf,0x3fa1,
-0x9f70,0xa0f5,0x33f9,0xbf69,
-0xf9f9,0x10b5,0xe65c,0x3f26,
-0x77b4,0x7de7,0x99cf,0xbed9,
-0xec09,0xf36c,0x5920,0x3e80,
-0x32e3,0xfba3,0xa89c,0xbe12,
-};
-static short B3[36] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xedf9,0x5b57,0x3889,0xbffe,
-0xcf1b,0x4d77,0x112b,0x3ff1,
-0x3643,0x38a2,0x9cbd,0xbfd1,
-0xc0b3,0x4ad3,0x203f,0x3fa4,
-0xdacc,0xd02b,0xf91c,0xbf6b,
-0x3d92,0x1a91,0x7817,0x3f28,
-0x644d,0x797e,0x9d0c,0xbeda,
-0x657c,0x675b,0xa3c3,0x3e80,
-0x2fcb,0xfba3,0xa89c,0xbe12,
-};
-#endif
-#if MIEEE
-static short A3[36] = {
-0xbfe8,0x814e,0xee7c,0xd369,
-0x3fe6,0x092b,0x383c,0x3b2e,
-0xbfcb,0x4c18,0xf5a8,0xce4a,
-0x3fa1,0x21cf,0x6220,0xb5d2,
-0xbf69,0x33f9,0xa0f5,0x9f70,
-0x3f26,0xe65c,0x10b5,0xf9f9,
-0xbed9,0x99cf,0x7de7,0x77b4,
-0x3e80,0x5920,0xf36c,0xec09,
-0xbe12,0xa89c,0xfba3,0x32e3,
-};
-static short B3[36] = {
-/* 0x3ff0,0x0000,0x0000,0x0000, */
-0xbffe,0x3889,0x5b57,0xedf9,
-0x3ff1,0x112b,0x4d77,0xcf1b,
-0xbfd1,0x9cbd,0x38a2,0x3643,
-0x3fa4,0x203f,0x4ad3,0xc0b3,
-0xbf6b,0xf91c,0xd02b,0xdacc,
-0x3f28,0x7817,0x1a91,0x3d92,
-0xbeda,0x9d0c,0x797e,0x644d,
-0x3e80,0xa3c3,0x675b,0x657c,
-0xbe12,0xa89c,0xfba3,0x2fcb,
-};
-#endif
-
-/* 16 <= x <= 32
- x exp(-x) Ei(x) - 1 = 1/x A4(1/x) / B4(1/x)
- Theoretical absolute error = 1.22e-17 */
-#if UNK
-static double A4[8] = {
--2.458119367674020323359E-1,
--1.483382253322077687183E-1,
- 7.248291795735551591813E-2,
--1.348315687380940523823E-2,
- 1.342775069788636972294E-3,
--7.942465637159712264564E-5,
- 2.644179518984235952241E-6,
--4.239473659313765177195E-8,
-};
-static double B4[8] = {
- /* 1.000000000000000000000E0, */
--1.044225908443871106315E-1,
--2.676453128101402655055E-1,
- 9.695000254621984627876E-2,
--1.601745692712991078208E-2,
- 1.496414899205908021882E-3,
--8.462452563778485013756E-5,
- 2.728938403476726394024E-6,
--4.239462431819542051337E-8,
-};
-#endif
-#if DEC
-static short A4[32] = {
-0137573,0133037,0152607,0113356,
-0137427,0162771,0145061,0126345,
-0037224,0070754,0110451,0174104,
-0136534,0164165,0072170,0063753,
-0035660,0000016,0002560,0147751,
-0134646,0110311,0123316,0047432,
-0033461,0071250,0101031,0075202,
-0132066,0012601,0077305,0170177,
-};
-static short B4[32] = {
- /* 0040200,0000000,0000000,0000000, */
-0137325,0155602,0162437,0030710,
-0137611,0004316,0071344,0176361,
-0037306,0106671,0011103,0155053,
-0136603,0033412,0132530,0175171,
-0035704,0021532,0015516,0166130,
-0134661,0074162,0036741,0073466,
-0033467,0021316,0003100,0171325,
-0132066,0012541,0162202,0150160,
-};
-#endif
-#if IBMPC
-static short A4[] = {
-0xf2de,0xfab0,0x76c3,0xbfcf,
-0x359d,0x3946,0xfcbf,0xbfc2,
-0x3f09,0x9225,0x8e3d,0x3fb2,
-0x0cfd,0xae8f,0x9d0e,0xbf8b,
-0x19fd,0xc0ae,0x0001,0x3f56,
-0xc9e3,0x34d9,0xd219,0xbf14,
-0x2f50,0x1043,0x2e55,0x3ec6,
-0xbe10,0x2fd8,0xc2b0,0xbe66,
-};
-static short B4[] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xe639,0x5ca3,0xbb70,0xbfba,
-0x9f9e,0xce5c,0x2119,0xbfd1,
-0x7b45,0x2248,0xd1b7,0x3fb8,
-0x1f4f,0x56ab,0x66e1,0xbf90,
-0xdd8b,0x4369,0x846b,0x3f58,
-0x2ee7,0x47bc,0x2f0e,0xbf16,
-0x1e5b,0xc0c8,0xe459,0x3ec6,
-0x5a0e,0x3c90,0xc2ac,0xbe66,
-};
-#endif
-#if MIEEE
-static short A4[32] = {
-0xbfcf,0x76c3,0xfab0,0xf2de,
-0xbfc2,0xfcbf,0x3946,0x359d,
-0x3fb2,0x8e3d,0x9225,0x3f09,
-0xbf8b,0x9d0e,0xae8f,0x0cfd,
-0x3f56,0x0001,0xc0ae,0x19fd,
-0xbf14,0xd219,0x34d9,0xc9e3,
-0x3ec6,0x2e55,0x1043,0x2f50,
-0xbe66,0xc2b0,0x2fd8,0xbe10,
-};
-static short B4[32] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xbfba,0xbb70,0x5ca3,0xe639,
-0xbfd1,0x2119,0xce5c,0x9f9e,
-0x3fb8,0xd1b7,0x2248,0x7b45,
-0xbf90,0x66e1,0x56ab,0x1f4f,
-0x3f58,0x846b,0x4369,0xdd8b,
-0xbf16,0x2f0e,0x47bc,0x2ee7,
-0x3ec6,0xe459,0xc0c8,0x1e5b,
-0xbe66,0xc2ac,0x3c90,0x5a0e,
-};
-#endif
-
-
-#if 0
-/* 20 <= x <= 40
- x exp(-x) Ei(x) - 1 = 1/x A4(1/x) / B4(1/x)
- Theoretical absolute error = 1.78e-17 */
-#if UNK
-static double A4[8] = {
- 2.067245813525780707978E-1,
--5.153749551345223645670E-1,
- 1.928289589546695033096E-1,
--3.124468842857260044075E-2,
- 2.740283734277352539912E-3,
--1.377775664366875175601E-4,
- 3.803788980664744242323E-6,
--4.611038277393688031154E-8,
-};
-static double B4[8] = {
- /* 1.000000000000000000000E0, */
--8.544436025219516861531E-1,
- 2.507436807692907385181E-1,
--3.647688090228423114064E-2,
- 3.008576950332041388892E-3,
--1.452926405348421286334E-4,
- 3.896007735260115431965E-6,
--4.611037642697098234083E-8,
-};
-#endif
-#if DEC
-static short A4[32] = {
-0037523,0127633,0150301,0022031,
-0140003,0167634,0170572,0170420,
-0037505,0072364,0060672,0063220,
-0136777,0172334,0057456,0102640,
-0036063,0113125,0002476,0047251,
-0135020,0074142,0042600,0043630,
-0033577,0042230,0155372,0136105,
-0132106,0005346,0165333,0114541,
-};
-static short B4[28] = {
- /* 0040200,0000000,0000000,0000000, */
-0140132,0136320,0160433,0131535,
-0037600,0060571,0144452,0060214,
-0137025,0064310,0024220,0176472,
-0036105,0025613,0115762,0166605,
-0135030,0054662,0035454,0061763,
-0033602,0135163,0116430,0000066,
-0132106,0005345,0020602,0137133,
-};
-#endif
-#if IBMPC
-static short A4[32] = {
-0x2483,0x7a18,0x75f3,0x3fca,
-0x5e22,0x9e2f,0x7df3,0xbfe0,
-0x4cd2,0x8c37,0xae9e,0x3fc8,
-0xd0b4,0x8be5,0xfe9b,0xbf9f,
-0xc9d5,0xa0a7,0x72ca,0x3f66,
-0x08f3,0x48b0,0x0f0c,0xbf22,
-0x5789,0x1b5f,0xe893,0x3ecf,
-0x732c,0xdd5b,0xc15c,0xbe68,
-};
-static short B4[28] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0x766c,0x1c23,0x579a,0xbfeb,
-0x4c11,0x3925,0x0c2f,0x3fd0,
-0x1fa7,0x0512,0xad19,0xbfa2,
-0x5db1,0x737e,0xa571,0x3f68,
-0x8c7e,0x4765,0x0b36,0xbf23,
-0x0007,0x73a3,0x574e,0x3ed0,
-0x57cb,0xa430,0xc15c,0xbe68,
-};
-#endif
-#if MIEEE
-static short A4[32] = {
-0x3fca,0x75f3,0x7a18,0x2483,
-0xbfe0,0x7df3,0x9e2f,0x5e22,
-0x3fc8,0xae9e,0x8c37,0x4cd2,
-0xbf9f,0xfe9b,0x8be5,0xd0b4,
-0x3f66,0x72ca,0xa0a7,0xc9d5,
-0xbf22,0x0f0c,0x48b0,0x08f3,
-0x3ecf,0xe893,0x1b5f,0x5789,
-0xbe68,0xc15c,0xdd5b,0x732c,
-};
-static short B4[28] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xbfeb,0x579a,0x1c23,0x766c,
-0x3fd0,0x0c2f,0x3925,0x4c11,
-0xbfa2,0xad19,0x0512,0x1fa7,
-0x3f68,0xa571,0x737e,0x5db1,
-0xbf23,0x0b36,0x4765,0x8c7e,
-0x3ed0,0x574e,0x73a3,0x0007,
-0xbe68,0xc15c,0xa430,0x57cb,
-};
-#endif
-#endif /* 0 */
-
-/* 4 <= x <= 8
- x exp(-x) Ei(x) - 1 = 1/x A5(1/x) / B5(1/x)
- Theoretical absolute error = 2.20e-17 */
-#if UNK
-static double A5[8] = {
--1.373215375871208729803E0,
--7.084559133740838761406E-1,
- 1.580806855547941010501E0,
--2.601500427425622944234E-1,
- 2.994674694113713763365E-2,
--1.038086040188744005513E-3,
- 4.371064420753005429514E-5,
- 2.141783679522602903795E-6,
-};
-static double B5[8] = {
- /* 1.000000000000000000000E0, */
- 8.585231423622028380768E-1,
- 4.483285822873995129957E-1,
- 7.687932158124475434091E-2,
- 2.449868241021887685904E-2,
- 8.832165941927796567926E-4,
- 4.590952299511353531215E-4,
--4.729848351866523044863E-6,
- 2.665195537390710170105E-6,
-};
-#endif
-#if DEC
-static short A5[32] = {
-0140257,0142605,0076335,0113632,
-0140065,0056535,0161231,0074311,
-0040312,0053741,0004357,0076405,
-0137605,0031142,0165503,0136705,
-0036765,0051341,0053573,0007602,
-0135610,0010143,0027643,0110522,
-0034467,0052762,0062024,0120161,
-0033417,0135620,0036500,0062647,
-};
-static short B[32] = {
- /* 0040200,0000000,0000000,0000000, */
-0040133,0144054,0031516,0004100,
-0037745,0105522,0166622,0123146,
-0037235,0071347,0157560,0157464,
-0036710,0130565,0173747,0041670,
-0035547,0103651,0106243,0101240,
-0035360,0131267,0176263,0140257,
-0133636,0132426,0102537,0102531,
-0033462,0155665,0167503,0176350,
-};
-#endif
-#if IBMPC
-static short A5[32] = {
-0xb2f3,0xaf9b,0xf8b0,0xbff5,
-0x2f19,0xbc53,0xabab,0xbfe6,
-0xefa1,0x211d,0x4afc,0x3ff9,
-0x77b9,0x5d68,0xa64c,0xbfd0,
-0x61f0,0x2aef,0xaa5c,0x3f9e,
-0x722a,0x65f4,0x020c,0xbf51,
-0x940e,0x4c82,0xeabe,0x3f06,
-0x0cb5,0x07a8,0xf772,0x3ec1,
-};
-static short B5[32] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xc108,0x8669,0x7905,0x3feb,
-0x54cd,0x5db2,0xb16a,0x3fdc,
-0x1be7,0xfbee,0xae5c,0x3fb3,
-0xe877,0xbefc,0x162e,0x3f99,
-0x7054,0x3194,0xf0f5,0x3f4c,
-0x7816,0xff96,0x1656,0x3f3e,
-0xf0ab,0xd0ab,0xd6a2,0xbed3,
-0x7f9d,0xbde8,0x5b76,0x3ec6,
-};
-#endif
-#if MIEEE
-static short A5[32] = {
-0xbff5,0xf8b0,0xaf9b,0xb2f3,
-0xbfe6,0xabab,0xbc53,0x2f19,
-0x3ff9,0x4afc,0x211d,0xefa1,
-0xbfd0,0xa64c,0x5d68,0x77b9,
-0x3f9e,0xaa5c,0x2aef,0x61f0,
-0xbf51,0x020c,0x65f4,0x722a,
-0x3f06,0xeabe,0x4c82,0x940e,
-0x3ec1,0xf772,0x07a8,0x0cb5,
-};
-static short B5[32] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0x3feb,0x7905,0x8669,0xc108,
-0x3fdc,0xb16a,0x5db2,0x54cd,
-0x3fb3,0xae5c,0xfbee,0x1be7,
-0x3f99,0x162e,0xbefc,0xe877,
-0x3f4c,0xf0f5,0x3194,0x7054,
-0x3f3e,0x1656,0xff96,0x7816,
-0xbed3,0xd6a2,0xd0ab,0xf0ab,
-0x3ec6,0x5b76,0xbde8,0x7f9d,
-};
-#endif
-/* 2 <= x <= 4
- x exp(-x) Ei(x) - 1 = 1/x A6(1/x) / B6(1/x)
- Theoretical absolute error = 4.89e-17 */
-#if UNK
-static double A6[8] = {
- 1.981808503259689673238E-2,
--1.271645625984917501326E0,
--2.088160335681228318920E0,
- 2.755544509187936721172E0,
--4.409507048701600257171E-1,
- 4.665623805935891391017E-2,
--1.545042679673485262580E-3,
- 7.059980605299617478514E-5,
-};
-static double B6[7] = {
- /* 1.000000000000000000000E0, */
- 1.476498670914921440652E0,
- 5.629177174822436244827E-1,
- 1.699017897879307263248E-1,
- 2.291647179034212017463E-2,
- 4.450150439728752875043E-3,
- 1.727439612206521482874E-4,
- 3.953167195549672482304E-5,
-};
-#endif
-#if DEC
-static short A6[32] = {
-0036642,0054611,0061263,0000140,
-0140242,0142510,0125732,0072035,
-0140405,0122153,0037643,0104527,
-0040460,0055327,0055550,0116240,
-0137741,0142112,0070441,0103510,
-0037077,0015234,0104750,0146765,
-0135712,0101407,0107554,0020253,
-0034624,0007373,0072621,0063735,
-};
-static short B6[28] = {
- /* 0040200,0000000,0000000,0000000, */
-0040274,0176750,0110025,0061006,
-0040020,0015540,0021354,0155050,
-0037455,0175274,0015257,0021112,
-0036673,0135523,0016042,0117203,
-0036221,0151221,0046352,0144174,
-0035065,0021232,0117727,0152432,
-0034445,0147317,0037300,0067123,
-};
-#endif
-#if IBMPC
-static short A6[32] = {
-0x600c,0x2c56,0x4b31,0x3f94,
-0x4e84,0x157b,0x58a9,0xbff4,
-0x712b,0x67f4,0xb48d,0xc000,
-0x1394,0xeb6d,0x0b5a,0x4006,
-0x30e9,0x4e24,0x3889,0xbfdc,
-0x19bf,0x913d,0xe353,0x3fa7,
-0x8415,0xf1ed,0x5060,0xbf59,
-0x2cfc,0x6eb2,0x81df,0x3f12,
-};
-static short B6[28] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xac41,0x1202,0x9fbd,0x3ff7,
-0x9b45,0x045d,0x036c,0x3fe2,
-0xe449,0x8355,0xbf57,0x3fc5,
-0x53d0,0x6384,0x776a,0x3f97,
-0x590f,0x299d,0x3a52,0x3f72,
-0xfaa3,0x53fa,0xa453,0x3f26,
-0x0dca,0xe7d8,0xb9d9,0x3f04,
-};
-#endif
-#if MIEEE
-static short A6[32] = {
-0x3f94,0x4b31,0x2c56,0x600c,
-0xbff4,0x58a9,0x157b,0x4e84,
-0xc000,0xb48d,0x67f4,0x712b,
-0x4006,0x0b5a,0xeb6d,0x1394,
-0xbfdc,0x3889,0x4e24,0x30e9,
-0x3fa7,0xe353,0x913d,0x19bf,
-0xbf59,0x5060,0xf1ed,0x8415,
-0x3f12,0x81df,0x6eb2,0x2cfc,
-};
-static short B6[28] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0x3ff7,0x9fbd,0x1202,0xac41,
-0x3fe2,0x036c,0x045d,0x9b45,
-0x3fc5,0xbf57,0x8355,0xe449,
-0x3f97,0x776a,0x6384,0x53d0,
-0x3f72,0x3a52,0x299d,0x590f,
-0x3f26,0xa453,0x53fa,0xfaa3,
-0x3f04,0xb9d9,0xe7d8,0x0dca,
-};
-#endif
-/* 32 <= x <= 64
- x exp(-x) Ei(x) - 1 = 1/x A7(1/x) / B7(1/x)
- Theoretical absolute error = 7.71e-18 */
-#if UNK
-static double A7[6] = {
- 1.212561118105456670844E-1,
--5.823133179043894485122E-1,
- 2.348887314557016779211E-1,
--3.040034318113248237280E-2,
- 1.510082146865190661777E-3,
--2.523137095499571377122E-5,
-};
-static double B7[5] = {
- /* 1.000000000000000000000E0, */
--1.002252150365854016662E0,
- 2.928709694872224144953E-1,
--3.337004338674007801307E-2,
- 1.560544881127388842819E-3,
--2.523137093603234562648E-5,
-};
-#endif
-#if DEC
-static short A7[24] = {
-0037370,0052437,0152524,0150125,
-0140025,0011174,0050154,0131330,
-0037560,0103253,0167464,0062245,
-0136771,0005043,0174001,0023345,
-0035705,0166762,0157300,0016451,
-0134323,0123764,0157767,0134477,
-};
-static short B7[20] = {
- /* 0040200,0000000,0000000,0000000, */
-0140200,0044714,0064025,0060324,
-0037625,0171457,0003712,0073131,
-0137010,0127406,0150061,0141746,
-0035714,0105462,0072356,0103712,
-0134323,0123764,0156514,0077414,
-};
-#endif
-#if IBMPC
-static short A7[24] = {
-0x9a0b,0xfaaa,0x0aa3,0x3fbf,
-0x965b,0x8a0d,0xa24f,0xbfe2,
-0x8c95,0x7de6,0x10d5,0x3fce,
-0x24dd,0x7f00,0x2144,0xbf9f,
-0x03a5,0x5bd8,0xbdbe,0x3f58,
-0xf728,0x9bfe,0x74fe,0xbefa,
-};
-static short B7[20] = {
- /* 0x0000,0x0000,0x0000,0x3ff0, */
-0xac1a,0x8d02,0x0939,0xbff0,
-0x4ecb,0xe0f9,0xbe65,0x3fd2,
-0x387d,0xda06,0x15e0,0xbfa1,
-0xd0f9,0x4e9d,0x9166,0x3f59,
-0x8fe2,0x9ba9,0x74fe,0xbefa,
-};
-#endif
-#if MIEEE
-static short A7[24] = {
-0x3fbf,0x0aa3,0xfaaa,0x9a0b,
-0xbfe2,0xa24f,0x8a0d,0x965b,
-0x3fce,0x10d5,0x7de6,0x8c95,
-0xbf9f,0x2144,0x7f00,0x24dd,
-0x3f58,0xbdbe,0x5bd8,0x03a5,
-0xbefa,0x74fe,0x9bfe,0xf728,
-};
-static short B7[20] = {
- /* 0x3ff0,0x0000,0x0000,0x0000, */
-0xbff0,0x0939,0x8d02,0xac1a,
-0x3fd2,0xbe65,0xe0f9,0x4ecb,
-0xbfa1,0x15e0,0xda06,0x387d,
-0x3f59,0x9166,0x4e9d,0xd0f9,
-0xbefa,0x74fe,0x9ba9,0x8fe2,
-};
-#endif
-
-double ei (x)
-double x;
-{
- double f, w;
-
- if (x <= 0.0)
- {
- mtherr("ei", DOMAIN);
- return 0.0;
- }
- else if (x < 2.0)
- {
- /* Power series.
- inf n
- - x
- Ei(x) = EUL + ln x + > ----
- - n n!
- n=1
- */
- f = polevl(x,A,5) / p1evl(x,B,6);
- /* f = polevl(x,A,6) / p1evl(x,B,7); */
- /* f = polevl(x,A,8) / p1evl(x,B,9); */
- return (EUL + log(x) + x * f);
- }
- else if (x < 4.0)
- {
- /* Asymptotic expansion.
- 1 2 6
- x exp(-x) Ei(x) = 1 + --- + --- + ---- + ...
- x 2 3
- x x
- */
- w = 1.0/x;
- f = polevl(w,A6,7) / p1evl(w,B6,7);
- return (exp(x) * w * (1.0 + w * f));
- }
- else if (x < 8.0)
- {
- w = 1.0/x;
- f = polevl(w,A5,7) / p1evl(w,B5,8);
- return (exp(x) * w * (1.0 + w * f));
- }
- else if (x < 16.0)
- {
- w = 1.0/x;
- f = polevl(w,A2,9) / p1evl(w,B2,9);
- return (exp(x) * w * (1.0 + w * f));
- }
- else if (x < 32.0)
- {
- w = 1.0/x;
- f = polevl(w,A4,7) / p1evl(w,B4,8);
- return (exp(x) * w * (1.0 + w * f));
- }
- else if (x < 64.0)
- {
- w = 1.0/x;
- f = polevl(w,A7,5) / p1evl(w,B7,5);
- return (exp(x) * w * (1.0 + w * f));
- }
- else
- {
- w = 1.0/x;
- f = polevl(w,A3,8) / p1evl(w,B3,9);
- return (exp(x) * w * (1.0 + w * f));
- }
-}
+++ /dev/null
-/* eigens.c
- *
- * Eigenvalues and eigenvectors of a real symmetric matrix
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double A[n*(n+1)/2], EV[n*n], E[n];
- * void eigens( A, EV, E, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * The algorithm is due to J. vonNeumann.
- *
- * A[] is a symmetric matrix stored in lower triangular form.
- * That is, A[ row, column ] = A[ (row*row+row)/2 + column ]
- * or equivalently with row and column interchanged. The
- * indices row and column run from 0 through n-1.
- *
- * EV[] is the output matrix of eigenvectors stored columnwise.
- * That is, the elements of each eigenvector appear in sequential
- * memory order. The jth element of the ith eigenvector is
- * EV[ n*i+j ] = EV[i][j].
- *
- * E[] is the output matrix of eigenvalues. The ith element
- * of E corresponds to the ith eigenvector (the ith row of EV).
- *
- * On output, the matrix A will have been diagonalized and its
- * orginal contents are destroyed.
- *
- * ACCURACY:
- *
- * The error is controlled by an internal parameter called RANGE
- * which is set to 1e-10. After diagonalization, the
- * off-diagonal elements of A will have been reduced by
- * this factor.
- *
- * ERROR MESSAGES:
- *
- * None.
- *
- */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double fabs ( double );
-#else
-double sqrt(), fabs();
-#endif
-
-void eigens( A, RR, E, N )
-double A[], RR[], E[];
-int N;
-{
-int IND, L, LL, LM, M, MM, MQ, I, J, IA, LQ;
-int IQ, IM, IL, NLI, NMI;
-double ANORM, ANORMX, AIA, THR, ALM, ALL, AMM, X, Y;
-double SINX, SINX2, COSX, COSX2, SINCS, AIL, AIM;
-double RLI, RMI;
-static double RANGE = 1.0e-10; /*3.0517578e-5;*/
-
-
-/* Initialize identity matrix in RR[] */
-for( J=0; J<N*N; J++ )
- RR[J] = 0.0;
-MM = 0;
-for( J=0; J<N; J++ )
- {
- RR[MM + J] = 1.0;
- MM += N;
- }
-
-ANORM=0.0;
-for( I=0; I<N; I++ )
- {
- for( J=0; J<N; J++ )
- {
- if( I != J )
- {
- IA = I + (J*J+J)/2;
- AIA = A[IA];
- ANORM += AIA * AIA;
- }
- }
- }
-if( ANORM <= 0.0 )
- goto done;
-ANORM = sqrt( ANORM + ANORM );
-ANORMX = ANORM * RANGE / N;
-THR = ANORM;
-
-while( THR > ANORMX )
-{
-THR=THR/N;
-
-do
-{ /* while IND != 0 */
-IND = 0;
-
-for( L=0; L<N-1; L++ )
- {
-
-for( M=L+1; M<N; M++ )
- {
- MQ=(M*M+M)/2;
- LM=L+MQ;
- ALM=A[LM];
- if( fabs(ALM) < THR )
- continue;
-
- IND=1;
- LQ=(L*L+L)/2;
- LL=L+LQ;
- MM=M+MQ;
- ALL=A[LL];
- AMM=A[MM];
- X=(ALL-AMM)/2.0;
- Y=-ALM/sqrt(ALM*ALM+X*X);
- if(X < 0.0)
- Y=-Y;
- SINX = Y / sqrt( 2.0 * (1.0 + sqrt( 1.0-Y*Y)) );
- SINX2=SINX*SINX;
- COSX=sqrt(1.0-SINX2);
- COSX2=COSX*COSX;
- SINCS=SINX*COSX;
-
-/* ROTATE L AND M COLUMNS */
-for( I=0; I<N; I++ )
- {
- IQ=(I*I+I)/2;
- if( (I != M) && (I != L) )
- {
- if(I > M)
- IM=M+IQ;
- else
- IM=I+MQ;
- if(I >= L)
- IL=L+IQ;
- else
- IL=I+LQ;
- AIL=A[IL];
- AIM=A[IM];
- X=AIL*COSX-AIM*SINX;
- A[IM]=AIL*SINX+AIM*COSX;
- A[IL]=X;
- }
- NLI = N*L + I;
- NMI = N*M + I;
- RLI = RR[ NLI ];
- RMI = RR[ NMI ];
- RR[NLI]=RLI*COSX-RMI*SINX;
- RR[NMI]=RLI*SINX+RMI*COSX;
- }
-
- X=2.0*ALM*SINCS;
- A[LL]=ALL*COSX2+AMM*SINX2-X;
- A[MM]=ALL*SINX2+AMM*COSX2+X;
- A[LM]=(ALL-AMM)*SINCS+ALM*(COSX2-SINX2);
- } /* for M=L+1 to N-1 */
- } /* for L=0 to N-2 */
-
- }
-while( IND != 0 );
-
-} /* while THR > ANORMX */
-
-done: ;
-
-/* Extract eigenvalues from the reduced matrix */
-L=0;
-for( J=1; J<=N; J++ )
- {
- L=L+J;
- E[J-1]=A[L-1];
- }
-}
+++ /dev/null
-/* ellie.c
- *
- * Incomplete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double phi, m, y, ellie();
- *
- * y = ellie( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * phi
- * -
- * | |
- * | 2
- * E(phi_\m) = | sqrt( 1 - m sin t ) dt
- * |
- * | |
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random arguments with phi in [-10, 10] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,2 2000 1.9e-16 3.4e-17
- * IEEE -10,10 150000 3.3e-15 1.4e-16
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1993, 2000 by Stephen L. Moshier
-*/
-
-/* Incomplete elliptic integral of second kind */
-#include <math.h>
-extern double PI, PIO2, MACHEP;
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double sin ( double x );
-extern double tan ( double x );
-extern double atan ( double );
-extern double floor ( double );
-extern double ellpe ( double );
-extern double ellpk ( double );
-double ellie ( double, double );
-#else
-double sqrt(), fabs(), log(), sin(), tan(), atan(), floor();
-double ellpe(), ellpk(), ellie();
-#endif
-
-double ellie( phi, m )
-double phi, m;
-{
-double a, b, c, e, temp;
-double lphi, t, E;
-int d, mod, npio2, sign;
-
-if( m == 0.0 )
- return( phi );
-lphi = phi;
-npio2 = floor( lphi/PIO2 );
-if( npio2 & 1 )
- npio2 += 1;
-lphi = lphi - npio2 * PIO2;
-if( lphi < 0.0 )
- {
- lphi = -lphi;
- sign = -1;
- }
-else
- {
- sign = 1;
- }
-a = 1.0 - m;
-E = ellpe( a );
-if( a == 0.0 )
- {
- temp = sin( lphi );
- goto done;
- }
-t = tan( lphi );
-b = sqrt(a);
-/* Thanks to Brian Fitzgerald <fitzgb@mml0.meche.rpi.edu>
- for pointing out an instability near odd multiples of pi/2. */
-if( fabs(t) > 10.0 )
- {
- /* Transform the amplitude */
- e = 1.0/(b*t);
- /* ... but avoid multiple recursions. */
- if( fabs(e) < 10.0 )
- {
- e = atan(e);
- temp = E + m * sin( lphi ) * sin( e ) - ellie( e, m );
- goto done;
- }
- }
-c = sqrt(m);
-a = 1.0;
-d = 1;
-e = 0.0;
-mod = 0;
-
-while( fabs(c/a) > MACHEP )
- {
- temp = b/a;
- lphi = lphi + atan(t*temp) + mod * PI;
- mod = (lphi + PIO2)/PI;
- t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
- c = ( a - b )/2.0;
- temp = sqrt( a * b );
- a = ( a + b )/2.0;
- b = temp;
- d += d;
- e += c * sin(lphi);
- }
-
-temp = E / ellpk( 1.0 - m );
-temp *= (atan(t) + mod * PI)/(d * a);
-temp += e;
-
-done:
-
-if( sign < 0 )
- temp = -temp;
-temp += npio2 * E;
-return( temp );
-}
+++ /dev/null
-/* ellik.c
- *
- * Incomplete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double phi, m, y, ellik();
- *
- * y = ellik( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * phi
- * -
- * | |
- * | dt
- * F(phi_\m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points with m in [0, 1] and phi as indicated.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 200000 7.4e-16 1.0e-16
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-/* Incomplete elliptic integral of first kind */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double tan ( double );
-extern double atan ( double );
-extern double floor ( double );
-extern double ellpk ( double );
-double ellik ( double, double );
-#else
-double sqrt(), fabs(), log(), tan(), atan(), floor(), ellpk();
-double ellik();
-#endif
-extern double PI, PIO2, MACHEP, MAXNUM;
-
-double ellik( phi, m )
-double phi, m;
-{
-double a, b, c, e, temp, t, K;
-int d, mod, sign, npio2;
-
-if( m == 0.0 )
- return( phi );
-a = 1.0 - m;
-if( a == 0.0 )
- {
- if( fabs(phi) >= PIO2 )
- {
- mtherr( "ellik", SING );
- return( MAXNUM );
- }
- return( log( tan( (PIO2 + phi)/2.0 ) ) );
- }
-npio2 = floor( phi/PIO2 );
-if( npio2 & 1 )
- npio2 += 1;
-if( npio2 )
- {
- K = ellpk( a );
- phi = phi - npio2 * PIO2;
- }
-else
- K = 0.0;
-if( phi < 0.0 )
- {
- phi = -phi;
- sign = -1;
- }
-else
- sign = 0;
-b = sqrt(a);
-t = tan( phi );
-if( fabs(t) > 10.0 )
- {
- /* Transform the amplitude */
- e = 1.0/(b*t);
- /* ... but avoid multiple recursions. */
- if( fabs(e) < 10.0 )
- {
- e = atan(e);
- if( npio2 == 0 )
- K = ellpk( a );
- temp = K - ellik( e, m );
- goto done;
- }
- }
-a = 1.0;
-c = sqrt(m);
-d = 1;
-mod = 0;
-
-while( fabs(c/a) > MACHEP )
- {
- temp = b/a;
- phi = phi + atan(t*temp) + mod * PI;
- mod = (phi + PIO2)/PI;
- t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
- c = ( a - b )/2.0;
- temp = sqrt( a * b );
- a = ( a + b )/2.0;
- b = temp;
- d += d;
- }
-
-temp = (atan(t) + mod * PI)/(d * a);
-
-done:
-if( sign < 0 )
- temp = -temp;
-temp += npio2 * K;
-return( temp );
-}
+++ /dev/null
-/* ellpe.c
- *
- * Complete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double m1, y, ellpe();
- *
- * y = ellpe( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * pi/2
- * -
- * | | 2
- * E(m) = | sqrt( 1 - m sin t ) dt
- * | |
- * -
- * 0
- *
- * Where m = 1 - m1, using the approximation
- *
- * P(x) - x log x Q(x).
- *
- * Though there are no singularities, the argument m1 is used
- * rather than m for compatibility with ellpk().
- *
- * E(1) = 1; E(0) = pi/2.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 1 13000 3.1e-17 9.4e-18
- * IEEE 0, 1 10000 2.1e-16 7.3e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpe domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpe.c */
-
-/* Elliptic integral of second kind */
-
-/*
-Cephes Math Library, Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
- 1.53552577301013293365E-4,
- 2.50888492163602060990E-3,
- 8.68786816565889628429E-3,
- 1.07350949056076193403E-2,
- 7.77395492516787092951E-3,
- 7.58395289413514708519E-3,
- 1.15688436810574127319E-2,
- 2.18317996015557253103E-2,
- 5.68051945617860553470E-2,
- 4.43147180560990850618E-1,
- 1.00000000000000000299E0
-};
-static double Q[] = {
- 3.27954898576485872656E-5,
- 1.00962792679356715133E-3,
- 6.50609489976927491433E-3,
- 1.68862163993311317300E-2,
- 2.61769742454493659583E-2,
- 3.34833904888224918614E-2,
- 4.27180926518931511717E-2,
- 5.85936634471101055642E-2,
- 9.37499997197644278445E-2,
- 2.49999999999888314361E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0035041,0001364,0141572,0117555,
-0036044,0066032,0130027,0033404,
-0036416,0053617,0064456,0102632,
-0036457,0161100,0061177,0122612,
-0036376,0136251,0012403,0124162,
-0036370,0101316,0151715,0131613,
-0036475,0105477,0050317,0133272,
-0036662,0154232,0024645,0171552,
-0037150,0126220,0047054,0030064,
-0037742,0162057,0167645,0165612,
-0040200,0000000,0000000,0000000
-};
-static unsigned short Q[] = {
-0034411,0106743,0115771,0055462,
-0035604,0052575,0155171,0045540,
-0036325,0030424,0064332,0167756,
-0036612,0052366,0063006,0115175,
-0036726,0070430,0004533,0124654,
-0037011,0022741,0030675,0030711,
-0037056,0174452,0127062,0132122,
-0037157,0177750,0142041,0072523,
-0037277,0177777,0173137,0002627,
-0037577,0177777,0177777,0101101
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x53ee,0x986f,0x205e,0x3f24,
-0xe6e0,0x5602,0x8d83,0x3f64,
-0xd0b3,0xed25,0xcaf1,0x3f81,
-0xf4b1,0x0c4f,0xfc48,0x3f85,
-0x750e,0x22a0,0xd795,0x3f7f,
-0xb671,0xda79,0x1059,0x3f7f,
-0xf6d7,0xea19,0xb167,0x3f87,
-0xbe6d,0x4534,0x5b13,0x3f96,
-0x8607,0x09c5,0x1592,0x3fad,
-0xbd71,0xfdf4,0x5c85,0x3fdc,
-0x0000,0x0000,0x0000,0x3ff0
-};
-static unsigned short Q[] = {
-0x2b66,0x737f,0x31bc,0x3f01,
-0x296c,0xbb4f,0x8aaf,0x3f50,
-0x5dfe,0x8d1b,0xa622,0x3f7a,
-0xd350,0xccc0,0x4a9e,0x3f91,
-0x7535,0x012b,0xce23,0x3f9a,
-0xa639,0x2637,0x24bc,0x3fa1,
-0x568a,0x55c6,0xdf25,0x3fa5,
-0x2eaa,0x1884,0xfffd,0x3fad,
-0xe0b3,0xfecb,0xffff,0x3fb7,
-0xf048,0xffff,0xffff,0x3fcf
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f24,0x205e,0x986f,0x53ee,
-0x3f64,0x8d83,0x5602,0xe6e0,
-0x3f81,0xcaf1,0xed25,0xd0b3,
-0x3f85,0xfc48,0x0c4f,0xf4b1,
-0x3f7f,0xd795,0x22a0,0x750e,
-0x3f7f,0x1059,0xda79,0xb671,
-0x3f87,0xb167,0xea19,0xf6d7,
-0x3f96,0x5b13,0x4534,0xbe6d,
-0x3fad,0x1592,0x09c5,0x8607,
-0x3fdc,0x5c85,0xfdf4,0xbd71,
-0x3ff0,0x0000,0x0000,0x0000
-};
-static unsigned short Q[] = {
-0x3f01,0x31bc,0x737f,0x2b66,
-0x3f50,0x8aaf,0xbb4f,0x296c,
-0x3f7a,0xa622,0x8d1b,0x5dfe,
-0x3f91,0x4a9e,0xccc0,0xd350,
-0x3f9a,0xce23,0x012b,0x7535,
-0x3fa1,0x24bc,0x2637,0xa639,
-0x3fa5,0xdf25,0x55c6,0x568a,
-0x3fad,0xfffd,0x1884,0x2eaa,
-0x3fb7,0xffff,0xfecb,0xe0b3,
-0x3fcf,0xffff,0xffff,0xf048
-};
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double log ( double );
-#else
-double polevl(), log();
-#endif
-
-double ellpe(x)
-double x;
-{
-
-if( (x <= 0.0) || (x > 1.0) )
- {
- if( x == 0.0 )
- return( 1.0 );
- mtherr( "ellpe", DOMAIN );
- return( 0.0 );
- }
-return( polevl(x,P,10) - log(x) * (x * polevl(x,Q,9)) );
-}
+++ /dev/null
-/* ellpj.c
- *
- * Jacobian Elliptic Functions
- *
- *
- *
- * SYNOPSIS:
- *
- * double u, m, sn, cn, dn, phi;
- * int ellpj();
- *
- * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
- * and dn(u|m) of parameter m between 0 and 1, and real
- * argument u.
- *
- * These functions are periodic, with quarter-period on the
- * real axis equal to the complete elliptic integral
- * ellpk(1.0-m).
- *
- * Relation to incomplete elliptic integral:
- * If u = ellik(phi,m), then sn(u|m) = sin(phi),
- * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
- *
- * Computation is by means of the arithmetic-geometric mean
- * algorithm, except when m is within 1e-9 of 0 or 1. In the
- * latter case with m close to 1, the approximation applies
- * only for phi < pi/2.
- *
- * ACCURACY:
- *
- * Tested at random points with u between 0 and 10, m between
- * 0 and 1.
- *
- * Absolute error (* = relative error):
- * arithmetic function # trials peak rms
- * DEC sn 1800 4.5e-16 8.7e-17
- * IEEE phi 10000 9.2e-16* 1.4e-16*
- * IEEE sn 50000 4.1e-15 4.6e-16
- * IEEE cn 40000 3.6e-15 4.4e-16
- * IEEE dn 10000 1.3e-12 1.8e-14
- *
- * Peak error observed in consistency check using addition
- * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
- * the above relation to the incomplete elliptic integral.
- * Accuracy deteriorates when u is large.
- *
- */
-\f
-/* ellpj.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern double asin ( double );
-extern double tanh ( double );
-extern double sinh ( double );
-extern double cosh ( double );
-extern double atan ( double );
-extern double exp ( double );
-#else
-double sqrt(), fabs(), sin(), cos(), asin(), tanh();
-double sinh(), cosh(), atan(), exp();
-#endif
-extern double PIO2, MACHEP;
-
-int ellpj( u, m, sn, cn, dn, ph )
-double u, m;
-double *sn, *cn, *dn, *ph;
-{
-double ai, b, phi, t, twon;
-double a[9], c[9];
-int i;
-
-
-/* Check for special cases */
-
-if( m < 0.0 || m > 1.0 )
- {
- mtherr( "ellpj", DOMAIN );
- *sn = 0.0;
- *cn = 0.0;
- *ph = 0.0;
- *dn = 0.0;
- return(-1);
- }
-if( m < 1.0e-9 )
- {
- t = sin(u);
- b = cos(u);
- ai = 0.25 * m * (u - t*b);
- *sn = t - ai*b;
- *cn = b + ai*t;
- *ph = u - ai;
- *dn = 1.0 - 0.5*m*t*t;
- return(0);
- }
-
-if( m >= 0.9999999999 )
- {
- ai = 0.25 * (1.0-m);
- b = cosh(u);
- t = tanh(u);
- phi = 1.0/b;
- twon = b * sinh(u);
- *sn = t + ai * (twon - u)/(b*b);
- *ph = 2.0*atan(exp(u)) - PIO2 + ai*(twon - u)/b;
- ai *= t * phi;
- *cn = phi - ai * (twon - u);
- *dn = phi + ai * (twon + u);
- return(0);
- }
-
-
-/* A. G. M. scale */
-a[0] = 1.0;
-b = sqrt(1.0 - m);
-c[0] = sqrt(m);
-twon = 1.0;
-i = 0;
-
-while( fabs(c[i]/a[i]) > MACHEP )
- {
- if( i > 7 )
- {
- mtherr( "ellpj", OVERFLOW );
- goto done;
- }
- ai = a[i];
- ++i;
- c[i] = ( ai - b )/2.0;
- t = sqrt( ai * b );
- a[i] = ( ai + b )/2.0;
- b = t;
- twon *= 2.0;
- }
-
-done:
-
-/* backward recurrence */
-phi = twon * a[i] * u;
-do
- {
- t = c[i] * sin(phi) / a[i];
- b = phi;
- phi = (asin(t) + phi)/2.0;
- }
-while( --i );
-
-*sn = sin(phi);
-t = cos(phi);
-*cn = t;
-*dn = t/cos(phi-b);
-*ph = phi;
-return(0);
-}
+++ /dev/null
-/* ellpk.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double m1, y, ellpk();
- *
- * y = ellpk( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * pi/2
- * -
- * | |
- * | dt
- * K(m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * where m = 1 - m1, using the approximation
- *
- * P(x) - log x Q(x).
- *
- * The argument m1 is used rather than m so that the logarithmic
- * singularity at m = 1 will be shifted to the origin; this
- * preserves maximum accuracy.
- *
- * K(0) = pi/2.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,1 16000 3.5e-17 1.1e-17
- * IEEE 0,1 30000 2.5e-16 6.8e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpk domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpk.c */
-
-
-/*
-Cephes Math Library, Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef DEC
-static unsigned short P[] =
-{
-0035020,0127576,0040430,0051544,
-0036025,0070136,0042703,0153716,
-0036402,0122614,0062555,0077777,
-0036441,0102130,0072334,0025172,
-0036341,0043320,0117242,0172076,
-0036312,0146456,0077242,0154141,
-0036420,0003467,0013727,0035407,
-0036564,0137263,0110651,0020237,
-0036775,0001330,0144056,0020305,
-0037305,0144137,0157521,0141734,
-0040261,0071027,0173721,0147572
-};
-static unsigned short Q[] =
-{
-0034366,0130371,0103453,0077633,
-0035557,0122745,0173515,0113016,
-0036302,0124470,0167304,0074473,
-0036575,0132403,0117226,0117576,
-0036703,0156271,0047124,0147733,
-0036766,0137465,0002053,0157312,
-0037031,0014423,0154274,0176515,
-0037107,0177747,0143216,0016145,
-0037217,0177777,0172621,0074000,
-0037377,0177777,0177776,0156435,
-0040000,0000000,0000000,0000000
-};
-static unsigned short ac1[] = {0040261,0071027,0173721,0147572};
-#define C1 (*(double *)ac1)
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] =
-{
-0x0a6d,0xc823,0x15ef,0x3f22,
-0x7afa,0xc8b8,0xae0b,0x3f62,
-0xb000,0x8cad,0x54b1,0x3f80,
-0x854f,0x0e9b,0x308b,0x3f84,
-0x5e88,0x13d4,0x28da,0x3f7c,
-0x5b0c,0xcfd4,0x59a5,0x3f79,
-0xe761,0xe2fa,0x00e6,0x3f82,
-0x2414,0x7235,0x97d6,0x3f8e,
-0xc419,0x1905,0xa05b,0x3f9f,
-0x387c,0xfbea,0xb90b,0x3fb8,
-0x39ef,0xfefa,0x2e42,0x3ff6
-};
-static unsigned short Q[] =
-{
-0x6ff3,0x30e5,0xd61f,0x3efe,
-0xb2c2,0xbee9,0xf4bc,0x3f4d,
-0x8f27,0x1dd8,0x5527,0x3f78,
-0xd3f0,0x73d2,0xb6a0,0x3f8f,
-0x99fb,0x29ca,0x7b97,0x3f98,
-0x7bd9,0xa085,0xd7e6,0x3f9e,
-0x9faa,0x7b17,0x2322,0x3fa3,
-0xc38d,0xf8d1,0xfffc,0x3fa8,
-0x2f00,0xfeb2,0xffff,0x3fb1,
-0xdba4,0xffff,0xffff,0x3fbf,
-0x0000,0x0000,0x0000,0x3fe0
-};
-static unsigned short ac1[] = {0x39ef,0xfefa,0x2e42,0x3ff6};
-#define C1 (*(double *)ac1)
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] =
-{
-0x3f22,0x15ef,0xc823,0x0a6d,
-0x3f62,0xae0b,0xc8b8,0x7afa,
-0x3f80,0x54b1,0x8cad,0xb000,
-0x3f84,0x308b,0x0e9b,0x854f,
-0x3f7c,0x28da,0x13d4,0x5e88,
-0x3f79,0x59a5,0xcfd4,0x5b0c,
-0x3f82,0x00e6,0xe2fa,0xe761,
-0x3f8e,0x97d6,0x7235,0x2414,
-0x3f9f,0xa05b,0x1905,0xc419,
-0x3fb8,0xb90b,0xfbea,0x387c,
-0x3ff6,0x2e42,0xfefa,0x39ef
-};
-static unsigned short Q[] =
-{
-0x3efe,0xd61f,0x30e5,0x6ff3,
-0x3f4d,0xf4bc,0xbee9,0xb2c2,
-0x3f78,0x5527,0x1dd8,0x8f27,
-0x3f8f,0xb6a0,0x73d2,0xd3f0,
-0x3f98,0x7b97,0x29ca,0x99fb,
-0x3f9e,0xd7e6,0xa085,0x7bd9,
-0x3fa3,0x2322,0x7b17,0x9faa,
-0x3fa8,0xfffc,0xf8d1,0xc38d,
-0x3fb1,0xffff,0xfeb2,0x2f00,
-0x3fbf,0xffff,0xffff,0xdba4,
-0x3fe0,0x0000,0x0000,0x0000
-};
-static unsigned short ac1[] = {
-0x3ff6,0x2e42,0xfefa,0x39ef
-};
-#define C1 (*(double *)ac1)
-#endif
-
-#ifdef UNK
-static double P[] =
-{
- 1.37982864606273237150E-4,
- 2.28025724005875567385E-3,
- 7.97404013220415179367E-3,
- 9.85821379021226008714E-3,
- 6.87489687449949877925E-3,
- 6.18901033637687613229E-3,
- 8.79078273952743772254E-3,
- 1.49380448916805252718E-2,
- 3.08851465246711995998E-2,
- 9.65735902811690126535E-2,
- 1.38629436111989062502E0
-};
-
-static double Q[] =
-{
- 2.94078955048598507511E-5,
- 9.14184723865917226571E-4,
- 5.94058303753167793257E-3,
- 1.54850516649762399335E-2,
- 2.39089602715924892727E-2,
- 3.01204715227604046988E-2,
- 3.73774314173823228969E-2,
- 4.88280347570998239232E-2,
- 7.03124996963957469739E-2,
- 1.24999999999870820058E-1,
- 4.99999999999999999821E-1
-};
-static double C1 = 1.3862943611198906188E0; /* log(4) */
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-#else
-double polevl(), p1evl(), log();
-#endif
-extern double MACHEP, MAXNUM;
-
-double ellpk(x)
-double x;
-{
-
-if( (x < 0.0) || (x > 1.0) )
- {
- mtherr( "ellpk", DOMAIN );
- return( 0.0 );
- }
-
-if( x > MACHEP )
- {
- return( polevl(x,P,10) - log(x) * polevl(x,Q,10) );
- }
-else
- {
- if( x == 0.0 )
- {
- mtherr( "ellpk", SING );
- return( MAXNUM );
- }
- else
- {
- return( C1 - 0.5 * log(x) );
- }
- }
-}
+++ /dev/null
-extern double MACHEP, PIO2, PI;
-double ellie(), ellpe(), floor(), fabs();
-double ellie2();
-
-main()
-{
-double y, m, phi, e, E, phipi, y1;
-int i, j, npi;
-
-/* dprec(); */
-m = 0.9;
-E = ellpe(0.1);
-for( j=-10; j<=10; j++ )
- {
- printf( "%d * PIO2\n", j );
- for( i=-2; i<=2; i++ )
- {
- phi = PIO2 * j + 50 * MACHEP * i;
- npi = floor(phi/PIO2);
- if( npi & 1 )
- npi += 1;
- phipi = phi - npi * PIO2;
- npi = floor(phi/PIO2);
- if( npi & 1 )
- npi += 1;
- phipi = phi - npi * PIO2;
- printf( "phi %.9e npi %d ", phi, npi );
- y1 = E * npi + ellie(phipi,m);
- y = ellie2( phi, m );
- printf( "y %.9e ", y );
- e = fabs(y - y1);
- if( y1 != 0.0 )
- e /= y1;
- printf( "e %.4e\n", e );
- }
- }
-}
+++ /dev/null
-/* euclid.c
- *
- * Rational arithmetic routines
- *
- *
- *
- * SYNOPSIS:
- *
- *
- * typedef struct
- * {
- * double n; numerator
- * double d; denominator
- * }fract;
- *
- * radd( a, b, c ) c = b + a
- * rsub( a, b, c ) c = b - a
- * rmul( a, b, c ) c = b * a
- * rdiv( a, b, c ) c = b / a
- * euclid( &n, &d ) Reduce n/d to lowest terms,
- * return greatest common divisor.
- *
- * Arguments of the routines are pointers to the structures.
- * The double precision numbers are assumed, without checking,
- * to be integer valued. Overflow conditions are reported.
- */
- \f
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double floor ( double );
-double euclid( double *, double * );
-#else
-double fabs(), floor(), euclid();
-#endif
-
-extern double MACHEP;
-#define BIG (1.0/MACHEP)
-
-typedef struct
- {
- double n; /* numerator */
- double d; /* denominator */
- }fract;
-
-/* Add fractions. */
-
-void radd( f1, f2, f3 )
-fract *f1, *f2, *f3;
-{
-double gcd, d1, d2, gcn, n1, n2;
-
-n1 = f1->n;
-d1 = f1->d;
-n2 = f2->n;
-d2 = f2->d;
-if( n1 == 0.0 )
- {
- f3->n = n2;
- f3->d = d2;
- return;
- }
-if( n2 == 0.0 )
- {
- f3->n = n1;
- f3->d = d1;
- return;
- }
-
-gcd = euclid( &d1, &d2 ); /* common divisors of denominators */
-gcn = euclid( &n1, &n2 ); /* common divisors of numerators */
-/* Note, factoring the numerators
- * makes overflow slightly less likely.
- */
-f3->n = ( n1 * d2 + n2 * d1) * gcn;
-f3->d = d1 * d2 * gcd;
-euclid( &f3->n, &f3->d );
-}
-
-
-/* Subtract fractions. */
-
-void rsub( f1, f2, f3 )
-fract *f1, *f2, *f3;
-{
-double gcd, d1, d2, gcn, n1, n2;
-
-n1 = f1->n;
-d1 = f1->d;
-n2 = f2->n;
-d2 = f2->d;
-if( n1 == 0.0 )
- {
- f3->n = n2;
- f3->d = d2;
- return;
- }
-if( n2 == 0.0 )
- {
- f3->n = -n1;
- f3->d = d1;
- return;
- }
-
-gcd = euclid( &d1, &d2 );
-gcn = euclid( &n1, &n2 );
-f3->n = (n2 * d1 - n1 * d2) * gcn;
-f3->d = d1 * d2 * gcd;
-euclid( &f3->n, &f3->d );
-}
-
-
-
-
-/* Multiply fractions. */
-
-void rmul( ff1, ff2, ff3 )
-fract *ff1, *ff2, *ff3;
-{
-double d1, d2, n1, n2;
-
-n1 = ff1->n;
-d1 = ff1->d;
-n2 = ff2->n;
-d2 = ff2->d;
-
-if( (n1 == 0.0) || (n2 == 0.0) )
- {
- ff3->n = 0.0;
- ff3->d = 1.0;
- return;
- }
-euclid( &n1, &d2 ); /* cross cancel common divisors */
-euclid( &n2, &d1 );
-ff3->n = n1 * n2;
-ff3->d = d1 * d2;
-/* Report overflow. */
-if( (fabs(ff3->n) >= BIG) || (fabs(ff3->d) >= BIG) )
- {
- mtherr( "rmul", OVERFLOW );
- return;
- }
-/* euclid( &ff3->n, &ff3->d );*/
-}
-
-
-
-/* Divide fractions. */
-
-void rdiv( ff1, ff2, ff3 )
-fract *ff1, *ff2, *ff3;
-{
-double d1, d2, n1, n2;
-
-n1 = ff1->d; /* Invert ff1, then multiply */
-d1 = ff1->n;
-if( d1 < 0.0 )
- { /* keep denominator positive */
- n1 = -n1;
- d1 = -d1;
- }
-n2 = ff2->n;
-d2 = ff2->d;
-if( (n1 == 0.0) || (n2 == 0.0) )
- {
- ff3->n = 0.0;
- ff3->d = 1.0;
- return;
- }
-
-euclid( &n1, &d2 ); /* cross cancel any common divisors */
-euclid( &n2, &d1 );
-ff3->n = n1 * n2;
-ff3->d = d1 * d2;
-/* Report overflow. */
-if( (fabs(ff3->n) >= BIG) || (fabs(ff3->d) >= BIG) )
- {
- mtherr( "rdiv", OVERFLOW );
- return;
- }
-/* euclid( &ff3->n, &ff3->d );*/
-}
-
-
-
-
-
-/* Euclidean algorithm
- * reduces fraction to lowest terms,
- * returns greatest common divisor.
- */
-
-
-double euclid( num, den )
-double *num, *den;
-{
-double n, d, q, r;
-
-n = *num; /* Numerator. */
-d = *den; /* Denominator. */
-
-/* Make numbers positive, locally. */
-if( n < 0.0 )
- n = -n;
-if( d < 0.0 )
- d = -d;
-
-/* Abort if numbers are too big for integer arithmetic. */
-if( (n >= BIG) || (d >= BIG) )
- {
- mtherr( "euclid", OVERFLOW );
- return(1.0);
- }
-
-/* Divide by zero, gcd = 1. */
-if(d == 0.0)
- return( 1.0 );
-
-/* Zero. Return 0/1, gcd = denominator. */
-if(n == 0.0)
- {
-/*
- if( *den < 0.0 )
- *den = -1.0;
- else
- *den = 1.0;
-*/
- *den = 1.0;
- return( d );
- }
-
-while( d > 0.5 )
- {
-/* Find integer part of n divided by d. */
- q = floor( n/d );
-/* Find remainder after dividing n by d. */
- r = n - d * q;
-/* The next fraction is d/r. */
- n = d;
- d = r;
- }
-
-if( n < 0.0 )
- mtherr( "euclid", UNDERFLOW );
-
-*num /= n;
-*den /= n;
-return( n );
-}
-
+++ /dev/null
-/* exp.c
- *
- * Exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, exp();
- *
- * y = exp( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns e (2.71828...) raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- *
- * x k f
- * e = 2 e.
- *
- * A Pade' form 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- * of degree 2/3 is used to approximate exp(f) in the basic
- * interval [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +- 88 50000 2.8e-17 7.0e-18
- * IEEE +- 708 40000 2.0e-16 5.6e-17
- *
- *
- * Error amplification in the exponential function can be
- * a serious matter. The error propagation involves
- * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
- * which shows that a 1 lsb error in representing X produces
- * a relative error of X times 1 lsb in the function.
- * While the routine gives an accurate result for arguments
- * that are exactly represented by a double precision
- * computer number, the result contains amplified roundoff
- * error for large arguments not exactly represented.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < MINLOG 0.0
- * exp overflow x > MAXLOG INFINITY
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-/* Exponential function */
-
-#include <math.h>
-
-#ifdef UNK
-
-static double P[] = {
- 1.26177193074810590878E-4,
- 3.02994407707441961300E-2,
- 9.99999999999999999910E-1,
-};
-static double Q[] = {
- 3.00198505138664455042E-6,
- 2.52448340349684104192E-3,
- 2.27265548208155028766E-1,
- 2.00000000000000000009E0,
-};
-static double C1 = 6.93145751953125E-1;
-static double C2 = 1.42860682030941723212E-6;
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0035004,0047156,0127442,0057502,
-0036770,0033210,0063121,0061764,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short Q[] = {
-0033511,0072665,0160662,0176377,
-0036045,0070715,0124105,0132777,
-0037550,0134114,0142077,0001637,
-0040400,0000000,0000000,0000000,
-};
-static unsigned short sc1[] = {0040061,0071000,0000000,0000000};
-#define C1 (*(double *)sc1)
-static unsigned short sc2[] = {0033277,0137216,0075715,0057117};
-#define C2 (*(double *)sc2)
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x4be8,0xd5e4,0x89cd,0x3f20,
-0x2c7e,0x0cca,0x06d1,0x3f9f,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short Q[] = {
-0x5fa0,0xbc36,0x2eb6,0x3ec9,
-0xb6c0,0xb508,0xae39,0x3f64,
-0xe074,0x9887,0x1709,0x3fcd,
-0x0000,0x0000,0x0000,0x4000,
-};
-static unsigned short sc1[] = {0x0000,0x0000,0x2e40,0x3fe6};
-#define C1 (*(double *)sc1)
-static unsigned short sc2[] = {0xabca,0xcf79,0xf7d1,0x3eb7};
-#define C2 (*(double *)sc2)
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f20,0x89cd,0xd5e4,0x4be8,
-0x3f9f,0x06d1,0x0cca,0x2c7e,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short Q[] = {
-0x3ec9,0x2eb6,0xbc36,0x5fa0,
-0x3f64,0xae39,0xb508,0xb6c0,
-0x3fcd,0x1709,0x9887,0xe074,
-0x4000,0x0000,0x0000,0x0000,
-};
-static unsigned short sc1[] = {0x3fe6,0x2e40,0x0000,0x0000};
-#define C1 (*(double *)sc1)
-static unsigned short sc2[] = {0x3eb7,0xf7d1,0xcf79,0xabca};
-#define C2 (*(double *)sc2)
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double ldexp ( double, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double polevl(), p1evl(), floor(), ldexp();
-int isnan(), isfinite();
-#endif
-extern double LOGE2, LOG2E, MAXLOG, MINLOG, MAXNUM;
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-
-double exp(x)
-double x;
-{
-double px, xx;
-int n;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-if( x > MAXLOG)
- {
-#ifdef INFINITIES
- return( INFINITY );
-#else
- mtherr( "exp", OVERFLOW );
- return( MAXNUM );
-#endif
- }
-
-if( x < MINLOG )
- {
-#ifndef INFINITIES
- mtherr( "exp", UNDERFLOW );
-#endif
- return(0.0);
- }
-
-/* Express e**x = e**g 2**n
- * = e**g e**( n loge(2) )
- * = e**( g + n loge(2) )
- */
-px = floor( LOG2E * x + 0.5 ); /* floor() truncates toward -infinity. */
-n = px;
-x -= px * C1;
-x -= px * C2;
-
-/* rational approximation for exponential
- * of the fractional part:
- * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
-xx = x * x;
-px = x * polevl( xx, P, 2 );
-x = px/( polevl( xx, Q, 3 ) - px );
-x = 1.0 + 2.0 * x;
-
-/* multiply by power of 2 */
-x = ldexp( x, n );
-return(x);
-}
+++ /dev/null
-/* exp10.c
- *
- * Base 10 exponential function
- * (Common antilogarithm)
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, exp10();
- *
- * y = exp10( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 10 raised to the x power.
- *
- * Range reduction is accomplished by expressing the argument
- * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
- * The Pade' form
- *
- * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- *
- * is used to approximate 10**f.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -307,+307 30000 2.2e-16 5.5e-17
- * Test result from an earlier version (2.1):
- * DEC -38,+38 70000 3.1e-17 7.0e-18
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp10 underflow x < -MAXL10 0.0
- * exp10 overflow x > MAXL10 MAXNUM
- *
- * DEC arithmetic: MAXL10 = 38.230809449325611792.
- * IEEE arithmetic: MAXL10 = 308.2547155599167.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1991, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
- 4.09962519798587023075E-2,
- 1.17452732554344059015E1,
- 4.06717289936872725516E2,
- 2.39423741207388267439E3,
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 8.50936160849306532625E1,
- 1.27209271178345121210E3,
- 2.07960819286001865907E3,
-};
-/* static double LOG102 = 3.01029995663981195214e-1; */
-static double LOG210 = 3.32192809488736234787e0;
-static double LG102A = 3.01025390625000000000E-1;
-static double LG102B = 4.60503898119521373889E-6;
-/* static double MAXL10 = 38.230809449325611792; */
-static double MAXL10 = 308.2547155599167;
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0037047,0165657,0114061,0067234,
-0041073,0166243,0123052,0144643,
-0042313,0055720,0024032,0047443,
-0043025,0121714,0070232,0050007,
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041652,0027756,0071216,0050075,
-0042637,0001367,0077263,0136017,
-0043001,0174673,0024157,0133416,
-};
-/*
-static unsigned short L102[] = {0037632,0020232,0102373,0147770};
-#define LOG102 *(double *)L102
-*/
-static unsigned short L210[] = {0040524,0115170,0045715,0015613};
-#define LOG210 *(double *)L210
-static unsigned short L102A[] = {0037632,0020000,0000000,0000000,};
-#define LG102A *(double *)L102A
-static unsigned short L102B[] = {0033632,0102373,0147767,0114220,};
-#define LG102B *(double *)L102B
-static unsigned short MXL[] = {0041430,0166131,0047761,0154130,};
-#define MAXL10 ( *(double *)MXL )
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x2dd4,0xf306,0xfd75,0x3fa4,
-0x5934,0x74c5,0x7d94,0x4027,
-0x49e4,0x0503,0x6b7a,0x4079,
-0x4a01,0x8e13,0xb479,0x40a2,
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xca08,0xce51,0x45fd,0x4055,
-0x7782,0xefd6,0xe05e,0x4093,
-0xf6e2,0x650d,0x3f37,0x40a0,
-};
-/*
-static unsigned short L102[] = {0x79ff,0x509f,0x4413,0x3fd3};
-#define LOG102 *(double *)L102
-*/
-static unsigned short L210[] = {0xa371,0x0979,0x934f,0x400a};
-#define LOG210 *(double *)L210
-static unsigned short L102A[] = {0x0000,0x0000,0x4400,0x3fd3,};
-#define LG102A *(double *)L102A
-static unsigned short L102B[] = {0xf312,0x79fe,0x509f,0x3ed3,};
-#define LG102B *(double *)L102B
-static double MAXL10 = 308.2547155599167;
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3fa4,0xfd75,0xf306,0x2dd4,
-0x4027,0x7d94,0x74c5,0x5934,
-0x4079,0x6b7a,0x0503,0x49e4,
-0x40a2,0xb479,0x8e13,0x4a01,
-};
-static unsigned short Q[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4055,0x45fd,0xce51,0xca08,
-0x4093,0xe05e,0xefd6,0x7782,
-0x40a0,0x3f37,0x650d,0xf6e2,
-};
-/*
-static unsigned short L102[] = {0x3fd3,0x4413,0x509f,0x79ff};
-#define LOG102 *(double *)L102
-*/
-static unsigned short L210[] = {0x400a,0x934f,0x0979,0xa371};
-#define LOG210 *(double *)L210
-static unsigned short L102A[] = {0x3fd3,0x4400,0x0000,0x0000,};
-#define LG102A *(double *)L102A
-static unsigned short L102B[] = {0x3ed3,0x509f,0x79fe,0xf312,};
-#define LG102B *(double *)L102B
-static double MAXL10 = 308.2547155599167;
-#endif
-
-#ifdef ANSIPROT
-extern double floor ( double );
-extern double ldexp ( double, int );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double floor(), ldexp(), polevl(), p1evl();
-int isnan(), isfinite();
-#endif
-extern double MAXNUM;
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-
-double exp10(x)
-double x;
-{
-double px, xx;
-short n;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-if( x > MAXL10 )
- {
-#ifdef INFINITIES
- return( INFINITY );
-#else
- mtherr( "exp10", OVERFLOW );
- return( MAXNUM );
-#endif
- }
-
-if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
- {
-#ifndef INFINITIES
- mtherr( "exp10", UNDERFLOW );
-#endif
- return(0.0);
- }
-
-/* Express 10**x = 10**g 2**n
- * = 10**g 10**( n log10(2) )
- * = 10**( g + n log10(2) )
- */
-px = floor( LOG210 * x + 0.5 );
-n = px;
-x -= px * LG102A;
-x -= px * LG102B;
-
-/* rational approximation for exponential
- * of the fractional part:
- * 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
-xx = x * x;
-px = x * polevl( xx, P, 3 );
-x = px/( p1evl( xx, Q, 3 ) - px );
-x = 1.0 + ldexp( x, 1 );
-
-/* multiply by power of 2 */
-x = ldexp( x, n );
-
-return(x);
-}
+++ /dev/null
-/* exp2.c
- *
- * Base 2 exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, exp2();
- *
- * y = exp2( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 2 raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- * x k f
- * 2 = 2 2.
- *
- * A Pade' form
- *
- * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
- *
- * approximates 2**x in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1022,+1024 30000 1.8e-16 5.4e-17
- *
- *
- * See exp.c for comments on error amplification.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < -MAXL2 0.0
- * exp overflow x > MAXL2 MAXNUM
- *
- * For DEC arithmetic, MAXL2 = 127.
- * For IEEE arithmetic, MAXL2 = 1024.
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
- 2.30933477057345225087E-2,
- 2.02020656693165307700E1,
- 1.51390680115615096133E3,
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 2.33184211722314911771E2,
- 4.36821166879210612817E3,
-};
-#define MAXL2 1024.0
-#define MINL2 -1024.0
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0036675,0027102,0122327,0053227,
-0041241,0116724,0115412,0157355,
-0042675,0036404,0101733,0132226,
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0042151,0027450,0077732,0160744,
-0043210,0100661,0077550,0056560,
-};
-#define MAXL2 127.0
-#define MINL2 -127.0
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0xead3,0x549a,0xa5c8,0x3f97,
-0x5bde,0x9361,0x33ba,0x4034,
-0x7693,0x907b,0xa7a0,0x4097,
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x5c3c,0x0ffb,0x25e5,0x406d,
-0x0bae,0x2fed,0x1036,0x40b1,
-};
-#define MAXL2 1024.0
-#define MINL2 -1022.0
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f97,0xa5c8,0x549a,0xead3,
-0x4034,0x33ba,0x9361,0x5bde,
-0x4097,0xa7a0,0x907b,0x7693,
-};
-static unsigned short Q[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x406d,0x25e5,0x0ffb,0x5c3c,
-0x40b1,0x1036,0x2fed,0x0bae,
-};
-#define MAXL2 1024.0
-#define MINL2 -1022.0
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double ldexp ( double, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double polevl(), p1evl(), floor(), ldexp();
-int isnan(), isfinite();
-#endif
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-extern double MAXNUM;
-
-double exp2(x)
-double x;
-{
-double px, xx;
-short n;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-if( x > MAXL2)
- {
-#ifdef INFINITIES
- return( INFINITY );
-#else
- mtherr( "exp2", OVERFLOW );
- return( MAXNUM );
-#endif
- }
-
-if( x < MINL2 )
- {
-#ifndef INFINITIES
- mtherr( "exp2", UNDERFLOW );
-#endif
- return(0.0);
- }
-
-xx = x; /* save x */
-/* separate into integer and fractional parts */
-px = floor(x+0.5);
-n = px;
-x = x - px;
-
-/* rational approximation
- * exp2(x) = 1 + 2xP(xx)/(Q(xx) - P(xx))
- * where xx = x**2
- */
-xx = x * x;
-px = x * polevl( xx, P, 2 );
-x = px / ( p1evl( xx, Q, 2 ) - px );
-x = 1.0 + ldexp( x, 1 );
-
-/* scale by power of 2 */
-x = ldexp( x, n );
-return(x);
-}
+++ /dev/null
-/* expn.c
- *
- * Exponential integral En
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double x, y, expn();
- *
- * y = expn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the exponential integral
- *
- * inf.
- * -
- * | | -xt
- * | e
- * E (x) = | ---- dt.
- * n | n
- * | | t
- * -
- * 1
- *
- *
- * Both n and x must be nonnegative.
- *
- * The routine employs either a power series, a continued
- * fraction, or an asymptotic formula depending on the
- * relative values of n and x.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 5000 2.0e-16 4.6e-17
- * IEEE 0, 30 10000 1.7e-15 3.6e-16
- *
- */
-\f
-/* expn.c */
-
-/* Cephes Math Library Release 2.8: June, 2000
- Copyright 1985, 2000 by Stephen L. Moshier */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double pow ( double, double );
-extern double gamma ( double );
-extern double log ( double );
-extern double exp ( double );
-extern double fabs ( double );
-#else
-double pow(), gamma(), log(), exp(), fabs();
-#endif
-#define EUL 0.57721566490153286060
-#define BIG 1.44115188075855872E+17
-extern double MAXNUM, MACHEP, MAXLOG;
-
-double expn( n, x )
-int n;
-double x;
-{
-double ans, r, t, yk, xk;
-double pk, pkm1, pkm2, qk, qkm1, qkm2;
-double psi, z;
-int i, k;
-static double big = BIG;
-
-if( n < 0 )
- goto domerr;
-
-if( x < 0 )
- {
-domerr: mtherr( "expn", DOMAIN );
- return( MAXNUM );
- }
-
-if( x > MAXLOG )
- return( 0.0 );
-
-if( x == 0.0 )
- {
- if( n < 2 )
- {
- mtherr( "expn", SING );
- return( MAXNUM );
- }
- else
- return( 1.0/(n-1.0) );
- }
-
-if( n == 0 )
- return( exp(-x)/x );
-\f
-/* expn.c */
-/* Expansion for large n */
-
-if( n > 5000 )
- {
- xk = x + n;
- yk = 1.0 / (xk * xk);
- t = n;
- ans = yk * t * (6.0 * x * x - 8.0 * t * x + t * t);
- ans = yk * (ans + t * (t - 2.0 * x));
- ans = yk * (ans + t);
- ans = (ans + 1.0) * exp( -x ) / xk;
- goto done;
- }
-
-if( x > 1.0 )
- goto cfrac;
-\f
-/* expn.c */
-
-/* Power series expansion */
-
-psi = -EUL - log(x);
-for( i=1; i<n; i++ )
- psi = psi + 1.0/i;
-
-z = -x;
-xk = 0.0;
-yk = 1.0;
-pk = 1.0 - n;
-if( n == 1 )
- ans = 0.0;
-else
- ans = 1.0/pk;
-do
- {
- xk += 1.0;
- yk *= z/xk;
- pk += 1.0;
- if( pk != 0.0 )
- {
- ans += yk/pk;
- }
- if( ans != 0.0 )
- t = fabs(yk/ans);
- else
- t = 1.0;
- }
-while( t > MACHEP );
-k = xk;
-t = n;
-r = n - 1;
-ans = (pow(z, r) * psi / gamma(t)) - ans;
-goto done;
-\f
-/* expn.c */
-/* continued fraction */
-cfrac:
-k = 1;
-pkm2 = 1.0;
-qkm2 = x;
-pkm1 = 1.0;
-qkm1 = x + n;
-ans = pkm1/qkm1;
-
-do
- {
- k += 1;
- if( k & 1 )
- {
- yk = 1.0;
- xk = n + (k-1)/2;
- }
- else
- {
- yk = x;
- xk = k/2;
- }
- pk = pkm1 * yk + pkm2 * xk;
- qk = qkm1 * yk + qkm2 * xk;
- if( qk != 0 )
- {
- r = pk/qk;
- t = fabs( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-if( fabs(pk) > big )
- {
- pkm2 /= big;
- pkm1 /= big;
- qkm2 /= big;
- qkm1 /= big;
- }
- }
-while( t > MACHEP );
-
-ans *= exp( -x );
-
-done:
-return( ans );
-}
-
+++ /dev/null
-/* fabs.c
- *
- * Absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y;
- *
- * y = fabs( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the absolute value of the argument.
- *
- */
-\f
-
-#include <math.h>
-/* Avoid using UNK if possible. */
-#ifdef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-#endif
-
-double fabs(x)
-double x;
-{
-union
- {
- double d;
- short i[4];
- } u;
-
-u.d = x;
-#ifdef IBMPC
- u.i[3] &= 0x7fff;
-#endif
-#ifdef MIEEE
- u.i[0] &= 0x7fff;
-#endif
-#ifdef DEC
- u.i[3] &= 0x7fff;
-#endif
-#ifdef UNK
-if( u.d < 0 )
- u.d = -u.d;
-#endif
-return( u.d );
-}
+++ /dev/null
-/* fac.c
- *
- * Factorial function
- *
- *
- *
- * SYNOPSIS:
- *
- * double y, fac();
- * int i;
- *
- * y = fac( i );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns factorial of i = 1 * 2 * 3 * ... * i.
- * fac(0) = 1.0.
- *
- * Due to machine arithmetic bounds the largest value of
- * i accepted is 33 in DEC arithmetic or 170 in IEEE
- * arithmetic. Greater values, or negative ones,
- * produce an error message and return MAXNUM.
- *
- *
- *
- * ACCURACY:
- *
- * For i < 34 the values are simply tabulated, and have
- * full machine accuracy. If i > 55, fac(i) = gamma(i+1);
- * see gamma.c.
- *
- * Relative error:
- * arithmetic domain peak
- * IEEE 0, 170 1.4e-15
- * DEC 0, 33 1.4e-17
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Factorials of integers from 0 through 33 */
-#ifdef UNK
-static double factbl[] = {
- 1.00000000000000000000E0,
- 1.00000000000000000000E0,
- 2.00000000000000000000E0,
- 6.00000000000000000000E0,
- 2.40000000000000000000E1,
- 1.20000000000000000000E2,
- 7.20000000000000000000E2,
- 5.04000000000000000000E3,
- 4.03200000000000000000E4,
- 3.62880000000000000000E5,
- 3.62880000000000000000E6,
- 3.99168000000000000000E7,
- 4.79001600000000000000E8,
- 6.22702080000000000000E9,
- 8.71782912000000000000E10,
- 1.30767436800000000000E12,
- 2.09227898880000000000E13,
- 3.55687428096000000000E14,
- 6.40237370572800000000E15,
- 1.21645100408832000000E17,
- 2.43290200817664000000E18,
- 5.10909421717094400000E19,
- 1.12400072777760768000E21,
- 2.58520167388849766400E22,
- 6.20448401733239439360E23,
- 1.55112100433309859840E25,
- 4.03291461126605635584E26,
- 1.0888869450418352160768E28,
- 3.04888344611713860501504E29,
- 8.841761993739701954543616E30,
- 2.6525285981219105863630848E32,
- 8.22283865417792281772556288E33,
- 2.6313083693369353016721801216E35,
- 8.68331761881188649551819440128E36
-};
-#define MAXFAC 33
-#endif
-
-#ifdef DEC
-static unsigned short factbl[] = {
-0040200,0000000,0000000,0000000,
-0040200,0000000,0000000,0000000,
-0040400,0000000,0000000,0000000,
-0040700,0000000,0000000,0000000,
-0041300,0000000,0000000,0000000,
-0041760,0000000,0000000,0000000,
-0042464,0000000,0000000,0000000,
-0043235,0100000,0000000,0000000,
-0044035,0100000,0000000,0000000,
-0044661,0030000,0000000,0000000,
-0045535,0076000,0000000,0000000,
-0046430,0042500,0000000,0000000,
-0047344,0063740,0000000,0000000,
-0050271,0112146,0000000,0000000,
-0051242,0060731,0040000,0000000,
-0052230,0035673,0126000,0000000,
-0053230,0035673,0126000,0000000,
-0054241,0137567,0063300,0000000,
-0055265,0173546,0051630,0000000,
-0056330,0012711,0101504,0100000,
-0057407,0006635,0171012,0150000,
-0060461,0040737,0046656,0030400,
-0061563,0135223,0005317,0101540,
-0062657,0027031,0127705,0023155,
-0064003,0061223,0041723,0156322,
-0065115,0045006,0014773,0004410,
-0066246,0146044,0172433,0173526,
-0067414,0136077,0027317,0114261,
-0070566,0044556,0110753,0045465,
-0071737,0031214,0032075,0036050,
-0073121,0037543,0070371,0064146,
-0074312,0132550,0052561,0116443,
-0075512,0132550,0052561,0116443,
-0076721,0005423,0114035,0025014
-};
-#define MAXFAC 33
-#endif
-
-#ifdef IBMPC
-static unsigned short factbl[] = {
-0x0000,0x0000,0x0000,0x3ff0,
-0x0000,0x0000,0x0000,0x3ff0,
-0x0000,0x0000,0x0000,0x4000,
-0x0000,0x0000,0x0000,0x4018,
-0x0000,0x0000,0x0000,0x4038,
-0x0000,0x0000,0x0000,0x405e,
-0x0000,0x0000,0x8000,0x4086,
-0x0000,0x0000,0xb000,0x40b3,
-0x0000,0x0000,0xb000,0x40e3,
-0x0000,0x0000,0x2600,0x4116,
-0x0000,0x0000,0xaf80,0x414b,
-0x0000,0x0000,0x08a8,0x4183,
-0x0000,0x0000,0x8cfc,0x41bc,
-0x0000,0xc000,0x328c,0x41f7,
-0x0000,0x2800,0x4c3b,0x4234,
-0x0000,0x7580,0x0777,0x4273,
-0x0000,0x7580,0x0777,0x42b3,
-0x0000,0xecd8,0x37ee,0x42f4,
-0x0000,0xca73,0xbeec,0x4336,
-0x9000,0x3068,0x02b9,0x437b,
-0x5a00,0xbe41,0xe1b3,0x43c0,
-0xc620,0xe9b5,0x283b,0x4406,
-0xf06c,0x6159,0x7752,0x444e,
-0xa4ce,0x35f8,0xe5c3,0x4495,
-0x7b9a,0x687a,0x6c52,0x44e0,
-0x6121,0xc33f,0xa940,0x4529,
-0x7eeb,0x9ea3,0xd984,0x4574,
-0xf316,0xe5d9,0x9787,0x45c1,
-0x6967,0xd23d,0xc92d,0x460e,
-0xa785,0x8687,0xe651,0x465b,
-0x2d0d,0x6e1f,0x27ec,0x46aa,
-0x33a4,0x0aae,0x56ad,0x46f9,
-0x33a4,0x0aae,0x56ad,0x4749,
-0xa541,0x7303,0x2162,0x479a
-};
-#define MAXFAC 170
-#endif
-
-#ifdef MIEEE
-static unsigned short factbl[] = {
-0x3ff0,0x0000,0x0000,0x0000,
-0x3ff0,0x0000,0x0000,0x0000,
-0x4000,0x0000,0x0000,0x0000,
-0x4018,0x0000,0x0000,0x0000,
-0x4038,0x0000,0x0000,0x0000,
-0x405e,0x0000,0x0000,0x0000,
-0x4086,0x8000,0x0000,0x0000,
-0x40b3,0xb000,0x0000,0x0000,
-0x40e3,0xb000,0x0000,0x0000,
-0x4116,0x2600,0x0000,0x0000,
-0x414b,0xaf80,0x0000,0x0000,
-0x4183,0x08a8,0x0000,0x0000,
-0x41bc,0x8cfc,0x0000,0x0000,
-0x41f7,0x328c,0xc000,0x0000,
-0x4234,0x4c3b,0x2800,0x0000,
-0x4273,0x0777,0x7580,0x0000,
-0x42b3,0x0777,0x7580,0x0000,
-0x42f4,0x37ee,0xecd8,0x0000,
-0x4336,0xbeec,0xca73,0x0000,
-0x437b,0x02b9,0x3068,0x9000,
-0x43c0,0xe1b3,0xbe41,0x5a00,
-0x4406,0x283b,0xe9b5,0xc620,
-0x444e,0x7752,0x6159,0xf06c,
-0x4495,0xe5c3,0x35f8,0xa4ce,
-0x44e0,0x6c52,0x687a,0x7b9a,
-0x4529,0xa940,0xc33f,0x6121,
-0x4574,0xd984,0x9ea3,0x7eeb,
-0x45c1,0x9787,0xe5d9,0xf316,
-0x460e,0xc92d,0xd23d,0x6967,
-0x465b,0xe651,0x8687,0xa785,
-0x46aa,0x27ec,0x6e1f,0x2d0d,
-0x46f9,0x56ad,0x0aae,0x33a4,
-0x4749,0x56ad,0x0aae,0x33a4,
-0x479a,0x2162,0x7303,0xa541
-};
-#define MAXFAC 170
-#endif
-
-#ifdef ANSIPROT
-double gamma ( double );
-#else
-double gamma();
-#endif
-extern double MAXNUM;
-
-double fac(i)
-int i;
-{
-double x, f, n;
-int j;
-
-if( i < 0 )
- {
- mtherr( "fac", SING );
- return( MAXNUM );
- }
-
-if( i > MAXFAC )
- {
- mtherr( "fac", OVERFLOW );
- return( MAXNUM );
- }
-
-/* Get answer from table for small i. */
-if( i < 34 )
- {
-#ifdef UNK
- return( factbl[i] );
-#else
- return( *(double *)(&factbl[4*i]) );
-#endif
- }
-/* Use gamma function for large i. */
-if( i > 55 )
- {
- x = i + 1;
- return( gamma(x) );
- }
-/* Compute directly for intermediate i. */
-n = 34.0;
-f = 34.0;
-for( j=35; j<=i; j++ )
- {
- n += 1.0;
- f *= n;
- }
-#ifdef UNK
- f *= factbl[33];
-#else
- f *= *(double *)(&factbl[4*33]);
-#endif
-return( f );
-}
+++ /dev/null
-/* fdtr.c
- *
- * F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * double x, y, fdtr();
- *
- * y = fdtr( df1, df2, x );
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density). This is the density
- * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
- * variables having Chi square distributions with df1
- * and df2 degrees of freedom, respectively.
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
- *
- *
- * The arguments a and b are greater than zero, and x is
- * nonnegative.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x).
- *
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 0,100 100000 9.8e-15 1.7e-15
- * IEEE 1,5 0,100 100000 6.5e-15 3.5e-16
- * IEEE 0,1 1,10000 100000 2.2e-11 3.3e-12
- * IEEE 1,5 1,10000 100000 1.1e-11 1.7e-13
- * See also incbet.c.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtr domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrc()
- *
- * Complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * double x, y, fdtrc();
- *
- * y = fdtrc( df1, df2, x );
- *
- * DESCRIPTION:
- *
- * Returns the area from x to infinity under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density).
- *
- *
- * inf.
- * -
- * 1 | | a-1 b-1
- * 1-P(x) = ------ | t (1-t) dt
- * B(a,b) | |
- * -
- * x
- *
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
- *
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) in the indicated intervals.
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 1,100 100000 3.7e-14 5.9e-16
- * IEEE 1,5 1,100 100000 8.0e-15 1.6e-15
- * IEEE 0,1 1,10000 100000 1.8e-11 3.5e-13
- * IEEE 1,5 1,10000 100000 2.0e-11 3.0e-12
- * See also incbet.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrc domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtri()
- *
- * Inverse of complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * double x, p, fdtri();
- *
- * x = fdtri( df1, df2, p );
- *
- * DESCRIPTION:
- *
- * Finds the F density argument x such that the integral
- * from x to infinity of the F density is equal to the
- * given probability p.
- *
- * This is accomplished using the inverse beta integral
- * function and the relations
- *
- * z = incbi( df2/2, df1/2, p )
- * x = df2 (1-z) / (df1 z).
- *
- * Note: the following relations hold for the inverse of
- * the uncomplemented F distribution:
- *
- * z = incbi( df1/2, df2/2, p )
- * x = df2 z / (df1 (1-z)).
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between .001 and 1:
- * IEEE 1,100 100000 8.3e-15 4.7e-16
- * IEEE 1,10000 100000 2.1e-11 1.4e-13
- * For p between 10^-6 and 10^-3:
- * IEEE 1,100 50000 1.3e-12 8.4e-15
- * IEEE 1,10000 50000 3.0e-12 4.8e-14
- * See also fdtrc.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtri domain p <= 0 or p > 1 0.0
- * v < 1
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double incbet ( double, double, double );
-extern double incbi ( double, double, double );
-#else
-double incbet(), incbi();
-#endif
-
-double fdtrc( ia, ib, x )
-int ia, ib;
-double x;
-{
-double a, b, w;
-
-if( (ia < 1) || (ib < 1) || (x < 0.0) )
- {
- mtherr( "fdtrc", DOMAIN );
- return( 0.0 );
- }
-a = ia;
-b = ib;
-w = b / (b + a * x);
-return( incbet( 0.5*b, 0.5*a, w ) );
-}
-
-
-
-double fdtr( ia, ib, x )
-int ia, ib;
-double x;
-{
-double a, b, w;
-
-if( (ia < 1) || (ib < 1) || (x < 0.0) )
- {
- mtherr( "fdtr", DOMAIN );
- return( 0.0 );
- }
-a = ia;
-b = ib;
-w = a * x;
-w = w / (b + w);
-return( incbet(0.5*a, 0.5*b, w) );
-}
-
-
-double fdtri( ia, ib, y )
-int ia, ib;
-double y;
-{
-double a, b, w, x;
-
-if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
- {
- mtherr( "fdtri", DOMAIN );
- return( 0.0 );
- }
-a = ia;
-b = ib;
-/* Compute probability for x = 0.5. */
-w = incbet( 0.5*b, 0.5*a, 0.5 );
-/* If that is greater than y, then the solution w < .5.
- Otherwise, solve at 1-y to remove cancellation in (b - b*w). */
-if( w > y || y < 0.001)
- {
- w = incbi( 0.5*b, 0.5*a, y );
- x = (b - b*w)/(a*w);
- }
-else
- {
- w = incbi( 0.5*a, 0.5*b, 1.0-y );
- x = b*w/(a*(1.0-w));
- }
-return(x);
-}
+++ /dev/null
-/* fftr.c
- *
- * FFT of Real Valued Sequence
- *
- *
- *
- * SYNOPSIS:
- *
- * double x[], sine[];
- * int m;
- *
- * fftr( x, m, sine );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the (complex valued) discrete Fourier transform of
- * the real valued sequence x[]. The input sequence x[] contains
- * n = 2**m samples. The program fills array sine[k] with
- * n/4 + 1 values of sin( 2 PI k / n ).
- *
- * Data format for complex valued output is real part followed
- * by imaginary part. The output is developed in the input
- * array x[].
- *
- * The algorithm takes advantage of the fact that the FFT of an
- * n point real sequence can be obtained from an n/2 point
- * complex FFT.
- *
- * A radix 2 FFT algorithm is used.
- *
- * Execution time on an LSI-11/23 with floating point chip
- * is 1.0 sec for n = 256.
- *
- *
- *
- * REFERENCE:
- *
- * E. Oran Brigham, The Fast Fourier Transform;
- * Prentice-Hall, Inc., 1974
- *
- */
-\f
-
-#include <math.h>
-
-static short n0 = 0;
-static short n4 = 0;
-static short msav = 0;
-
-extern double PI;
-
-#ifdef ANSIPROT
-extern double sin ( double );
-static int bitrv(int, int);
-#else
-double sin();
-static int bitrv();
-#endif
-
-fftr( x, m0, sine )
-double x[];
-int m0;
-double sine[];
-{
-int th, nd, pth, nj, dth, m;
-int n, n2, j, k, l, r;
-double xr, xi, tr, ti, co, si;
-double a, b, c, d, bc, cs, bs, cc;
-double *p, *q;
-
-/* Array x assumed filled with real-valued data */
-/* m0 = log2(n0) */
-/* n0 is the number of real data samples */
-
-if( m0 != msav )
- {
- msav = m0;
-
- /* Find n0 = 2**m0 */
- n0 = 1;
- for( j=0; j<m0; j++ )
- n0 <<= 1;
-
- n4 = n0 >> 2;
-
- /* Calculate array of sines */
- xr = 2.0 * PI / n0;
- for( j=0; j<=n4; j++ )
- sine[j] = sin( j * xr );
- }
-
-n = n0 >> 1; /* doing half length transform */
-m = m0 - 1;
-
-\f
-/* fftr.c */
-
-/* Complex Fourier Transform of n Complex Data Points */
-
-/* First, bit reverse the input data */
-
-for( k=0; k<n; k++ )
- {
- j = bitrv( k, m );
- if( j > k )
- { /* executed approx. n/2 times */
- p = &x[2*k];
- tr = *p++;
- ti = *p;
- q = &x[2*j+1];
- *p = *q;
- *(--p) = *(--q);
- *q++ = tr;
- *q = ti;
- }
- }
-\f
-/* fftr.c */
-/* Radix 2 Complex FFT */
-n2 = n/2;
-nj = 1;
-pth = 1;
-dth = 0;
-th = 0;
-
-for( l=0; l<m; l++ )
- { /* executed log2(n) times, total */
- j = 0;
- do
- { /* executed n-1 times, total */
- r = th << 1;
- si = sine[r];
- co = sine[ n4 - r ];
- if( j >= pth )
- {
- th -= dth;
- co = -co;
- }
- else
- th += dth;
-
- nd = j;
-
- do
- { /* executed n/2 log2(n) times, total */
- r = (nd << 1) + (nj << 1);
- p = &x[ r ];
- xr = *p++;
- xi = *p;
- tr = xr * co + xi * si;
- ti = xi * co - xr * si;
- r = nd << 1;
- q = &x[ r ];
- xr = *q++;
- xi = *q;
- *p = xi - ti;
- *(--p) = xr - tr;
- *q = xi + ti;
- *(--q) = xr + tr;
- nd += nj << 1;
- }
- while( nd < n );
- }
- while( ++j < nj );
-
- n2 >>= 1;
- dth = n2;
- pth = nj;
- nj <<= 1;
- }
-\f
-/* fftr.c */
-
-/* Special trick algorithm */
-/* converts to spectrum of real series */
-
-/* Highest frequency term; add space to input array if wanted */
-/*
-x[2*n] = x[0] - x[1];
-x[2*n+1] = 0.0;
-*/
-
-/* Zero frequency term */
-x[0] = x[0] + x[1];
-x[1] = 0.0;
-n2 = n/2;
-
-for( j=1; j<=n2; j++ )
- { /* executed n/2 times */
- si = sine[j];
- co = sine[ n4 - j ];
- p = &x[ 2*j ];
- xr = *p++;
- xi = *p;
- q = &x[ 2*(n-j) ];
- tr = *q++;
- ti = *q;
- a = xr + tr;
- b = xi + ti;
- c = xr - tr;
- d = xi - ti;
- bc = b * co;
- cs = c * si;
- bs = b * si;
- cc = c * co;
- *p = ( d - bs - cc )/2.0;
- *(--p) = ( a + bc - cs )/2.0;
- *q = -( d + bs + cc )/2.0;
- *(--q) = ( a - bc + cs )/2.0;
- }
-
-return(0);
-}
-\f
-/* fftr.c */
-
-/* Bit reverser */
-
-int bitrv( j, m )
-int j, m;
-{
-register int j1, ans;
-short k;
-
-ans = 0;
-j1 = j;
-
-for( k=0; k<m; k++ )
- {
- ans = (ans << 1) + (j1 & 1);
- j1 >>= 1;
- }
-
-return( ans );
-}
+++ /dev/null
-/* ceil()
- * floor()
- * frexp()
- * ldexp()
- * signbit()
- * isnan()
- * isfinite()
- *
- * Floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * double ceil(), floor(), frexp(), ldexp();
- * int signbit(), isnan(), isfinite();
- * double x, y;
- * int expnt, n;
- *
- * y = floor(x);
- * y = ceil(x);
- * y = frexp( x, &expnt );
- * y = ldexp( x, n );
- * n = signbit(x);
- * n = isnan(x);
- * n = isfinite(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * All four routines return a double precision floating point
- * result.
- *
- * floor() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * ceil() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * frexp() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * ldexp() multiplies x by 2**n.
- *
- * signbit(x) returns 1 if the sign bit of x is 1, else 0.
- *
- * These functions are part of the standard C run time library
- * for many but not all C compilers. The ones supplied are
- * written in C for either DEC or IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
-#undef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-#endif
-
-#ifdef DEC
-#define EXPMSK 0x807f
-#define MEXP 255
-#define NBITS 56
-#endif
-
-#ifdef IBMPC
-#define EXPMSK 0x800f
-#define MEXP 0x7ff
-#define NBITS 53
-#endif
-
-#ifdef MIEEE
-#define EXPMSK 0x800f
-#define MEXP 0x7ff
-#define NBITS 53
-#endif
-
-extern double MAXNUM, NEGZERO;
-#ifdef ANSIPROT
-double floor ( double );
-int isnan ( double );
-int isfinite ( double );
-double ldexp ( double, int );
-#else
-double floor();
-int isnan(), isfinite();
-double ldexp();
-#endif
-
-double ceil(x)
-double x;
-{
-double y;
-
-#ifdef UNK
-mtherr( "ceil", DOMAIN );
-return(0.0);
-#endif
-#ifdef NANS
-if( isnan(x) )
- return( x );
-#endif
-#ifdef INFINITIES
-if(!isfinite(x))
- return(x);
-#endif
-
-y = floor(x);
-if( y < x )
- y += 1.0;
-#ifdef MINUSZERO
-if( y == 0.0 && x < 0.0 )
- return( NEGZERO );
-#endif
-return(y);
-}
-
-
-
-
-/* Bit clearing masks: */
-
-static unsigned short bmask[] = {
-0xffff,
-0xfffe,
-0xfffc,
-0xfff8,
-0xfff0,
-0xffe0,
-0xffc0,
-0xff80,
-0xff00,
-0xfe00,
-0xfc00,
-0xf800,
-0xf000,
-0xe000,
-0xc000,
-0x8000,
-0x0000,
-};
-
-
-
-
-
-double floor(x)
-double x;
-{
-union
- {
- double y;
- unsigned short sh[4];
- } u;
-unsigned short *p;
-int e;
-
-#ifdef UNK
-mtherr( "floor", DOMAIN );
-return(0.0);
-#endif
-#ifdef NANS
-if( isnan(x) )
- return( x );
-#endif
-#ifdef INFINITIES
-if(!isfinite(x))
- return(x);
-#endif
-#ifdef MINUSZERO
-if(x == 0.0L)
- return(x);
-#endif
-u.y = x;
-/* find the exponent (power of 2) */
-#ifdef DEC
-p = (unsigned short *)&u.sh[0];
-e = (( *p >> 7) & 0377) - 0201;
-p += 3;
-#endif
-
-#ifdef IBMPC
-p = (unsigned short *)&u.sh[3];
-e = (( *p >> 4) & 0x7ff) - 0x3ff;
-p -= 3;
-#endif
-
-#ifdef MIEEE
-p = (unsigned short *)&u.sh[0];
-e = (( *p >> 4) & 0x7ff) - 0x3ff;
-p += 3;
-#endif
-
-if( e < 0 )
- {
- if( u.y < 0.0 )
- return( -1.0 );
- else
- return( 0.0 );
- }
-
-e = (NBITS -1) - e;
-/* clean out 16 bits at a time */
-while( e >= 16 )
- {
-#ifdef IBMPC
- *p++ = 0;
-#endif
-
-#ifdef DEC
- *p-- = 0;
-#endif
-
-#ifdef MIEEE
- *p-- = 0;
-#endif
- e -= 16;
- }
-
-/* clear the remaining bits */
-if( e > 0 )
- *p &= bmask[e];
-
-if( (x < 0) && (u.y != x) )
- u.y -= 1.0;
-
-return(u.y);
-}
-
-
-
-
-double frexp( x, pw2 )
-double x;
-int *pw2;
-{
-union
- {
- double y;
- unsigned short sh[4];
- } u;
-int i;
-#ifdef DENORMAL
-int k;
-#endif
-short *q;
-
-u.y = x;
-
-#ifdef UNK
-mtherr( "frexp", DOMAIN );
-return(0.0);
-#endif
-
-#ifdef IBMPC
-q = (short *)&u.sh[3];
-#endif
-
-#ifdef DEC
-q = (short *)&u.sh[0];
-#endif
-
-#ifdef MIEEE
-q = (short *)&u.sh[0];
-#endif
-
-/* find the exponent (power of 2) */
-#ifdef DEC
-i = ( *q >> 7) & 0377;
-if( i == 0 )
- {
- *pw2 = 0;
- return(0.0);
- }
-i -= 0200;
-*pw2 = i;
-*q &= 0x807f; /* strip all exponent bits */
-*q |= 040000; /* mantissa between 0.5 and 1 */
-return(u.y);
-#endif
-
-#ifdef IBMPC
-i = ( *q >> 4) & 0x7ff;
-if( i != 0 )
- goto ieeedon;
-#endif
-
-#ifdef MIEEE
-i = *q >> 4;
-i &= 0x7ff;
-if( i != 0 )
- goto ieeedon;
-#ifdef DENORMAL
-
-#else
-*pw2 = 0;
-return(0.0);
-#endif
-
-#endif
-
-
-#ifndef DEC
-/* Number is denormal or zero */
-#ifdef DENORMAL
-if( u.y == 0.0 )
- {
- *pw2 = 0;
- return( 0.0 );
- }
-
-
-/* Handle denormal number. */
-do
- {
- u.y *= 2.0;
- i -= 1;
- k = ( *q >> 4) & 0x7ff;
- }
-while( k == 0 );
-i = i + k;
-#endif /* DENORMAL */
-
-ieeedon:
-
-i -= 0x3fe;
-*pw2 = i;
-*q &= 0x800f;
-*q |= 0x3fe0;
-return( u.y );
-#endif
-}
-
-
-
-
-
-
-
-double ldexp( x, pw2 )
-double x;
-int pw2;
-{
-union
- {
- double y;
- unsigned short sh[4];
- } u;
-short *q;
-int e;
-
-#ifdef UNK
-mtherr( "ldexp", DOMAIN );
-return(0.0);
-#endif
-
-u.y = x;
-#ifdef DEC
-q = (short *)&u.sh[0];
-e = ( *q >> 7) & 0377;
-if( e == 0 )
- return(0.0);
-#else
-
-#ifdef IBMPC
-q = (short *)&u.sh[3];
-#endif
-#ifdef MIEEE
-q = (short *)&u.sh[0];
-#endif
-while( (e = (*q & 0x7ff0) >> 4) == 0 )
- {
- if( u.y == 0.0 )
- {
- return( 0.0 );
- }
-/* Input is denormal. */
- if( pw2 > 0 )
- {
- u.y *= 2.0;
- pw2 -= 1;
- }
- if( pw2 < 0 )
- {
- if( pw2 < -53 )
- return(0.0);
- u.y /= 2.0;
- pw2 += 1;
- }
- if( pw2 == 0 )
- return(u.y);
- }
-#endif /* not DEC */
-
-e += pw2;
-
-/* Handle overflow */
-#ifdef DEC
-if( e > MEXP )
- return( MAXNUM );
-#else
-if( e >= MEXP )
- return( 2.0*MAXNUM );
-#endif
-
-/* Handle denormalized results */
-if( e < 1 )
- {
-#ifdef DENORMAL
- if( e < -53 )
- return(0.0);
- *q &= 0x800f;
- *q |= 0x10;
- /* For denormals, significant bits may be lost even
- when dividing by 2. Construct 2^-(1-e) so the result
- is obtained with only one multiplication. */
- u.y *= ldexp(1.0, e-1);
- return(u.y);
-#else
- return(0.0);
-#endif
- }
-else
- {
-#ifdef DEC
- *q &= 0x807f; /* strip all exponent bits */
- *q |= (e & 0xff) << 7;
-#else
- *q &= 0x800f;
- *q |= (e & 0x7ff) << 4;
-#endif
- return(u.y);
- }
-}
-
-/**********************************************************************/
-/*
- * trunc is just a slightly modified version of floor above.
- */
-
-double trunc(double x)
-{
- union {
- double y;
- unsigned short sh[4];
- } u;
- unsigned short *p;
- int e;
-
-#ifdef UNK
- mtherr( "trunc", DOMAIN );
- return(0.0);
-#endif
-#ifdef NANS
- if( isnan(x) )
- return( x );
-#endif
-#ifdef INFINITIES
- if(!isfinite(x))
- return(x);
-#endif
-#ifdef MINUSZERO
- if(x == 0.0L)
- return(x);
-#endif
- u.y = x;
- /* find the exponent (power of 2) */
-#ifdef DEC
- p = (unsigned short *)&u.sh[0];
- e = (( *p >> 7) & 0377) - 0201;
- p += 3;
-#endif
-
-#ifdef IBMPC
- p = (unsigned short *)&u.sh[3];
- e = (( *p >> 4) & 0x7ff) - 0x3ff;
- p -= 3;
-#endif
-
-#ifdef MIEEE
- p = (unsigned short *)&u.sh[0];
- e = (( *p >> 4) & 0x7ff) - 0x3ff;
- p += 3;
-#endif
-
- if( e < 0 )
- return( 0.0 );
-
- e = (NBITS -1) - e;
- /* clean out 16 bits at a time */
- while( e >= 16 )
- {
-#ifdef IBMPC
- *p++ = 0;
-#endif
-
-#ifdef DEC
- *p-- = 0;
-#endif
-
-#ifdef MIEEE
- *p-- = 0;
-#endif
- e -= 16;
- }
-
- /* clear the remaining bits */
- if( e > 0 )
- *p &= bmask[e];
-
- return(u.y);
-}
+++ /dev/null
-/* fltest.c
- * Test program for floor(), frexp(), ldexp()
- */
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-
-#include <math.h>
-extern double MACHEP;
-#define UTH -1023
-
-main()
-{
-double x, y, y0, z, f, x00, y00;
-int i, j, k, e, e0;
-int errfr, errld, errfl, underexp, err, errth, e00;
-double frexp(), ldexp(), floor();
-
-
-/*
-if( 1 )
- goto flrtst;
-*/
-
-printf( "Testing frexp() and ldexp().\n" );
-errfr = 0;
-errld = 0;
-underexp = 0;
-f = 1.0;
-x00 = 2.0;
-y00 = 0.5;
-e00 = 2;
-
-for( j=0; j<20; j++ )
-{
-if( j == 10 )
- {
- f = 1.0;
- x00 = 2.0;
- e00 = 1;
-/* Find 2**(2**10) / 2 */
-#ifdef DEC
- for( i=0; i<5; i++ )
-#else
- for( i=0; i<9; i++ )
-#endif
- {
- x00 *= x00;
- e00 += e00;
- }
- y00 = x00/2.0;
- x00 = x00 * y00;
- e00 += e00;
- y00 = 0.5;
- }
-x = x00 * f;
-y0 = y00 * f;
-e0 = e00;
-for( i=0; i<2200; i++ )
- {
- x /= 2.0;
- e0 -= 1;
- if( x == 0.0 )
- {
- if( f == 1.0 )
- underexp = e0;
- y0 = 0.0;
- e0 = 0;
- }
- y = frexp( x, &e );
- if( (e0 < -1023) && (e != e0) )
- {
- if( e == (e0 - 1) )
- {
- e += 1;
- y /= 2.0;
- }
- if( e == (e0 + 1) )
- {
- e -= 1;
- y *= 2.0;
- }
- }
- err = y - y0;
- if( y0 != 0.0 )
- err /= y0;
- if( err < 0.0 )
- err = -err;
- if( e0 > -1023 )
- errth = 0.0;
- else
- {/* Denormal numbers may have rounding errors */
- if( e0 == -1023 )
- {
- errth = 2.0 * MACHEP;
- }
- else
- {
- errth *= 2.0;
- }
- }
-
- if( (x != 0.0) && ((err > errth) || (e != e0)) )
- {
- printf( "Test %d: ", j+1 );
- printf( " frexp( %.15e) =?= %.15e * 2**%d;", x, y, e );
- printf( " should be %.15e * 2**%d\n", y0, e0 );
- errfr += 1;
- }
- y = ldexp( x, 1-e0 );
- err = y - 1.0;
- if( err < 0.0 )
- err = -err;
- if( (err > errth) && ((x == 0.0) && (y != 0.0)) )
- {
- printf( "Test %d: ", j+1 );
- printf( "ldexp( %.15e, %d ) =?= %.15e;", x, 1-e0, y );
- if( x != 0.0 )
- printf( " should be %.15e\n", f );
- else
- printf( " should be %.15e\n", 0.0 );
- errld += 1;
- }
- if( x == 0.0 )
- {
- break;
- }
- }
-f = f * 1.08005973889;
-}
-
-
-x = 2.22507385850720138309e-308;
-for (i = 0; i < 52; i++)
- {
- y = ldexp (x, -i);
- z = ldexp (y, i);
- if (x != z)
- {
- printf ("x %.16e, i %d, y %.16e, z %.16e\n", x, i, y, z);
- errld += 1;
- }
- }
-
-
-if( (errld == 0) && (errfr == 0) )
- {
- printf( "No errors found.\n" );
- }
-
-flrtst:
-
-printf( "Testing floor().\n" );
-errfl = 0;
-
-f = 1.0/MACHEP;
-x00 = 1.0;
-for( j=0; j<57; j++ )
-{
-x = x00 - 1.0;
-for( i=0; i<128; i++ )
- {
- y = floor(x);
- if( y != x )
- {
- flierr( x, y, j );
- errfl += 1;
- }
-/* Warning! the if() statement is compiler dependent,
- * since x-0.49 may be held in extra precision accumulator
- * so would never compare equal to x! The subroutine call
- * y = floor() forces z to be stored as a double and reloaded
- * for the if() statement.
- */
- z = x - 0.49;
- y = floor(z);
- if( z == x )
- break;
- if( y != (x - 1.0) )
- {
- flierr( z, y, j );
- errfl += 1;
- }
-
- z = x + 0.49;
- y = floor(z);
- if( z != x )
- {
- if( y != x )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- x = -x;
- y = floor(x);
- if( z != x )
- {
- if( y != x )
- {
- flierr( x, y, j );
- errfl += 1;
- }
- }
- z = x + 0.49;
- y = floor(z);
- if( z != x )
- {
- if( y != x )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- z = x - 0.49;
- y = floor(z);
- if( z != x )
- {
- if( y != (x - 1.0) )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- x = -x;
- x += 1.0;
- }
-x00 = x00 + x00;
-}
-y = floor(0.0);
-if( y != 0.0 )
- {
- flierr( 0.0, y, 57 );
- errfl += 1;
- }
-y = floor(-0.0);
-if( y != 0.0 )
- {
- flierr( -0.0, y, 58 );
- errfl += 1;
- }
-y = floor(-1.0);
-if( y != -1.0 )
- {
- flierr( -1.0, y, 59 );
- errfl += 1;
- }
-y = floor(-0.1);
-if( y != -1.0 )
- {
- flierr( -0.1, y, 60 );
- errfl += 1;
- }
-
-if( errfl == 0 )
- printf( "No errors found in floor().\n" );
-
-}
-
-
-flierr( x, y, k )
-double x, y;
-int k;
-{
-printf( "Test %d: ", k+1 );
-printf( "floor(%.15e) =?= %.15e\n", x, y );
-}
+++ /dev/null
-int drand();
-double exp(), frexp(), ldexp();
-volatile double x, y, z;
-
-main()
-{
-int i, e;
-
-for( i=0; i<100000; i++ )
- {
- drand(&x);
- x = exp( 10.0*(x - 1.5) );
- y = frexp( x, &e );
- z = ldexp( y, e );
- if( z != x )
- abort();
- }
-}
+++ /dev/null
-/* fltest.c
- * Test program for floor(), frexp(), ldexp()
- */
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-
-#include <math.h>
-/*extern double MACHEP;*/
-#define MACHEP 2.3e-16
-#define UTH -1023
-
-main()
-{
-double x, y, y0, z, f, x00, y00;
-int i, j, k, e, e0;
-int errfr, errld, errfl, underexp, err, errth, e00;
-double frexp(), ldexp(), floor();
-
-
-/*
-if( 1 )
- goto flrtst;
-*/
-
-printf( "Testing frexp() and ldexp().\n" );
-errfr = 0;
-errld = 0;
-underexp = 0;
-f = 1.0;
-x00 = 2.0;
-y00 = 0.5;
-e00 = 2;
-
-for( j=0; j<20; j++ )
-{
-if( j == 10 )
- {
- f = 1.0;
- x00 = 2.0;
- e00 = 1;
-/* Find 2**(2**10) / 2 */
-#ifdef DEC
- for( i=0; i<5; i++ )
-#else
- for( i=0; i<9; i++ )
-#endif
- {
- x00 *= x00;
- e00 += e00;
- }
- y00 = x00/2.0;
- x00 = x00 * y00;
- e00 += e00;
- y00 = 0.5;
- }
-x = x00 * f;
-y0 = y00 * f;
-e0 = e00;
-for( i=0; i<2200; i++ )
- {
- x /= 2.0;
- e0 -= 1;
- if( x == 0.0 )
- {
- if( f == 1.0 )
- underexp = e0;
- y0 = 0.0;
- e0 = 0;
- }
- y = frexp( x, &e );
- if( (e0 < -1023) && (e != e0) )
- {
- if( e == (e0 - 1) )
- {
- e += 1;
- y /= 2.0;
- }
- if( e == (e0 + 1) )
- {
- e -= 1;
- y *= 2.0;
- }
- }
- err = y - y0;
- if( y0 != 0.0 )
- err /= y0;
- if( err < 0.0 )
- err = -err;
- if( e0 > -1023 )
- errth = 0.0;
- else
- {/* Denormal numbers may have rounding errors */
- if( e0 == -1023 )
- {
- errth = 2.0 * MACHEP;
- }
- else
- {
- errth *= 2.0;
- }
- }
-
- if( (x != 0.0) && ((err > errth) || (e != e0)) )
- {
- printf( "Test %d: ", j+1 );
- printf( " frexp( %.15e) =?= %.15e * 2**%d;", x, y, e );
- printf( " should be %.15e * 2**%d\n", y0, e0 );
- errfr += 1;
- }
- y = ldexp( x, 1-e0 );
- err = y - 1.0;
- if( err < 0.0 )
- err = -err;
- if( (err > errth) && ((x == 0.0) && (y != 0.0)) )
- {
- printf( "Test %d: ", j+1 );
- printf( "ldexp( %.15e, %d ) =?= %.15e;", x, 1-e0, y );
- if( x != 0.0 )
- printf( " should be %.15e\n", f );
- else
- printf( " should be %.15e\n", 0.0 );
- errld += 1;
- }
- if( x == 0.0 )
- {
- break;
- }
- }
-f = f * 1.08005973889;
-}
-
-if( (errld == 0) && (errfr == 0) )
- {
- printf( "No errors found.\n" );
- }
-
-flrtst:
-
-printf( "Testing floor().\n" );
-errfl = 0;
-
-f = 1.0/MACHEP;
-x00 = 1.0;
-for( j=0; j<57; j++ )
-{
-x = x00 - 1.0;
-for( i=0; i<128; i++ )
- {
- y = floor(x);
- if( y != x )
- {
- flierr( x, y, j );
- errfl += 1;
- }
-/* Warning! the if() statement is compiler dependent,
- * since x-0.49 may be held in extra precision accumulator
- * so would never compare equal to x! The subroutine call
- * y = floor() forces z to be stored as a double and reloaded
- * for the if() statement.
- */
- z = x - 0.49;
- y = floor(z);
- if( z == x )
- break;
- if( y != (x - 1.0) )
- {
- flierr( z, y, j );
- errfl += 1;
- }
-
- z = x + 0.49;
- y = floor(z);
- if( z != x )
- {
- if( y != x )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- x = -x;
- y = floor(x);
- if( z != x )
- {
- if( y != x )
- {
- flierr( x, y, j );
- errfl += 1;
- }
- }
- z = x + 0.49;
- y = floor(z);
- if( z != x )
- {
- if( y != x )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- z = x - 0.49;
- y = floor(z);
- if( z != x )
- {
- if( y != (x - 1.0) )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- x = -x;
- x += 1.0;
- }
-x00 = x00 + x00;
-}
-y = floor(0.0);
-if( y != 0.0 )
- {
- flierr( 0.0, y, 57 );
- errfl += 1;
- }
-y = floor(-0.0);
-if( y != 0.0 )
- {
- flierr( -0.0, y, 58 );
- errfl += 1;
- }
-y = floor(-1.0);
-if( y != -1.0 )
- {
- flierr( -1.0, y, 59 );
- errfl += 1;
- }
-y = floor(-0.1);
-if( y != -1.0 )
- {
- flierr( -0.1, y, 60 );
- errfl += 1;
- }
-
-if( errfl == 0 )
- printf( "No errors found in floor().\n" );
-
-}
-
-
-flierr( x, y, k )
-double x, y;
-int k;
-{
-printf( "Test %d: ", k+1 );
-printf( "floor(%.15e) =?= %.15e\n", x, y );
-}
+++ /dev/null
-/* fresnl.c
- *
- * Fresnel integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, S, C;
- * void fresnl();
- *
- * fresnl( x, _&S, _&C );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the Fresnel integrals
- *
- * x
- * -
- * | |
- * C(x) = | cos(pi/2 t**2) dt,
- * | |
- * -
- * 0
- *
- * x
- * -
- * | |
- * S(x) = | sin(pi/2 t**2) dt.
- * | |
- * -
- * 0
- *
- *
- * The integrals are evaluated by a power series for x < 1.
- * For x >= 1 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
- * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
- *
- *
- *
- * ACCURACY:
- *
- * Relative error.
- *
- * Arithmetic function domain # trials peak rms
- * IEEE S(x) 0, 10 10000 2.0e-15 3.2e-16
- * IEEE C(x) 0, 10 10000 1.8e-15 3.3e-16
- * DEC S(x) 0, 10 6000 2.2e-16 3.9e-17
- * DEC C(x) 0, 10 5000 2.3e-16 3.9e-17
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* S(x) for small x */
-#ifdef UNK
-static double sn[6] = {
--2.99181919401019853726E3,
- 7.08840045257738576863E5,
--6.29741486205862506537E7,
- 2.54890880573376359104E9,
--4.42979518059697779103E10,
- 3.18016297876567817986E11,
-};
-static double sd[6] = {
-/* 1.00000000000000000000E0,*/
- 2.81376268889994315696E2,
- 4.55847810806532581675E4,
- 5.17343888770096400730E6,
- 4.19320245898111231129E8,
- 2.24411795645340920940E10,
- 6.07366389490084639049E11,
-};
-#endif
-#ifdef DEC
-static unsigned short sn[24] = {
-0143072,0176433,0065455,0127034,
-0045055,0007200,0134540,0026661,
-0146560,0035061,0023667,0127545,
-0050027,0166503,0002673,0153756,
-0151045,0002721,0121737,0102066,
-0051624,0013177,0033451,0021271,
-};
-static unsigned short sd[24] = {
-/*0040200,0000000,0000000,0000000,*/
-0042214,0130051,0112070,0101617,
-0044062,0010307,0172346,0152510,
-0045635,0160575,0143200,0136642,
-0047307,0171215,0127457,0052361,
-0050647,0031447,0032621,0013510,
-0052015,0064733,0117362,0012653,
-};
-#endif
-#ifdef IBMPC
-static unsigned short sn[24] = {
-0xb5c3,0x6d65,0x5fa3,0xc0a7,
-0x05b6,0x172c,0xa1d0,0x4125,
-0xf5ed,0x24f6,0x0746,0xc18e,
-0x7afe,0x60b7,0xfda8,0x41e2,
-0xf087,0x347b,0xa0ba,0xc224,
-0x2457,0xe6e5,0x82cf,0x4252,
-};
-static unsigned short sd[24] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x1072,0x3287,0x9605,0x4071,
-0xdaa9,0xfe9c,0x4218,0x40e6,
-0x17b4,0xb8d0,0xbc2f,0x4153,
-0xea9e,0xb5e5,0xfe51,0x41b8,
-0x22e9,0xe6b2,0xe664,0x4214,
-0x42b5,0x73de,0xad3b,0x4261,
-};
-#endif
-#ifdef MIEEE
-static unsigned short sn[24] = {
-0xc0a7,0x5fa3,0x6d65,0xb5c3,
-0x4125,0xa1d0,0x172c,0x05b6,
-0xc18e,0x0746,0x24f6,0xf5ed,
-0x41e2,0xfda8,0x60b7,0x7afe,
-0xc224,0xa0ba,0x347b,0xf087,
-0x4252,0x82cf,0xe6e5,0x2457,
-};
-static unsigned short sd[24] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4071,0x9605,0x3287,0x1072,
-0x40e6,0x4218,0xfe9c,0xdaa9,
-0x4153,0xbc2f,0xb8d0,0x17b4,
-0x41b8,0xfe51,0xb5e5,0xea9e,
-0x4214,0xe664,0xe6b2,0x22e9,
-0x4261,0xad3b,0x73de,0x42b5,
-};
-#endif
-
-/* C(x) for small x */
-#ifdef UNK
-static double cn[6] = {
--4.98843114573573548651E-8,
- 9.50428062829859605134E-6,
--6.45191435683965050962E-4,
- 1.88843319396703850064E-2,
--2.05525900955013891793E-1,
- 9.99999999999999998822E-1,
-};
-static double cd[7] = {
- 3.99982968972495980367E-12,
- 9.15439215774657478799E-10,
- 1.25001862479598821474E-7,
- 1.22262789024179030997E-5,
- 8.68029542941784300606E-4,
- 4.12142090722199792936E-2,
- 1.00000000000000000118E0,
-};
-#endif
-#ifdef DEC
-static unsigned short cn[24] = {
-0132126,0040141,0063733,0013231,
-0034037,0072223,0010200,0075637,
-0135451,0021020,0073264,0036057,
-0036632,0131520,0101316,0060233,
-0137522,0072541,0136124,0132202,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short cd[28] = {
-0026614,0135503,0051776,0032631,
-0030573,0121116,0154033,0126712,
-0032406,0034100,0012442,0106212,
-0034115,0017567,0150520,0164623,
-0035543,0106171,0177336,0146351,
-0037050,0150073,0000607,0171635,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short cn[24] = {
-0x62d3,0x2cfb,0xc80c,0xbe6a,
-0x0f74,0x6210,0xee92,0x3ee3,
-0x8786,0x0ed6,0x2442,0xbf45,
-0xcc13,0x1059,0x566a,0x3f93,
-0x9690,0x378a,0x4eac,0xbfca,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short cd[28] = {
-0xc6b3,0x6a7f,0x9768,0x3d91,
-0x75b9,0xdb03,0x7449,0x3e0f,
-0x5191,0x02a4,0xc708,0x3e80,
-0x1d32,0xfa2a,0xa3ee,0x3ee9,
-0xd99d,0x3fdb,0x718f,0x3f4c,
-0xfe74,0x6030,0x1a07,0x3fa5,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short cn[24] = {
-0xbe6a,0xc80c,0x2cfb,0x62d3,
-0x3ee3,0xee92,0x6210,0x0f74,
-0xbf45,0x2442,0x0ed6,0x8786,
-0x3f93,0x566a,0x1059,0xcc13,
-0xbfca,0x4eac,0x378a,0x9690,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short cd[28] = {
-0x3d91,0x9768,0x6a7f,0xc6b3,
-0x3e0f,0x7449,0xdb03,0x75b9,
-0x3e80,0xc708,0x02a4,0x5191,
-0x3ee9,0xa3ee,0xfa2a,0x1d32,
-0x3f4c,0x718f,0x3fdb,0xd99d,
-0x3fa5,0x1a07,0x6030,0xfe74,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-/* Auxiliary function f(x) */
-#ifdef UNK
-static double fn[10] = {
- 4.21543555043677546506E-1,
- 1.43407919780758885261E-1,
- 1.15220955073585758835E-2,
- 3.45017939782574027900E-4,
- 4.63613749287867322088E-6,
- 3.05568983790257605827E-8,
- 1.02304514164907233465E-10,
- 1.72010743268161828879E-13,
- 1.34283276233062758925E-16,
- 3.76329711269987889006E-20,
-};
-static double fd[10] = {
-/* 1.00000000000000000000E0,*/
- 7.51586398353378947175E-1,
- 1.16888925859191382142E-1,
- 6.44051526508858611005E-3,
- 1.55934409164153020873E-4,
- 1.84627567348930545870E-6,
- 1.12699224763999035261E-8,
- 3.60140029589371370404E-11,
- 5.88754533621578410010E-14,
- 4.52001434074129701496E-17,
- 1.25443237090011264384E-20,
-};
-#endif
-#ifdef DEC
-static unsigned short fn[40] = {
-0037727,0152216,0106601,0016214,
-0037422,0154606,0112710,0071355,
-0036474,0143453,0154253,0166545,
-0035264,0161606,0022250,0073743,
-0033633,0110036,0024653,0136246,
-0032003,0036652,0041164,0036413,
-0027740,0174122,0046305,0036726,
-0025501,0125270,0121317,0167667,
-0023032,0150555,0076175,0047443,
-0020061,0133570,0070130,0027657,
-};
-static unsigned short fd[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0040100,0063767,0054413,0151452,
-0037357,0061566,0007243,0065754,
-0036323,0005365,0033552,0133625,
-0035043,0101123,0000275,0165402,
-0033367,0146614,0110623,0023647,
-0031501,0116644,0125222,0144263,
-0027436,0062051,0117235,0001411,
-0025204,0111543,0056370,0036201,
-0022520,0071351,0015227,0122144,
-0017554,0172240,0112713,0005006,
-};
-#endif
-#ifdef IBMPC
-static unsigned short fn[40] = {
-0x2391,0xd1b0,0xfa91,0x3fda,
-0x0e5e,0xd2b9,0x5b30,0x3fc2,
-0x7dad,0x7b15,0x98e5,0x3f87,
-0x0efc,0xc495,0x9c70,0x3f36,
-0x7795,0xc535,0x7203,0x3ed3,
-0x87a1,0x484e,0x67b5,0x3e60,
-0xa7bb,0x4998,0x1f0a,0x3ddc,
-0xfdf7,0x1459,0x3557,0x3d48,
-0xa9e4,0xaf8f,0x5a2d,0x3ca3,
-0x05f6,0x0e0b,0x36ef,0x3be6,
-};
-static unsigned short fd[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x7a65,0xeb21,0x0cfe,0x3fe8,
-0x6d7d,0xc1d4,0xec6e,0x3fbd,
-0x56f3,0xa6ed,0x615e,0x3f7a,
-0xbd60,0x6017,0x704a,0x3f24,
-0x64f5,0x9232,0xf9b1,0x3ebe,
-0x5916,0x9552,0x33b4,0x3e48,
-0xa061,0x33d3,0xcc85,0x3dc3,
-0x0790,0x6b9f,0x926c,0x3d30,
-0xf48d,0x2352,0x0e5d,0x3c8a,
-0x6141,0x12b9,0x9e94,0x3bcd,
-};
-#endif
-#ifdef MIEEE
-static unsigned short fn[40] = {
-0x3fda,0xfa91,0xd1b0,0x2391,
-0x3fc2,0x5b30,0xd2b9,0x0e5e,
-0x3f87,0x98e5,0x7b15,0x7dad,
-0x3f36,0x9c70,0xc495,0x0efc,
-0x3ed3,0x7203,0xc535,0x7795,
-0x3e60,0x67b5,0x484e,0x87a1,
-0x3ddc,0x1f0a,0x4998,0xa7bb,
-0x3d48,0x3557,0x1459,0xfdf7,
-0x3ca3,0x5a2d,0xaf8f,0xa9e4,
-0x3be6,0x36ef,0x0e0b,0x05f6,
-};
-static unsigned short fd[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3fe8,0x0cfe,0xeb21,0x7a65,
-0x3fbd,0xec6e,0xc1d4,0x6d7d,
-0x3f7a,0x615e,0xa6ed,0x56f3,
-0x3f24,0x704a,0x6017,0xbd60,
-0x3ebe,0xf9b1,0x9232,0x64f5,
-0x3e48,0x33b4,0x9552,0x5916,
-0x3dc3,0xcc85,0x33d3,0xa061,
-0x3d30,0x926c,0x6b9f,0x0790,
-0x3c8a,0x0e5d,0x2352,0xf48d,
-0x3bcd,0x9e94,0x12b9,0x6141,
-};
-#endif
-
-
-/* Auxiliary function g(x) */
-#ifdef UNK
-static double gn[11] = {
- 5.04442073643383265887E-1,
- 1.97102833525523411709E-1,
- 1.87648584092575249293E-2,
- 6.84079380915393090172E-4,
- 1.15138826111884280931E-5,
- 9.82852443688422223854E-8,
- 4.45344415861750144738E-10,
- 1.08268041139020870318E-12,
- 1.37555460633261799868E-15,
- 8.36354435630677421531E-19,
- 1.86958710162783235106E-22,
-};
-static double gd[11] = {
-/* 1.00000000000000000000E0,*/
- 1.47495759925128324529E0,
- 3.37748989120019970451E-1,
- 2.53603741420338795122E-2,
- 8.14679107184306179049E-4,
- 1.27545075667729118702E-5,
- 1.04314589657571990585E-7,
- 4.60680728146520428211E-10,
- 1.10273215066240270757E-12,
- 1.38796531259578871258E-15,
- 8.39158816283118707363E-19,
- 1.86958710162783236342E-22,
-};
-#endif
-#ifdef DEC
-static unsigned short gn[44] = {
-0040001,0021435,0120406,0053123,
-0037511,0152523,0037703,0122011,
-0036631,0134302,0122721,0110235,
-0035463,0051712,0043215,0114732,
-0034101,0025677,0147725,0057630,
-0032323,0010342,0067523,0002206,
-0030364,0152247,0110007,0054107,
-0026230,0057654,0035464,0047124,
-0023706,0036401,0167705,0045440,
-0021166,0154447,0105632,0142461,
-0016142,0002353,0011175,0170530,
-};
-static unsigned short gd[44] = {
-/*0040200,0000000,0000000,0000000,*/
-0040274,0145551,0016742,0127005,
-0037654,0166557,0076416,0015165,
-0036717,0140217,0030675,0050111,
-0035525,0110060,0076405,0070502,
-0034125,0176061,0060120,0031730,
-0032340,0001615,0054343,0120501,
-0030375,0041414,0070747,0107060,
-0026233,0031034,0160757,0074526,
-0023710,0003341,0137100,0144664,
-0021167,0126414,0023774,0015435,
-0016142,0002353,0011175,0170530,
-};
-#endif
-#ifdef IBMPC
-static unsigned short gn[44] = {
-0xcaca,0xb420,0x2463,0x3fe0,
-0x7481,0x67f8,0x3aaa,0x3fc9,
-0x3214,0x54ba,0x3718,0x3f93,
-0xb33b,0x48d1,0x6a79,0x3f46,
-0xabf3,0xf9fa,0x2577,0x3ee8,
-0x6091,0x4dea,0x621c,0x3e7a,
-0xeb09,0xf200,0x9a94,0x3dfe,
-0x89cb,0x8766,0x0bf5,0x3d73,
-0xa964,0x3df8,0xc7a0,0x3cd8,
-0x58a6,0xf173,0xdb24,0x3c2e,
-0xbe2b,0x624f,0x409d,0x3b6c,
-};
-static unsigned short gd[44] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x55c1,0x23bc,0x996d,0x3ff7,
-0xc34f,0xefa1,0x9dad,0x3fd5,
-0xaa09,0xe637,0xf811,0x3f99,
-0xae28,0x0fa0,0xb206,0x3f4a,
-0x067b,0x2c0a,0xbf86,0x3eea,
-0x7428,0xab1c,0x0071,0x3e7c,
-0xf1c6,0x8e3c,0xa861,0x3dff,
-0xef2b,0x9c3d,0x6643,0x3d73,
-0x1936,0x37c8,0x00dc,0x3cd9,
-0x8364,0x84ff,0xf5a1,0x3c2e,
-0xbe2b,0x624f,0x409d,0x3b6c,
-};
-#endif
-#ifdef MIEEE
-static unsigned short gn[44] = {
-0x3fe0,0x2463,0xb420,0xcaca,
-0x3fc9,0x3aaa,0x67f8,0x7481,
-0x3f93,0x3718,0x54ba,0x3214,
-0x3f46,0x6a79,0x48d1,0xb33b,
-0x3ee8,0x2577,0xf9fa,0xabf3,
-0x3e7a,0x621c,0x4dea,0x6091,
-0x3dfe,0x9a94,0xf200,0xeb09,
-0x3d73,0x0bf5,0x8766,0x89cb,
-0x3cd8,0xc7a0,0x3df8,0xa964,
-0x3c2e,0xdb24,0xf173,0x58a6,
-0x3b6c,0x409d,0x624f,0xbe2b,
-};
-static unsigned short gd[44] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3ff7,0x996d,0x23bc,0x55c1,
-0x3fd5,0x9dad,0xefa1,0xc34f,
-0x3f99,0xf811,0xe637,0xaa09,
-0x3f4a,0xb206,0x0fa0,0xae28,
-0x3eea,0xbf86,0x2c0a,0x067b,
-0x3e7c,0x0071,0xab1c,0x7428,
-0x3dff,0xa861,0x8e3c,0xf1c6,
-0x3d73,0x6643,0x9c3d,0xef2b,
-0x3cd9,0x00dc,0x37c8,0x1936,
-0x3c2e,0xf5a1,0x84ff,0x8364,
-0x3b6c,0x409d,0x624f,0xbe2b,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double cos ( double );
-extern double sin ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double fabs(), cos(), sin(), polevl(), p1evl();
-#endif
-extern double PI, PIO2, MACHEP;
-
-int fresnl( xxa, ssa, cca )
-double xxa, *ssa, *cca;
-{
-double f, g, cc, ss, c, s, t, u;
-double x, x2;
-
-x = fabs(xxa);
-x2 = x * x;
-if( x2 < 2.5625 )
- {
- t = x2 * x2;
- ss = x * x2 * polevl( t, sn, 5)/p1evl( t, sd, 6 );
- cc = x * polevl( t, cn, 5)/polevl(t, cd, 6 );
- goto done;
- }
-
-
-
-
-
-
-if( x > 36974.0 )
- {
- cc = 0.5;
- ss = 0.5;
- goto done;
- }
-
-
-/* Asymptotic power series auxiliary functions
- * for large argument
- */
- x2 = x * x;
- t = PI * x2;
- u = 1.0/(t * t);
- t = 1.0/t;
- f = 1.0 - u * polevl( u, fn, 9)/p1evl(u, fd, 10);
- g = t * polevl( u, gn, 10)/p1evl(u, gd, 11);
-
- t = PIO2 * x2;
- c = cos(t);
- s = sin(t);
- t = PI * x;
- cc = 0.5 + (f * s - g * c)/t;
- ss = 0.5 - (f * c + g * s)/t;
-
-done:
-if( xxa < 0.0 )
- {
- cc = -cc;
- ss = -ss;
- }
-
-*cca = cc;
-*ssa = ss;
-return(0);
-}
+++ /dev/null
-/* gamma.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, gamma();
- * extern int sgngam;
- *
- * y = gamma( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
- *
- * Arguments |x| <= 34 are reduced by recurrence and the function
- * approximated by a rational function of degree 6/7 in the
- * interval (2,3). Large arguments are handled by Stirling's
- * formula. Large negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -34, 34 10000 1.3e-16 2.5e-17
- * IEEE -170,-33 20000 2.3e-15 3.3e-16
- * IEEE -33, 33 20000 9.4e-16 2.2e-16
- * IEEE 33, 171.6 20000 2.3e-15 3.2e-16
- *
- * Error for arguments outside the test range will be larger
- * owing to error amplification by the exponential function.
- *
- */\f
-/* lgam()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, lgam();
- * extern int sgngam;
- *
- * y = lgam( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
- *
- * For arguments greater than 13, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula using a polynomial approximation of
- * degree 4. Arguments between -33 and +33 are reduced by
- * recurrence to the interval [2,3] of a rational approximation.
- * The cosecant reflection formula is employed for arguments
- * less than -33.
- *
- * Arguments greater than MAXLGM return MAXNUM and an error
- * message. MAXLGM = 2.035093e36 for DEC
- * arithmetic or 2.556348e305 for IEEE arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- *
- * arithmetic domain # trials peak rms
- * DEC 0, 3 7000 5.2e-17 1.3e-17
- * DEC 2.718, 2.035e36 5000 3.9e-17 9.9e-18
- * IEEE 0, 3 28000 5.4e-16 1.1e-16
- * IEEE 2.718, 2.556e305 40000 3.5e-16 8.3e-17
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- *
- * The following test used the relative error criterion, though
- * at certain points the relative error could be much higher than
- * indicated.
- * IEEE -200, -4 10000 4.8e-16 1.3e-16
- *
- */
-\f
-/* gamma.c */
-/* gamma function */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
- 1.60119522476751861407E-4,
- 1.19135147006586384913E-3,
- 1.04213797561761569935E-2,
- 4.76367800457137231464E-2,
- 2.07448227648435975150E-1,
- 4.94214826801497100753E-1,
- 9.99999999999999996796E-1
-};
-static double Q[] = {
--2.31581873324120129819E-5,
- 5.39605580493303397842E-4,
--4.45641913851797240494E-3,
- 1.18139785222060435552E-2,
- 3.58236398605498653373E-2,
--2.34591795718243348568E-1,
- 7.14304917030273074085E-2,
- 1.00000000000000000320E0
-};
-#define MAXGAM 171.624376956302725
-static double LOGPI = 1.14472988584940017414;
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0035047,0162701,0146301,0005234,
-0035634,0023437,0032065,0176530,
-0036452,0137157,0047330,0122574,
-0037103,0017310,0143041,0017232,
-0037524,0066516,0162563,0164605,
-0037775,0004671,0146237,0014222,
-0040200,0000000,0000000,0000000
-};
-static unsigned short Q[] = {
-0134302,0041724,0020006,0116565,
-0035415,0072121,0044251,0025634,
-0136222,0003447,0035205,0121114,
-0036501,0107552,0154335,0104271,
-0037022,0135717,0014776,0171471,
-0137560,0034324,0165024,0037021,
-0037222,0045046,0047151,0161213,
-0040200,0000000,0000000,0000000
-};
-#define MAXGAM 34.84425627277176174
-static unsigned short LPI[4] = {
-0040222,0103202,0043475,0006750,
-};
-#define LOGPI *(double *)LPI
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x2153,0x3998,0xfcb8,0x3f24,
-0xbfab,0xe686,0x84e3,0x3f53,
-0x14b0,0xe9db,0x57cd,0x3f85,
-0x23d3,0x18c4,0x63d9,0x3fa8,
-0x7d31,0xdcae,0x8da9,0x3fca,
-0xe312,0x3993,0xa137,0x3fdf,
-0x0000,0x0000,0x0000,0x3ff0
-};
-static unsigned short Q[] = {
-0xd3af,0x8400,0x487a,0xbef8,
-0x2573,0x2915,0xae8a,0x3f41,
-0xb44a,0xe750,0x40e4,0xbf72,
-0xb117,0x5b1b,0x31ed,0x3f88,
-0xde67,0xe33f,0x5779,0x3fa2,
-0x87c2,0x9d42,0x071a,0xbfce,
-0x3c51,0xc9cd,0x4944,0x3fb2,
-0x0000,0x0000,0x0000,0x3ff0
-};
-#define MAXGAM 171.624376956302725
-static unsigned short LPI[4] = {
-0xa1bd,0x48e7,0x50d0,0x3ff2,
-};
-#define LOGPI *(double *)LPI
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f24,0xfcb8,0x3998,0x2153,
-0x3f53,0x84e3,0xe686,0xbfab,
-0x3f85,0x57cd,0xe9db,0x14b0,
-0x3fa8,0x63d9,0x18c4,0x23d3,
-0x3fca,0x8da9,0xdcae,0x7d31,
-0x3fdf,0xa137,0x3993,0xe312,
-0x3ff0,0x0000,0x0000,0x0000
-};
-static unsigned short Q[] = {
-0xbef8,0x487a,0x8400,0xd3af,
-0x3f41,0xae8a,0x2915,0x2573,
-0xbf72,0x40e4,0xe750,0xb44a,
-0x3f88,0x31ed,0x5b1b,0xb117,
-0x3fa2,0x5779,0xe33f,0xde67,
-0xbfce,0x071a,0x9d42,0x87c2,
-0x3fb2,0x4944,0xc9cd,0x3c51,
-0x3ff0,0x0000,0x0000,0x0000
-};
-#define MAXGAM 171.624376956302725
-static unsigned short LPI[4] = {
-0x3ff2,0x50d0,0x48e7,0xa1bd,
-};
-#define LOGPI *(double *)LPI
-#endif
-
-/* Stirling's formula for the gamma function */
-#if UNK
-static double STIR[5] = {
- 7.87311395793093628397E-4,
--2.29549961613378126380E-4,
--2.68132617805781232825E-3,
- 3.47222221605458667310E-3,
- 8.33333333333482257126E-2,
-};
-#define MAXSTIR 143.01608
-static double SQTPI = 2.50662827463100050242E0;
-#endif
-#if DEC
-static unsigned short STIR[20] = {
-0035516,0061622,0144553,0112224,
-0135160,0131531,0037460,0165740,
-0136057,0134460,0037242,0077270,
-0036143,0107070,0156306,0027751,
-0037252,0125252,0125252,0146064,
-};
-#define MAXSTIR 26.77
-static unsigned short SQT[4] = {
-0040440,0066230,0177661,0034055,
-};
-#define SQTPI *(double *)SQT
-#endif
-#if IBMPC
-static unsigned short STIR[20] = {
-0x7293,0x592d,0xcc72,0x3f49,
-0x1d7c,0x27e6,0x166b,0xbf2e,
-0x4fd7,0x07d4,0xf726,0xbf65,
-0xc5fd,0x1b98,0x71c7,0x3f6c,
-0x5986,0x5555,0x5555,0x3fb5,
-};
-#define MAXSTIR 143.01608
-static unsigned short SQT[4] = {
-0x2706,0x1ff6,0x0d93,0x4004,
-};
-#define SQTPI *(double *)SQT
-#endif
-#if MIEEE
-static unsigned short STIR[20] = {
-0x3f49,0xcc72,0x592d,0x7293,
-0xbf2e,0x166b,0x27e6,0x1d7c,
-0xbf65,0xf726,0x07d4,0x4fd7,
-0x3f6c,0x71c7,0x1b98,0xc5fd,
-0x3fb5,0x5555,0x5555,0x5986,
-};
-#define MAXSTIR 143.01608
-static unsigned short SQT[4] = {
-0x4004,0x0d93,0x1ff6,0x2706,
-};
-#define SQTPI *(double *)SQT
-#endif
-
-int sgngam = 0;
-extern int sgngam;
-extern double MAXLOG, MAXNUM, PI;
-#ifdef ANSIPROT
-extern double pow ( double, double );
-extern double log ( double );
-extern double exp ( double );
-extern double sin ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double fabs ( double );
-extern int isnan ( double );
-extern int isfinite ( double );
-static double stirf ( double );
-double lgam ( double );
-#else
-double pow(), log(), exp(), sin(), polevl(), p1evl(), floor(), fabs();
-int isnan(), isfinite();
-static double stirf();
-double lgam();
-#endif
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-#ifdef NANS
-extern double NAN;
-#endif
-
-/* Gamma function computed by Stirling's formula.
- * The polynomial STIR is valid for 33 <= x <= 172.
- */
-static double stirf(x)
-double x;
-{
-double y, w, v;
-
-w = 1.0/x;
-w = 1.0 + w * polevl( w, STIR, 4 );
-y = exp(x);
-if( x > MAXSTIR )
- { /* Avoid overflow in pow() */
- v = pow( x, 0.5 * x - 0.25 );
- y = v * (v / y);
- }
-else
- {
- y = pow( x, x - 0.5 ) / y;
- }
-y = SQTPI * y * w;
-return( y );
-}
-
-
-
-double gamma(x)
-double x;
-{
-double p, q, z;
-int i;
-
-sgngam = 1;
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-#ifdef NANS
-if( x == INFINITY )
- return(x);
-if( x == -INFINITY )
- return(NAN);
-#else
-if( !isfinite(x) )
- return(x);
-#endif
-#endif
-q = fabs(x);
-
-if( q > 33.0 )
- {
- if( x < 0.0 )
- {
- p = floor(q);
- if( p == q )
- {
-#ifdef NANS
-gamnan:
- mtherr( "gamma", DOMAIN );
- return (NAN);
-#else
- goto goverf;
-#endif
- }
- i = p;
- if( (i & 1) == 0 )
- sgngam = -1;
- z = q - p;
- if( z > 0.5 )
- {
- p += 1.0;
- z = q - p;
- }
- z = q * sin( PI * z );
- if( z == 0.0 )
- {
-#ifdef INFINITIES
- return( sgngam * INFINITY);
-#else
-goverf:
- mtherr( "gamma", OVERFLOW );
- return( sgngam * MAXNUM);
-#endif
- }
- z = fabs(z);
- z = PI/(z * stirf(q) );
- }
- else
- {
- z = stirf(x);
- }
- return( sgngam * z );
- }
-
-z = 1.0;
-while( x >= 3.0 )
- {
- x -= 1.0;
- z *= x;
- }
-
-while( x < 0.0 )
- {
- if( x > -1.E-9 )
- goto small;
- z /= x;
- x += 1.0;
- }
-
-while( x < 2.0 )
- {
- if( x < 1.e-9 )
- goto small;
- z /= x;
- x += 1.0;
- }
-
-if( x == 2.0 )
- return(z);
-
-x -= 2.0;
-p = polevl( x, P, 6 );
-q = polevl( x, Q, 7 );
-return( z * p / q );
-
-small:
-if( x == 0.0 )
- {
-#ifdef INFINITIES
-#ifdef NANS
- goto gamnan;
-#else
- return( INFINITY );
-#endif
-#else
- mtherr( "gamma", SING );
- return( MAXNUM );
-#endif
- }
-else
- return( z/((1.0 + 0.5772156649015329 * x) * x) );
-}
-
-
-
-/* A[]: Stirling's formula expansion of log gamma
- * B[], C[]: log gamma function between 2 and 3
- */
-#ifdef UNK
-static double A[] = {
- 8.11614167470508450300E-4,
--5.95061904284301438324E-4,
- 7.93650340457716943945E-4,
--2.77777777730099687205E-3,
- 8.33333333333331927722E-2
-};
-static double B[] = {
--1.37825152569120859100E3,
--3.88016315134637840924E4,
--3.31612992738871184744E5,
--1.16237097492762307383E6,
--1.72173700820839662146E6,
--8.53555664245765465627E5
-};
-static double C[] = {
-/* 1.00000000000000000000E0, */
--3.51815701436523470549E2,
--1.70642106651881159223E4,
--2.20528590553854454839E5,
--1.13933444367982507207E6,
--2.53252307177582951285E6,
--2.01889141433532773231E6
-};
-/* log( sqrt( 2*pi ) ) */
-static double LS2PI = 0.91893853320467274178;
-#define MAXLGM 2.556348e305
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0035524,0141201,0034633,0031405,
-0135433,0176755,0126007,0045030,
-0035520,0006371,0003342,0172730,
-0136066,0005540,0132605,0026407,
-0037252,0125252,0125252,0125132
-};
-static unsigned short B[] = {
-0142654,0044014,0077633,0035410,
-0144027,0110641,0125335,0144760,
-0144641,0165637,0142204,0047447,
-0145215,0162027,0146246,0155211,
-0145322,0026110,0010317,0110130,
-0145120,0061472,0120300,0025363
-};
-static unsigned short C[] = {
-/*0040200,0000000,0000000,0000000*/
-0142257,0164150,0163630,0112622,
-0143605,0050153,0156116,0135272,
-0144527,0056045,0145642,0062332,
-0145213,0012063,0106250,0001025,
-0145432,0111254,0044577,0115142,
-0145366,0071133,0050217,0005122
-};
-/* log( sqrt( 2*pi ) ) */
-static unsigned short LS2P[] = {040153,037616,041445,0172645,};
-#define LS2PI *(double *)LS2P
-#define MAXLGM 2.035093e36
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0x6661,0x2733,0x9850,0x3f4a,
-0xe943,0xb580,0x7fbd,0xbf43,
-0x5ebb,0x20dc,0x019f,0x3f4a,
-0xa5a1,0x16b0,0xc16c,0xbf66,
-0x554b,0x5555,0x5555,0x3fb5
-};
-static unsigned short B[] = {
-0x6761,0x8ff3,0x8901,0xc095,
-0xb93e,0x355b,0xf234,0xc0e2,
-0x89e5,0xf890,0x3d73,0xc114,
-0xdb51,0xf994,0xbc82,0xc131,
-0xf20b,0x0219,0x4589,0xc13a,
-0x055e,0x5418,0x0c67,0xc12a
-};
-static unsigned short C[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x12b2,0x1cf3,0xfd0d,0xc075,
-0xd757,0x7b89,0xaa0d,0xc0d0,
-0x4c9b,0xb974,0xeb84,0xc10a,
-0x0043,0x7195,0x6286,0xc131,
-0xf34c,0x892f,0x5255,0xc143,
-0xe14a,0x6a11,0xce4b,0xc13e
-};
-/* log( sqrt( 2*pi ) ) */
-static unsigned short LS2P[] = {
-0xbeb5,0xc864,0x67f1,0x3fed
-};
-#define LS2PI *(double *)LS2P
-#define MAXLGM 2.556348e305
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0x3f4a,0x9850,0x2733,0x6661,
-0xbf43,0x7fbd,0xb580,0xe943,
-0x3f4a,0x019f,0x20dc,0x5ebb,
-0xbf66,0xc16c,0x16b0,0xa5a1,
-0x3fb5,0x5555,0x5555,0x554b
-};
-static unsigned short B[] = {
-0xc095,0x8901,0x8ff3,0x6761,
-0xc0e2,0xf234,0x355b,0xb93e,
-0xc114,0x3d73,0xf890,0x89e5,
-0xc131,0xbc82,0xf994,0xdb51,
-0xc13a,0x4589,0x0219,0xf20b,
-0xc12a,0x0c67,0x5418,0x055e
-};
-static unsigned short C[] = {
-0xc075,0xfd0d,0x1cf3,0x12b2,
-0xc0d0,0xaa0d,0x7b89,0xd757,
-0xc10a,0xeb84,0xb974,0x4c9b,
-0xc131,0x6286,0x7195,0x0043,
-0xc143,0x5255,0x892f,0xf34c,
-0xc13e,0xce4b,0x6a11,0xe14a
-};
-/* log( sqrt( 2*pi ) ) */
-static unsigned short LS2P[] = {
-0x3fed,0x67f1,0xc864,0xbeb5
-};
-#define LS2PI *(double *)LS2P
-#define MAXLGM 2.556348e305
-#endif
-
-
-/* Logarithm of gamma function */
-
-
-double lgam(x)
-double x;
-{
-double p, q, u, w, z;
-int i;
-
-sgngam = 1;
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-
-#ifdef INFINITIES
-if( !isfinite(x) )
- return(INFINITY);
-#endif
-
-if( x < -34.0 )
- {
- q = -x;
- w = lgam(q); /* note this modifies sgngam! */
- p = floor(q);
- if( p == q )
- {
-lgsing:
-#ifdef INFINITIES
- mtherr( "lgam", SING );
- return (INFINITY);
-#else
- goto loverf;
-#endif
- }
- i = p;
- if( (i & 1) == 0 )
- sgngam = -1;
- else
- sgngam = 1;
- z = q - p;
- if( z > 0.5 )
- {
- p += 1.0;
- z = p - q;
- }
- z = q * sin( PI * z );
- if( z == 0.0 )
- goto lgsing;
-/* z = log(PI) - log( z ) - w;*/
- z = LOGPI - log( z ) - w;
- return( z );
- }
-
-if( x < 13.0 )
- {
- z = 1.0;
- p = 0.0;
- u = x;
- while( u >= 3.0 )
- {
- p -= 1.0;
- u = x + p;
- z *= u;
- }
- while( u < 2.0 )
- {
- if( u == 0.0 )
- goto lgsing;
- z /= u;
- p += 1.0;
- u = x + p;
- }
- if( z < 0.0 )
- {
- sgngam = -1;
- z = -z;
- }
- else
- sgngam = 1;
- if( u == 2.0 )
- return( log(z) );
- p -= 2.0;
- x = x + p;
- p = x * polevl( x, B, 5 ) / p1evl( x, C, 6);
- return( log(z) + p );
- }
-
-if( x > MAXLGM )
- {
-#ifdef INFINITIES
- return( sgngam * INFINITY );
-#else
-loverf:
- mtherr( "lgam", OVERFLOW );
- return( sgngam * MAXNUM );
-#endif
- }
-
-q = ( x - 0.5 ) * log(x) - x + LS2PI;
-if( x > 1.0e8 )
- return( q );
-
-p = 1.0/(x*x);
-if( x >= 1000.0 )
- q += (( 7.9365079365079365079365e-4 * p
- - 2.7777777777777777777778e-3) *p
- + 0.0833333333333333333333) / x;
-else
- q += polevl( p, A, 4 ) / x;
-return( q );
-}
+++ /dev/null
-/* gdtr.c
- *
- * Gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, gdtr();
- *
- * y = gdtr( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from zero to x of the gamma probability
- * density function:
- *
- *
- * x
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * 0
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igam( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtr domain x < 0 0.0
- *
- */
-\f/* gdtrc.c
- *
- * Complemented gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, gdtrc();
- *
- * y = gdtrc( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from x to infinity of the gamma
- * probability density function:
- *
- *
- * inf.
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * x
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igamc( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrc domain x < 0 0.0
- *
- */
-\f
-/* gdtr() */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double igam ( double, double );
-extern double igamc ( double, double );
-#else
-double igam(), igamc();
-#endif
-
-double gdtr( a, b, x )
-double a, b, x;
-{
-
-if( x < 0.0 )
- {
- mtherr( "gdtr", DOMAIN );
- return( 0.0 );
- }
-return( igam( b, a * x ) );
-}
-
-
-
-double gdtrc( a, b, x )
-double a, b, x;
-{
-
-if( x < 0.0 )
- {
- mtherr( "gdtrc", DOMAIN );
- return( 0.0 );
- }
-return( igamc( b, a * x ) );
-}
+++ /dev/null
-/*
-C
-C ..................................................................
-C
-C SUBROUTINE GELS
-C
-C PURPOSE
-C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
-C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
-C IS ASSUMED TO BE STORED COLUMNWISE.
-C
-C USAGE
-C CALL GELS(R,A,M,N,EPS,IER,AUX)
-C
-C DESCRIPTION OF PARAMETERS
-C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
-C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
-C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
-C M BY M COEFFICIENT MATRIX. (DESTROYED)
-C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
-C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
-C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
-C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
-C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
-C IER=0 - NO ERROR,
-C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
-C PIVOT ELEMENT AT ANY ELIMINATION STEP
-C EQUAL TO 0,
-C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
-C CANCE INDICATED AT ELIMINATION STEP K+1,
-C WHERE PIVOT ELEMENT WAS LESS THAN OR
-C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
-C ABSOLUTELY GREATEST MAIN DIAGONAL
-C ELEMENT OF MATRIX A.
-C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
-C
-C REMARKS
-C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
-C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
-C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
-C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
-C TOO.
-C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
-C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
-C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
-C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
-C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
-C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
-C GIVEN IN CASE M=1.
-C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
-C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
-C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
-C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
-C
-C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
-C NONE
-C
-C METHOD
-C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
-C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
-C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
-C
-C ..................................................................
-C
-*/
-#include <math.h>
-#ifdef ANSIPROT
-extern double fabs ( double );
-#else
-double fabs();
-#endif
-
-gels( A, R, M, EPS, AUX )
-double A[],R[];
-int M;
-double EPS;
-double AUX[];
-{
-int I, J, K, L, IER;
-int II, LL, LLD, LR, LT, LST, LLST, LEND;
-double tb, piv, tol, pivi;
-
-if( M <= 0 )
- {
-fatal:
- IER = -1;
- goto done;
- }
-/* SEARCH FOR GREATEST MAIN DIAGONAL ELEMENT */
-
-/* Diagonal elements are at A(i,i) = 1, 3, 6, 10, ...
- * A(i,j) = A( i(i-1)/2 + j )
- */
-IER = 0;
-piv = 0.0;
-L = 0;
-for( K=1; K<=M; K++ )
- {
- L += K;
- tb = fabs( A[L-1] );
- if( tb > piv )
- {
- piv = tb;
- I = L;
- J = K;
- }
- }
-tol = EPS * piv;
-
-/*
-C MAIN DIAGONAL ELEMENT A(I)=A(J,J) IS FIRST PIVOT ELEMENT.
-C PIV CONTAINS THE ABSOLUTE VALUE OF A(I).
-*/
-
-/* START ELIMINATION LOOP */
-LST = 0;
-LEND = M - 1;
-for( K=1; K<=M; K++ )
- {
-/* TEST ON USEFULNESS OF SYMMETRIC ALGORITHM */
- if( piv <= 0.0 )
- goto fatal;
- if( IER == 0 )
- {
- if( piv <= tol )
- {
- IER = K - 1;
- }
- }
- LT = J - K;
- LST += K;
-
-/* PIVOT ROW REDUCTION AND ROW INTERCHANGE IN RIGHT HAND SIDE R */
- pivi = 1.0 / A[I-1];
- L = K;
- LL = L + LT;
- tb = pivi * R[LL-1];
- R[LL-1] = R[L-1];
- R[L-1] = tb;
-/* IS ELIMINATION TERMINATED */
- if( K >= M )
- break;
-/*
-C ROW AND COLUMN INTERCHANGE AND PIVOT ROW REDUCTION IN MATRIX A.
-C ELEMENTS OF PIVOT COLUMN ARE SAVED IN AUXILIARY VECTOR AUX.
-*/
- LR = LST + (LT*(K+J-1))/2;
- LL = LR;
- L=LST;
- for( II=K; II<=LEND; II++ )
- {
- L += II;
- LL += 1;
- if( L == LR )
- {
- A[LL-1] = A[LST-1];
- tb = A[L-1];
- goto lab13;
- }
- if( L > LR )
- LL = L + LT;
-
- tb = A[LL-1];
- A[LL-1] = A[L-1];
-lab13:
- AUX[II-1] = tb;
- A[L-1] = pivi * tb;
- }
-/* SAVE COLUMN INTERCHANGE INFORMATION */
- A[LST-1] = LT;
-/* ELEMENT REDUCTION AND SEARCH FOR NEXT PIVOT */
- piv = 0.0;
- LLST = LST;
- LT = 0;
- for( II=K; II<=LEND; II++ )
- {
- pivi = -AUX[II-1];
- LL = LLST;
- LT += 1;
- for( LLD=II; LLD<=LEND; LLD++ )
- {
- LL += LLD;
- L = LL + LT;
- A[L-1] += pivi * A[LL-1];
- }
- LLST += II;
- LR = LLST + LT;
- tb =fabs( A[LR-1] );
- if( tb > piv )
- {
- piv = tb;
- I = LR;
- J = II + 1;
- }
- LR = K;
- LL = LR + LT;
- R[LL-1] += pivi * R[LR-1];
- }
- }
-/* END OF ELIMINATION LOOP */
-
-/* BACK SUBSTITUTION AND BACK INTERCHANGE */
-
-if( LEND <= 0 )
- {
- if( LEND < 0 )
- goto fatal;
- goto done;
- }
-II = M;
-for( I=2; I<=M; I++ )
- {
- LST -= II;
- II -= 1;
- L = A[LST-1] + 0.5;
- J = II;
- tb = R[J-1];
- LL = J;
- K = LST;
- for( LT=II; LT<=LEND; LT++ )
- {
- LL += 1;
- K += LT;
- tb -= A[K-1] * R[LL-1];
- }
- K = J + L;
- R[J-1] = R[K-1];
- R[K-1] = tb;
- }
-done:
-return( IER );
-}
+++ /dev/null
-/* hyp2f1.c
- *
- * Gauss hypergeometric function F
- * 2 1
- *
- *
- * SYNOPSIS:
- *
- * double a, b, c, x, y, hyp2f1();
- *
- * y = hyp2f1( a, b, c, x );
- *
- *
- * DESCRIPTION:
- *
- *
- * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
- * 2 1
- *
- * inf.
- * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
- * = 1 + > ----------------------------- x .
- * - c(c+1)...(c+k) (k+1)!
- * k = 0
- *
- * Cases addressed are
- * Tests and escapes for negative integer a, b, or c
- * Linear transformation if c - a or c - b negative integer
- * Special case c = a or c = b
- * Linear transformation for x near +1
- * Transformation for x < -0.5
- * Psi function expansion if x > 0.5 and c - a - b integer
- * Conditionally, a recurrence on c to make c-a-b > 0
- *
- * |x| > 1 is rejected.
- *
- * The parameters a, b, c are considered to be integer
- * valued if they are within 1.0e-14 of the nearest integer
- * (1.0e-13 for IEEE arithmetic).
- *
- * ACCURACY:
- *
- *
- * Relative error (-1 < x < 1):
- * arithmetic domain # trials peak rms
- * IEEE -1,7 230000 1.2e-11 5.2e-14
- *
- * Several special cases also tested with a, b, c in
- * the range -7 to 7.
- *
- * ERROR MESSAGES:
- *
- * A "partial loss of precision" message is printed if
- * the internally estimated relative error exceeds 1^-12.
- * A "singularity" message is printed on overflow or
- * in cases not addressed (such as x < -1).
- */
-\f
-/* hyp2f1 */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef DEC
-#define EPS 1.0e-14
-#define EPS2 1.0e-11
-#endif
-
-#ifdef IBMPC
-#define EPS 1.0e-13
-#define EPS2 1.0e-10
-#endif
-
-#ifdef MIEEE
-#define EPS 1.0e-13
-#define EPS2 1.0e-10
-#endif
-
-#ifdef UNK
-#define EPS 1.0e-13
-#define EPS2 1.0e-10
-#endif
-
-#define ETHRESH 1.0e-12
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double pow ( double, double );
-extern double round ( double );
-extern double gamma ( double );
-extern double log ( double );
-extern double exp ( double );
-extern double psi ( double );
-static double hyt2f1(double, double, double, double, double *);
-static double hys2f1(double, double, double, double, double *);
-double hyp2f1(double, double, double, double);
-#else
-double fabs(), pow(), round(), gamma(), log(), exp(), psi();
-static double hyt2f1();
-static double hys2f1();
-double hyp2f1();
-#endif
-extern double MAXNUM, MACHEP;
-
-double hyp2f1( a, b, c, x )
-double a, b, c, x;
-{
-double d, d1, d2, e;
-double p, q, r, s, y, ax;
-double ia, ib, ic, id, err;
-int flag, i, aid;
-
-err = 0.0;
-ax = fabs(x);
-s = 1.0 - x;
-flag = 0;
-ia = round(a); /* nearest integer to a */
-ib = round(b);
-
-if( a <= 0 )
- {
- if( fabs(a-ia) < EPS ) /* a is a negative integer */
- flag |= 1;
- }
-
-if( b <= 0 )
- {
- if( fabs(b-ib) < EPS ) /* b is a negative integer */
- flag |= 2;
- }
-
-if( ax < 1.0 )
- {
- if( fabs(b-c) < EPS ) /* b = c */
- {
- y = pow( s, -a ); /* s to the -a power */
- goto hypdon;
- }
- if( fabs(a-c) < EPS ) /* a = c */
- {
- y = pow( s, -b ); /* s to the -b power */
- goto hypdon;
- }
- }
-
-
-
-if( c <= 0.0 )
- {
- ic = round(c); /* nearest integer to c */
- if( fabs(c-ic) < EPS ) /* c is a negative integer */
- {
- /* check if termination before explosion */
- if( (flag & 1) && (ia > ic) )
- goto hypok;
- if( (flag & 2) && (ib > ic) )
- goto hypok;
- goto hypdiv;
- }
- }
-
-if( flag ) /* function is a polynomial */
- goto hypok;
-
-if( ax > 1.0 ) /* series diverges */
- goto hypdiv;
-
-p = c - a;
-ia = round(p); /* nearest integer to c-a */
-if( (ia <= 0.0) && (fabs(p-ia) < EPS) ) /* negative int c - a */
- flag |= 4;
-
-r = c - b;
-ib = round(r); /* nearest integer to c-b */
-if( (ib <= 0.0) && (fabs(r-ib) < EPS) ) /* negative int c - b */
- flag |= 8;
-
-d = c - a - b;
-id = round(d); /* nearest integer to d */
-q = fabs(d-id);
-
-/* Thanks to Christian Burger <BURGER@DMRHRZ11.HRZ.Uni-Marburg.DE>
- * for reporting a bug here. */
-if( fabs(ax-1.0) < EPS ) /* |x| == 1.0 */
- {
- if( x > 0.0 )
- {
- if( flag & 12 ) /* negative int c-a or c-b */
- {
- if( d >= 0.0 )
- goto hypf;
- else
- goto hypdiv;
- }
- if( d <= 0.0 )
- goto hypdiv;
- y = gamma(c)*gamma(d)/(gamma(p)*gamma(r));
- goto hypdon;
- }
-
- if( d <= -1.0 )
- goto hypdiv;
-
- }
-
-/* Conditionally make d > 0 by recurrence on c
- * AMS55 #15.2.27
- */
-if( d < 0.0 )
- {
-/* Try the power series first */
- y = hyt2f1( a, b, c, x, &err );
- if( err < ETHRESH )
- goto hypdon;
-/* Apply the recurrence if power series fails */
- err = 0.0;
- aid = 2 - id;
- e = c + aid;
- d2 = hyp2f1(a,b,e,x);
- d1 = hyp2f1(a,b,e+1.0,x);
- q = a + b + 1.0;
- for( i=0; i<aid; i++ )
- {
- r = e - 1.0;
- y = (e*(r-(2.0*e-q)*x)*d2 + (e-a)*(e-b)*x*d1)/(e*r*s);
- e = r;
- d1 = d2;
- d2 = y;
- }
- goto hypdon;
- }
-
-
-if( flag & 12 )
- goto hypf; /* negative integer c-a or c-b */
-
-hypok:
-y = hyt2f1( a, b, c, x, &err );
-
-
-hypdon:
-if( err > ETHRESH )
- {
- mtherr( "hyp2f1", PLOSS );
-/* printf( "Estimated err = %.2e\n", err ); */
- }
-return(y);
-
-/* The transformation for c-a or c-b negative integer
- * AMS55 #15.3.3
- */
-hypf:
-y = pow( s, d ) * hys2f1( c-a, c-b, c, x, &err );
-goto hypdon;
-
-/* The alarm exit */
-hypdiv:
-mtherr( "hyp2f1", OVERFLOW );
-return( MAXNUM );
-}
-
-
-
-
-
-
-/* Apply transformations for |x| near 1
- * then call the power series
- */
-static double hyt2f1( a, b, c, x, loss )
-double a, b, c, x;
-double *loss;
-{
-double p, q, r, s, t, y, d, err, err1;
-double ax, id, d1, d2, e, y1;
-int i, aid;
-
-err = 0.0;
-s = 1.0 - x;
-if( x < -0.5 )
- {
- if( b > a )
- y = pow( s, -a ) * hys2f1( a, c-b, c, -x/s, &err );
-
- else
- y = pow( s, -b ) * hys2f1( c-a, b, c, -x/s, &err );
-
- goto done;
- }
-
-d = c - a - b;
-id = round(d); /* nearest integer to d */
-
-if( x > 0.9 )
-{
-if( fabs(d-id) > EPS ) /* test for integer c-a-b */
- {
-/* Try the power series first */
- y = hys2f1( a, b, c, x, &err );
- if( err < ETHRESH )
- goto done;
-/* If power series fails, then apply AMS55 #15.3.6 */
- q = hys2f1( a, b, 1.0-d, s, &err );
- q *= gamma(d) /(gamma(c-a) * gamma(c-b));
- r = pow(s,d) * hys2f1( c-a, c-b, d+1.0, s, &err1 );
- r *= gamma(-d)/(gamma(a) * gamma(b));
- y = q + r;
-
- q = fabs(q); /* estimate cancellation error */
- r = fabs(r);
- if( q > r )
- r = q;
- err += err1 + (MACHEP*r)/y;
-
- y *= gamma(c);
- goto done;
- }
-else
- {
-/* Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12 */
- if( id >= 0.0 )
- {
- e = d;
- d1 = d;
- d2 = 0.0;
- aid = id;
- }
- else
- {
- e = -d;
- d1 = 0.0;
- d2 = d;
- aid = -id;
- }
-
- ax = log(s);
-
- /* sum for t = 0 */
- y = psi(1.0) + psi(1.0+e) - psi(a+d1) - psi(b+d1) - ax;
- y /= gamma(e+1.0);
-
- p = (a+d1) * (b+d1) * s / gamma(e+2.0); /* Poch for t=1 */
- t = 1.0;
- do
- {
- r = psi(1.0+t) + psi(1.0+t+e) - psi(a+t+d1)
- - psi(b+t+d1) - ax;
- q = p * r;
- y += q;
- p *= s * (a+t+d1) / (t+1.0);
- p *= (b+t+d1) / (t+1.0+e);
- t += 1.0;
- }
- while( fabs(q/y) > EPS );
-
-
- if( id == 0.0 )
- {
- y *= gamma(c)/(gamma(a)*gamma(b));
- goto psidon;
- }
-
- y1 = 1.0;
-
- if( aid == 1 )
- goto nosum;
-
- t = 0.0;
- p = 1.0;
- for( i=1; i<aid; i++ )
- {
- r = 1.0-e+t;
- p *= s * (a+t+d2) * (b+t+d2) / r;
- t += 1.0;
- p /= t;
- y1 += p;
- }
-nosum:
- p = gamma(c);
- y1 *= gamma(e) * p / (gamma(a+d1) * gamma(b+d1));
-
- y *= p / (gamma(a+d2) * gamma(b+d2));
- if( (aid & 1) != 0 )
- y = -y;
-
- q = pow( s, id ); /* s to the id power */
- if( id > 0.0 )
- y *= q;
- else
- y1 *= q;
-
- y += y1;
-psidon:
- goto done;
- }
-
-}
-
-/* Use defining power series if no special cases */
-y = hys2f1( a, b, c, x, &err );
-
-done:
-*loss = err;
-return(y);
-}
-
-
-
-
-
-/* Defining power series expansion of Gauss hypergeometric function */
-
-static double hys2f1( a, b, c, x, loss )
-double a, b, c, x;
-double *loss; /* estimates loss of significance */
-{
-double f, g, h, k, m, s, u, umax;
-int i;
-
-i = 0;
-umax = 0.0;
-f = a;
-g = b;
-h = c;
-s = 1.0;
-u = 1.0;
-k = 0.0;
-do
- {
- if( fabs(h) < EPS )
- {
- *loss = 1.0;
- return( MAXNUM );
- }
- m = k + 1.0;
- u = u * ((f+k) * (g+k) * x / ((h+k) * m));
- s += u;
- k = fabs(u); /* remember largest term summed */
- if( k > umax )
- umax = k;
- k = m;
- if( ++i > 10000 ) /* should never happen */
- {
- *loss = 1.0;
- return(s);
- }
- }
-while( fabs(u/s) > MACHEP );
-
-/* return estimated relative error */
-*loss = (MACHEP*umax)/fabs(s) + (MACHEP*i);
-
-return(s);
-}
+++ /dev/null
-/* hyperg.c
- *
- * Confluent hypergeometric function
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, hyperg();
- *
- * y = hyperg( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the confluent hypergeometric function
- *
- * 1 2
- * a x a(a+1) x
- * F ( a,b;x ) = 1 + ---- + --------- + ...
- * 1 1 b 1! b(b+1) 2!
- *
- * Many higher transcendental functions are special cases of
- * this power series.
- *
- * As is evident from the formula, b must not be a negative
- * integer or zero unless a is an integer with 0 >= a > b.
- *
- * The routine attempts both a direct summation of the series
- * and an asymptotic expansion. In each case error due to
- * roundoff, cancellation, and nonconvergence is estimated.
- * The result with smaller estimated error is returned.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (a, b, x), all three variables
- * ranging from 0 to 30.
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 2000 1.2e-15 1.3e-16
- qtst1:
- 21800 max = 1.4200E-14 rms = 1.0841E-15 ave = -5.3640E-17
- ltstd:
- 25500 max = 1.2759e-14 rms = 3.7155e-16 ave = 1.5384e-18
- * IEEE 0,30 30000 1.8e-14 1.1e-15
- *
- * Larger errors can be observed when b is near a negative
- * integer or zero. Certain combinations of arguments yield
- * serious cancellation error in the power series summation
- * and also are not in the region of near convergence of the
- * asymptotic series. An error message is printed if the
- * self-estimated relative error is greater than 1.0e-12.
- *
- */
-\f
-/* hyperg.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef ANSIPROT
-extern double exp ( double );
-extern double log ( double );
-extern double gamma ( double );
-extern double lgam ( double );
-extern double fabs ( double );
-double hyp2f0 ( double, double, double, int, double * );
-static double hy1f1p(double, double, double, double *);
-static double hy1f1a(double, double, double, double *);
-double hyperg (double, double, double);
-#else
-double exp(), log(), gamma(), lgam(), fabs(), hyp2f0();
-static double hy1f1p();
-static double hy1f1a();
-double hyperg();
-#endif
-extern double MAXNUM, MACHEP;
-
-double hyperg( a, b, x)
-double a, b, x;
-{
-double asum, psum, acanc, pcanc, temp;
-
-/* See if a Kummer transformation will help */
-temp = b - a;
-if( fabs(temp) < 0.001 * fabs(a) )
- return( exp(x) * hyperg( temp, b, -x ) );
-
-
-psum = hy1f1p( a, b, x, &pcanc );
-if( pcanc < 1.0e-15 )
- goto done;
-
-
-/* try asymptotic series */
-
-asum = hy1f1a( a, b, x, &acanc );
-
-
-/* Pick the result with less estimated error */
-
-if( acanc < pcanc )
- {
- pcanc = acanc;
- psum = asum;
- }
-
-done:
-if( pcanc > 1.0e-12 )
- mtherr( "hyperg", PLOSS );
-
-return( psum );
-}
-
-
-
-
-/* Power series summation for confluent hypergeometric function */
-
-
-static double hy1f1p( a, b, x, err )
-double a, b, x;
-double *err;
-{
-double n, a0, sum, t, u, temp;
-double an, bn, maxt, pcanc;
-
-
-/* set up for power series summation */
-an = a;
-bn = b;
-a0 = 1.0;
-sum = 1.0;
-n = 1.0;
-t = 1.0;
-maxt = 0.0;
-
-
-while( t > MACHEP )
- {
- if( bn == 0 ) /* check bn first since if both */
- {
- mtherr( "hyperg", SING );
- return( MAXNUM ); /* an and bn are zero it is */
- }
- if( an == 0 ) /* a singularity */
- return( sum );
- if( n > 200 )
- goto pdone;
- u = x * ( an / (bn * n) );
-
- /* check for blowup */
- temp = fabs(u);
- if( (temp > 1.0 ) && (maxt > (MAXNUM/temp)) )
- {
- pcanc = 1.0; /* estimate 100% error */
- goto blowup;
- }
-
- a0 *= u;
- sum += a0;
- t = fabs(a0);
- if( t > maxt )
- maxt = t;
-/*
- if( (maxt/fabs(sum)) > 1.0e17 )
- {
- pcanc = 1.0;
- goto blowup;
- }
-*/
- an += 1.0;
- bn += 1.0;
- n += 1.0;
- }
-
-pdone:
-
-/* estimate error due to roundoff and cancellation */
-if( sum != 0.0 )
- maxt /= fabs(sum);
-maxt *= MACHEP; /* this way avoids multiply overflow */
-pcanc = fabs( MACHEP * n + maxt );
-
-blowup:
-
-*err = pcanc;
-
-return( sum );
-}
-
-
-/* hy1f1a() */
-/* asymptotic formula for hypergeometric function:
- *
- * ( -a
- * -- ( |z|
- * | (b) ( -------- 2f0( a, 1+a-b, -1/x )
- * ( --
- * ( | (b-a)
- *
- *
- * x a-b )
- * e |x| )
- * + -------- 2f0( b-a, 1-a, 1/x ) )
- * -- )
- * | (a) )
- */
-
-static double hy1f1a( a, b, x, err )
-double a, b, x;
-double *err;
-{
-double h1, h2, t, u, temp, acanc, asum, err1, err2;
-
-if( x == 0 )
- {
- acanc = 1.0;
- asum = MAXNUM;
- goto adone;
- }
-temp = log( fabs(x) );
-t = x + temp * (a-b);
-u = -temp * a;
-
-if( b > 0 )
- {
- temp = lgam(b);
- t += temp;
- u += temp;
- }
-
-h1 = hyp2f0( a, a-b+1, -1.0/x, 1, &err1 );
-
-temp = exp(u) / gamma(b-a);
-h1 *= temp;
-err1 *= temp;
-
-h2 = hyp2f0( b-a, 1.0-a, 1.0/x, 2, &err2 );
-
-if( a < 0 )
- temp = exp(t) / gamma(a);
-else
- temp = exp( t - lgam(a) );
-
-h2 *= temp;
-err2 *= temp;
-
-if( x < 0.0 )
- asum = h1;
-else
- asum = h2;
-
-acanc = fabs(err1) + fabs(err2);
-
-
-if( b < 0 )
- {
- temp = gamma(b);
- asum *= temp;
- acanc *= fabs(temp);
- }
-
-
-if( asum != 0.0 )
- acanc /= fabs(asum);
-
-acanc *= 30.0; /* fudge factor, since error of asymptotic formula
- * often seems this much larger than advertised */
-
-adone:
-
-
-*err = acanc;
-return( asum );
-}
-\f
-/* hyp2f0() */
-
-double hyp2f0( a, b, x, type, err )
-double a, b, x;
-int type; /* determines what converging factor to use */
-double *err;
-{
-double a0, alast, t, tlast, maxt;
-double n, an, bn, u, sum, temp;
-
-an = a;
-bn = b;
-a0 = 1.0e0;
-alast = 1.0e0;
-sum = 0.0;
-n = 1.0e0;
-t = 1.0e0;
-tlast = 1.0e9;
-maxt = 0.0;
-
-do
- {
- if( an == 0 )
- goto pdone;
- if( bn == 0 )
- goto pdone;
-
- u = an * (bn * x / n);
-
- /* check for blowup */
- temp = fabs(u);
- if( (temp > 1.0 ) && (maxt > (MAXNUM/temp)) )
- goto error;
-
- a0 *= u;
- t = fabs(a0);
-
- /* terminating condition for asymptotic series */
- if( t > tlast )
- goto ndone;
-
- tlast = t;
- sum += alast; /* the sum is one term behind */
- alast = a0;
-
- if( n > 200 )
- goto ndone;
-
- an += 1.0e0;
- bn += 1.0e0;
- n += 1.0e0;
- if( t > maxt )
- maxt = t;
- }
-while( t > MACHEP );
-
-
-pdone: /* series converged! */
-
-/* estimate error due to roundoff and cancellation */
-*err = fabs( MACHEP * (n + maxt) );
-
-alast = a0;
-goto done;
-
-ndone: /* series did not converge */
-
-/* The following "Converging factors" are supposed to improve accuracy,
- * but do not actually seem to accomplish very much. */
-
-n -= 1.0;
-x = 1.0/x;
-
-switch( type ) /* "type" given as subroutine argument */
-{
-case 1:
- alast *= ( 0.5 + (0.125 + 0.25*b - 0.5*a + 0.25*x - 0.25*n)/x );
- break;
-
-case 2:
- alast *= 2.0/3.0 - b + 2.0*a + x - n;
- break;
-
-default:
- ;
-}
-
-/* estimate error due to roundoff, cancellation, and nonconvergence */
-*err = MACHEP * (n + maxt) + fabs ( a0 );
-
-
-done:
-sum += alast;
-return( sum );
-
-/* series blew up: */
-error:
-*err = MAXNUM;
-mtherr( "hyperg", TLOSS );
-return( sum );
-}
+++ /dev/null
-/* i0.c
- *
- * Modified Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i0();
- *
- * y = i0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order zero of the
- * argument.
- *
- * The function is defined as i0(x) = j0( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 6000 8.2e-17 1.9e-17
- * IEEE 0,30 30000 5.8e-16 1.4e-16
- *
- */
-\f/* i0e.c
- *
- * Modified Bessel function of order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i0e();
- *
- * y = i0e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order zero of the argument.
- *
- * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 5.4e-16 1.2e-16
- * See i0().
- *
- */
-\f
-/* i0.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for exp(-x) I0(x)
- * in the interval [0,8].
- *
- * lim(x->0){ exp(-x) I0(x) } = 1.
- */
-
-#ifdef UNK
-static double A[] =
-{
--4.41534164647933937950E-18,
- 3.33079451882223809783E-17,
--2.43127984654795469359E-16,
- 1.71539128555513303061E-15,
--1.16853328779934516808E-14,
- 7.67618549860493561688E-14,
--4.85644678311192946090E-13,
- 2.95505266312963983461E-12,
--1.72682629144155570723E-11,
- 9.67580903537323691224E-11,
--5.18979560163526290666E-10,
- 2.65982372468238665035E-9,
--1.30002500998624804212E-8,
- 6.04699502254191894932E-8,
--2.67079385394061173391E-7,
- 1.11738753912010371815E-6,
--4.41673835845875056359E-6,
- 1.64484480707288970893E-5,
--5.75419501008210370398E-5,
- 1.88502885095841655729E-4,
--5.76375574538582365885E-4,
- 1.63947561694133579842E-3,
--4.32430999505057594430E-3,
- 1.05464603945949983183E-2,
--2.37374148058994688156E-2,
- 4.93052842396707084878E-2,
--9.49010970480476444210E-2,
- 1.71620901522208775349E-1,
--3.04682672343198398683E-1,
- 6.76795274409476084995E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0121642,0162671,0004646,0103567,
-0022431,0115424,0135755,0026104,
-0123214,0023533,0110365,0156635,
-0023767,0033304,0117662,0172716,
-0124522,0100426,0012277,0157531,
-0025254,0155062,0054461,0030465,
-0126010,0131143,0013560,0153604,
-0026517,0170577,0006336,0114437,
-0127227,0162253,0152243,0052734,
-0027724,0142766,0061641,0160200,
-0130416,0123760,0116564,0125262,
-0031066,0144035,0021246,0054641,
-0131537,0053664,0060131,0102530,
-0032201,0155664,0165153,0020652,
-0132617,0061434,0074423,0176145,
-0033225,0174444,0136147,0122542,
-0133624,0031576,0056453,0020470,
-0034211,0175305,0172321,0041314,
-0134561,0054462,0147040,0165315,
-0035105,0124333,0120203,0162532,
-0135427,0013750,0174257,0055221,
-0035726,0161654,0050220,0100162,
-0136215,0131361,0000325,0041110,
-0036454,0145417,0117357,0017352,
-0136702,0072367,0104415,0133574,
-0037111,0172126,0072505,0014544,
-0137302,0055601,0120550,0033523,
-0037457,0136543,0136544,0043002,
-0137633,0177536,0001276,0066150,
-0040055,0041164,0100655,0010521
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0xd0ef,0x2134,0x5cb7,0xbc54,
-0xa589,0x977d,0x3362,0x3c83,
-0xbbb4,0x721e,0x84eb,0xbcb1,
-0x5eba,0x93f6,0xe6d8,0x3cde,
-0xfbeb,0xc297,0x5022,0xbd0a,
-0x2627,0x4b26,0x9b46,0x3d35,
-0x1af0,0x62ee,0x164c,0xbd61,
-0xd324,0xe19b,0xfe2f,0x3d89,
-0x6abc,0x7a94,0xfc95,0xbdb2,
-0x3c10,0xcc74,0x98be,0x3dda,
-0x9556,0x13ae,0xd4fe,0xbe01,
-0xcb34,0xa454,0xd903,0x3e26,
-0x30ab,0x8c0b,0xeaf6,0xbe4b,
-0x6435,0x9d4d,0x3b76,0x3e70,
-0x7f8d,0x8f22,0xec63,0xbe91,
-0xf4ac,0x978c,0xbf24,0x3eb2,
-0x6427,0xcba5,0x866f,0xbed2,
-0x2859,0xbe9a,0x3f58,0x3ef1,
-0x1d5a,0x59c4,0x2b26,0xbf0e,
-0x7cab,0x7410,0xb51b,0x3f28,
-0xeb52,0x1f15,0xe2fd,0xbf42,
-0x100e,0x8a12,0xdc75,0x3f5a,
-0xa849,0x201a,0xb65e,0xbf71,
-0xe3dd,0xf3dd,0x9961,0x3f85,
-0xb6f0,0xf121,0x4e9e,0xbf98,
-0xa32d,0xcea8,0x3e8a,0x3fa9,
-0x06ea,0x342d,0x4b70,0xbfb8,
-0x88c0,0x77ac,0xf7ac,0x3fc5,
-0xcd8d,0xc057,0x7feb,0xbfd3,
-0xa22a,0x9035,0xa84e,0x3fe5,
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0xbc54,0x5cb7,0x2134,0xd0ef,
-0x3c83,0x3362,0x977d,0xa589,
-0xbcb1,0x84eb,0x721e,0xbbb4,
-0x3cde,0xe6d8,0x93f6,0x5eba,
-0xbd0a,0x5022,0xc297,0xfbeb,
-0x3d35,0x9b46,0x4b26,0x2627,
-0xbd61,0x164c,0x62ee,0x1af0,
-0x3d89,0xfe2f,0xe19b,0xd324,
-0xbdb2,0xfc95,0x7a94,0x6abc,
-0x3dda,0x98be,0xcc74,0x3c10,
-0xbe01,0xd4fe,0x13ae,0x9556,
-0x3e26,0xd903,0xa454,0xcb34,
-0xbe4b,0xeaf6,0x8c0b,0x30ab,
-0x3e70,0x3b76,0x9d4d,0x6435,
-0xbe91,0xec63,0x8f22,0x7f8d,
-0x3eb2,0xbf24,0x978c,0xf4ac,
-0xbed2,0x866f,0xcba5,0x6427,
-0x3ef1,0x3f58,0xbe9a,0x2859,
-0xbf0e,0x2b26,0x59c4,0x1d5a,
-0x3f28,0xb51b,0x7410,0x7cab,
-0xbf42,0xe2fd,0x1f15,0xeb52,
-0x3f5a,0xdc75,0x8a12,0x100e,
-0xbf71,0xb65e,0x201a,0xa849,
-0x3f85,0x9961,0xf3dd,0xe3dd,
-0xbf98,0x4e9e,0xf121,0xb6f0,
-0x3fa9,0x3e8a,0xcea8,0xa32d,
-0xbfb8,0x4b70,0x342d,0x06ea,
-0x3fc5,0xf7ac,0x77ac,0x88c0,
-0xbfd3,0x7feb,0xc057,0xcd8d,
-0x3fe5,0xa84e,0x9035,0xa22a
-};
-#endif
-
-
-/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
- * in the inverted interval [8,infinity].
- *
- * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
- */
-
-#ifdef UNK
-static double B[] =
-{
--7.23318048787475395456E-18,
--4.83050448594418207126E-18,
- 4.46562142029675999901E-17,
- 3.46122286769746109310E-17,
--2.82762398051658348494E-16,
--3.42548561967721913462E-16,
- 1.77256013305652638360E-15,
- 3.81168066935262242075E-15,
--9.55484669882830764870E-15,
--4.15056934728722208663E-14,
- 1.54008621752140982691E-14,
- 3.85277838274214270114E-13,
- 7.18012445138366623367E-13,
--1.79417853150680611778E-12,
--1.32158118404477131188E-11,
--3.14991652796324136454E-11,
- 1.18891471078464383424E-11,
- 4.94060238822496958910E-10,
- 3.39623202570838634515E-9,
- 2.26666899049817806459E-8,
- 2.04891858946906374183E-7,
- 2.89137052083475648297E-6,
- 6.88975834691682398426E-5,
- 3.36911647825569408990E-3,
- 8.04490411014108831608E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short B[] = {
-0122005,0066672,0123124,0054311,
-0121662,0033323,0030214,0104602,
-0022515,0170300,0113314,0020413,
-0022437,0117350,0035402,0007146,
-0123243,0000135,0057220,0177435,
-0123305,0073476,0144106,0170702,
-0023777,0071755,0017527,0154373,
-0024211,0052214,0102247,0033270,
-0124454,0017763,0171453,0012322,
-0125072,0166316,0075505,0154616,
-0024612,0133770,0065376,0025045,
-0025730,0162143,0056036,0001632,
-0026112,0015077,0150464,0063542,
-0126374,0101030,0014274,0065457,
-0127150,0077271,0125763,0157617,
-0127412,0104350,0040713,0120445,
-0027121,0023765,0057500,0001165,
-0030407,0147146,0003643,0075644,
-0031151,0061445,0044422,0156065,
-0031702,0132224,0003266,0125551,
-0032534,0000076,0147153,0005555,
-0033502,0004536,0004016,0026055,
-0034620,0076433,0142314,0171215,
-0036134,0146145,0013454,0101104,
-0040115,0171425,0062500,0047133
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short B[] = {
-0x8b19,0x54ca,0xadb7,0xbc60,
-0x9130,0x6611,0x46da,0xbc56,
-0x8421,0x12d9,0xbe18,0x3c89,
-0x41cd,0x0760,0xf3dd,0x3c83,
-0x1fe4,0xabd2,0x600b,0xbcb4,
-0xde38,0xd908,0xaee7,0xbcb8,
-0xfb1f,0xa3ea,0xee7d,0x3cdf,
-0xe6d7,0x9094,0x2a91,0x3cf1,
-0x629a,0x7e65,0x83fe,0xbd05,
-0xbb32,0xcf68,0x5d99,0xbd27,
-0xc545,0x0d5f,0x56ff,0x3d11,
-0xc073,0x6b83,0x1c8c,0x3d5b,
-0x8cec,0xfa26,0x4347,0x3d69,
-0x8d66,0x0317,0x9043,0xbd7f,
-0x7bf2,0x357e,0x0fd7,0xbdad,
-0x7425,0x0839,0x511d,0xbdc1,
-0x004f,0xabe8,0x24fe,0x3daa,
-0x6f75,0xc0f4,0xf9cc,0x3e00,
-0x5b87,0xa922,0x2c64,0x3e2d,
-0xd56d,0x80d6,0x5692,0x3e58,
-0x616e,0xd9cd,0x8007,0x3e8b,
-0xc586,0xc101,0x412b,0x3ec8,
-0x9e52,0x7899,0x0fa3,0x3f12,
-0x9049,0xa2e5,0x998c,0x3f6b,
-0x09cb,0xaca8,0xbe62,0x3fe9
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short B[] = {
-0xbc60,0xadb7,0x54ca,0x8b19,
-0xbc56,0x46da,0x6611,0x9130,
-0x3c89,0xbe18,0x12d9,0x8421,
-0x3c83,0xf3dd,0x0760,0x41cd,
-0xbcb4,0x600b,0xabd2,0x1fe4,
-0xbcb8,0xaee7,0xd908,0xde38,
-0x3cdf,0xee7d,0xa3ea,0xfb1f,
-0x3cf1,0x2a91,0x9094,0xe6d7,
-0xbd05,0x83fe,0x7e65,0x629a,
-0xbd27,0x5d99,0xcf68,0xbb32,
-0x3d11,0x56ff,0x0d5f,0xc545,
-0x3d5b,0x1c8c,0x6b83,0xc073,
-0x3d69,0x4347,0xfa26,0x8cec,
-0xbd7f,0x9043,0x0317,0x8d66,
-0xbdad,0x0fd7,0x357e,0x7bf2,
-0xbdc1,0x511d,0x0839,0x7425,
-0x3daa,0x24fe,0xabe8,0x004f,
-0x3e00,0xf9cc,0xc0f4,0x6f75,
-0x3e2d,0x2c64,0xa922,0x5b87,
-0x3e58,0x5692,0x80d6,0xd56d,
-0x3e8b,0x8007,0xd9cd,0x616e,
-0x3ec8,0x412b,0xc101,0xc586,
-0x3f12,0x0fa3,0x7899,0x9e52,
-0x3f6b,0x998c,0xa2e5,0x9049,
-0x3fe9,0xbe62,0xaca8,0x09cb
-};
-#endif
-
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double exp ( double );
-extern double sqrt ( double );
-#else
-double chbevl(), exp(), sqrt();
-#endif
-
-double i0(x)
-double x;
-{
-double y;
-
-if( x < 0 )
- x = -x;
-if( x <= 8.0 )
- {
- y = (x/2.0) - 2.0;
- return( exp(x) * chbevl( y, A, 30 ) );
- }
-
-return( exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
-
-}
-
-
-
-
-double i0e( x )
-double x;
-{
-double y;
-
-if( x < 0 )
- x = -x;
-if( x <= 8.0 )
- {
- y = (x/2.0) - 2.0;
- return( chbevl( y, A, 30 ) );
- }
-
-return( chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
-
-}
+++ /dev/null
-/* i1.c
- *
- * Modified Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i1();
- *
- * y = i1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order one of the
- * argument.
- *
- * The function is defined as i1(x) = -i j1( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 3400 1.2e-16 2.3e-17
- * IEEE 0, 30 30000 1.9e-15 2.1e-16
- *
- *
- */
-\f/* i1e.c
- *
- * Modified Bessel function of order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i1e();
- *
- * y = i1e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order one of the argument.
- *
- * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 2.0e-15 2.0e-16
- * See i1().
- *
- */
-\f
-/* i1.c 2 */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1985, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for exp(-x) I1(x) / x
- * in the interval [0,8].
- *
- * lim(x->0){ exp(-x) I1(x) / x } = 1/2.
- */
-
-#ifdef UNK
-static double A[] =
-{
- 2.77791411276104639959E-18,
--2.11142121435816608115E-17,
- 1.55363195773620046921E-16,
--1.10559694773538630805E-15,
- 7.60068429473540693410E-15,
--5.04218550472791168711E-14,
- 3.22379336594557470981E-13,
--1.98397439776494371520E-12,
- 1.17361862988909016308E-11,
--6.66348972350202774223E-11,
- 3.62559028155211703701E-10,
--1.88724975172282928790E-9,
- 9.38153738649577178388E-9,
--4.44505912879632808065E-8,
- 2.00329475355213526229E-7,
--8.56872026469545474066E-7,
- 3.47025130813767847674E-6,
--1.32731636560394358279E-5,
- 4.78156510755005422638E-5,
--1.61760815825896745588E-4,
- 5.12285956168575772895E-4,
--1.51357245063125314899E-3,
- 4.15642294431288815669E-3,
--1.05640848946261981558E-2,
- 2.47264490306265168283E-2,
--5.29459812080949914269E-2,
- 1.02643658689847095384E-1,
--1.76416518357834055153E-1,
- 2.52587186443633654823E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0021514,0174520,0060742,0000241,
-0122302,0137206,0016120,0025663,
-0023063,0017437,0026235,0176536,
-0123637,0052523,0170150,0125632,
-0024410,0165770,0030251,0044134,
-0125143,0012160,0162170,0054727,
-0025665,0075702,0035716,0145247,
-0126413,0116032,0176670,0015462,
-0027116,0073425,0110351,0105242,
-0127622,0104034,0137530,0037364,
-0030307,0050645,0120776,0175535,
-0131001,0130331,0043523,0037455,
-0031441,0026160,0010712,0100174,
-0132076,0164761,0022706,0017500,
-0032527,0015045,0115076,0104076,
-0133146,0001714,0015434,0144520,
-0033550,0161166,0124215,0077050,
-0134136,0127715,0143365,0157170,
-0034510,0106652,0013070,0064130,
-0135051,0117126,0117264,0123761,
-0035406,0045355,0133066,0175751,
-0135706,0061420,0054746,0122440,
-0036210,0031232,0047235,0006640,
-0136455,0012373,0144235,0011523,
-0036712,0107437,0036731,0015111,
-0137130,0156742,0115744,0172743,
-0037322,0033326,0124667,0124740,
-0137464,0123210,0021510,0144556,
-0037601,0051433,0111123,0177721
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0x4014,0x0c3c,0x9f2a,0x3c49,
-0x0576,0xc38a,0x57d0,0xbc78,
-0xbfac,0xe593,0x63e3,0x3ca6,
-0x1573,0x7e0d,0xeaaa,0xbcd3,
-0x290c,0x0615,0x1d7f,0x3d01,
-0x0b3b,0x1c8f,0x628e,0xbd2c,
-0xd955,0x4779,0xaf78,0x3d56,
-0x0366,0x5fb7,0x7383,0xbd81,
-0x3154,0xb21d,0xcee2,0x3da9,
-0x07de,0x97eb,0x5103,0xbdd2,
-0xdf6c,0xb43f,0xea34,0x3df8,
-0x67e6,0x28ea,0x361b,0xbe20,
-0x5010,0x0239,0x258e,0x3e44,
-0xc3e8,0x24b8,0xdd3e,0xbe67,
-0xd108,0xb347,0xe344,0x3e8a,
-0x992a,0x8363,0xc079,0xbeac,
-0xafc5,0xd511,0x1c4e,0x3ecd,
-0xbbcf,0xb8de,0xd5f9,0xbeeb,
-0x0d0b,0x42c7,0x11b5,0x3f09,
-0x94fe,0xd3d6,0x33ca,0xbf25,
-0xdf7d,0xb6c6,0xc95d,0x3f40,
-0xd4a4,0x0b3c,0xcc62,0xbf58,
-0xa1b4,0x49d3,0x0653,0x3f71,
-0xa26a,0x7913,0xa29f,0xbf85,
-0x2349,0xe7bb,0x51e3,0x3f99,
-0x9ebc,0x537c,0x1bbc,0xbfab,
-0xf53c,0xd536,0x46da,0x3fba,
-0x192e,0x0469,0x94d1,0xbfc6,
-0x7ffa,0x724a,0x2a63,0x3fd0
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0x3c49,0x9f2a,0x0c3c,0x4014,
-0xbc78,0x57d0,0xc38a,0x0576,
-0x3ca6,0x63e3,0xe593,0xbfac,
-0xbcd3,0xeaaa,0x7e0d,0x1573,
-0x3d01,0x1d7f,0x0615,0x290c,
-0xbd2c,0x628e,0x1c8f,0x0b3b,
-0x3d56,0xaf78,0x4779,0xd955,
-0xbd81,0x7383,0x5fb7,0x0366,
-0x3da9,0xcee2,0xb21d,0x3154,
-0xbdd2,0x5103,0x97eb,0x07de,
-0x3df8,0xea34,0xb43f,0xdf6c,
-0xbe20,0x361b,0x28ea,0x67e6,
-0x3e44,0x258e,0x0239,0x5010,
-0xbe67,0xdd3e,0x24b8,0xc3e8,
-0x3e8a,0xe344,0xb347,0xd108,
-0xbeac,0xc079,0x8363,0x992a,
-0x3ecd,0x1c4e,0xd511,0xafc5,
-0xbeeb,0xd5f9,0xb8de,0xbbcf,
-0x3f09,0x11b5,0x42c7,0x0d0b,
-0xbf25,0x33ca,0xd3d6,0x94fe,
-0x3f40,0xc95d,0xb6c6,0xdf7d,
-0xbf58,0xcc62,0x0b3c,0xd4a4,
-0x3f71,0x0653,0x49d3,0xa1b4,
-0xbf85,0xa29f,0x7913,0xa26a,
-0x3f99,0x51e3,0xe7bb,0x2349,
-0xbfab,0x1bbc,0x537c,0x9ebc,
-0x3fba,0x46da,0xd536,0xf53c,
-0xbfc6,0x94d1,0x0469,0x192e,
-0x3fd0,0x2a63,0x724a,0x7ffa
-};
-#endif
-\f
-/* i1.c */
-
-/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
- * in the inverted interval [8,infinity].
- *
- * lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
- */
-
-#ifdef UNK
-static double B[] =
-{
- 7.51729631084210481353E-18,
- 4.41434832307170791151E-18,
--4.65030536848935832153E-17,
--3.20952592199342395980E-17,
- 2.96262899764595013876E-16,
- 3.30820231092092828324E-16,
--1.88035477551078244854E-15,
--3.81440307243700780478E-15,
- 1.04202769841288027642E-14,
- 4.27244001671195135429E-14,
--2.10154184277266431302E-14,
--4.08355111109219731823E-13,
--7.19855177624590851209E-13,
- 2.03562854414708950722E-12,
- 1.41258074366137813316E-11,
- 3.25260358301548823856E-11,
--1.89749581235054123450E-11,
--5.58974346219658380687E-10,
--3.83538038596423702205E-9,
--2.63146884688951950684E-8,
--2.51223623787020892529E-7,
--3.88256480887769039346E-6,
--1.10588938762623716291E-4,
--9.76109749136146840777E-3,
- 7.78576235018280120474E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short B[] = {
-0022012,0125555,0115227,0043456,
-0021642,0156127,0052075,0145203,
-0122526,0072435,0111231,0011664,
-0122424,0001544,0161671,0114403,
-0023252,0144257,0163532,0142121,
-0023276,0132162,0174045,0013204,
-0124007,0077154,0057046,0110517,
-0124211,0066650,0116127,0157073,
-0024473,0133413,0130551,0107504,
-0025100,0064741,0032631,0040364,
-0124675,0045101,0071551,0012400,
-0125745,0161054,0071637,0011247,
-0126112,0117410,0035525,0122231,
-0026417,0037237,0131034,0176427,
-0027170,0100373,0024742,0025725,
-0027417,0006417,0105303,0141446,
-0127246,0163716,0121202,0060137,
-0130431,0123122,0120436,0166000,
-0131203,0144134,0153251,0124500,
-0131742,0005234,0122732,0033006,
-0132606,0157751,0072362,0121031,
-0133602,0043372,0047120,0015626,
-0134747,0165774,0001125,0046462,
-0136437,0166402,0117746,0155137,
-0040107,0050305,0125330,0124241
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short B[] = {
-0xe8e6,0xb352,0x556d,0x3c61,
-0xb950,0xea87,0x5b8a,0x3c54,
-0x2277,0xb253,0xcea3,0xbc8a,
-0x3320,0x9c77,0x806c,0xbc82,
-0x588a,0xfceb,0x5915,0x3cb5,
-0xa2d1,0x5f04,0xd68e,0x3cb7,
-0xd22a,0x8bc4,0xefcd,0xbce0,
-0xfbc7,0x138a,0x2db5,0xbcf1,
-0x31e8,0x762d,0x76e1,0x3d07,
-0x281e,0x26b3,0x0d3c,0x3d28,
-0x22a0,0x2e6d,0xa948,0xbd17,
-0xe255,0x8e73,0xbc45,0xbd5c,
-0xb493,0x076a,0x53e1,0xbd69,
-0x9fa3,0xf643,0xe7d3,0x3d81,
-0x457b,0x653c,0x101f,0x3daf,
-0x7865,0xf158,0xe1a1,0x3dc1,
-0x4c0c,0xd450,0xdcf9,0xbdb4,
-0xdd80,0x5423,0x34ca,0xbe03,
-0x3528,0x9ad5,0x790b,0xbe30,
-0x46c1,0x94bb,0x4153,0xbe5c,
-0x5443,0x2e9e,0xdbfd,0xbe90,
-0x0373,0x49ca,0x48df,0xbed0,
-0xa9a6,0x804a,0xfd7f,0xbf1c,
-0xdb4c,0x53fc,0xfda0,0xbf83,
-0x1514,0xb55b,0xea18,0x3fe8
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short B[] = {
-0x3c61,0x556d,0xb352,0xe8e6,
-0x3c54,0x5b8a,0xea87,0xb950,
-0xbc8a,0xcea3,0xb253,0x2277,
-0xbc82,0x806c,0x9c77,0x3320,
-0x3cb5,0x5915,0xfceb,0x588a,
-0x3cb7,0xd68e,0x5f04,0xa2d1,
-0xbce0,0xefcd,0x8bc4,0xd22a,
-0xbcf1,0x2db5,0x138a,0xfbc7,
-0x3d07,0x76e1,0x762d,0x31e8,
-0x3d28,0x0d3c,0x26b3,0x281e,
-0xbd17,0xa948,0x2e6d,0x22a0,
-0xbd5c,0xbc45,0x8e73,0xe255,
-0xbd69,0x53e1,0x076a,0xb493,
-0x3d81,0xe7d3,0xf643,0x9fa3,
-0x3daf,0x101f,0x653c,0x457b,
-0x3dc1,0xe1a1,0xf158,0x7865,
-0xbdb4,0xdcf9,0xd450,0x4c0c,
-0xbe03,0x34ca,0x5423,0xdd80,
-0xbe30,0x790b,0x9ad5,0x3528,
-0xbe5c,0x4153,0x94bb,0x46c1,
-0xbe90,0xdbfd,0x2e9e,0x5443,
-0xbed0,0x48df,0x49ca,0x0373,
-0xbf1c,0xfd7f,0x804a,0xa9a6,
-0xbf83,0xfda0,0x53fc,0xdb4c,
-0x3fe8,0xea18,0xb55b,0x1514
-};
-#endif
-\f
-/* i1.c */
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double exp ( double );
-extern double sqrt ( double );
-extern double fabs ( double );
-#else
-double chbevl(), exp(), sqrt(), fabs();
-#endif
-
-double i1(x)
-double x;
-{
-double y, z;
-
-z = fabs(x);
-if( z <= 8.0 )
- {
- y = (z/2.0) - 2.0;
- z = chbevl( y, A, 29 ) * z * exp(z);
- }
-else
- {
- z = exp(z) * chbevl( 32.0/z - 2.0, B, 25 ) / sqrt(z);
- }
-if( x < 0.0 )
- z = -z;
-return( z );
-}
-\f
-/* i1e() */
-
-double i1e( x )
-double x;
-{
-double y, z;
-
-z = fabs(x);
-if( z <= 8.0 )
- {
- y = (z/2.0) - 2.0;
- z = chbevl( y, A, 29 ) * z;
- }
-else
- {
- z = chbevl( 32.0/z - 2.0, B, 25 ) / sqrt(z);
- }
-if( x < 0.0 )
- z = -z;
-return( z );
-}
+++ /dev/null
-/* igam.c
- *
- * Incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, y, igam();
- *
- * y = igam( a, x );
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 200000 3.6e-14 2.9e-15
- * IEEE 0,100 300000 9.9e-14 1.5e-14
- */
-\f/* igamc()
- *
- * Complemented incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, y, igamc();
- *
- * y = igamc( a, x );
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- * ACCURACY:
- *
- * Tested at random a, x.
- * a x Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
- * IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1985, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double lgam ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double fabs ( double );
-extern double igam ( double, double );
-extern double igamc ( double, double );
-#else
-double lgam(), exp(), log(), fabs(), igam(), igamc();
-#endif
-
-extern double MACHEP, MAXLOG;
-static double big = 4.503599627370496e15;
-static double biginv = 2.22044604925031308085e-16;
-
-double igamc( a, x )
-double a, x;
-{
-double ans, ax, c, yc, r, t, y, z;
-double pk, pkm1, pkm2, qk, qkm1, qkm2;
-
-if( (x <= 0) || ( a <= 0) )
- return( 1.0 );
-
-if( (x < 1.0) || (x < a) )
- return( 1.0 - igam(a,x) );
-
-ax = a * log(x) - x - lgam(a);
-if( ax < -MAXLOG )
- {
- mtherr( "igamc", UNDERFLOW );
- return( 0.0 );
- }
-ax = exp(ax);
-
-/* continued fraction */
-y = 1.0 - a;
-z = x + y + 1.0;
-c = 0.0;
-pkm2 = 1.0;
-qkm2 = x;
-pkm1 = x + 1.0;
-qkm1 = z * x;
-ans = pkm1/qkm1;
-
-do
- {
- c += 1.0;
- y += 1.0;
- z += 2.0;
- yc = y * c;
- pk = pkm1 * z - pkm2 * yc;
- qk = qkm1 * z - qkm2 * yc;
- if( qk != 0 )
- {
- r = pk/qk;
- t = fabs( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
- if( fabs(pk) > big )
- {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
- }
- }
-while( t > MACHEP );
-
-return( ans * ax );
-}
-
-
-
-/* left tail of incomplete gamma function:
- *
- * inf. k
- * a -x - x
- * x e > ----------
- * - -
- * k=0 | (a+k+1)
- *
- */
-
-double igam( a, x )
-double a, x;
-{
-double ans, ax, c, r;
-
-if( (x <= 0) || ( a <= 0) )
- return( 0.0 );
-
-if( (x > 1.0) && (x > a ) )
- return( 1.0 - igamc(a,x) );
-
-/* Compute x**a * exp(-x) / gamma(a) */
-ax = a * log(x) - x - lgam(a);
-if( ax < -MAXLOG )
- {
- mtherr( "igam", UNDERFLOW );
- return( 0.0 );
- }
-ax = exp(ax);
-
-/* power series */
-r = a;
-c = 1.0;
-ans = 1.0;
-
-do
- {
- r += 1.0;
- c *= x/r;
- ans += c;
- }
-while( c/ans > MACHEP );
-
-return( ans * ax/a );
-}
+++ /dev/null
-/* igami()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, p, igami();
- *
- * x = igami( a, p );
- *
- * DESCRIPTION:
- *
- * Given p, the function finds x such that
- *
- * igamc( a, x ) = p.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(p) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - p = 0.
- *
- * ACCURACY:
- *
- * Tested at random a, p in the intervals indicated.
- *
- * a p Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15
- * IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15
- * IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
-#ifdef ANSIPROT
-extern double igamc ( double, double );
-extern double ndtri ( double );
-extern double exp ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double sqrt ( double );
-extern double lgam ( double );
-#else
-double igamc(), ndtri(), exp(), fabs(), log(), sqrt(), lgam();
-#endif
-
-double igami( a, y0 )
-double a, y0;
-{
-double x0, x1, x, yl, yh, y, d, lgm, dithresh;
-int i, dir;
-
-/* bound the solution */
-x0 = MAXNUM;
-yl = 0;
-x1 = 0;
-yh = 1.0;
-dithresh = 5.0 * MACHEP;
-
-/* approximation to inverse function */
-d = 1.0/(9.0*a);
-y = ( 1.0 - d - ndtri(y0) * sqrt(d) );
-x = a * y * y * y;
-
-lgm = lgam(a);
-
-for( i=0; i<10; i++ )
- {
- if( x > x0 || x < x1 )
- goto ihalve;
- y = igamc(a,x);
- if( y < yl || y > yh )
- goto ihalve;
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- }
- else
- {
- x1 = x;
- yh = y;
- }
-/* compute the derivative of the function at this point */
- d = (a - 1.0) * log(x) - x - lgm;
- if( d < -MAXLOG )
- goto ihalve;
- d = -exp(d);
-/* compute the step to the next approximation of x */
- d = (y - y0)/d;
- if( fabs(d/x) < MACHEP )
- goto done;
- x = x - d;
- }
-
-/* Resort to interval halving if Newton iteration did not converge. */
-ihalve:
-
-d = 0.0625;
-if( x0 == MAXNUM )
- {
- if( x <= 0.0 )
- x = 1.0;
- while( x0 == MAXNUM )
- {
- x = (1.0 + d) * x;
- y = igamc( a, x );
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- break;
- }
- d = d + d;
- }
- }
-d = 0.5;
-dir = 0;
-
-for( i=0; i<400; i++ )
- {
- x = x1 + d * (x0 - x1);
- y = igamc( a, x );
- lgm = (x0 - x1)/(x1 + x0);
- if( fabs(lgm) < dithresh )
- break;
- lgm = (y - y0)/y0;
- if( fabs(lgm) < dithresh )
- break;
- if( x <= 0.0 )
- break;
- if( y >= y0 )
- {
- x1 = x;
- yh = y;
- if( dir < 0 )
- {
- dir = 0;
- d = 0.5;
- }
- else if( dir > 1 )
- d = 0.5 * d + 0.5;
- else
- d = (y0 - yl)/(yh - yl);
- dir += 1;
- }
- else
- {
- x0 = x;
- yl = y;
- if( dir > 0 )
- {
- dir = 0;
- d = 0.5;
- }
- else if( dir < -1 )
- d = 0.5 * d;
- else
- d = (y0 - yl)/(yh - yl);
- dir -= 1;
- }
- }
-if( x == 0.0 )
- mtherr( "igami", UNDERFLOW );
-
-done:
-return( x );
-}
+++ /dev/null
-/* incbet.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, incbet();
- *
- * y = incbet( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion
- * or, when b*x is small, by a power series.
- *
- * ACCURACY:
- *
- * Tested at uniformly distributed random points (a,b,x) with a and b
- * in "domain" and x between 0 and 1.
- * Relative error
- * arithmetic domain # trials peak rms
- * IEEE 0,5 10000 6.9e-15 4.5e-16
- * IEEE 0,85 250000 2.2e-13 1.7e-14
- * IEEE 0,1000 30000 5.3e-12 6.3e-13
- * IEEE 0,10000 250000 9.3e-11 7.1e-12
- * IEEE 0,100000 10000 8.7e-10 4.8e-11
- * Outputs smaller than the IEEE gradual underflow threshold
- * were excluded from these statistics.
- *
- * ERROR MESSAGES:
- * message condition value returned
- * incbet domain x<0, x>1 0.0
- * incbet underflow 0.0
- */
-\f
-
-/*
-Cephes Math Library, Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef DEC
-#define MAXGAM 34.84425627277176174
-#else
-#define MAXGAM 171.624376956302725
-#endif
-
-extern double MACHEP, MINLOG, MAXLOG;
-#ifdef ANSIPROT
-extern double gamma ( double );
-extern double lgam ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double pow ( double, double );
-extern double fabs ( double );
-static double incbcf(double, double, double);
-static double incbd(double, double, double);
-static double pseries(double, double, double);
-#else
-double gamma(), lgam(), exp(), log(), pow(), fabs();
-static double incbcf(), incbd(), pseries();
-#endif
-
-static double big = 4.503599627370496e15;
-static double biginv = 2.22044604925031308085e-16;
-
-
-double incbet( aa, bb, xx )
-double aa, bb, xx;
-{
-double a, b, t, x, xc, w, y;
-int flag;
-
-if( aa <= 0.0 || bb <= 0.0 )
- goto domerr;
-
-if( (xx <= 0.0) || ( xx >= 1.0) )
- {
- if( xx == 0.0 )
- return(0.0);
- if( xx == 1.0 )
- return( 1.0 );
-domerr:
- mtherr( "incbet", DOMAIN );
- return( 0.0 );
- }
-
-flag = 0;
-if( (bb * xx) <= 1.0 && xx <= 0.95)
- {
- t = pseries(aa, bb, xx);
- goto done;
- }
-
-w = 1.0 - xx;
-
-/* Reverse a and b if x is greater than the mean. */
-if( xx > (aa/(aa+bb)) )
- {
- flag = 1;
- a = bb;
- b = aa;
- xc = xx;
- x = w;
- }
-else
- {
- a = aa;
- b = bb;
- xc = w;
- x = xx;
- }
-
-if( flag == 1 && (b * x) <= 1.0 && x <= 0.95)
- {
- t = pseries(a, b, x);
- goto done;
- }
-
-/* Choose expansion for better convergence. */
-y = x * (a+b-2.0) - (a-1.0);
-if( y < 0.0 )
- w = incbcf( a, b, x );
-else
- w = incbd( a, b, x ) / xc;
-
-/* Multiply w by the factor
- a b _ _ _
- x (1-x) | (a+b) / ( a | (a) | (b) ) . */
-
-y = a * log(x);
-t = b * log(xc);
-if( (a+b) < MAXGAM && fabs(y) < MAXLOG && fabs(t) < MAXLOG )
- {
- t = pow(xc,b);
- t *= pow(x,a);
- t /= a;
- t *= w;
- t *= gamma(a+b) / (gamma(a) * gamma(b));
- goto done;
- }
-/* Resort to logarithms. */
-y += t + lgam(a+b) - lgam(a) - lgam(b);
-y += log(w/a);
-if( y < MINLOG )
- t = 0.0;
-else
- t = exp(y);
-
-done:
-
-if( flag == 1 )
- {
- if( t <= MACHEP )
- t = 1.0 - MACHEP;
- else
- t = 1.0 - t;
- }
-return( t );
-}
-\f
-/* Continued fraction expansion #1
- * for incomplete beta integral
- */
-
-static double incbcf( a, b, x )
-double a, b, x;
-{
-double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
-double k1, k2, k3, k4, k5, k6, k7, k8;
-double r, t, ans, thresh;
-int n;
-
-k1 = a;
-k2 = a + b;
-k3 = a;
-k4 = a + 1.0;
-k5 = 1.0;
-k6 = b - 1.0;
-k7 = k4;
-k8 = a + 2.0;
-
-pkm2 = 0.0;
-qkm2 = 1.0;
-pkm1 = 1.0;
-qkm1 = 1.0;
-ans = 1.0;
-r = 1.0;
-n = 0;
-thresh = 3.0 * MACHEP;
-do
- {
-
- xk = -( x * k1 * k2 )/( k3 * k4 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = ( x * k5 * k6 )/( k7 * k8 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if( qk != 0 )
- r = pk/qk;
- if( r != 0 )
- {
- t = fabs( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
-
- if( t < thresh )
- goto cdone;
-
- k1 += 1.0;
- k2 += 1.0;
- k3 += 2.0;
- k4 += 2.0;
- k5 += 1.0;
- k6 -= 1.0;
- k7 += 2.0;
- k8 += 2.0;
-
- if( (fabs(qk) + fabs(pk)) > big )
- {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
- }
- if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
- {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- }
-while( ++n < 300 );
-
-cdone:
-return(ans);
-}
-
-\f
-/* Continued fraction expansion #2
- * for incomplete beta integral
- */
-
-static double incbd( a, b, x )
-double a, b, x;
-{
-double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
-double k1, k2, k3, k4, k5, k6, k7, k8;
-double r, t, ans, z, thresh;
-int n;
-
-k1 = a;
-k2 = b - 1.0;
-k3 = a;
-k4 = a + 1.0;
-k5 = 1.0;
-k6 = a + b;
-k7 = a + 1.0;;
-k8 = a + 2.0;
-
-pkm2 = 0.0;
-qkm2 = 1.0;
-pkm1 = 1.0;
-qkm1 = 1.0;
-z = x / (1.0-x);
-ans = 1.0;
-r = 1.0;
-n = 0;
-thresh = 3.0 * MACHEP;
-do
- {
-
- xk = -( z * k1 * k2 )/( k3 * k4 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = ( z * k5 * k6 )/( k7 * k8 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if( qk != 0 )
- r = pk/qk;
- if( r != 0 )
- {
- t = fabs( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
-
- if( t < thresh )
- goto cdone;
-
- k1 += 1.0;
- k2 -= 1.0;
- k3 += 2.0;
- k4 += 2.0;
- k5 += 1.0;
- k6 += 1.0;
- k7 += 2.0;
- k8 += 2.0;
-
- if( (fabs(qk) + fabs(pk)) > big )
- {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
- }
- if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
- {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- }
-while( ++n < 300 );
-cdone:
-return(ans);
-}
-\f
-/* Power series for incomplete beta integral.
- Use when b*x is small and x not too close to 1. */
-
-static double pseries( a, b, x )
-double a, b, x;
-{
-double s, t, u, v, n, t1, z, ai;
-
-ai = 1.0 / a;
-u = (1.0 - b) * x;
-v = u / (a + 1.0);
-t1 = v;
-t = u;
-n = 2.0;
-s = 0.0;
-z = MACHEP * ai;
-while( fabs(v) > z )
- {
- u = (n - b) * x / n;
- t *= u;
- v = t / (a + n);
- s += v;
- n += 1.0;
- }
-s += t1;
-s += ai;
-
-u = a * log(x);
-if( (a+b) < MAXGAM && fabs(u) < MAXLOG )
- {
- t = gamma(a+b)/(gamma(a)*gamma(b));
- s = s * t * pow(x,a);
- }
-else
- {
- t = lgam(a+b) - lgam(a) - lgam(b) + u + log(s);
- if( t < MINLOG )
- s = 0.0;
- else
- s = exp(t);
- }
-return(s);
-}
+++ /dev/null
-/* incbi()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, incbi();
- *
- * x = incbi( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y .
- *
- * The routine performs interval halving or Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 .5,10000 50000 5.8e-12 1.3e-13
- * IEEE 0,1 .25,100 100000 1.8e-13 3.9e-15
- * IEEE 0,1 0,5 50000 1.1e-12 5.5e-15
- * VAX 0,1 .5,100 25000 3.5e-14 1.1e-15
- * With a and b constrained to half-integer or integer values:
- * IEEE 0,1 .5,10000 50000 5.8e-12 1.1e-13
- * IEEE 0,1 .5,100 100000 1.7e-14 7.9e-16
- * With a = .5, b constrained to half-integer or integer values:
- * IEEE 0,1 .5,10000 10000 8.3e-11 1.0e-11
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1996, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
-#ifdef ANSIPROT
-extern double ndtri ( double );
-extern double exp ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double sqrt ( double );
-extern double lgam ( double );
-extern double incbet ( double, double, double );
-#else
-double ndtri(), exp(), fabs(), log(), sqrt(), lgam(), incbet();
-#endif
-
-double incbi( aa, bb, yy0 )
-double aa, bb, yy0;
-{
-double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
-int i, rflg, dir, nflg;
-
-
-i = 0;
-if( yy0 <= 0 )
- return(0.0);
-if( yy0 >= 1.0 )
- return(1.0);
-x0 = 0.0;
-yl = 0.0;
-x1 = 1.0;
-yh = 1.0;
-nflg = 0;
-
-if( aa <= 1.0 || bb <= 1.0 )
- {
- dithresh = 1.0e-6;
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- x = a/(a+b);
- y = incbet( a, b, x );
- goto ihalve;
- }
-else
- {
- dithresh = 1.0e-4;
- }
-/* approximation to inverse function */
-
-yp = -ndtri(yy0);
-
-if( yy0 > 0.5 )
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0 - yy0;
- yp = -yp;
- }
-else
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
-
-lgm = (yp * yp - 3.0)/6.0;
-x = 2.0/( 1.0/(2.0*a-1.0) + 1.0/(2.0*b-1.0) );
-d = yp * sqrt( x + lgm ) / x
- - ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
- * (lgm + 5.0/6.0 - 2.0/(3.0*x));
-d = 2.0 * d;
-if( d < MINLOG )
- {
- x = 1.0;
- goto under;
- }
-x = a/( a + b * exp(d) );
-y = incbet( a, b, x );
-yp = (y - y0)/y0;
-if( fabs(yp) < 0.2 )
- goto newt;
-
-/* Resort to interval halving if not close enough. */
-ihalve:
-
-dir = 0;
-di = 0.5;
-for( i=0; i<100; i++ )
- {
- if( i != 0 )
- {
- x = x0 + di * (x1 - x0);
- if( x == 1.0 )
- x = 1.0 - MACHEP;
- if( x == 0.0 )
- {
- di = 0.5;
- x = x0 + di * (x1 - x0);
- if( x == 0.0 )
- goto under;
- }
- y = incbet( a, b, x );
- yp = (x1 - x0)/(x1 + x0);
- if( fabs(yp) < dithresh )
- goto newt;
- yp = (y-y0)/y0;
- if( fabs(yp) < dithresh )
- goto newt;
- }
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- if( dir < 0 )
- {
- dir = 0;
- di = 0.5;
- }
- else if( dir > 3 )
- di = 1.0 - (1.0 - di) * (1.0 - di);
- else if( dir > 1 )
- di = 0.5 * di + 0.5;
- else
- di = (y0 - y)/(yh - yl);
- dir += 1;
- if( x0 > 0.75 )
- {
- if( rflg == 1 )
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
- else
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0 - yy0;
- }
- x = 1.0 - x;
- y = incbet( a, b, x );
- x0 = 0.0;
- yl = 0.0;
- x1 = 1.0;
- yh = 1.0;
- goto ihalve;
- }
- }
- else
- {
- x1 = x;
- if( rflg == 1 && x1 < MACHEP )
- {
- x = 0.0;
- goto done;
- }
- yh = y;
- if( dir > 0 )
- {
- dir = 0;
- di = 0.5;
- }
- else if( dir < -3 )
- di = di * di;
- else if( dir < -1 )
- di = 0.5 * di;
- else
- di = (y - y0)/(yh - yl);
- dir -= 1;
- }
- }
-mtherr( "incbi", PLOSS );
-if( x0 >= 1.0 )
- {
- x = 1.0 - MACHEP;
- goto done;
- }
-if( x <= 0.0 )
- {
-under:
- mtherr( "incbi", UNDERFLOW );
- x = 0.0;
- goto done;
- }
-
-newt:
-
-if( nflg )
- goto done;
-nflg = 1;
-lgm = lgam(a+b) - lgam(a) - lgam(b);
-
-for( i=0; i<8; i++ )
- {
- /* Compute the function at this point. */
- if( i != 0 )
- y = incbet(a,b,x);
- if( y < yl )
- {
- x = x0;
- y = yl;
- }
- else if( y > yh )
- {
- x = x1;
- y = yh;
- }
- else if( y < y0 )
- {
- x0 = x;
- yl = y;
- }
- else
- {
- x1 = x;
- yh = y;
- }
- if( x == 1.0 || x == 0.0 )
- break;
- /* Compute the derivative of the function at this point. */
- d = (a - 1.0) * log(x) + (b - 1.0) * log(1.0-x) + lgm;
- if( d < MINLOG )
- goto done;
- if( d > MAXLOG )
- break;
- d = exp(d);
- /* Compute the step to the next approximation of x. */
- d = (y - y0)/d;
- xt = x - d;
- if( xt <= x0 )
- {
- y = (x - x0) / (x1 - x0);
- xt = x0 + 0.5 * y * (x - x0);
- if( xt <= 0.0 )
- break;
- }
- if( xt >= x1 )
- {
- y = (x1 - x) / (x1 - x0);
- xt = x1 - 0.5 * y * (x1 - x);
- if( xt >= 1.0 )
- break;
- }
- x = xt;
- if( fabs(d/x) < 128.0 * MACHEP )
- goto done;
- }
-/* Did not converge. */
-dithresh = 256.0 * MACHEP;
-goto ihalve;
-
-done:
-
-if( rflg )
- {
- if( x <= MACHEP )
- x = 1.0 - MACHEP;
- else
- x = 1.0 - x;
- }
-return( x );
-}
+++ /dev/null
-/* isnan()
- * signbit()
- * isfinite()
- *
- * Floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * double ceil(), floor(), frexp(), ldexp();
- * int signbit(), isnan(), isfinite();
- * double x, y;
- * int expnt, n;
- *
- * y = floor(x);
- * y = ceil(x);
- * y = frexp( x, &expnt );
- * y = ldexp( x, n );
- * n = signbit(x);
- * n = isnan(x);
- * n = isfinite(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * All four routines return a double precision floating point
- * result.
- *
- * floor() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * ceil() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * frexp() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * ldexp() multiplies x by 2**n.
- *
- * signbit(x) returns 1 if the sign bit of x is 1, else 0.
- *
- * These functions are part of the standard C run time library
- * for many but not all C compilers. The ones supplied are
- * written in C for either DEC or IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
-#undef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-#endif
-
-
-/* Return 1 if the sign bit of x is 1, else 0. */
-
-int signbit(x)
-double x;
-{
-union
- {
- double d;
- short s[4];
- int i[2];
- } u;
-
-u.d = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- return( u.i[1] < 0 );
-#endif
-#ifdef DEC
- return( u.s[3] < 0 );
-#endif
-#ifdef MIEEE
- return( u.i[0] < 0 );
-#endif
- }
-else
- {
-#ifdef IBMPC
- return( u.s[3] < 0 );
-#endif
-#ifdef DEC
- return( u.s[3] < 0 );
-#endif
-#ifdef MIEEE
- return( u.s[0] < 0 );
-#endif
- }
-}
-
-
-/* Return 1 if x is a number that is Not a Number, else return 0. */
-
-int isnan(x)
-double x;
-{
-#ifdef NANS
-union
- {
- double d;
- unsigned short s[4];
- unsigned int i[2];
- } u;
-
-u.d = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- if( ((u.i[1] & 0x7ff00000) == 0x7ff00000)
- && (((u.i[1] & 0x000fffff) != 0) || (u.i[0] != 0)))
- return 1;
-#endif
-#ifdef DEC
- if( (u.s[1] & 0x7fff) == 0)
- {
- if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( ((u.i[0] & 0x7ff00000) == 0x7ff00000)
- && (((u.i[0] & 0x000fffff) != 0) || (u.i[1] != 0)))
- return 1;
-#endif
- return(0);
- }
-else
- { /* size int not 4 */
-#ifdef IBMPC
- if( (u.s[3] & 0x7ff0) == 0x7ff0)
- {
- if( ((u.s[3] & 0x000f) | u.s[2] | u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef DEC
- if( (u.s[3] & 0x7fff) == 0)
- {
- if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( (u.s[0] & 0x7ff0) == 0x7ff0)
- {
- if( ((u.s[0] & 0x000f) | u.s[1] | u.s[2] | u.s[3]) != 0 )
- return(1);
- }
-#endif
- return(0);
- } /* size int not 4 */
-
-#else
-/* No NANS. */
-return(0);
-#endif
-}
-
-
-/* Return 1 if x is not infinite and is not a NaN. */
-
-int isfinite(x)
-double x;
-{
-#ifdef INFINITIES
-union
- {
- double d;
- unsigned short s[4];
- unsigned int i[2];
- } u;
-
-u.d = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- if( (u.i[1] & 0x7ff00000) != 0x7ff00000)
- return 1;
-#endif
-#ifdef DEC
- if( (u.s[3] & 0x7fff) != 0)
- return 1;
-#endif
-#ifdef MIEEE
- if( (u.i[0] & 0x7ff00000) != 0x7ff00000)
- return 1;
-#endif
- return(0);
- }
-else
- {
-#ifdef IBMPC
- if( (u.s[3] & 0x7ff0) != 0x7ff0)
- return 1;
-#endif
-#ifdef DEC
- if( (u.s[3] & 0x7fff) != 0)
- return 1;
-#endif
-#ifdef MIEEE
- if( (u.s[0] & 0x7ff0) != 0x7ff0)
- return 1;
-#endif
- return(0);
- }
-#else
-/* No INFINITY. */
-return(1);
-#endif
-}
+++ /dev/null
-/* iv.c
- *
- * Modified Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, iv();
- *
- * y = iv( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order v of the
- * argument. If x is negative, v must be integer valued.
- *
- * The function is defined as Iv(x) = Jv( ix ). It is
- * here computed in terms of the confluent hypergeometric
- * function, according to the formula
- *
- * v -x
- * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
- *
- * If v is a negative integer, then v is replaced by -v.
- *
- *
- * ACCURACY:
- *
- * Tested at random points (v, x), with v between 0 and
- * 30, x between 0 and 28.
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 2000 3.1e-15 5.4e-16
- * IEEE 0,30 10000 1.7e-14 2.7e-15
- *
- * Accuracy is diminished if v is near a negative integer.
- *
- * See also hyperg.c.
- *
- */
-\f/* iv.c */
-/* Modified Bessel function of noninteger order */
-/* If x < 0, then v must be an integer. */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double hyperg ( double, double, double );
-extern double exp ( double );
-extern double gamma ( double );
-extern double log ( double );
-extern double fabs ( double );
-extern double floor ( double );
-#else
-double hyperg(), exp(), gamma(), log(), fabs(), floor();
-#endif
-extern double MACHEP, MAXNUM;
-
-double iv( v, x )
-double v, x;
-{
-int sign;
-double t, ax;
-
-/* If v is a negative integer, invoke symmetry */
-t = floor(v);
-if( v < 0.0 )
- {
- if( t == v )
- {
- v = -v; /* symmetry */
- t = -t;
- }
- }
-/* If x is negative, require v to be an integer */
-sign = 1;
-if( x < 0.0 )
- {
- if( t != v )
- {
- mtherr( "iv", DOMAIN );
- return( 0.0 );
- }
- if( v != 2.0 * floor(v/2.0) )
- sign = -1;
- }
-
-/* Avoid logarithm singularity */
-if( x == 0.0 )
- {
- if( v == 0.0 )
- return( 1.0 );
- if( v < 0.0 )
- {
- mtherr( "iv", OVERFLOW );
- return( MAXNUM );
- }
- else
- return( 0.0 );
- }
-
-ax = fabs(x);
-t = v * log( 0.5 * ax ) - x;
-t = sign * exp(t) / gamma( v + 1.0 );
-ax = v + 0.5;
-return( t * hyperg( ax, 2.0 * ax, 2.0 * x ) );
-}
+++ /dev/null
-/* j0.c
- *
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j0();
- *
- * y = j0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval the following rational
- * approximation is used:
- *
- *
- * 2 2
- * (w - r ) (w - r ) P (w) / Q (w)
- * 1 2 3 8
- *
- * 2
- * where w = x and the two r's are zeros of the function.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.4e-17 6.3e-18
- * IEEE 0, 30 60000 4.2e-16 1.1e-16
- *
- */
-\f/* y0.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y0();
- *
- * y = y0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
- * Thus a call to j0() is required.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * DEC 0, 30 9400 7.0e-17 7.9e-18
- * IEEE 0, 30 30000 1.3e-15 1.6e-16
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-/* Note: all coefficients satisfy the relative error criterion
- * except YP, YQ which are designed for absolute error. */
-
-#include <math.h>
-
-#ifdef UNK
-static double PP[7] = {
- 7.96936729297347051624E-4,
- 8.28352392107440799803E-2,
- 1.23953371646414299388E0,
- 5.44725003058768775090E0,
- 8.74716500199817011941E0,
- 5.30324038235394892183E0,
- 9.99999999999999997821E-1,
-};
-static double PQ[7] = {
- 9.24408810558863637013E-4,
- 8.56288474354474431428E-2,
- 1.25352743901058953537E0,
- 5.47097740330417105182E0,
- 8.76190883237069594232E0,
- 5.30605288235394617618E0,
- 1.00000000000000000218E0,
-};
-#endif
-#ifdef DEC
-static unsigned short PP[28] = {
-0035520,0164604,0140733,0054470,
-0037251,0122605,0115356,0107170,
-0040236,0124412,0071500,0056303,
-0040656,0047737,0045720,0045263,
-0041013,0172143,0045004,0142103,
-0040651,0132045,0026241,0026406,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short PQ[28] = {
-0035562,0052006,0070034,0134666,
-0037257,0057055,0055242,0123424,
-0040240,0071626,0046630,0032371,
-0040657,0011077,0032013,0012731,
-0041014,0030307,0050331,0006414,
-0040651,0145457,0065021,0150304,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short PP[28] = {
-0x6b27,0x983b,0x1d30,0x3f4a,
-0xd1cf,0xb35d,0x34b0,0x3fb5,
-0x0b98,0x4e68,0xd521,0x3ff3,
-0x0956,0xe97a,0xc9fb,0x4015,
-0x9888,0x6940,0x7e8c,0x4021,
-0x25a1,0xa594,0x3684,0x4015,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short PQ[28] = {
-0x9737,0xce03,0x4a80,0x3f4e,
-0x54e3,0xab54,0xebc5,0x3fb5,
-0x069f,0xc9b3,0x0e72,0x3ff4,
-0x62bb,0xe681,0xe247,0x4015,
-0x21a1,0xea1b,0x8618,0x4021,
-0x3a19,0xed42,0x3965,0x4015,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short PP[28] = {
-0x3f4a,0x1d30,0x983b,0x6b27,
-0x3fb5,0x34b0,0xb35d,0xd1cf,
-0x3ff3,0xd521,0x4e68,0x0b98,
-0x4015,0xc9fb,0xe97a,0x0956,
-0x4021,0x7e8c,0x6940,0x9888,
-0x4015,0x3684,0xa594,0x25a1,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short PQ[28] = {
-0x3f4e,0x4a80,0xce03,0x9737,
-0x3fb5,0xebc5,0xab54,0x54e3,
-0x3ff4,0x0e72,0xc9b3,0x069f,
-0x4015,0xe247,0xe681,0x62bb,
-0x4021,0x8618,0xea1b,0x21a1,
-0x4015,0x3965,0xed42,0x3a19,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef UNK
-static double QP[8] = {
--1.13663838898469149931E-2,
--1.28252718670509318512E0,
--1.95539544257735972385E1,
--9.32060152123768231369E1,
--1.77681167980488050595E2,
--1.47077505154951170175E2,
--5.14105326766599330220E1,
--6.05014350600728481186E0,
-};
-static double QQ[7] = {
-/* 1.00000000000000000000E0,*/
- 6.43178256118178023184E1,
- 8.56430025976980587198E2,
- 3.88240183605401609683E3,
- 7.24046774195652478189E3,
- 5.93072701187316984827E3,
- 2.06209331660327847417E3,
- 2.42005740240291393179E2,
-};
-#endif
-#ifdef DEC
-static unsigned short QP[32] = {
-0136472,0035021,0142451,0141115,
-0140244,0024731,0150620,0105642,
-0141234,0067177,0124161,0060141,
-0141672,0064572,0151557,0043036,
-0142061,0127141,0003127,0043517,
-0142023,0011727,0060271,0144544,
-0141515,0122142,0126620,0143150,
-0140701,0115306,0106715,0007344,
-};
-static unsigned short QQ[28] = {
-/*0040200,0000000,0000000,0000000,*/
-0041600,0121272,0004741,0026544,
-0042526,0015605,0105654,0161771,
-0043162,0123155,0165644,0062645,
-0043342,0041675,0167576,0130756,
-0043271,0052720,0165631,0154214,
-0043000,0160576,0034614,0172024,
-0042162,0000570,0030500,0051235,
-};
-#endif
-#ifdef IBMPC
-static unsigned short QP[32] = {
-0x384a,0x38a5,0x4742,0xbf87,
-0x1174,0x3a32,0x853b,0xbff4,
-0x2c0c,0xf50e,0x8dcf,0xc033,
-0xe8c4,0x5a6d,0x4d2f,0xc057,
-0xe8ea,0x20ca,0x35cc,0xc066,
-0x392d,0xec17,0x627a,0xc062,
-0x18cd,0x55b2,0xb48c,0xc049,
-0xa1dd,0xd1b9,0x3358,0xc018,
-};
-static unsigned short QQ[28] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x25ac,0x413c,0x1457,0x4050,
-0x9c7f,0xb175,0xc370,0x408a,
-0x8cb5,0xbd74,0x54cd,0x40ae,
-0xd63e,0xbdef,0x4877,0x40bc,
-0x3b11,0x1d73,0x2aba,0x40b7,
-0x9e82,0xc731,0x1c2f,0x40a0,
-0x0a54,0x0628,0x402f,0x406e,
-};
-#endif
-#ifdef MIEEE
-static unsigned short QP[32] = {
-0xbf87,0x4742,0x38a5,0x384a,
-0xbff4,0x853b,0x3a32,0x1174,
-0xc033,0x8dcf,0xf50e,0x2c0c,
-0xc057,0x4d2f,0x5a6d,0xe8c4,
-0xc066,0x35cc,0x20ca,0xe8ea,
-0xc062,0x627a,0xec17,0x392d,
-0xc049,0xb48c,0x55b2,0x18cd,
-0xc018,0x3358,0xd1b9,0xa1dd,
-};
-static unsigned short QQ[28] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4050,0x1457,0x413c,0x25ac,
-0x408a,0xc370,0xb175,0x9c7f,
-0x40ae,0x54cd,0xbd74,0x8cb5,
-0x40bc,0x4877,0xbdef,0xd63e,
-0x40b7,0x2aba,0x1d73,0x3b11,
-0x40a0,0x1c2f,0xc731,0x9e82,
-0x406e,0x402f,0x0628,0x0a54,
-};
-#endif
-
-
-#ifdef UNK
-static double YP[8] = {
- 1.55924367855235737965E4,
--1.46639295903971606143E7,
- 5.43526477051876500413E9,
--9.82136065717911466409E11,
- 8.75906394395366999549E13,
--3.46628303384729719441E15,
- 4.42733268572569800351E16,
--1.84950800436986690637E16,
-};
-static double YQ[7] = {
-/* 1.00000000000000000000E0,*/
- 1.04128353664259848412E3,
- 6.26107330137134956842E5,
- 2.68919633393814121987E8,
- 8.64002487103935000337E10,
- 2.02979612750105546709E13,
- 3.17157752842975028269E15,
- 2.50596256172653059228E17,
-};
-#endif
-#ifdef DEC
-static unsigned short YP[32] = {
-0043563,0120677,0042264,0046166,
-0146137,0140371,0113444,0042260,
-0050241,0175707,0100502,0063344,
-0152144,0125737,0007265,0164526,
-0053637,0051621,0163035,0060546,
-0155105,0004416,0107306,0060023,
-0056035,0045133,0030132,0000024,
-0155603,0065132,0144061,0131732,
-};
-static unsigned short YQ[28] = {
-/*0040200,0000000,0000000,0000000,*/
-0042602,0024422,0135557,0162663,
-0045030,0155665,0044075,0160135,
-0047200,0035432,0105446,0104005,
-0051240,0167331,0056063,0022743,
-0053223,0127746,0025764,0012160,
-0055064,0044206,0177532,0145545,
-0056536,0111375,0163715,0127201,
-};
-#endif
-#ifdef IBMPC
-static unsigned short YP[32] = {
-0x898f,0xe896,0x7437,0x40ce,
-0x8896,0x32e4,0xf81f,0xc16b,
-0x4cdd,0xf028,0x3f78,0x41f4,
-0xbd2b,0xe1d6,0x957b,0xc26c,
-0xac2d,0x3cc3,0xea72,0x42d3,
-0xcc02,0xd1d8,0xa121,0xc328,
-0x4003,0x660b,0xa94b,0x4363,
-0x367b,0x5906,0x6d4b,0xc350,
-};
-static unsigned short YQ[28] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xfcb6,0x576d,0x4522,0x4090,
-0xbc0c,0xa907,0x1b76,0x4123,
-0xd101,0x5164,0x0763,0x41b0,
-0x64bc,0x2b86,0x1ddb,0x4234,
-0x828e,0xc57e,0x75fc,0x42b2,
-0x596d,0xdfeb,0x8910,0x4326,
-0xb5d0,0xbcf9,0xd25f,0x438b,
-};
-#endif
-#ifdef MIEEE
-static unsigned short YP[32] = {
-0x40ce,0x7437,0xe896,0x898f,
-0xc16b,0xf81f,0x32e4,0x8896,
-0x41f4,0x3f78,0xf028,0x4cdd,
-0xc26c,0x957b,0xe1d6,0xbd2b,
-0x42d3,0xea72,0x3cc3,0xac2d,
-0xc328,0xa121,0xd1d8,0xcc02,
-0x4363,0xa94b,0x660b,0x4003,
-0xc350,0x6d4b,0x5906,0x367b,
-};
-static unsigned short YQ[28] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4090,0x4522,0x576d,0xfcb6,
-0x4123,0x1b76,0xa907,0xbc0c,
-0x41b0,0x0763,0x5164,0xd101,
-0x4234,0x1ddb,0x2b86,0x64bc,
-0x42b2,0x75fc,0xc57e,0x828e,
-0x4326,0x8910,0xdfeb,0x596d,
-0x438b,0xd25f,0xbcf9,0xb5d0,
-};
-#endif
-
-#ifdef UNK
-/* 5.783185962946784521175995758455807035071 */
-static double DR1 = 5.78318596294678452118E0;
-/* 30.47126234366208639907816317502275584842 */
-static double DR2 = 3.04712623436620863991E1;
-#endif
-
-#ifdef DEC
-static unsigned short R1[] = {0040671,0007734,0001061,0056734};
-#define DR1 *(double *)R1
-static unsigned short R2[] = {0041363,0142445,0030416,0165567};
-#define DR2 *(double *)R2
-#endif
-
-#ifdef IBMPC
-static unsigned short R1[] = {0x2bbb,0x8046,0x21fb,0x4017};
-#define DR1 *(double *)R1
-static unsigned short R2[] = {0xdd6f,0xa621,0x78a4,0x403e};
-#define DR2 *(double *)R2
-#endif
-
-#ifdef MIEEE
-static unsigned short R1[] = {0x4017,0x21fb,0x8046,0x2bbb};
-#define DR1 *(double *)R1
-static unsigned short R2[] = {0x403e,0x78a4,0xa621,0xdd6f};
-#define DR2 *(double *)R2
-#endif
-
-#ifdef UNK
-static double RP[4] = {
--4.79443220978201773821E9,
- 1.95617491946556577543E12,
--2.49248344360967716204E14,
- 9.70862251047306323952E15,
-};
-static double RQ[8] = {
-/* 1.00000000000000000000E0,*/
- 4.99563147152651017219E2,
- 1.73785401676374683123E5,
- 4.84409658339962045305E7,
- 1.11855537045356834862E10,
- 2.11277520115489217587E12,
- 3.10518229857422583814E14,
- 3.18121955943204943306E16,
- 1.71086294081043136091E18,
-};
-#endif
-#ifdef DEC
-static unsigned short RP[16] = {
-0150216,0161235,0064344,0014450,
-0052343,0135216,0035624,0144153,
-0154142,0130247,0003310,0003667,
-0055411,0173703,0047772,0176635,
-};
-static unsigned short RQ[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0042371,0144025,0032265,0136137,
-0044451,0133131,0132420,0151466,
-0046470,0144641,0072540,0030636,
-0050446,0126600,0045042,0044243,
-0052365,0172633,0110301,0071063,
-0054215,0032424,0062272,0043513,
-0055742,0005013,0171731,0072335,
-0057275,0170646,0036663,0013134,
-};
-#endif
-#ifdef IBMPC
-static unsigned short RP[16] = {
-0x8325,0xad1c,0xdc53,0xc1f1,
-0x990d,0xc772,0x7751,0x427c,
-0x00f7,0xe0d9,0x5614,0xc2ec,
-0x5fb4,0x69ff,0x3ef8,0x4341,
-};
-static unsigned short RQ[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xb78c,0xa696,0x3902,0x407f,
-0x1a67,0x36a2,0x36cb,0x4105,
-0x0634,0x2eac,0x1934,0x4187,
-0x4914,0x0944,0xd5b0,0x4204,
-0x2e46,0x7218,0xbeb3,0x427e,
-0x48e9,0x8c97,0xa6a2,0x42f1,
-0x2e9c,0x7e7b,0x4141,0x435c,
-0x62cc,0xc7b6,0xbe34,0x43b7,
-};
-#endif
-#ifdef MIEEE
-static unsigned short RP[16] = {
-0xc1f1,0xdc53,0xad1c,0x8325,
-0x427c,0x7751,0xc772,0x990d,
-0xc2ec,0x5614,0xe0d9,0x00f7,
-0x4341,0x3ef8,0x69ff,0x5fb4,
-};
-static unsigned short RQ[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x407f,0x3902,0xa696,0xb78c,
-0x4105,0x36cb,0x36a2,0x1a67,
-0x4187,0x1934,0x2eac,0x0634,
-0x4204,0xd5b0,0x0944,0x4914,
-0x427e,0xbeb3,0x7218,0x2e46,
-0x42f1,0xa6a2,0x8c97,0x48e9,
-0x435c,0x4141,0x7e7b,0x2e9c,
-0x43b7,0xbe34,0xc7b6,0x62cc,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern double sqrt ( double );
-double j0 ( double );
-#else
-double polevl(), p1evl(), log(), sin(), cos(), sqrt();
-double j0();
-#endif
-extern double TWOOPI, SQ2OPI, PIO4;
-
-double j0(x)
-double x;
-{
-double w, z, p, q, xn;
-
-if( x < 0 )
- x = -x;
-
-if( x <= 5.0 )
- {
- z = x * x;
- if( x < 1.0e-5 )
- return( 1.0 - z/4.0 );
-
- p = (z - DR1) * (z - DR2);
- p = p * polevl( z, RP, 3)/p1evl( z, RQ, 8 );
- return( p );
- }
-
-w = 5.0/x;
-q = 25.0/(x*x);
-p = polevl( q, PP, 6)/polevl( q, PQ, 6 );
-q = polevl( q, QP, 7)/p1evl( q, QQ, 7 );
-xn = x - PIO4;
-p = p * cos(xn) - w * q * sin(xn);
-return( p * SQ2OPI / sqrt(x) );
-}
-\f
-/* y0() 2 */
-/* Bessel function of second kind, order zero */
-
-/* Rational approximation coefficients YP[], YQ[] are used here.
- * The function computed is y0(x) - 2 * log(x) * j0(x) / PI,
- * whose value at x = 0 is 2 * ( log(0.5) + EUL ) / PI
- * = 0.073804295108687225.
- */
-
-/*
-#define PIO4 .78539816339744830962
-#define SQ2OPI .79788456080286535588
-*/
-extern double MAXNUM;
-
-double y0(x)
-double x;
-{
-double w, z, p, q, xn;
-
-if( x <= 5.0 )
- {
- if( x <= 0.0 )
- {
- mtherr( "y0", DOMAIN );
- return( -MAXNUM );
- }
- z = x * x;
- w = polevl( z, YP, 7) / p1evl( z, YQ, 7 );
- w += TWOOPI * log(x) * j0(x);
- return( w );
- }
-
-w = 5.0/x;
-z = 25.0 / (x * x);
-p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
-q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
-xn = x - PIO4;
-p = p * sin(xn) + w * q * cos(xn);
-return( p * SQ2OPI / sqrt(x) );
-}
+++ /dev/null
-/* j1.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j1();
- *
- * y = j1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 24 term Chebyshev
- * expansion is used. In the second, the asymptotic
- * trigonometric representation is employed using two
- * rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.0e-17 1.1e-17
- * IEEE 0, 30 30000 2.6e-16 1.1e-16
- *
- *
- */
-\f/* y1.c
- *
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 25 term Chebyshev
- * expansion is used, and a call to j1() is required.
- * In the second, the asymptotic trigonometric representation
- * is employed using two rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 8.6e-17 1.3e-17
- * IEEE 0, 30 30000 1.0e-15 1.3e-16
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-/*
-#define PIO4 .78539816339744830962
-#define THPIO4 2.35619449019234492885
-#define SQ2OPI .79788456080286535588
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double RP[4] = {
--8.99971225705559398224E8,
- 4.52228297998194034323E11,
--7.27494245221818276015E13,
- 3.68295732863852883286E15,
-};
-static double RQ[8] = {
-/* 1.00000000000000000000E0,*/
- 6.20836478118054335476E2,
- 2.56987256757748830383E5,
- 8.35146791431949253037E7,
- 2.21511595479792499675E10,
- 4.74914122079991414898E12,
- 7.84369607876235854894E14,
- 8.95222336184627338078E16,
- 5.32278620332680085395E18,
-};
-#endif
-#ifdef DEC
-static unsigned short RP[16] = {
-0147526,0110742,0063322,0077052,
-0051722,0112720,0065034,0061530,
-0153604,0052227,0033147,0105650,
-0055121,0055025,0032276,0022015,
-};
-static unsigned short RQ[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0042433,0032610,0155604,0033473,
-0044572,0173320,0067270,0006616,
-0046637,0045246,0162225,0006606,
-0050645,0004773,0157577,0053004,
-0052612,0033734,0001667,0176501,
-0054462,0054121,0173147,0121367,
-0056237,0002777,0121451,0176007,
-0057623,0136253,0131601,0044710,
-};
-#endif
-#ifdef IBMPC
-static unsigned short RP[16] = {
-0x4fc5,0x4cda,0xd23c,0xc1ca,
-0x8c6b,0x0d43,0x52ba,0x425a,
-0xf175,0xe6cc,0x8a92,0xc2d0,
-0xc482,0xa697,0x2b42,0x432a,
-};
-static unsigned short RQ[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x86e7,0x1b70,0x66b1,0x4083,
-0x01b2,0x0dd7,0x5eda,0x410f,
-0xa1b1,0xdc92,0xe954,0x4193,
-0xeac1,0x7bef,0xa13f,0x4214,
-0xffa8,0x8076,0x46fb,0x4291,
-0xf45f,0x3ecc,0x4b0a,0x4306,
-0x3f81,0xf465,0xe0bf,0x4373,
-0x2939,0x7670,0x7795,0x43d2,
-};
-#endif
-#ifdef MIEEE
-static unsigned short RP[16] = {
-0xc1ca,0xd23c,0x4cda,0x4fc5,
-0x425a,0x52ba,0x0d43,0x8c6b,
-0xc2d0,0x8a92,0xe6cc,0xf175,
-0x432a,0x2b42,0xa697,0xc482,
-};
-static unsigned short RQ[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4083,0x66b1,0x1b70,0x86e7,
-0x410f,0x5eda,0x0dd7,0x01b2,
-0x4193,0xe954,0xdc92,0xa1b1,
-0x4214,0xa13f,0x7bef,0xeac1,
-0x4291,0x46fb,0x8076,0xffa8,
-0x4306,0x4b0a,0x3ecc,0xf45f,
-0x4373,0xe0bf,0xf465,0x3f81,
-0x43d2,0x7795,0x7670,0x2939,
-};
-#endif
-
-#ifdef UNK
-static double PP[7] = {
- 7.62125616208173112003E-4,
- 7.31397056940917570436E-2,
- 1.12719608129684925192E0,
- 5.11207951146807644818E0,
- 8.42404590141772420927E0,
- 5.21451598682361504063E0,
- 1.00000000000000000254E0,
-};
-static double PQ[7] = {
- 5.71323128072548699714E-4,
- 6.88455908754495404082E-2,
- 1.10514232634061696926E0,
- 5.07386386128601488557E0,
- 8.39985554327604159757E0,
- 5.20982848682361821619E0,
- 9.99999999999999997461E-1,
-};
-#endif
-#ifdef DEC
-static unsigned short PP[28] = {
-0035507,0144542,0061543,0024326,
-0037225,0145105,0017766,0022661,
-0040220,0043766,0010254,0133255,
-0040643,0113047,0142611,0151521,
-0041006,0144344,0055351,0074261,
-0040646,0156520,0120574,0006416,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short PQ[28] = {
-0035425,0142330,0115041,0165514,
-0037214,0177352,0145105,0052026,
-0040215,0072515,0141207,0073255,
-0040642,0056427,0137222,0106405,
-0041006,0062716,0166427,0165450,
-0040646,0133352,0035425,0123304,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short PP[28] = {
-0x651b,0x4c6c,0xf92c,0x3f48,
-0xc4b6,0xa3fe,0xb948,0x3fb2,
-0x96d6,0xc215,0x08fe,0x3ff2,
-0x3a6a,0xf8b1,0x72c4,0x4014,
-0x2f16,0x8b5d,0xd91c,0x4020,
-0x81a2,0x142f,0xdbaa,0x4014,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short PQ[28] = {
-0x3d69,0x1344,0xb89b,0x3f42,
-0xaa83,0x5948,0x9fdd,0x3fb1,
-0xeed6,0xb850,0xaea9,0x3ff1,
-0x51a1,0xf7d2,0x4ba2,0x4014,
-0xfd65,0xdda2,0xccb9,0x4020,
-0xb4d9,0x4762,0xd6dd,0x4014,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short PP[28] = {
-0x3f48,0xf92c,0x4c6c,0x651b,
-0x3fb2,0xb948,0xa3fe,0xc4b6,
-0x3ff2,0x08fe,0xc215,0x96d6,
-0x4014,0x72c4,0xf8b1,0x3a6a,
-0x4020,0xd91c,0x8b5d,0x2f16,
-0x4014,0xdbaa,0x142f,0x81a2,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short PQ[28] = {
-0x3f42,0xb89b,0x1344,0x3d69,
-0x3fb1,0x9fdd,0x5948,0xaa83,
-0x3ff1,0xaea9,0xb850,0xeed6,
-0x4014,0x4ba2,0xf7d2,0x51a1,
-0x4020,0xccb9,0xdda2,0xfd65,
-0x4014,0xd6dd,0x4762,0xb4d9,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef UNK
-static double QP[8] = {
- 5.10862594750176621635E-2,
- 4.98213872951233449420E0,
- 7.58238284132545283818E1,
- 3.66779609360150777800E2,
- 7.10856304998926107277E2,
- 5.97489612400613639965E2,
- 2.11688757100572135698E2,
- 2.52070205858023719784E1,
-};
-static double QQ[7] = {
-/* 1.00000000000000000000E0,*/
- 7.42373277035675149943E1,
- 1.05644886038262816351E3,
- 4.98641058337653607651E3,
- 9.56231892404756170795E3,
- 7.99704160447350683650E3,
- 2.82619278517639096600E3,
- 3.36093607810698293419E2,
-};
-#endif
-#ifdef DEC
-static unsigned short QP[32] = {
-0037121,0037723,0055605,0151004,
-0040637,0066656,0031554,0077264,
-0041627,0122714,0153170,0161466,
-0042267,0061712,0036520,0140145,
-0042461,0133315,0131573,0071176,
-0042425,0057525,0147500,0013201,
-0042123,0130122,0061245,0154131,
-0041311,0123772,0064254,0172650,
-};
-static unsigned short QQ[28] = {
-/*0040200,0000000,0000000,0000000,*/
-0041624,0074603,0002112,0101670,
-0042604,0007135,0010162,0175565,
-0043233,0151510,0157757,0172010,
-0043425,0064506,0112006,0104276,
-0043371,0164125,0032271,0164242,
-0043060,0121425,0122750,0136013,
-0042250,0005773,0053472,0146267,
-};
-#endif
-#ifdef IBMPC
-static unsigned short QP[32] = {
-0xba40,0x6b70,0x27fa,0x3faa,
-0x8fd6,0xc66d,0xedb5,0x4013,
-0x1c67,0x9acf,0xf4b9,0x4052,
-0x180d,0x47aa,0xec79,0x4076,
-0x6e50,0xb66f,0x36d9,0x4086,
-0x02d0,0xb9e8,0xabea,0x4082,
-0xbb0b,0x4c54,0x760a,0x406a,
-0x9eb5,0x4d15,0x34ff,0x4039,
-};
-static unsigned short QQ[28] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x5077,0x6089,0x8f30,0x4052,
-0x5f6f,0xa20e,0x81cb,0x4090,
-0xfe81,0x1bfd,0x7a69,0x40b3,
-0xd118,0xd280,0xad28,0x40c2,
-0x3d14,0xa697,0x3d0a,0x40bf,
-0x1781,0xb4bd,0x1462,0x40a6,
-0x5997,0x6ae7,0x017f,0x4075,
-};
-#endif
-#ifdef MIEEE
-static unsigned short QP[32] = {
-0x3faa,0x27fa,0x6b70,0xba40,
-0x4013,0xedb5,0xc66d,0x8fd6,
-0x4052,0xf4b9,0x9acf,0x1c67,
-0x4076,0xec79,0x47aa,0x180d,
-0x4086,0x36d9,0xb66f,0x6e50,
-0x4082,0xabea,0xb9e8,0x02d0,
-0x406a,0x760a,0x4c54,0xbb0b,
-0x4039,0x34ff,0x4d15,0x9eb5,
-};
-static unsigned short QQ[28] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4052,0x8f30,0x6089,0x5077,
-0x4090,0x81cb,0xa20e,0x5f6f,
-0x40b3,0x7a69,0x1bfd,0xfe81,
-0x40c2,0xad28,0xd280,0xd118,
-0x40bf,0x3d0a,0xa697,0x3d14,
-0x40a6,0x1462,0xb4bd,0x1781,
-0x4075,0x017f,0x6ae7,0x5997,
-};
-#endif
-
-#ifdef UNK
-static double YP[6] = {
- 1.26320474790178026440E9,
--6.47355876379160291031E11,
- 1.14509511541823727583E14,
--8.12770255501325109621E15,
- 2.02439475713594898196E17,
--7.78877196265950026825E17,
-};
-static double YQ[8] = {
-/* 1.00000000000000000000E0,*/
- 5.94301592346128195359E2,
- 2.35564092943068577943E5,
- 7.34811944459721705660E7,
- 1.87601316108706159478E10,
- 3.88231277496238566008E12,
- 6.20557727146953693363E14,
- 6.87141087355300489866E16,
- 3.97270608116560655612E18,
-};
-#endif
-#ifdef DEC
-static unsigned short YP[24] = {
-0047626,0112763,0013715,0133045,
-0152026,0134552,0142033,0024411,
-0053720,0045245,0102210,0077565,
-0155347,0000321,0136415,0102031,
-0056463,0146550,0055633,0032605,
-0157054,0171012,0167361,0054265,
-};
-static unsigned short YQ[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0042424,0111515,0044773,0153014,
-0044546,0005405,0171307,0075774,
-0046614,0023575,0047105,0063556,
-0050613,0143034,0101533,0156026,
-0052541,0175367,0166514,0114257,
-0054415,0014466,0134350,0171154,
-0056164,0017436,0025075,0022101,
-0057534,0103614,0103663,0121772,
-};
-#endif
-#ifdef IBMPC
-static unsigned short YP[24] = {
-0xb6c5,0x62f9,0xd2be,0x41d2,
-0x6521,0x5883,0xd72d,0xc262,
-0x0fef,0xb091,0x0954,0x42da,
-0xb083,0x37a1,0xe01a,0xc33c,
-0x66b1,0x0b73,0x79ad,0x4386,
-0x2b17,0x5dde,0x9e41,0xc3a5,
-};
-static unsigned short YQ[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x7ac2,0xa93f,0x9269,0x4082,
-0xef7f,0xbe58,0xc160,0x410c,
-0xacee,0xa9c8,0x84ef,0x4191,
-0x7b83,0x906b,0x78c3,0x4211,
-0x9316,0xfda9,0x3f5e,0x428c,
-0x1e4e,0xd71d,0xa326,0x4301,
-0xa488,0xc547,0x83e3,0x436e,
-0x747f,0x90f6,0x90f1,0x43cb,
-};
-#endif
-#ifdef MIEEE
-static unsigned short YP[24] = {
-0x41d2,0xd2be,0x62f9,0xb6c5,
-0xc262,0xd72d,0x5883,0x6521,
-0x42da,0x0954,0xb091,0x0fef,
-0xc33c,0xe01a,0x37a1,0xb083,
-0x4386,0x79ad,0x0b73,0x66b1,
-0xc3a5,0x9e41,0x5dde,0x2b17,
-};
-static unsigned short YQ[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4082,0x9269,0xa93f,0x7ac2,
-0x410c,0xc160,0xbe58,0xef7f,
-0x4191,0x84ef,0xa9c8,0xacee,
-0x4211,0x78c3,0x906b,0x7b83,
-0x428c,0x3f5e,0xfda9,0x9316,
-0x4301,0xa326,0xd71d,0x1e4e,
-0x436e,0x83e3,0xc547,0xa488,
-0x43cb,0x90f1,0x90f6,0x747f,
-};
-#endif
-
-
-#ifdef UNK
-static double Z1 = 1.46819706421238932572E1;
-static double Z2 = 4.92184563216946036703E1;
-#endif
-
-#ifdef DEC
-static unsigned short DZ1[] = {0041152,0164532,0006114,0010540};
-static unsigned short DZ2[] = {0041504,0157663,0001625,0020621};
-#define Z1 (*(double *)DZ1)
-#define Z2 (*(double *)DZ2)
-#endif
-
-#ifdef IBMPC
-static unsigned short DZ1[] = {0x822c,0x4189,0x5d2b,0x402d};
-static unsigned short DZ2[] = {0xa432,0x6072,0x9bf6,0x4048};
-#define Z1 (*(double *)DZ1)
-#define Z2 (*(double *)DZ2)
-#endif
-
-#ifdef MIEEE
-static unsigned short DZ1[] = {0x402d,0x5d2b,0x4189,0x822c};
-static unsigned short DZ2[] = {0x4048,0x9bf6,0x6072,0xa432};
-#define Z1 (*(double *)DZ1)
-#define Z2 (*(double *)DZ2)
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern double sqrt ( double );
-double j1 ( double );
-#else
-double polevl(), p1evl(), log(), sin(), cos(), sqrt();
-double j1();
-#endif
-extern double TWOOPI, THPIO4, SQ2OPI;
-
-double j1(x)
-double x;
-{
-double w, z, p, q, xn;
-
-w = x;
-if( x < 0 )
- w = -x;
-
-if( w <= 5.0 )
- {
- z = x * x;
- w = polevl( z, RP, 3 ) / p1evl( z, RQ, 8 );
- w = w * x * (z - Z1) * (z - Z2);
- return( w );
- }
-
-w = 5.0/x;
-z = w * w;
-p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
-q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
-xn = x - THPIO4;
-p = p * cos(xn) - w * q * sin(xn);
-return( p * SQ2OPI / sqrt(x) );
-}
-
-
-extern double MAXNUM;
-
-double y1(x)
-double x;
-{
-double w, z, p, q, xn;
-
-if( x <= 5.0 )
- {
- if( x <= 0.0 )
- {
- mtherr( "y1", DOMAIN );
- return( -MAXNUM );
- }
- z = x * x;
- w = x * (polevl( z, YP, 5 ) / p1evl( z, YQ, 8 ));
- w += TWOOPI * ( j1(x) * log(x) - 1.0/x );
- return( w );
- }
-
-w = 5.0/x;
-z = w * w;
-p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
-q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
-xn = x - THPIO4;
-p = p * sin(xn) + w * q * cos(xn);
-return( p * SQ2OPI / sqrt(x) );
-}
+++ /dev/null
-/* jn.c
- *
- * Bessel function of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double x, y, jn();
- *
- * y = jn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The ratio of jn(x) to j0(x) is computed by backward
- * recurrence. First the ratio jn/jn-1 is found by a
- * continued fraction expansion. Then the recurrence
- * relating successive orders is applied until j0 or j1 is
- * reached.
- *
- * If n = 0 or 1 the routine for j0 or j1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic range # trials peak rms
- * DEC 0, 30 5500 6.9e-17 9.3e-18
- * IEEE 0, 30 5000 4.4e-16 7.9e-17
- *
- *
- * Not suitable for large n or x. Use jv() instead.
- *
- */
-\f
-/* jn.c
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-#include <math.h>
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double j0 ( double );
-extern double j1 ( double );
-#else
-double fabs(), j0(), j1();
-#endif
-extern double MACHEP;
-
-double jn( n, x )
-int n;
-double x;
-{
-double pkm2, pkm1, pk, xk, r, ans;
-int k, sign;
-
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) == 0 ) /* -1**n */
- sign = 1;
- else
- sign = -1;
- }
-else
- sign = 1;
-
-if( x < 0.0 )
- {
- if( n & 1 )
- sign = -sign;
- x = -x;
- }
-
-if( n == 0 )
- return( sign * j0(x) );
-if( n == 1 )
- return( sign * j1(x) );
-if( n == 2 )
- return( sign * (2.0 * j1(x) / x - j0(x)) );
-
-if( x < MACHEP )
- return( 0.0 );
-
-/* continued fraction */
-#ifdef DEC
-k = 56;
-#else
-k = 53;
-#endif
-
-pk = 2 * (n + k);
-ans = pk;
-xk = x * x;
-
-do
- {
- pk -= 2.0;
- ans = pk - (xk/ans);
- }
-while( --k > 0 );
-ans = x/ans;
-
-/* backward recurrence */
-
-pk = 1.0;
-pkm1 = 1.0/ans;
-k = n-1;
-r = 2 * k;
-
-do
- {
- pkm2 = (pkm1 * r - pk * x) / x;
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0;
- }
-while( --k > 0 );
-
-if( fabs(pk) > fabs(pkm1) )
- ans = j1(x)/pk;
-else
- ans = j0(x)/pkm1;
-return( sign * ans );
-}
+++ /dev/null
-/* jv.c
- *
- * Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, jv();
- *
- * y = jv( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order v of the argument,
- * where v is real. Negative x is allowed if v is an integer.
- *
- * Several expansions are included: the ascending power
- * series, the Hankel expansion, and two transitional
- * expansions for large v. If v is not too large, it
- * is reduced by recurrence to a region of best accuracy.
- * The transitional expansions give 12D accuracy for v > 500.
- *
- *
- *
- * ACCURACY:
- * Results for integer v are indicated by *, where x and v
- * both vary from -125 to +125. Otherwise,
- * x ranges from 0 to 125, v ranges as indicated by "domain."
- * Error criterion is absolute, except relative when |jv()| > 1.
- *
- * arithmetic v domain x domain # trials peak rms
- * IEEE 0,125 0,125 100000 4.6e-15 2.2e-16
- * IEEE -125,0 0,125 40000 5.4e-11 3.7e-13
- * IEEE 0,500 0,500 20000 4.4e-15 4.0e-16
- * Integer v:
- * IEEE -125,125 -125,125 50000 3.5e-15* 1.9e-16*
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-#define DEBUG 0
-
-#ifdef DEC
-#define MAXGAM 34.84425627277176174
-#else
-#define MAXGAM 171.624376956302725
-#endif
-
-#ifdef ANSIPROT
-extern int airy ( double, double *, double *, double *, double * );
-extern double fabs ( double );
-extern double floor ( double );
-extern double frexp ( double, int * );
-extern double polevl ( double, void *, int );
-extern double j0 ( double );
-extern double j1 ( double );
-extern double sqrt ( double );
-extern double cbrt ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern double acos ( double );
-extern double pow ( double, double );
-extern double gamma ( double );
-extern double lgam ( double );
-static double recur(double *, double, double *, int);
-static double jvs(double, double);
-static double hankel(double, double);
-static double jnx(double, double);
-static double jnt(double, double);
-#else
-int airy();
-double fabs(), floor(), frexp(), polevl(), j0(), j1(), sqrt(), cbrt();
-double exp(), log(), sin(), cos(), acos(), pow(), gamma(), lgam();
-static double recur(), jvs(), hankel(), jnx(), jnt();
-#endif
-
-extern double MAXNUM, MACHEP, MINLOG, MAXLOG;
-#define BIG 1.44115188075855872E+17
-
-double jv( n, x )
-double n, x;
-{
-double k, q, t, y, an;
-int i, sign, nint;
-
-nint = 0; /* Flag for integer n */
-sign = 1; /* Flag for sign inversion */
-an = fabs( n );
-y = floor( an );
-if( y == an )
- {
- nint = 1;
- i = an - 16384.0 * floor( an/16384.0 );
- if( n < 0.0 )
- {
- if( i & 1 )
- sign = -sign;
- n = an;
- }
- if( x < 0.0 )
- {
- if( i & 1 )
- sign = -sign;
- x = -x;
- }
- if( n == 0.0 )
- return( j0(x) );
- if( n == 1.0 )
- return( sign * j1(x) );
- }
-
-if( (x < 0.0) && (y != an) )
- {
- mtherr( "Jv", DOMAIN );
- y = 0.0;
- goto done;
- }
-
-y = fabs(x);
-
-if( y < MACHEP )
- goto underf;
-
-k = 3.6 * sqrt(y);
-t = 3.6 * sqrt(an);
-if( (y < t) && (an > 21.0) )
- return( sign * jvs(n,x) );
-if( (an < k) && (y > 21.0) )
- return( sign * hankel(n,x) );
-
-if( an < 500.0 )
- {
-/* Note: if x is too large, the continued
- * fraction will fail; but then the
- * Hankel expansion can be used.
- */
- if( nint != 0 )
- {
- k = 0.0;
- q = recur( &n, x, &k, 1 );
- if( k == 0.0 )
- {
- y = j0(x)/q;
- goto done;
- }
- if( k == 1.0 )
- {
- y = j1(x)/q;
- goto done;
- }
- }
-
-if( an > 2.0 * y )
- goto rlarger;
-
- if( (n >= 0.0) && (n < 20.0)
- && (y > 6.0) && (y < 20.0) )
- {
-/* Recur backwards from a larger value of n
- */
-rlarger:
- k = n;
-
- y = y + an + 1.0;
- if( y < 30.0 )
- y = 30.0;
- y = n + floor(y-n);
- q = recur( &y, x, &k, 0 );
- y = jvs(y,x) * q;
- goto done;
- }
-
- if( k <= 30.0 )
- {
- k = 2.0;
- }
- else if( k < 90.0 )
- {
- k = (3*k)/4;
- }
- if( an > (k + 3.0) )
- {
- if( n < 0.0 )
- k = -k;
- q = n - floor(n);
- k = floor(k) + q;
- if( n > 0.0 )
- q = recur( &n, x, &k, 1 );
- else
- {
- t = k;
- k = n;
- q = recur( &t, x, &k, 1 );
- k = t;
- }
- if( q == 0.0 )
- {
-underf:
- y = 0.0;
- goto done;
- }
- }
- else
- {
- k = n;
- q = 1.0;
- }
-
-/* boundary between convergence of
- * power series and Hankel expansion
- */
- y = fabs(k);
- if( y < 26.0 )
- t = (0.0083*y + 0.09)*y + 12.9;
- else
- t = 0.9 * y;
-
- if( x > t )
- y = hankel(k,x);
- else
- y = jvs(k,x);
-#if DEBUG
-printf( "y = %.16e, recur q = %.16e\n", y, q );
-#endif
- if( n > 0.0 )
- y /= q;
- else
- y *= q;
- }
-
-else
- {
-/* For large n, use the uniform expansion
- * or the transitional expansion.
- * But if x is of the order of n**2,
- * these may blow up, whereas the
- * Hankel expansion will then work.
- */
- if( n < 0.0 )
- {
- mtherr( "Jv", TLOSS );
- y = 0.0;
- goto done;
- }
- t = x/n;
- t /= n;
- if( t > 0.3 )
- y = hankel(n,x);
- else
- y = jnx(n,x);
- }
-
-done: return( sign * y);
-}
-\f
-/* Reduce the order by backward recurrence.
- * AMS55 #9.1.27 and 9.1.73.
- */
-
-static double recur( n, x, newn, cancel )
-double *n;
-double x;
-double *newn;
-int cancel;
-{
-double pkm2, pkm1, pk, qkm2, qkm1;
-/* double pkp1; */
-double k, ans, qk, xk, yk, r, t, kf;
-static double big = BIG;
-int nflag, ctr;
-
-/* continued fraction for Jn(x)/Jn-1(x) */
-if( *n < 0.0 )
- nflag = 1;
-else
- nflag = 0;
-
-fstart:
-
-#if DEBUG
-printf( "recur: n = %.6e, newn = %.6e, cfrac = ", *n, *newn );
-#endif
-
-pkm2 = 0.0;
-qkm2 = 1.0;
-pkm1 = x;
-qkm1 = *n + *n;
-xk = -x * x;
-yk = qkm1;
-ans = 1.0;
-ctr = 0;
-do
- {
- yk += 2.0;
- pk = pkm1 * yk + pkm2 * xk;
- qk = qkm1 * yk + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
- if( qk != 0 )
- r = pk/qk;
- else
- r = 0.0;
- if( r != 0 )
- {
- t = fabs( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
-
- if( ++ctr > 1000 )
- {
- mtherr( "jv", UNDERFLOW );
- goto done;
- }
- if( t < MACHEP )
- goto done;
-
- if( fabs(pk) > big )
- {
- pkm2 /= big;
- pkm1 /= big;
- qkm2 /= big;
- qkm1 /= big;
- }
- }
-while( t > MACHEP );
-
-done:
-
-#if DEBUG
-printf( "%.6e\n", ans );
-#endif
-
-/* Change n to n-1 if n < 0 and the continued fraction is small
- */
-if( nflag > 0 )
- {
- if( fabs(ans) < 0.125 )
- {
- nflag = -1;
- *n = *n - 1.0;
- goto fstart;
- }
- }
-
-
-kf = *newn;
-
-/* backward recurrence
- * 2k
- * J (x) = --- J (x) - J (x)
- * k-1 x k k+1
- */
-
-pk = 1.0;
-pkm1 = 1.0/ans;
-k = *n - 1.0;
-r = 2 * k;
-do
- {
- pkm2 = (pkm1 * r - pk * x) / x;
- /* pkp1 = pk; */
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0;
-/*
- t = fabs(pkp1) + fabs(pk);
- if( (k > (kf + 2.5)) && (fabs(pkm1) < 0.25*t) )
- {
- k -= 1.0;
- t = x*x;
- pkm2 = ( (r*(r+2.0)-t)*pk - r*x*pkp1 )/t;
- pkp1 = pk;
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0;
- }
-*/
- k -= 1.0;
- }
-while( k > (kf + 0.5) );
-
-/* Take the larger of the last two iterates
- * on the theory that it may have less cancellation error.
- */
-
-if( cancel )
- {
- if( (kf >= 0.0) && (fabs(pk) > fabs(pkm1)) )
- {
- k += 1.0;
- pkm2 = pk;
- }
- }
-*newn = k;
-#if DEBUG
-printf( "newn %.6e rans %.6e\n", k, pkm2 );
-#endif
-return( pkm2 );
-}
-
-
-
-/* Ascending power series for Jv(x).
- * AMS55 #9.1.10.
- */
-
-extern double PI;
-extern int sgngam;
-
-static double jvs( n, x )
-double n, x;
-{
-double t, u, y, z, k;
-int ex;
-
-z = -x * x / 4.0;
-u = 1.0;
-y = u;
-k = 1.0;
-t = 1.0;
-
-while( t > MACHEP )
- {
- u *= z / (k * (n+k));
- y += u;
- k += 1.0;
- if( y != 0 )
- t = fabs( u/y );
- }
-#if DEBUG
-printf( "power series=%.5e ", y );
-#endif
-t = frexp( 0.5*x, &ex );
-ex = ex * n;
-if( (ex > -1023)
- && (ex < 1023)
- && (n > 0.0)
- && (n < (MAXGAM-1.0)) )
- {
- t = pow( 0.5*x, n ) / gamma( n + 1.0 );
-#if DEBUG
-printf( "pow(.5*x, %.4e)/gamma(n+1)=%.5e\n", n, t );
-#endif
- y *= t;
- }
-else
- {
-#if DEBUG
- z = n * log(0.5*x);
- k = lgam( n+1.0 );
- t = z - k;
- printf( "log pow=%.5e, lgam(%.4e)=%.5e\n", z, n+1.0, k );
-#else
- t = n * log(0.5*x) - lgam(n + 1.0);
-#endif
- if( y < 0 )
- {
- sgngam = -sgngam;
- y = -y;
- }
- t += log(y);
-#if DEBUG
-printf( "log y=%.5e\n", log(y) );
-#endif
- if( t < -MAXLOG )
- {
- return( 0.0 );
- }
- if( t > MAXLOG )
- {
- mtherr( "Jv", OVERFLOW );
- return( MAXNUM );
- }
- y = sgngam * exp( t );
- }
-return(y);
-}
-\f
-/* Hankel's asymptotic expansion
- * for large x.
- * AMS55 #9.2.5.
- */
-
-static double hankel( n, x )
-double n, x;
-{
-double t, u, z, k, sign, conv;
-double p, q, j, m, pp, qq;
-int flag;
-
-m = 4.0*n*n;
-j = 1.0;
-z = 8.0 * x;
-k = 1.0;
-p = 1.0;
-u = (m - 1.0)/z;
-q = u;
-sign = 1.0;
-conv = 1.0;
-flag = 0;
-t = 1.0;
-pp = 1.0e38;
-qq = 1.0e38;
-
-while( t > MACHEP )
- {
- k += 2.0;
- j += 1.0;
- sign = -sign;
- u *= (m - k * k)/(j * z);
- p += sign * u;
- k += 2.0;
- j += 1.0;
- u *= (m - k * k)/(j * z);
- q += sign * u;
- t = fabs(u/p);
- if( t < conv )
- {
- conv = t;
- qq = q;
- pp = p;
- flag = 1;
- }
-/* stop if the terms start getting larger */
- if( (flag != 0) && (t > conv) )
- {
-#if DEBUG
- printf( "Hankel: convergence to %.4E\n", conv );
-#endif
- goto hank1;
- }
- }
-
-hank1:
-u = x - (0.5*n + 0.25) * PI;
-t = sqrt( 2.0/(PI*x) ) * ( pp * cos(u) - qq * sin(u) );
-#if DEBUG
-printf( "hank: %.6e\n", t );
-#endif
-return( t );
-}
-\f
-
-/* Asymptotic expansion for large n.
- * AMS55 #9.3.35.
- */
-
-static double lambda[] = {
- 1.0,
- 1.041666666666666666666667E-1,
- 8.355034722222222222222222E-2,
- 1.282265745563271604938272E-1,
- 2.918490264641404642489712E-1,
- 8.816272674437576524187671E-1,
- 3.321408281862767544702647E+0,
- 1.499576298686255465867237E+1,
- 7.892301301158651813848139E+1,
- 4.744515388682643231611949E+2,
- 3.207490090890661934704328E+3
-};
-static double mu[] = {
- 1.0,
- -1.458333333333333333333333E-1,
- -9.874131944444444444444444E-2,
- -1.433120539158950617283951E-1,
- -3.172272026784135480967078E-1,
- -9.424291479571202491373028E-1,
- -3.511203040826354261542798E+0,
- -1.572726362036804512982712E+1,
- -8.228143909718594444224656E+1,
- -4.923553705236705240352022E+2,
- -3.316218568547972508762102E+3
-};
-static double P1[] = {
- -2.083333333333333333333333E-1,
- 1.250000000000000000000000E-1
-};
-static double P2[] = {
- 3.342013888888888888888889E-1,
- -4.010416666666666666666667E-1,
- 7.031250000000000000000000E-2
-};
-static double P3[] = {
- -1.025812596450617283950617E+0,
- 1.846462673611111111111111E+0,
- -8.912109375000000000000000E-1,
- 7.324218750000000000000000E-2
-};
-static double P4[] = {
- 4.669584423426247427983539E+0,
- -1.120700261622299382716049E+1,
- 8.789123535156250000000000E+0,
- -2.364086914062500000000000E+0,
- 1.121520996093750000000000E-1
-};
-static double P5[] = {
- -2.8212072558200244877E1,
- 8.4636217674600734632E1,
- -9.1818241543240017361E1,
- 4.2534998745388454861E1,
- -7.3687943594796316964E0,
- 2.27108001708984375E-1
-};
-static double P6[] = {
- 2.1257013003921712286E2,
- -7.6525246814118164230E2,
- 1.0599904525279998779E3,
- -6.9957962737613254123E2,
- 2.1819051174421159048E2,
- -2.6491430486951555525E1,
- 5.7250142097473144531E-1
-};
-static double P7[] = {
- -1.9194576623184069963E3,
- 8.0617221817373093845E3,
- -1.3586550006434137439E4,
- 1.1655393336864533248E4,
- -5.3056469786134031084E3,
- 1.2009029132163524628E3,
- -1.0809091978839465550E2,
- 1.7277275025844573975E0
-};
-
-
-static double jnx( n, x )
-double n, x;
-{
-double zeta, sqz, zz, zp, np;
-double cbn, n23, t, z, sz;
-double pp, qq, z32i, zzi;
-double ak, bk, akl, bkl;
-int sign, doa, dob, nflg, k, s, tk, tkp1, m;
-static double u[8];
-static double ai, aip, bi, bip;
-
-/* Test for x very close to n.
- * Use expansion for transition region if so.
- */
-cbn = cbrt(n);
-z = (x - n)/cbn;
-if( fabs(z) <= 0.7 )
- return( jnt(n,x) );
-
-z = x/n;
-zz = 1.0 - z*z;
-if( zz == 0.0 )
- return(0.0);
-
-if( zz > 0.0 )
- {
- sz = sqrt( zz );
- t = 1.5 * (log( (1.0+sz)/z ) - sz ); /* zeta ** 3/2 */
- zeta = cbrt( t * t );
- nflg = 1;
- }
-else
- {
- sz = sqrt(-zz);
- t = 1.5 * (sz - acos(1.0/z));
- zeta = -cbrt( t * t );
- nflg = -1;
- }
-z32i = fabs(1.0/t);
-sqz = cbrt(t);
-
-/* Airy function */
-n23 = cbrt( n * n );
-t = n23 * zeta;
-
-#if DEBUG
-printf("zeta %.5E, Airy(%.5E)\n", zeta, t );
-#endif
-airy( t, &ai, &aip, &bi, &bip );
-
-/* polynomials in expansion */
-u[0] = 1.0;
-zzi = 1.0/zz;
-u[1] = polevl( zzi, P1, 1 )/sz;
-u[2] = polevl( zzi, P2, 2 )/zz;
-u[3] = polevl( zzi, P3, 3 )/(sz*zz);
-pp = zz*zz;
-u[4] = polevl( zzi, P4, 4 )/pp;
-u[5] = polevl( zzi, P5, 5 )/(pp*sz);
-pp *= zz;
-u[6] = polevl( zzi, P6, 6 )/pp;
-u[7] = polevl( zzi, P7, 7 )/(pp*sz);
-
-#if DEBUG
-for( k=0; k<=7; k++ )
- printf( "u[%d] = %.5E\n", k, u[k] );
-#endif
-
-pp = 0.0;
-qq = 0.0;
-np = 1.0;
-/* flags to stop when terms get larger */
-doa = 1;
-dob = 1;
-akl = MAXNUM;
-bkl = MAXNUM;
-
-for( k=0; k<=3; k++ )
- {
- tk = 2 * k;
- tkp1 = tk + 1;
- zp = 1.0;
- ak = 0.0;
- bk = 0.0;
- for( s=0; s<=tk; s++ )
- {
- if( doa )
- {
- if( (s & 3) > 1 )
- sign = nflg;
- else
- sign = 1;
- ak += sign * mu[s] * zp * u[tk-s];
- }
-
- if( dob )
- {
- m = tkp1 - s;
- if( ((m+1) & 3) > 1 )
- sign = nflg;
- else
- sign = 1;
- bk += sign * lambda[s] * zp * u[m];
- }
- zp *= z32i;
- }
-
- if( doa )
- {
- ak *= np;
- t = fabs(ak);
- if( t < akl )
- {
- akl = t;
- pp += ak;
- }
- else
- doa = 0;
- }
-
- if( dob )
- {
- bk += lambda[tkp1] * zp * u[0];
- bk *= -np/sqz;
- t = fabs(bk);
- if( t < bkl )
- {
- bkl = t;
- qq += bk;
- }
- else
- dob = 0;
- }
-#if DEBUG
- printf("a[%d] %.5E, b[%d] %.5E\n", k, ak, k, bk );
-#endif
- if( np < MACHEP )
- break;
- np /= n*n;
- }
-
-/* normalizing factor ( 4*zeta/(1 - z**2) )**1/4 */
-t = 4.0 * zeta/zz;
-t = sqrt( sqrt(t) );
-
-t *= ai*pp/cbrt(n) + aip*qq/(n23*n);
-return(t);
-}
-\f
-/* Asymptotic expansion for transition region,
- * n large and x close to n.
- * AMS55 #9.3.23.
- */
-
-static double PF2[] = {
- -9.0000000000000000000e-2,
- 8.5714285714285714286e-2
-};
-static double PF3[] = {
- 1.3671428571428571429e-1,
- -5.4920634920634920635e-2,
- -4.4444444444444444444e-3
-};
-static double PF4[] = {
- 1.3500000000000000000e-3,
- -1.6036054421768707483e-1,
- 4.2590187590187590188e-2,
- 2.7330447330447330447e-3
-};
-static double PG1[] = {
- -2.4285714285714285714e-1,
- 1.4285714285714285714e-2
-};
-static double PG2[] = {
- -9.0000000000000000000e-3,
- 1.9396825396825396825e-1,
- -1.1746031746031746032e-2
-};
-static double PG3[] = {
- 1.9607142857142857143e-2,
- -1.5983694083694083694e-1,
- 6.3838383838383838384e-3
-};
-
-
-static double jnt( n, x )
-double n, x;
-{
-double z, zz, z3;
-double cbn, n23, cbtwo;
-double ai, aip, bi, bip; /* Airy functions */
-double nk, fk, gk, pp, qq;
-double F[5], G[4];
-int k;
-
-cbn = cbrt(n);
-z = (x - n)/cbn;
-cbtwo = cbrt( 2.0 );
-
-/* Airy function */
-zz = -cbtwo * z;
-airy( zz, &ai, &aip, &bi, &bip );
-
-/* polynomials in expansion */
-zz = z * z;
-z3 = zz * z;
-F[0] = 1.0;
-F[1] = -z/5.0;
-F[2] = polevl( z3, PF2, 1 ) * zz;
-F[3] = polevl( z3, PF3, 2 );
-F[4] = polevl( z3, PF4, 3 ) * z;
-G[0] = 0.3 * zz;
-G[1] = polevl( z3, PG1, 1 );
-G[2] = polevl( z3, PG2, 2 ) * z;
-G[3] = polevl( z3, PG3, 2 ) * zz;
-#if DEBUG
-for( k=0; k<=4; k++ )
- printf( "F[%d] = %.5E\n", k, F[k] );
-for( k=0; k<=3; k++ )
- printf( "G[%d] = %.5E\n", k, G[k] );
-#endif
-pp = 0.0;
-qq = 0.0;
-nk = 1.0;
-n23 = cbrt( n * n );
-
-for( k=0; k<=4; k++ )
- {
- fk = F[k]*nk;
- pp += fk;
- if( k != 4 )
- {
- gk = G[k]*nk;
- qq += gk;
- }
-#if DEBUG
- printf("fk[%d] %.5E, gk[%d] %.5E\n", k, fk, k, gk );
-#endif
- nk /= n23;
- }
-
-fk = cbtwo * ai * pp/cbn + cbrt(4.0) * aip * qq/n;
-return(fk);
-}
+++ /dev/null
-/* k0.c
- *
- * Modified Bessel function, third kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k0();
- *
- * y = k0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order zero of the argument.
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at 2000 random points between 0 and 8. Peak absolute
- * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 3100 1.3e-16 2.1e-17
- * IEEE 0, 30 30000 1.2e-15 1.6e-16
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * K0 domain x <= 0 MAXNUM
- *
- */
-\f/* k0e()
- *
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k0e();
- *
- * y = k0e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.4e-15 1.4e-16
- * See k0().
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for K0(x) + log(x/2) I0(x)
- * in the interval [0,2]. The odd order coefficients are all
- * zero; only the even order coefficients are listed.
- *
- * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL.
- */
-
-#ifdef UNK
-static double A[] =
-{
- 1.37446543561352307156E-16,
- 4.25981614279661018399E-14,
- 1.03496952576338420167E-11,
- 1.90451637722020886025E-9,
- 2.53479107902614945675E-7,
- 2.28621210311945178607E-5,
- 1.26461541144692592338E-3,
- 3.59799365153615016266E-2,
- 3.44289899924628486886E-1,
--5.35327393233902768720E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0023036,0073417,0032477,0165673,
-0025077,0154126,0016046,0012517,
-0027066,0011342,0035211,0005041,
-0031002,0160233,0037454,0050224,
-0032610,0012747,0037712,0173741,
-0034277,0144007,0172147,0162375,
-0035645,0140563,0125431,0165626,
-0037023,0057662,0125124,0102051,
-0037660,0043304,0004411,0166707,
-0140011,0005467,0047227,0130370
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0xfd77,0xe6a7,0xcee1,0x3ca3,
-0xc2aa,0xc384,0xfb0a,0x3d27,
-0x2144,0x4751,0xc25c,0x3da6,
-0x8a13,0x67e5,0x5c13,0x3e20,
-0x5efc,0xe7f9,0x02bc,0x3e91,
-0xfca0,0xfe8c,0xf900,0x3ef7,
-0x3d73,0x7563,0xb82e,0x3f54,
-0x9085,0x554a,0x6bf6,0x3fa2,
-0x3db9,0x8121,0x08d8,0x3fd6,
-0xf61f,0xe9d2,0x2166,0xbfe1
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0x3ca3,0xcee1,0xe6a7,0xfd77,
-0x3d27,0xfb0a,0xc384,0xc2aa,
-0x3da6,0xc25c,0x4751,0x2144,
-0x3e20,0x5c13,0x67e5,0x8a13,
-0x3e91,0x02bc,0xe7f9,0x5efc,
-0x3ef7,0xf900,0xfe8c,0xfca0,
-0x3f54,0xb82e,0x7563,0x3d73,
-0x3fa2,0x6bf6,0x554a,0x9085,
-0x3fd6,0x08d8,0x8121,0x3db9,
-0xbfe1,0x2166,0xe9d2,0xf61f
-};
-#endif
-
-
-
-/* Chebyshev coefficients for exp(x) sqrt(x) K0(x)
- * in the inverted interval [2,infinity].
- *
- * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2).
- */
-
-#ifdef UNK
-static double B[] = {
- 5.30043377268626276149E-18,
--1.64758043015242134646E-17,
- 5.21039150503902756861E-17,
--1.67823109680541210385E-16,
- 5.51205597852431940784E-16,
--1.84859337734377901440E-15,
- 6.34007647740507060557E-15,
--2.22751332699166985548E-14,
- 8.03289077536357521100E-14,
--2.98009692317273043925E-13,
- 1.14034058820847496303E-12,
--4.51459788337394416547E-12,
- 1.85594911495471785253E-11,
--7.95748924447710747776E-11,
- 3.57739728140030116597E-10,
--1.69753450938905987466E-9,
- 8.57403401741422608519E-9,
--4.66048989768794782956E-8,
- 2.76681363944501510342E-7,
--1.83175552271911948767E-6,
- 1.39498137188764993662E-5,
--1.28495495816278026384E-4,
- 1.56988388573005337491E-3,
--3.14481013119645005427E-2,
- 2.44030308206595545468E0
-};
-#endif
-
-#ifdef DEC
-static unsigned short B[] = {
-0021703,0106456,0076144,0173406,
-0122227,0173144,0116011,0030033,
-0022560,0044562,0006506,0067642,
-0123101,0076243,0123273,0131013,
-0023436,0157713,0056243,0141331,
-0124005,0032207,0063726,0164664,
-0024344,0066342,0051756,0162300,
-0124710,0121365,0154053,0077022,
-0025264,0161166,0066246,0077420,
-0125647,0141671,0006443,0103212,
-0026240,0076431,0077147,0160445,
-0126636,0153741,0174002,0105031,
-0027243,0040102,0035375,0163073,
-0127656,0176256,0113476,0044653,
-0030304,0125544,0006377,0130104,
-0130751,0047257,0110537,0127324,
-0031423,0046400,0014772,0012164,
-0132110,0025240,0155247,0112570,
-0032624,0105314,0007437,0021574,
-0133365,0155243,0174306,0116506,
-0034152,0004776,0061643,0102504,
-0135006,0136277,0036104,0175023,
-0035715,0142217,0162474,0115022,
-0137000,0147671,0065177,0134356,
-0040434,0026754,0175163,0044070
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short B[] = {
-0x9ee1,0xcf8c,0x71a5,0x3c58,
-0x2603,0x9381,0xfecc,0xbc72,
-0xcdf4,0x41a8,0x092e,0x3c8e,
-0x7641,0x74d7,0x2f94,0xbca8,
-0x785b,0x6b94,0xdbf9,0x3cc3,
-0xdd36,0xecfa,0xa690,0xbce0,
-0xdc98,0x4a7d,0x8d9c,0x3cfc,
-0x6fc2,0xbb05,0x145e,0xbd19,
-0xcfe2,0xcd94,0x9c4e,0x3d36,
-0x70d1,0x21a4,0xf877,0xbd54,
-0xfc25,0x2fcc,0x0fa3,0x3d74,
-0x5143,0x3f00,0xdafc,0xbd93,
-0xbcc7,0x475f,0x6808,0x3db4,
-0xc935,0xd2e7,0xdf95,0xbdd5,
-0xf608,0x819f,0x956c,0x3df8,
-0xf5db,0xf22b,0x29d5,0xbe1d,
-0x428e,0x033f,0x69a0,0x3e42,
-0xf2af,0x1b54,0x0554,0xbe69,
-0xe46f,0x81e3,0x9159,0x3e92,
-0xd3a9,0x7f18,0xbb54,0xbebe,
-0x70a9,0xcc74,0x413f,0x3eed,
-0x9f42,0xe788,0xd797,0xbf20,
-0x9342,0xfca7,0xb891,0x3f59,
-0xf71e,0x2d4f,0x19f7,0xbfa0,
-0x6907,0x9f4e,0x85bd,0x4003
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short B[] = {
-0x3c58,0x71a5,0xcf8c,0x9ee1,
-0xbc72,0xfecc,0x9381,0x2603,
-0x3c8e,0x092e,0x41a8,0xcdf4,
-0xbca8,0x2f94,0x74d7,0x7641,
-0x3cc3,0xdbf9,0x6b94,0x785b,
-0xbce0,0xa690,0xecfa,0xdd36,
-0x3cfc,0x8d9c,0x4a7d,0xdc98,
-0xbd19,0x145e,0xbb05,0x6fc2,
-0x3d36,0x9c4e,0xcd94,0xcfe2,
-0xbd54,0xf877,0x21a4,0x70d1,
-0x3d74,0x0fa3,0x2fcc,0xfc25,
-0xbd93,0xdafc,0x3f00,0x5143,
-0x3db4,0x6808,0x475f,0xbcc7,
-0xbdd5,0xdf95,0xd2e7,0xc935,
-0x3df8,0x956c,0x819f,0xf608,
-0xbe1d,0x29d5,0xf22b,0xf5db,
-0x3e42,0x69a0,0x033f,0x428e,
-0xbe69,0x0554,0x1b54,0xf2af,
-0x3e92,0x9159,0x81e3,0xe46f,
-0xbebe,0xbb54,0x7f18,0xd3a9,
-0x3eed,0x413f,0xcc74,0x70a9,
-0xbf20,0xd797,0xe788,0x9f42,
-0x3f59,0xb891,0xfca7,0x9342,
-0xbfa0,0x19f7,0x2d4f,0xf71e,
-0x4003,0x85bd,0x9f4e,0x6907
-};
-#endif
-
-/* k0.c */
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double exp ( double );
-extern double i0 ( double );
-extern double log ( double );
-extern double sqrt ( double );
-#else
-double chbevl(), exp(), i0(), log(), sqrt();
-#endif
-extern double PI;
-extern double MAXNUM;
-
-double k0(x)
-double x;
-{
-double y, z;
-
-if( x <= 0.0 )
- {
- mtherr( "k0", DOMAIN );
- return( MAXNUM );
- }
-
-if( x <= 2.0 )
- {
- y = x * x - 2.0;
- y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x);
- return( y );
- }
-z = 8.0/x - 2.0;
-y = exp(-x) * chbevl( z, B, 25 ) / sqrt(x);
-return(y);
-}
-
-
-
-
-double k0e( x )
-double x;
-{
-double y;
-
-if( x <= 0.0 )
- {
- mtherr( "k0e", DOMAIN );
- return( MAXNUM );
- }
-
-if( x <= 2.0 )
- {
- y = x * x - 2.0;
- y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x);
- return( y * exp(x) );
- }
-
-y = chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x);
-return(y);
-}
+++ /dev/null
-/* k1.c
- *
- * Modified Bessel function, third kind, order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k1();
- *
- * y = k1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the modified Bessel function of the third kind
- * of order one of the argument.
- *
- * The range is partitioned into the two intervals [0,2] and
- * (2, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 3300 8.9e-17 2.2e-17
- * IEEE 0, 30 30000 1.2e-15 1.6e-16
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * k1 domain x <= 0 MAXNUM
- *
- */
-\f/* k1e.c
- *
- * Modified Bessel function, third kind, order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k1e();
- *
- * y = k1e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order one of the argument:
- *
- * k1e(x) = exp(x) * k1(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-16 1.2e-16
- * See k1().
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
- * in the interval [0,2].
- *
- * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
- */
-
-#ifdef UNK
-static double A[] =
-{
--7.02386347938628759343E-18,
--2.42744985051936593393E-15,
--6.66690169419932900609E-13,
--1.41148839263352776110E-10,
--2.21338763073472585583E-8,
--2.43340614156596823496E-6,
--1.73028895751305206302E-4,
--6.97572385963986435018E-3,
--1.22611180822657148235E-1,
--3.53155960776544875667E-1,
- 1.52530022733894777053E0
-};
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0122001,0110501,0164746,0151255,
-0124056,0165213,0150034,0147377,
-0126073,0124026,0167207,0001044,
-0130033,0030735,0141061,0033116,
-0131676,0020350,0121341,0107175,
-0133443,0046631,0062031,0070716,
-0135065,0067427,0026435,0164022,
-0136344,0112234,0165752,0006222,
-0137373,0015622,0017016,0155636,
-0137664,0150333,0125730,0067240,
-0040303,0036411,0130200,0043120
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0xda56,0x3d3c,0x3228,0xbc60,
-0x99e0,0x7a03,0xdd51,0xbce5,
-0xe045,0xddd0,0x7502,0xbd67,
-0x26ca,0xb846,0x663b,0xbde3,
-0x31d0,0x145c,0xc41d,0xbe57,
-0x2e3a,0x2c83,0x69b3,0xbec4,
-0xbd02,0xe5a3,0xade2,0xbf26,
-0x4192,0x9d7d,0x9293,0xbf7c,
-0xdb74,0x43c1,0x6372,0xbfbf,
-0x0dd4,0x757b,0x9a1b,0xbfd6,
-0x08ca,0x3610,0x67a1,0x3ff8
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0xbc60,0x3228,0x3d3c,0xda56,
-0xbce5,0xdd51,0x7a03,0x99e0,
-0xbd67,0x7502,0xddd0,0xe045,
-0xbde3,0x663b,0xb846,0x26ca,
-0xbe57,0xc41d,0x145c,0x31d0,
-0xbec4,0x69b3,0x2c83,0x2e3a,
-0xbf26,0xade2,0xe5a3,0xbd02,
-0xbf7c,0x9293,0x9d7d,0x4192,
-0xbfbf,0x6372,0x43c1,0xdb74,
-0xbfd6,0x9a1b,0x757b,0x0dd4,
-0x3ff8,0x67a1,0x3610,0x08ca
-};
-#endif
-
-
-
-/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
- * in the interval [2,infinity].
- *
- * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
- */
-
-#ifdef UNK
-static double B[] =
-{
--5.75674448366501715755E-18,
- 1.79405087314755922667E-17,
--5.68946255844285935196E-17,
- 1.83809354436663880070E-16,
--6.05704724837331885336E-16,
- 2.03870316562433424052E-15,
--7.01983709041831346144E-15,
- 2.47715442448130437068E-14,
--8.97670518232499435011E-14,
- 3.34841966607842919884E-13,
--1.28917396095102890680E-12,
- 5.13963967348173025100E-12,
--2.12996783842756842877E-11,
- 9.21831518760500529508E-11,
--4.19035475934189648750E-10,
- 2.01504975519703286596E-9,
--1.03457624656780970260E-8,
- 5.74108412545004946722E-8,
--3.50196060308781257119E-7,
- 2.40648494783721712015E-6,
--1.93619797416608296024E-5,
- 1.95215518471351631108E-4,
--2.85781685962277938680E-3,
- 1.03923736576817238437E-1,
- 2.72062619048444266945E0
-};
-#endif
-
-#ifdef DEC
-static unsigned short B[] = {
-0121724,0061352,0013041,0150076,
-0022245,0074324,0016172,0173232,
-0122603,0030250,0135670,0165221,
-0023123,0165362,0023561,0060124,
-0123456,0112436,0141654,0073623,
-0024022,0163557,0077564,0006753,
-0124374,0165221,0131014,0026524,
-0024737,0017512,0144250,0175451,
-0125312,0021456,0123136,0076633,
-0025674,0077720,0020125,0102607,
-0126265,0067543,0007744,0043701,
-0026664,0152702,0033002,0074202,
-0127273,0055234,0120016,0071733,
-0027712,0133200,0042441,0075515,
-0130346,0057000,0015456,0074470,
-0031012,0074441,0051636,0111155,
-0131461,0136444,0177417,0002101,
-0032166,0111743,0032176,0021410,
-0132674,0001224,0076555,0027060,
-0033441,0077430,0135226,0106663,
-0134242,0065610,0167155,0113447,
-0035114,0131304,0043664,0102163,
-0136073,0045065,0171465,0122123,
-0037324,0152767,0147401,0017732,
-0040456,0017275,0050061,0062120,
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short B[] = {
-0x3a08,0x42c4,0x8c5d,0xbc5a,
-0x5ed3,0x838f,0xaf1a,0x3c74,
-0x1d52,0x1777,0x6615,0xbc90,
-0x2c0b,0x44ee,0x7d5e,0x3caa,
-0x8ef2,0xd875,0xd2a3,0xbcc5,
-0x81bd,0xefee,0x5ced,0x3ce2,
-0x85ab,0x3641,0x9d52,0xbcff,
-0x1f65,0x5915,0xe3e9,0x3d1b,
-0xcfb3,0xd4cb,0x4465,0xbd39,
-0xb0b1,0x040a,0x8ffa,0x3d57,
-0x88f8,0x61fc,0xadec,0xbd76,
-0x4f10,0x46c0,0x9ab8,0x3d96,
-0xce7b,0x9401,0x6b53,0xbdb7,
-0x2f6a,0x08a4,0x56d0,0x3dd9,
-0xcf27,0x0365,0xcbc0,0xbdfc,
-0xd24e,0x2a73,0x4f24,0x3e21,
-0xe088,0x9fe1,0x37a4,0xbe46,
-0xc461,0x668f,0xd27c,0x3e6e,
-0xa5c6,0x8fad,0x8052,0xbe97,
-0xd1b6,0x1752,0x2fe3,0x3ec4,
-0xb2e5,0x1dcd,0x4d71,0xbef4,
-0x908e,0x88f6,0x9658,0x3f29,
-0xb48a,0xbe66,0x6946,0xbf67,
-0x23fb,0xf9e0,0x9abe,0x3fba,
-0x2c8a,0xaa06,0xc3d7,0x4005
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short B[] = {
-0xbc5a,0x8c5d,0x42c4,0x3a08,
-0x3c74,0xaf1a,0x838f,0x5ed3,
-0xbc90,0x6615,0x1777,0x1d52,
-0x3caa,0x7d5e,0x44ee,0x2c0b,
-0xbcc5,0xd2a3,0xd875,0x8ef2,
-0x3ce2,0x5ced,0xefee,0x81bd,
-0xbcff,0x9d52,0x3641,0x85ab,
-0x3d1b,0xe3e9,0x5915,0x1f65,
-0xbd39,0x4465,0xd4cb,0xcfb3,
-0x3d57,0x8ffa,0x040a,0xb0b1,
-0xbd76,0xadec,0x61fc,0x88f8,
-0x3d96,0x9ab8,0x46c0,0x4f10,
-0xbdb7,0x6b53,0x9401,0xce7b,
-0x3dd9,0x56d0,0x08a4,0x2f6a,
-0xbdfc,0xcbc0,0x0365,0xcf27,
-0x3e21,0x4f24,0x2a73,0xd24e,
-0xbe46,0x37a4,0x9fe1,0xe088,
-0x3e6e,0xd27c,0x668f,0xc461,
-0xbe97,0x8052,0x8fad,0xa5c6,
-0x3ec4,0x2fe3,0x1752,0xd1b6,
-0xbef4,0x4d71,0x1dcd,0xb2e5,
-0x3f29,0x9658,0x88f6,0x908e,
-0xbf67,0x6946,0xbe66,0xb48a,
-0x3fba,0x9abe,0xf9e0,0x23fb,
-0x4005,0xc3d7,0xaa06,0x2c8a
-};
-#endif
-
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double exp ( double );
-extern double i1 ( double );
-extern double log ( double );
-extern double sqrt ( double );
-#else
-double chbevl(), exp(), i1(), log(), sqrt();
-#endif
-extern double PI;
-extern double MINLOG, MAXNUM;
-
-double k1(x)
-double x;
-{
-double y, z;
-
-z = 0.5 * x;
-if( z <= 0.0 )
- {
- mtherr( "k1", DOMAIN );
- return( MAXNUM );
- }
-
-if( x <= 2.0 )
- {
- y = x * x - 2.0;
- y = log(z) * i1(x) + chbevl( y, A, 11 ) / x;
- return( y );
- }
-
-return( exp(-x) * chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
-}
-
-
-
-
-double k1e( x )
-double x;
-{
-double y;
-
-if( x <= 0.0 )
- {
- mtherr( "k1e", DOMAIN );
- return( MAXNUM );
- }
-
-if( x <= 2.0 )
- {
- y = x * x - 2.0;
- y = log( 0.5 * x ) * i1(x) + chbevl( y, A, 11 ) / x;
- return( y * exp(x) );
- }
-
-return( chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
-}
+++ /dev/null
-/* kn.c
- *
- * Modified Bessel function, third kind, integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, kn();
- * int n;
- *
- * y = kn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order n of the argument.
- *
- * The range is partitioned into the two intervals [0,9.55] and
- * (9.55, infinity). An ascending power series is used in the
- * low range, and an asymptotic expansion in the high range.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 3000 1.3e-9 5.8e-11
- * IEEE 0,30 90000 1.8e-8 3.0e-10
- *
- * Error is high only near the crossover point x = 9.55
- * between the two expansions used.
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
-*/
-
-
-/*
-Algorithm for Kn.
- n-1
- -n - (n-k-1)! 2 k
-K (x) = 0.5 (x/2) > -------- (-x /4)
- n - k!
- k=0
-
- inf. 2 k
- n n - (x /4)
- + (-1) 0.5(x/2) > {p(k+1) + p(n+k+1) - 2log(x/2)} ---------
- - k! (n+k)!
- k=0
-
-where p(m) is the psi function: p(1) = -EUL and
-
- m-1
- -
- p(m) = -EUL + > 1/k
- -
- k=1
-
-For large x,
- 2 2 2
- u-1 (u-1 )(u-3 )
-K (z) = sqrt(pi/2z) exp(-z) { 1 + ------- + ------------ + ...}
- v 1 2
- 1! (8z) 2! (8z)
-asymptotically, where
-
- 2
- u = 4 v .
-
-*/
-\f
-#include <math.h>
-
-#define EUL 5.772156649015328606065e-1
-#define MAXFAC 31
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double sqrt ( double );
-#else
-double fabs(), exp(), log(), sqrt();
-#endif
-extern double MACHEP, MAXNUM, MAXLOG, PI;
-
-double kn( nn, x )
-int nn;
-double x;
-{
-double k, kf, nk1f, nkf, zn, t, s, z0, z;
-double ans, fn, pn, pk, zmn, tlg, tox;
-int i, n;
-
-if( nn < 0 )
- n = -nn;
-else
- n = nn;
-
-if( n > MAXFAC )
- {
-overf:
- mtherr( "kn", OVERFLOW );
- return( MAXNUM );
- }
-
-if( x <= 0.0 )
- {
- if( x < 0.0 )
- mtherr( "kn", DOMAIN );
- else
- mtherr( "kn", SING );
- return( MAXNUM );
- }
-
-
-if( x > 9.55 )
- goto asymp;
-
-ans = 0.0;
-z0 = 0.25 * x * x;
-fn = 1.0;
-pn = 0.0;
-zmn = 1.0;
-tox = 2.0/x;
-
-if( n > 0 )
- {
- /* compute factorial of n and psi(n) */
- pn = -EUL;
- k = 1.0;
- for( i=1; i<n; i++ )
- {
- pn += 1.0/k;
- k += 1.0;
- fn *= k;
- }
-
- zmn = tox;
-
- if( n == 1 )
- {
- ans = 1.0/x;
- }
- else
- {
- nk1f = fn/n;
- kf = 1.0;
- s = nk1f;
- z = -z0;
- zn = 1.0;
- for( i=1; i<n; i++ )
- {
- nk1f = nk1f/(n-i);
- kf = kf * i;
- zn *= z;
- t = nk1f * zn / kf;
- s += t;
- if( (MAXNUM - fabs(t)) < fabs(s) )
- goto overf;
- if( (tox > 1.0) && ((MAXNUM/tox) < zmn) )
- goto overf;
- zmn *= tox;
- }
- s *= 0.5;
- t = fabs(s);
- if( (zmn > 1.0) && ((MAXNUM/zmn) < t) )
- goto overf;
- if( (t > 1.0) && ((MAXNUM/t) < zmn) )
- goto overf;
- ans = s * zmn;
- }
- }
-
-
-tlg = 2.0 * log( 0.5 * x );
-pk = -EUL;
-if( n == 0 )
- {
- pn = pk;
- t = 1.0;
- }
-else
- {
- pn = pn + 1.0/n;
- t = 1.0/fn;
- }
-s = (pk+pn-tlg)*t;
-k = 1.0;
-do
- {
- t *= z0 / (k * (k+n));
- pk += 1.0/k;
- pn += 1.0/(k+n);
- s += (pk+pn-tlg)*t;
- k += 1.0;
- }
-while( fabs(t/s) > MACHEP );
-
-s = 0.5 * s / zmn;
-if( n & 1 )
- s = -s;
-ans += s;
-
-return(ans);
-
-
-
-/* Asymptotic expansion for Kn(x) */
-/* Converges to 1.4e-17 for x > 18.4 */
-
-asymp:
-
-if( x > MAXLOG )
- {
- mtherr( "kn", UNDERFLOW );
- return(0.0);
- }
-k = n;
-pn = 4.0 * k * k;
-pk = 1.0;
-z0 = 8.0 * x;
-fn = 1.0;
-t = 1.0;
-s = t;
-nkf = MAXNUM;
-i = 0;
-do
- {
- z = pn - pk * pk;
- t = t * z /(fn * z0);
- nk1f = fabs(t);
- if( (i >= n) && (nk1f > nkf) )
- {
- goto adone;
- }
- nkf = nk1f;
- s += t;
- fn += 1.0;
- pk += 2.0;
- i += 1;
- }
-while( fabs(t/s) > MACHEP );
-
-adone:
-ans = exp(-x) * sqrt( PI/(2.0*x) ) * s;
-return(ans);
-}
+++ /dev/null
-
-/* Re Kolmogorov statistics, here is Birnbaum and Tingey's formula for the
- distribution of D+, the maximum of all positive deviations between a
- theoretical distribution function P(x) and an empirical one Sn(x)
- from n samples.
-
- +
- D = sup [P(x) - S (x)]
- n -inf < x < inf n
-
-
- [n(1-e)]
- + - v-1 n-v
- Pr{D > e} = > C e (e + v/n) (1 - e - v/n)
- n - n v
- v=0
-
- [n(1-e)] is the largest integer not exceeding n(1-e).
- nCv is the number of combinations of n things taken v at a time. */
-
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double pow ( double, double );
-extern double floor ( double );
-extern double lgam ( double );
-extern double exp ( double );
-extern double sqrt ( double );
-extern double log ( double );
-extern double fabs ( double );
-double smirnov ( int, double );
-double kolmogorov ( double );
-#else
-double pow (), floor (), lgam (), exp (), sqrt (), log (), fabs ();
-double smirnov (), kolmogorov ();
-#endif
-extern double MAXLOG;
-
-/* Exact Smirnov statistic, for one-sided test. */
-double
-smirnov (n, e)
- int n;
- double e;
-{
- int v, nn;
- double evn, omevn, p, t, c, lgamnp1;
-
- if (n <= 0 || e < 0.0 || e > 1.0)
- return (-1.0);
- nn = floor ((double) n * (1.0 - e));
- p = 0.0;
- if (n < 1013)
- {
- c = 1.0;
- for (v = 0; v <= nn; v++)
- {
- evn = e + ((double) v) / n;
- p += c * pow (evn, (double) (v - 1))
- * pow (1.0 - evn, (double) (n - v));
- /* Next combinatorial term; worst case error = 4e-15. */
- c *= ((double) (n - v)) / (v + 1);
- }
- }
- else
- {
- lgamnp1 = lgam ((double) (n + 1));
- for (v = 0; v <= nn; v++)
- {
- evn = e + ((double) v) / n;
- omevn = 1.0 - evn;
- if (fabs (omevn) > 0.0)
- {
- t = lgamnp1
- - lgam ((double) (v + 1))
- - lgam ((double) (n - v + 1))
- + (v - 1) * log (evn)
- + (n - v) * log (omevn);
- if (t > -MAXLOG)
- p += exp (t);
- }
- }
- }
- return (p * e);
-}
-
-
-/* Kolmogorov's limiting distribution of two-sided test, returns
- probability that sqrt(n) * max deviation > y,
- or that max deviation > y/sqrt(n).
- The approximation is useful for the tail of the distribution
- when n is large. */
-double
-kolmogorov (y)
- double y;
-{
- double p, t, r, sign, x;
-
- x = -2.0 * y * y;
- sign = 1.0;
- p = 0.0;
- r = 1.0;
- do
- {
- t = exp (x * r * r);
- p += sign * t;
- if (t == 0.0)
- break;
- r += 1.0;
- sign = -sign;
- }
- while ((t / p) > 1.1e-16);
- return (p + p);
-}
-
-/* Functional inverse of Smirnov distribution
- finds e such that smirnov(n,e) = p. */
-double
-smirnovi (n, p)
- int n;
- double p;
-{
- double e, t, dpde;
-
- if (p <= 0.0 || p > 1.0)
- {
- mtherr ("smirnovi", DOMAIN);
- return 0.0;
- }
- /* Start with approximation p = exp(-2 n e^2). */
- e = sqrt (-log (p) / (2.0 * n));
- do
- {
- /* Use approximate derivative in Newton iteration. */
- t = -2.0 * n * e;
- dpde = 2.0 * t * exp (t * e);
- if (fabs (dpde) > 0.0)
- t = (p - smirnov (n, e)) / dpde;
- else
- {
- mtherr ("smirnovi", UNDERFLOW);
- return 0.0;
- }
- e = e + t;
- if (e >= 1.0 || e <= 0.0)
- {
- mtherr ("smirnovi", OVERFLOW);
- return 0.0;
- }
- }
- while (fabs (t / e) > 1e-10);
- return (e);
-}
-
-
-/* Functional inverse of Kolmogorov statistic for two-sided test.
- Finds y such that kolmogorov(y) = p.
- If e = smirnovi (n,p), then kolmogi(2 * p) / sqrt(n) should
- be close to e. */
-double
-kolmogi (p)
- double p;
-{
- double y, t, dpdy;
-
- if (p <= 0.0 || p > 1.0)
- {
- mtherr ("kolmogi", DOMAIN);
- return 0.0;
- }
- /* Start with approximation p = 2 exp(-2 y^2). */
- y = sqrt (-0.5 * log (0.5 * p));
- do
- {
- /* Use approximate derivative in Newton iteration. */
- t = -2.0 * y;
- dpdy = 4.0 * t * exp (t * y);
- if (fabs (dpdy) > 0.0)
- t = (p - kolmogorov (y)) / dpdy;
- else
- {
- mtherr ("kolmogi", UNDERFLOW);
- return 0.0;
- }
- y = y + t;
- }
- while (fabs (t / y) > 1e-10);
- return (y);
-}
-
-
-#ifdef SALONE
-/* Type in a number. */
-void
-getnum (s, px)
- char *s;
- double *px;
-{
- char str[30];
-
- printf (" %s (%.15e) ? ", s, *px);
- gets (str);
- if (str[0] == '\0' || str[0] == '\n')
- return;
- sscanf (str, "%lf", px);
- printf ("%.15e\n", *px);
-}
-
-/* Type in values, get answers. */
-void
-main ()
-{
- int n;
- double e, p, ps, pk, ek, y;
-
- n = 5;
- e = 0.0;
- p = 0.1;
-loop:
- ps = n;
- getnum ("n", &ps);
- n = ps;
- if (n <= 0)
- {
- printf ("? Operator error.\n");
- goto loop;
- }
- /*
- getnum ("e", &e);
- ps = smirnov (n, e);
- y = sqrt ((double) n) * e;
- printf ("y = %.4e\n", y);
- pk = kolmogorov (y);
- printf ("Smirnov = %.15e, Kolmogorov/2 = %.15e\n", ps, pk / 2.0);
-*/
- getnum ("p", &p);
- e = smirnovi (n, p);
- printf ("Smirnov e = %.15e\n", e);
- y = kolmogi (2.0 * p);
- ek = y / sqrt ((double) n);
- printf ("Kolmogorov e = %.15e\n", ek);
- goto loop;
-}
-#endif
+++ /dev/null
-/* Levnsn.c */
-/* Levinson-Durbin LPC
- *
- * | R0 R1 R2 ... RN-1 | | A1 | | -R1 |
- * | R1 R0 R1 ... RN-2 | | A2 | | -R2 |
- * | R2 R1 R0 ... RN-3 | | A3 | = | -R3 |
- * | ... | | ...| | ... |
- * | RN-1 RN-2... R0 | | AN | | -RN |
- *
- * Ref: John Makhoul, "Linear Prediction, A Tutorial Review"
- * Proc. IEEE Vol. 63, PP 561-580 April, 1975.
- *
- * R is the input autocorrelation function. R0 is the zero lag
- * term. A is the output array of predictor coefficients. Note
- * that a filter impulse response has a coefficient of 1.0 preceding
- * A1. E is an array of mean square error for each prediction order
- * 1 to N. REFL is an output array of the reflection coefficients.
- */
-
-#define abs(x) ( (x) < 0 ? -(x) : (x) )
-
-int levnsn( n, r, a, e, refl )
-int n;
-double r[], a[], e[], refl[];
-{
-int k, km1, i, kmi, j;
-double ai, akk, err, err1, r0, t, akmi;
-double *pa, *pr;
-
-for( i=0; i<n; i++ )
- {
- a[i] = 0.0;
- e[i] = 0.0;
- refl[i] = 0.0;
- }
-r0 = r[0];
-e[0] = r0;
-err = r0;
-
-akk = -r[1]/err;
-err = (1.0 - akk*akk) * err;
-e[1] = err;
-a[1] = akk;
-refl[1] = akk;
-
-if( err < 1.0e-2 )
- return 0;
-
-for( k=2; k<n; k++ )
- {
- t = 0.0;
- pa = &a[1];
- pr = &r[k-1];
- for( j=1; j<k; j++ )
- t += *pa++ * *pr--;
- akk = -( r[k] + t )/err;
- refl[k] = akk;
- km1 = k/2;
- for( j=1; j<=km1; j++ )
- {
- kmi = k-j;
- ai = a[j];
- akmi = a[kmi];
- a[j] = ai + akk*akmi;
- if( i == kmi )
- goto nxtk;
- a[kmi] = akmi + akk*ai;
- }
-nxtk:
- a[k] = akk;
- err1 = (1.0 - akk*akk)*err;
- e[k] = err1;
- if( err1 < 0 )
- err1 = -err1;
-/* err1 = abs(err1);*/
-/* if( (err1 < 1.0e-2) || (err1 >= err) )*/
- if( err1 < 1.0e-2 )
- return 0;
- err = err1;
- }
- return 0;
-}
+++ /dev/null
-/* log.c
- *
- * Natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, log();
- *
- * y = log( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 150000 1.44e-16 5.06e-17
- * IEEE +-MAXNUM 30000 1.20e-16 4.78e-17
- * DEC 0, 10 170000 1.8e-17 6.3e-18
- *
- * In the tests over the interval [+-MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [0, MAXLOG].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITY
- * log domain: x < 0; returns NAN
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-static char fname[] = {"log"};
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-#ifdef UNK
-static double P[] = {
- 1.01875663804580931796E-4,
- 4.97494994976747001425E-1,
- 4.70579119878881725854E0,
- 1.44989225341610930846E1,
- 1.79368678507819816313E1,
- 7.70838733755885391666E0,
-};
-static double Q[] = {
-/* 1.00000000000000000000E0, */
- 1.12873587189167450590E1,
- 4.52279145837532221105E1,
- 8.29875266912776603211E1,
- 7.11544750618563894466E1,
- 2.31251620126765340583E1,
-};
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0037777,0127270,0162547,0057274,
-0041001,0054665,0164317,0005341,
-0041451,0034104,0031640,0105773,
-0041677,0011276,0123617,0160135,
-0041701,0126603,0053215,0117250,
-0041420,0115777,0135206,0030232,
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041220,0144332,0045272,0174241,
-0041742,0164566,0035720,0130431,
-0042246,0126327,0166065,0116357,
-0042372,0033420,0157525,0124560,
-0042271,0167002,0066537,0172303,
-0041730,0164777,0113711,0044407,
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x1bb0,0x93c3,0xb4c2,0x3f1a,
-0x52f2,0x3f56,0xd6f5,0x3fdf,
-0x6911,0xed92,0xd2ba,0x4012,
-0xeb2e,0xc63e,0xff72,0x402c,
-0xc84d,0x924b,0xefd6,0x4031,
-0xdcf8,0x7d7e,0xd563,0x401e,
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xef8e,0xae97,0x9320,0x4026,
-0xc033,0x4e19,0x9d2c,0x4046,
-0xbdbd,0xa326,0xbf33,0x4054,
-0xae21,0xeb5e,0xc9e2,0x4051,
-0x25b2,0x9e1f,0x200a,0x4037,
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f1a,0xb4c2,0x93c3,0x1bb0,
-0x3fdf,0xd6f5,0x3f56,0x52f2,
-0x4012,0xd2ba,0xed92,0x6911,
-0x402c,0xff72,0xc63e,0xeb2e,
-0x4031,0xefd6,0x924b,0xc84d,
-0x401e,0xd563,0x7d7e,0xdcf8,
-};
-static unsigned short Q[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4026,0x9320,0xae97,0xef8e,
-0x4046,0x9d2c,0x4e19,0xc033,
-0x4054,0xbf33,0xa326,0xbdbd,
-0x4051,0xc9e2,0xeb5e,0xae21,
-0x4037,0x200a,0x9e1f,0x25b2,
-};
-#endif
-
-/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/(x+1)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-
-#ifdef UNK
-static double R[3] = {
--7.89580278884799154124E-1,
- 1.63866645699558079767E1,
--6.41409952958715622951E1,
-};
-static double S[3] = {
-/* 1.00000000000000000000E0,*/
--3.56722798256324312549E1,
- 3.12093766372244180303E2,
--7.69691943550460008604E2,
-};
-#endif
-#ifdef DEC
-static unsigned short R[12] = {
-0140112,0020756,0161540,0072035,
-0041203,0013743,0114023,0155527,
-0141600,0044060,0104421,0050400,
-};
-static unsigned short S[12] = {
-/*0040200,0000000,0000000,0000000,*/
-0141416,0130152,0017543,0064122,
-0042234,0006000,0104527,0020155,
-0142500,0066110,0146631,0174731,
-};
-#endif
-#ifdef IBMPC
-static unsigned short R[12] = {
-0x0e84,0xdc6c,0x443d,0xbfe9,
-0x7b6b,0x7302,0x62fc,0x4030,
-0x2a20,0x1122,0x0906,0xc050,
-};
-static unsigned short S[12] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x6d0a,0x43ec,0xd60d,0xc041,
-0xe40e,0x112a,0x8180,0x4073,
-0x3f3b,0x19b3,0x0d89,0xc088,
-};
-#endif
-#ifdef MIEEE
-static unsigned short R[12] = {
-0xbfe9,0x443d,0xdc6c,0x0e84,
-0x4030,0x62fc,0x7302,0x7b6b,
-0xc050,0x0906,0x1122,0x2a20,
-};
-static unsigned short S[12] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc041,0xd60d,0x43ec,0x6d0a,
-0x4073,0x8180,0x112a,0xe40e,
-0xc088,0x0d89,0x19b3,0x3f3b,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double frexp(), ldexp(), polevl(), p1evl();
-int isnan(), isfinite();
-#endif
-#define SQRTH 0.70710678118654752440
-extern double INFINITY, NAN;
-
-double log(x)
-double x;
-{
-int e;
-#ifdef DEC
-short *q;
-#endif
-double y, z;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITY )
- return(x);
-#endif
-/* Test for domain */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- {
- mtherr( fname, SING );
- return( -INFINITY );
- }
- else
- {
- mtherr( fname, DOMAIN );
- return( NAN );
- }
- }
-
-/* separate mantissa from exponent */
-
-#ifdef DEC
-q = (short *)&x;
-e = *q; /* short containing exponent */
-e = ((e >> 7) & 0377) - 0200; /* the exponent */
-*q &= 0177; /* strip exponent from x */
-*q |= 040000; /* x now between 0.5 and 1 */
-#endif
-
-/* Note, frexp is used so that denormal numbers
- * will be handled properly.
- */
-#ifdef IBMPC
-x = frexp( x, &e );
-/*
-q = (short *)&x;
-q += 3;
-e = *q;
-e = ((e >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x0f;
-*q |= 0x3fe0;
-*/
-#endif
-
-/* Equivalent C language standard library function: */
-#ifdef UNK
-x = frexp( x, &e );
-#endif
-
-#ifdef MIEEE
-x = frexp( x, &e );
-#endif
-
-
-
-/* logarithm using log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/x+1)
- */
-
-if( (e > 2) || (e < -2) )
-{
-if( x < SQRTH )
- { /* 2( 2x-1 )/( 2x+1 ) */
- e -= 1;
- z = x - 0.5;
- y = 0.5 * z + 0.5;
- }
-else
- { /* 2 (x-1)/(x+1) */
- z = x - 0.5;
- z -= 0.5;
- y = 0.5 * x + 0.5;
- }
-
-x = z / y;
-
-
-/* rational form */
-z = x*x;
-z = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
-y = e;
-z = z - y * 2.121944400546905827679e-4;
-z = z + x;
-z = z + e * 0.693359375;
-goto ldone;
-}
-
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0;
- }
-
-
-/* rational form */
-z = x*x;
-#if DEC
-y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) );
-#else
-y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
-#endif
-if( e )
- y = y - e * 2.121944400546905827679e-4;
-y = y - ldexp( z, -1 ); /* y - 0.5 * z */
-z = x + y;
-if( e )
- z = z + e * 0.693359375;
-
-ldone:
-
-return( z );
-}
+++ /dev/null
-/* log10.c
- *
- * Common logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, log10();
- *
- * y = log10( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns logarithm to the base 10 of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. The logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 1.5e-16 5.0e-17
- * IEEE 0, MAXNUM 30000 1.4e-16 4.8e-17
- * DEC 1, MAXNUM 50000 2.5e-17 6.0e-18
- *
- * In the tests over the interval [1, MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [0, MAXLOG].
- *
- * ERROR MESSAGES:
- *
- * log10 singularity: x = 0; returns -INFINITY
- * log10 domain: x < 0; returns NAN
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-static char fname[] = {"log10"};
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-#ifdef UNK
-static double P[] = {
- 4.58482948458143443514E-5,
- 4.98531067254050724270E-1,
- 6.56312093769992875930E0,
- 2.97877425097986925891E1,
- 6.06127134467767258030E1,
- 5.67349287391754285487E1,
- 1.98892446572874072159E1
-};
-static double Q[] = {
-/* 1.00000000000000000000E0, */
- 1.50314182634250003249E1,
- 8.27410449222435217021E1,
- 2.20664384982121929218E2,
- 3.07254189979530058263E2,
- 2.14955586696422947765E2,
- 5.96677339718622216300E1
-};
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0034500,0046473,0051374,0135174,
-0037777,0037566,0145712,0150321,
-0040722,0002426,0031543,0123107,
-0041356,0046513,0170752,0004346,
-0041562,0071553,0023536,0163343,
-0041542,0170221,0024316,0114216,
-0041237,0016454,0046611,0104602
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041160,0100260,0067736,0102424,
-0041645,0075552,0036563,0147072,
-0042134,0125025,0021132,0025320,
-0042231,0120211,0046030,0103271,
-0042126,0172241,0052151,0120426,
-0041556,0125702,0072116,0047103
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x974f,0x6a5f,0x09a7,0x3f08,
-0x5a1a,0xd979,0xe7ee,0x3fdf,
-0x74c9,0xc66c,0x40a2,0x401a,
-0x411d,0x7e3d,0xc9a9,0x403d,
-0xdcdc,0x64eb,0x4e6d,0x404e,
-0xd312,0x2519,0x5e12,0x404c,
-0x3130,0x89b1,0xe3a5,0x4033
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xd0a2,0x0dfb,0x1016,0x402e,
-0x79c7,0x47ae,0xaf6d,0x4054,
-0x455a,0xa44b,0x9542,0x406b,
-0x10d7,0x2983,0x3411,0x4073,
-0x3423,0x2a8d,0xde94,0x406a,
-0xc9c8,0x4e89,0xd578,0x404d
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f08,0x09a7,0x6a5f,0x974f,
-0x3fdf,0xe7ee,0xd979,0x5a1a,
-0x401a,0x40a2,0xc66c,0x74c9,
-0x403d,0xc9a9,0x7e3d,0x411d,
-0x404e,0x4e6d,0x64eb,0xdcdc,
-0x404c,0x5e12,0x2519,0xd312,
-0x4033,0xe3a5,0x89b1,0x3130
-};
-static unsigned short Q[] = {
-0x402e,0x1016,0x0dfb,0xd0a2,
-0x4054,0xaf6d,0x47ae,0x79c7,
-0x406b,0x9542,0xa44b,0x455a,
-0x4073,0x3411,0x2983,0x10d7,
-0x406a,0xde94,0x2a8d,0x3423,
-0x404d,0xd578,0x4e89,0xc9c8
-};
-#endif
-
-#define SQRTH 0.70710678118654752440
-#define L102A 3.0078125E-1
-#define L102B 2.48745663981195213739E-4
-#define L10EA 4.3359375E-1
-#define L10EB 7.00731903251827651129E-4
-
-#ifdef ANSIPROT
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double frexp(), ldexp(), polevl(), p1evl();
-int isnan(), isfinite();
-#endif
-extern double LOGE2, SQRT2, INFINITY, NAN;
-
-double log10(x)
-double x;
-{
-VOLATILE double z;
-double y;
-#ifdef DEC
-short *q;
-#endif
-int e;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITY )
- return(x);
-#endif
-/* Test for domain */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- {
- mtherr( fname, SING );
- return( -INFINITY );
- }
- else
- {
- mtherr( fname, DOMAIN );
- return( NAN );
- }
- }
-
-/* separate mantissa from exponent */
-
-#ifdef DEC
-q = (short *)&x;
-e = *q; /* short containing exponent */
-e = ((e >> 7) & 0377) - 0200; /* the exponent */
-*q &= 0177; /* strip exponent from x */
-*q |= 040000; /* x now between 0.5 and 1 */
-#endif
-
-#ifdef IBMPC
-x = frexp( x, &e );
-/*
-q = (short *)&x;
-q += 3;
-e = *q;
-e = ((e >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x0f;
-*q |= 0x3fe0;
-*/
-#endif
-
-/* Equivalent C language standard library function: */
-#ifdef UNK
-x = frexp( x, &e );
-#endif
-
-#ifdef MIEEE
-x = frexp( x, &e );
-#endif
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0;
- }
-
-
-/* rational form */
-z = x*x;
-y = x * ( z * polevl( x, P, 6 ) / p1evl( x, Q, 6 ) );
-y = y - ldexp( z, -1 ); /* y - 0.5 * x**2 */
-
-/* multiply log of fraction by log10(e)
- * and base 2 exponent by log10(2)
- */
-z = (x + y) * L10EB; /* accumulate terms in order of size */
-z += y * L10EA;
-z += x * L10EA;
-z += e * L102B;
-z += e * L102A;
-
-
-return( z );
-}
+++ /dev/null
-/* log2.c
- *
- * Base 2 logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, log2();
- *
- * y = log2( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 2 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the base e
- * logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 2.0e-16 5.5e-17
- * IEEE exp(+-700) 40000 1.3e-16 4.6e-17
- *
- * In the tests over the interval [exp(+-700)], the logarithms
- * of the random arguments were uniformly distributed.
- *
- * ERROR MESSAGES:
- *
- * log2 singularity: x = 0; returns -INFINITY
- * log2 domain: x < 0; returns NAN
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-static char fname[] = {"log2"};
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-#ifdef UNK
-static double P[] = {
- 1.01875663804580931796E-4,
- 4.97494994976747001425E-1,
- 4.70579119878881725854E0,
- 1.44989225341610930846E1,
- 1.79368678507819816313E1,
- 7.70838733755885391666E0,
-};
-static double Q[] = {
-/* 1.00000000000000000000E0, */
- 1.12873587189167450590E1,
- 4.52279145837532221105E1,
- 8.29875266912776603211E1,
- 7.11544750618563894466E1,
- 2.31251620126765340583E1,
-};
-#define LOG2EA 0.44269504088896340735992
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0037777,0127270,0162547,0057274,
-0041001,0054665,0164317,0005341,
-0041451,0034104,0031640,0105773,
-0041677,0011276,0123617,0160135,
-0041701,0126603,0053215,0117250,
-0041420,0115777,0135206,0030232,
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041220,0144332,0045272,0174241,
-0041742,0164566,0035720,0130431,
-0042246,0126327,0166065,0116357,
-0042372,0033420,0157525,0124560,
-0042271,0167002,0066537,0172303,
-0041730,0164777,0113711,0044407,
-};
-static unsigned short L[5] = {0037742,0124354,0122560,0057703};
-#define LOG2EA (*(double *)(&L[0]))
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x1bb0,0x93c3,0xb4c2,0x3f1a,
-0x52f2,0x3f56,0xd6f5,0x3fdf,
-0x6911,0xed92,0xd2ba,0x4012,
-0xeb2e,0xc63e,0xff72,0x402c,
-0xc84d,0x924b,0xefd6,0x4031,
-0xdcf8,0x7d7e,0xd563,0x401e,
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xef8e,0xae97,0x9320,0x4026,
-0xc033,0x4e19,0x9d2c,0x4046,
-0xbdbd,0xa326,0xbf33,0x4054,
-0xae21,0xeb5e,0xc9e2,0x4051,
-0x25b2,0x9e1f,0x200a,0x4037,
-};
-static unsigned short L[5] = {0x0bf8,0x94ae,0x551d,0x3fdc};
-#define LOG2EA (*(double *)(&L[0]))
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3f1a,0xb4c2,0x93c3,0x1bb0,
-0x3fdf,0xd6f5,0x3f56,0x52f2,
-0x4012,0xd2ba,0xed92,0x6911,
-0x402c,0xff72,0xc63e,0xeb2e,
-0x4031,0xefd6,0x924b,0xc84d,
-0x401e,0xd563,0x7d7e,0xdcf8,
-};
-static unsigned short Q[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4026,0x9320,0xae97,0xef8e,
-0x4046,0x9d2c,0x4e19,0xc033,
-0x4054,0xbf33,0xa326,0xbdbd,
-0x4051,0xc9e2,0xeb5e,0xae21,
-0x4037,0x200a,0x9e1f,0x25b2,
-};
-static unsigned short L[5] = {0x3fdc,0x551d,0x94ae,0x0bf8};
-#define LOG2EA (*(double *)(&L[0]))
-#endif
-
-/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/(x+1)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-
-#ifdef UNK
-static double R[3] = {
--7.89580278884799154124E-1,
- 1.63866645699558079767E1,
--6.41409952958715622951E1,
-};
-static double S[3] = {
-/* 1.00000000000000000000E0,*/
--3.56722798256324312549E1,
- 3.12093766372244180303E2,
--7.69691943550460008604E2,
-};
-/* log2(e) - 1 */
-#define LOG2EA 0.44269504088896340735992
-#endif
-#ifdef DEC
-static unsigned short R[12] = {
-0140112,0020756,0161540,0072035,
-0041203,0013743,0114023,0155527,
-0141600,0044060,0104421,0050400,
-};
-static unsigned short S[12] = {
-/*0040200,0000000,0000000,0000000,*/
-0141416,0130152,0017543,0064122,
-0042234,0006000,0104527,0020155,
-0142500,0066110,0146631,0174731,
-};
-/* log2(e) - 1 */
-#define LOG2EA 0.44269504088896340735992L
-#endif
-#ifdef IBMPC
-static unsigned short R[12] = {
-0x0e84,0xdc6c,0x443d,0xbfe9,
-0x7b6b,0x7302,0x62fc,0x4030,
-0x2a20,0x1122,0x0906,0xc050,
-};
-static unsigned short S[12] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x6d0a,0x43ec,0xd60d,0xc041,
-0xe40e,0x112a,0x8180,0x4073,
-0x3f3b,0x19b3,0x0d89,0xc088,
-};
-#endif
-#ifdef MIEEE
-static unsigned short R[12] = {
-0xbfe9,0x443d,0xdc6c,0x0e84,
-0x4030,0x62fc,0x7302,0x7b6b,
-0xc050,0x0906,0x1122,0x2a20,
-};
-static unsigned short S[12] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc041,0xd60d,0x43ec,0x6d0a,
-0x4073,0x8180,0x112a,0xe40e,
-0xc088,0x0d89,0x19b3,0x3f3b,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double frexp(), ldexp(), polevl(), p1evl();
-int isnan(), isfinite();
-#endif
-#define SQRTH 0.70710678118654752440
-extern double LOGE2, INFINITY, NAN;
-
-double log2(x)
-double x;
-{
-int e;
-double y;
-VOLATILE double z;
-#ifdef DEC
-short *q;
-#endif
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITY )
- return(x);
-#endif
-/* Test for domain */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- {
- mtherr( fname, SING );
- return( -INFINITY );
- }
- else
- {
- mtherr( fname, DOMAIN );
- return( NAN );
- }
- }
-
-/* separate mantissa from exponent */
-
-#ifdef DEC
-q = (short *)&x;
-e = *q; /* short containing exponent */
-e = ((e >> 7) & 0377) - 0200; /* the exponent */
-*q &= 0177; /* strip exponent from x */
-*q |= 040000; /* x now between 0.5 and 1 */
-#endif
-
-/* Note, frexp is used so that denormal numbers
- * will be handled properly.
- */
-#ifdef IBMPC
-x = frexp( x, &e );
-/*
-q = (short *)&x;
-q += 3;
-e = *q;
-e = ((e >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x0f;
-*q |= 0x3fe0;
-*/
-#endif
-
-/* Equivalent C language standard library function: */
-#ifdef UNK
-x = frexp( x, &e );
-#endif
-
-#ifdef MIEEE
-x = frexp( x, &e );
-#endif
-
-
-/* logarithm using log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/x+1)
- */
-
-if( (e > 2) || (e < -2) )
-{
-if( x < SQRTH )
- { /* 2( 2x-1 )/( 2x+1 ) */
- e -= 1;
- z = x - 0.5;
- y = 0.5 * z + 0.5;
- }
-else
- { /* 2 (x-1)/(x+1) */
- z = x - 0.5;
- z -= 0.5;
- y = 0.5 * x + 0.5;
- }
-
-x = z / y;
-z = x*x;
-y = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
-goto ldone;
-}
-
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0;
- }
-
-z = x*x;
-#if DEC
-y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) ) - ldexp( z, -1 );
-#else
-y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) ) - ldexp( z, -1 );
-#endif
-
-ldone:
-
-/* Multiply log of fraction by log2(e)
- * and base 2 exponent by 1
- *
- * ***CAUTION***
- *
- * This sequence of operations is critical and it may
- * be horribly defeated by some compiler optimizers.
- */
-z = y * LOG2EA;
-z += x * LOG2EA;
-z += y;
-z += x;
-z += e;
-return( z );
-}
+++ /dev/null
-/* lrand.c
- *
- * Pseudorandom number generator
- *
- *
- *
- * SYNOPSIS:
- *
- * long y, drand();
- *
- * drand( &y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Yields a long integer random number.
- *
- * The three-generator congruential algorithm by Brian
- * Wichmann and David Hill (BYTE magazine, March, 1987,
- * pp 127-8) is used. The period, given by them, is
- * 6953607871644.
- *
- *
- */
-\f
-
-
-#include <math.h>
-
-
-/* Three-generator random number algorithm
- * of Brian Wichmann and David Hill
- * BYTE magazine, March, 1987 pp 127-8
- *
- * The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
- */
-
-static int sx = 1;
-static int sy = 10000;
-static int sz = 3000;
-
-/* This function implements the three
- * congruential generators.
- */
-
-long lrand()
-{
-int r, s;
-unsigned long ans;
-
-/*
-if( arg )
- {
- sx = 1;
- sy = 10000;
- sz = 3000;
- }
-*/
-
-/* sx = sx * 171 mod 30269 */
-r = sx/177;
-s = sx - 177 * r;
-sx = 171 * s - 2 * r;
-if( sx < 0 )
- sx += 30269;
-
-
-/* sy = sy * 172 mod 30307 */
-r = sy/176;
-s = sy - 176 * r;
-sy = 172 * s - 35 * r;
-if( sy < 0 )
- sy += 30307;
-
-/* sz = 170 * sz mod 30323 */
-r = sz/178;
-s = sz - 178 * r;
-sz = 170 * s - 63 * r;
-if( sz < 0 )
- sz += 30323;
-
-ans = sx * sy * sz;
-return(ans);
-}
-
+++ /dev/null
-/* lsqrt.c
- *
- * Integer square root
- *
- *
- *
- * SYNOPSIS:
- *
- * long x, y;
- * long lsqrt();
- *
- * y = lsqrt( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns a long integer square root of the long integer
- * argument. The computation is by binary long division.
- *
- * The largest possible result is lsqrt(2,147,483,647)
- * = 46341.
- *
- * If x < 0, the square root of |x| is returned, and an
- * error message is printed.
- *
- *
- * ACCURACY:
- *
- * An extra, roundoff, bit is computed; hence the result
- * is the nearest integer to the actual square root.
- * NOTE: only DEC arithmetic is currently supported.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-long lsqrt(x)
-long x;
-{
-long num, sq;
-long temp;
-int i, j, k, n;
-
-if( x < 0 )
- {
- mtherr( "lsqrt", DOMAIN );
- x = -x;
- }
-
-num = 0;
-sq = 0;
-k = 24;
-n = 4;
-
-for( j=0; j<4; j++ )
- {
- num |= (x >> k) & 0xff; /* bring in next byte of arg */
- if( j == 3 ) /* do roundoff bit at end */
- n = 5;
- for( i=0; i<n; i++ )
- {
- num <<= 2; /* next 2 bits of arg */
- sq <<= 1; /* shift up answer */
- temp = (sq << 1) + 256; /* trial divisor */
- temp = num - temp;
- if( temp >= 0 )
- {
- num = temp; /* it went in */
- sq += 256; /* answer bit = 1 */
- }
- }
- k -= 8; /* shift count to get next byte of arg */
- }
-
-sq += 256; /* add roundoff bit */
-sq >>= 9; /* truncate */
-return( sq );
-}
+++ /dev/null
-/* ltstd.c */
-/* Function test routine.
- * Requires long double type check routine and double precision function
- * under test. Indicate function name and range in #define statements
- * below. Modifications for two argument functions and absolute
- * rather than relative accuracy report are indicated.
- */
-
-#include <stdio.h>
-/* int printf(), gets(), sscanf(); */
-
-#include <math.h>
-#ifdef ANSIPROT
-int drand ( void );
-int dprec ( void );
-int ldprec ( void );
-double exp ( double );
-double sqrt ( double );
-double fabs ( double );
-double floor ( double );
-long double sqrtl ( long double );
-long double fabsl ( long double );
-#else
-int drand();
-int dprec(), ldprec();
-double exp(), sqrt(), fabs(), floor();
-long double sqrtl(), fabsl();
-#endif
-
-#define RELERR 1
-#define ONEARG 0
-#define ONEINT 0
-#define TWOARG 0
-#define TWOINT 0
-#define THREEARG 1
-#define THREEINT 0
-#define FOURARG 0
-#define VECARG 0
-#define FOURANS 0
-#define TWOANS 0
-#define PROB 0
-#define EXPSCALE 0
-#define EXPSC2 0
-/* insert function to be tested here: */
-#define FUNC hyperg
-double FUNC();
-#define QFUNC hypergl
-long double QFUNC();
-/*extern int aiconf;*/
-
-extern double MAXLOG;
-extern double MINLOG;
-extern double MAXNUM;
-#define LTS 3.258096538
-/* insert low end and width of test interval */
-#define LOW 0.0
-#define WIDTH 30.0
-#define LOWA 0.0
-#define WIDTHA 30.0
-/* 1.073741824e9 */
-/* 2.147483648e9 */
-long double qone = 1.0L;
-static long double q1, q2, q3, qa, qb, qc, qz, qy1, qy2, qy3, qy4;
-static double y2, y3, y4, a, b, c, x, y, z, e;
-static long double qe, qmax, qrmsa, qave;
-volatile double v;
-static long double lp[3], lq[3];
-static double dp[3], dq[3];
-
-char strave[20];
-char strrms[20];
-char strmax[20];
-double underthresh = 2.22507385850720138309E-308; /* 2^-1022 */
-
-void main()
-{
-char s[80];
-int i, j, k;
-long m, n;
-
-merror = 0;
-ldprec(); /* set up coprocessor. */
-/*aiconf = -1;*/ /* configure Airy function */
-x = 1.0;
-z = x * x;
-qmax = 0.0L;
-sprintf(strmax, "%.4Le", qmax );
-qrmsa = 0.0L;
-qave = 0.0L;
-
-#if 1
-printf(" Start at random number #:" );
-gets( s );
-sscanf( s, "%ld", &n );
-printf("%ld\n", n );
-#else
-n = 0;
-#endif
-
-for( m=0; m<n; m++ )
- drand( &x );
-n = 0;
-m = 0;
-x = floor( x );
-
-loop:
-
-for( i=0; i<500; i++ )
-{
-n++;
-m++;
-
-#if ONEARG || TWOARG || THREEARG || FOURARG
-/*ldprec();*/ /* set up floating point coprocessor */
-/* make random number in desired range */
-drand( &x );
-x = WIDTH * ( x - 1.0 ) + LOW;
-#if EXPSCALE
-x = exp(x);
-drand( &a );
-a = 1.0e-13 * x * a;
-if( x > 0.0 )
- x -= a;
-else
- x += a;
-#endif
-#if ONEINT
-k = x;
-x = k;
-#endif
-v = x;
-q1 = v; /* double number to q type */
-#endif
-
-/* do again if second argument required */
-
-#if TWOARG || THREEARG || FOURARG
-drand( &a );
-a = WIDTHA * ( a - 1.0 ) + LOWA;
-/*a /= 50.0;*/
-#if EXPSC2
-a = exp(a);
-drand( &y2 );
-y2 = 1.0e-13 * y2 * a;
-if( a > 0.0 )
- a -= y2;
-else
- a += y2;
-#endif
-#if TWOINT || THREEINT
-k = a + 0.25;
-a = k;
-#endif
-v = a;
-qy4 = v;
-#endif
-
-#if THREEARG || FOURARG
-drand( &b );
-#if PROB
-/*
-b = b - 1.0;
-b = a * b;
-*/
-#if 1
-/* This makes b <= a, for bdtr. */
-b = (a - LOWA) * ( b - 1.0 ) + LOWA;
-if( b > 1.0 && a > 1.0 )
- b -= 1.0;
-else
- {
- a += 1.0;
- k = a;
- a = k;
- v = a;
- qy4 = v;
- }
-#else
-b = WIDTHA * ( b - 1.0 ) + LOWA;
-#endif
-
-/* Half-integer a and b */
-/*
-a = 0.5*floor(2.0*a+1.0);
-b = 0.5*floor(2.0*b+1.0);
-*/
-v = a;
-qy4 = v;
-/*x = (a / (a+b));*/
-
-#else
-b = WIDTHA * ( b - 1.0 ) + LOWA;
-#endif
-#if THREEINT
-j = b + 0.25;
-b = j;
-#endif
-v = b;
-qb = v;
-#endif
-
-#if FOURARG
-drand( &c );
-c = WIDTHA * ( c - 1.0 ) + LOWA;
-/* for hyp2f1 to ensure c-a-b > -1 */
-/*
-z = c-a-b;
-if( z < -1.0 )
- c -= 1.6 * z;
-*/
-v = c;
-qc = v;
-#endif
-
-#if VECARG
-for( j=0; j<3; j++)
- {
- drand( &x );
- x = WIDTH * ( x - 1.0 ) + LOW;
- v = x;
- dp[j] = v;
- q1 = v; /* double number to q type */
- lp[j] = q1;
- drand( &x );
- x = WIDTH * ( x - 1.0 ) + LOW;
- v = x;
- dq[j] = v;
- q1 = v; /* double number to q type */
- lq[j] = q1;
- }
-#endif /* VECARG */
-
-/*printf("%.16E %.16E\n", a, x);*/
-/* compute function under test */
-/* Set to double precision */
-/*dprec();*/
-#if ONEARG
-#if FOURANS
-/*FUNC( x, &z, &y2, &y3, &y4 );*/
-FUNC( x, &y4, &y2, &y3, &z );
-#else
-#if TWOANS
-FUNC( x, &z, &y2 );
-/*FUNC( x, &y2, &z );*/
-#else
-#if ONEINT
-z = FUNC( k );
-#else
-z = FUNC( x );
-#endif
-#endif
-#endif
-#endif
-
-#if TWOARG
-#if TWOINT
-z = FUNC( k, x );
-/*z = FUNC( x, k );*/
-/*z = FUNC( a, x );*/
-#else
-#if FOURANS
-FUNC( a, x, &z, &y2, &y3, &y4 );
-#else
-z = FUNC( a, x );
-#endif
-#endif
-#endif
-
-#if THREEARG
-#if THREEINT
-z = FUNC( j, k, x );
-#else
-z = FUNC( a, b, x );
-#endif
-#endif
-
-#if FOURARG
-z = FUNC( a, b, c, x );
-#endif
-
-#if VECARG
-z = FUNC( dp, dq );
-#endif
-
-q2 = z;
-/* handle detected overflow */
-if( (z == MAXNUM) || (z == -MAXNUM) )
- {
- printf("detected overflow ");
-#if FOURARG
- printf("%.4E %.4E %.4E %.4E %.4E %6ld \n",
- a, b, c, x, y, n);
-#else
- printf("%.16E %.4E %.4E %6ld \n", x, a, z, n);
-#endif
- e = 0.0;
- m -= 1;
- goto endlup;
- }
-/* Skip high precision if underflow. */
-if( merror == UNDERFLOW )
- goto underf;
-
-/* compute high precision function */
-/*ldprec();*/
-#if ONEARG
-#if FOURANS
-/*qy4 = QFUNC( q1, qz, qy2, qy3 );*/
-qz = QFUNC( q1, qy4, qy2, qy3 );
-#else
-#if TWOANS
-qy2 = QFUNC( q1, qz );
-/*qz = QFUNC( q1, qy2 );*/
-#else
-/* qy4 = 0.0L;*/
-/* qy4 = 1.0L;*/
-/*qz = QFUNC( qy4, q1 );*/
-/*qz = QFUNC( 1, q1 );*/
-qz = QFUNC( q1 ); /* normal */
-#endif
-#endif
-#endif
-
-#if TWOARG
-#if TWOINT
-qz = QFUNC( k, q1 );
-/*qz = QFUNC( q1, qy4 );*/
-/*qz = QFUNC( qy4, q1 );*/
-#else
-#if FOURANS
-qc = QFUNC( qy4, q1, qz, qy2, qy3 );
-#else
-/*qy4 = 0.0L;;*/
-/*qy4 = 1.0L );*/
-qz = QFUNC( qy4, q1 );
-#endif
-#endif
-#endif
-
-#if THREEARG
-#if THREEINT
-qz = QFUNC( j, k, q1 );
-#else
-qz = QFUNC( qy4, qb, q1 );
-#endif
-#endif
-
-#if FOURARG
-qz = QFUNC( qy4, qb, qc, q1 );
-#endif
-
-#if VECARG
-qz = QFUNC( lp, lq );
-#endif
-
-y = qz; /* correct answer, in double precision */
-
-/* get absolute error, in extended precision */
-qe = q2 - qz;
-e = qe; /* the error in double precision */
-
-/* handle function result equal to zero
- or underflowed. */
-if( qz == 0.0L || merror == UNDERFLOW || fabs(z) < underthresh )
- {
-underf:
- merror = 0;
-/* Don't bother to print anything. */
-#if 0
- printf("ans 0 ");
-#if ONEARG
- printf("%.8E %.8E %.4E %6ld \n", x, y, e, n);
-#endif
-
-#if TWOARG
-#if TWOINT
- printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, e, n);
-#else
- printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, e, n);
-#endif
-#endif
-
-#if THREEARG
- printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, e, n);
-#endif
-
-#if FOURARG
- printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
- a, b, c, x, y, e, n);
-#endif
-#endif /* 0 */
- qe = 0.0L;
- e = 0.0;
- m -= 1;
- goto endlup;
- }
-
-else
-
-/* relative error */
-
-/* comment out the following two lines if absolute accuracy report */
-
-#if RELERR
- qe = qe / qz;
-#else
- {
- q2 = qz;
- q2 = fabsl(q2);
- if( q2 > 1.0L )
- qe = qe / qz;
- }
-#endif
-
-qave = qave + qe;
-/* absolute value of error */
-qe = fabs(qe);
-
-/* peak detect the error */
-if( qe > qmax )
- {
- qmax = qe;
- sprintf(strmax, "%.4Le", qmax );
-#if ONEARG
- printf("%.8E %.8E %s %6ld \n", x, y, strmax, n);
-#endif
-#if TWOARG
-#if TWOINT
- printf("%d %.8E %.8E %s %6ld \n", k, x, y, strmax, n);
-#else
- printf("%.6E %.6E %.6E %s %6ld \n", a, x, y, strmax, n);
-#endif
-#endif
-#if THREEARG
- printf("%.6E %.6E %.6E %.6E %s %6ld \n", a, b, x, y, strmax, n);
-#endif
-#if FOURARG
- printf("%.4E %.4E %.4E %.4E %.4E %s %6ld \n",
- a, b, c, x, y, strmax, n);
-#endif
-#if VECARG
- printf("%.8E %s %6ld \n", y, strmax, n);
-#endif
- }
-
-/* accumulate rms error */
-/* rmsa += e * e; accumulate the square of the error */
-q2 = qe * qe;
-qrmsa = qrmsa + q2;
-endlup: ;
-/*ldprec();*/
-}
-
-/* report every 500 trials */
-/* rms = sqrt( rmsa/m ); */
-q1 = m;
-q2 = qrmsa / q1;
-q2 = sqrtl(q2);
-sprintf(strrms, "%.4Le", q2 );
-
-q2 = qave / q1;
-sprintf(strave, "%.4Le", q2 );
-/*
-printf("%6ld max = %s rms = %s ave = %s \n", m, strmax, strrms, strave );
-*/
-printf("%6ld max = %s rms = %s ave = %s \r", m, strmax, strrms, strave );
-fflush(stdout);
-goto loop;
-}
+++ /dev/null
-/* minv.c
- *
- * Matrix inversion
- *
- *
- *
- * SYNOPSIS:
- *
- * int n, errcod;
- * double A[n*n], X[n*n];
- * double B[n];
- * int IPS[n];
- * int minv();
- *
- * errcod = minv( A, X, n, B, IPS );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the inverse of the n by n matrix A. The result goes
- * to X. B and IPS are scratch pad arrays of length n.
- * The contents of matrix A are destroyed.
- *
- * The routine returns nonzero on error; error messages are printed
- * by subroutine simq().
- *
- */
-\f
-minv( A, X, n, B, IPS )
-double A[], X[];
-int n;
-double B[];
-int IPS[];
-{
-double *pX;
-int i, j, k;
-
-for( i=1; i<n; i++ )
- B[i] = 0.0;
-B[0] = 1.0;
-/* Reduce the matrix and solve for first right hand side vector */
-pX = X;
-k = simq( A, B, pX, n, 1, IPS );
-if( k )
- return(-1);
-/* Solve for the remaining right hand side vectors */
-for( i=1; i<n; i++ )
- {
- B[i-1] = 0.0;
- B[i] = 1.0;
- pX += n;
- k = simq( A, B, pX, n, -1, IPS );
- if( k )
- return(-1);
- }
-/* Transpose the array of solution vectors */
-mtransp( n, X, X );
-return(0);
-}
-
+++ /dev/null
-/* Program to test range reduction of trigonometry functions
- *
- * -- Steve Moshier
- */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double floor ( double );
-extern double ldexp ( double, int );
-extern double sin ( double );
-#else
-double floor(), ldexp(), sin();
-#endif
-
-#define TPI 6.283185307179586476925
-
-main()
-{
-char s[40];
-double a, n, t, x, y, z;
-int lflg;
-
-x = TPI/4.0;
-t = 1.0;
-
-loop:
-
-t = 2.0 * t;
-
-/* Stop testing at a point beyond which the integer part of
- * x/2pi cannot be represented exactly by a double precision number.
- * The library trigonometry functions will probably give up long before
- * this point is reached.
- */
-if( t > 1.0e16 )
- exit(0);
-
-/* Adjust the following to choose a nontrivial x
- * where test function(x) has a slope of about 1 or more.
- */
-x = TPI * t + 0.5;
-
-z = x;
-lflg = 0;
-
-inlup:
-
-/* floor() returns the largest integer less than its argument.
- * If you do not have this, or AINT(), then you may convert x/TPI
- * to a long integer and then back to double; but in that case
- * x will be limited to the largest value that will fit into a
- * long integer.
- */
-n = floor( z/TPI );
-
-/* Carefully subtract 2 pi n from x.
- * This is done by subtracting n * 2**k in such a way that there
- * is no arithmetic cancellation error at any step. The k are the
- * bits in the number 2 pi.
- *
- * If you do not have ldexp(), then you may multiply or
- * divide n by an appropriate power of 2 after each step.
- * For example:
- * a = z - 4*n;
- * a -= 2*n;
- * n /= 4;
- * a -= n; n/4
- * n /= 8;
- * a -= n; n/32
- * etc.
- * This will only work if division by a power of 2 is exact.
- */
-
-a = z - ldexp(n, 2); /* 4n */
-a -= ldexp( n, 1); /* 2n */
-a -= ldexp( n, -2 ); /* n/4 */
-a -= ldexp( n, -5 ); /* n/32 */
-a -= ldexp( n, -9 ); /* n/512 */
-a += ldexp( n, -15 ); /* add n/32768 */
-a -= ldexp( n, -17 ); /* n/131072 */
-a -= ldexp( n, -18 );
-a -= ldexp( n, -20 );
-a -= ldexp( n, -22 );
-a -= ldexp( n, -24 );
-a -= ldexp( n, -28 );
-a -= ldexp( n, -32 );
-a -= ldexp( n, -37 );
-a -= ldexp( n, -39 );
-a -= ldexp( n, -40 );
-a -= ldexp( n, -42 );
-a -= ldexp( n, -46 );
-a -= ldexp( n, -47 );
-
-/* Subtract what is left of 2 pi n after all the above reductions.
- */
-a -= 2.44929359829470635445e-16 * n;
-
-/* If the test is extended too far, it is possible
- * to have chosen the wrong value of n. The following
- * will fix that, but at some reduction in accuracy.
- */
-if( (a > TPI) || (a < -1e-11) )
- {
- z = a;
- lflg += 1;
- printf( "Warning! Reduction failed on first try.\n" );
- goto inlup;
- }
-if( a < 0.0 )
- {
- printf( "Warning! Reduced value < 0\n" );
- a += TPI;
- }
-
-/* Compute the test function at x and at a = x mod 2 pi.
- */
-y = sin(x);
-z = sin(a);
-printf( "sin(%.15e) error = %.3e\n", x, y-z );
-goto loop;
-}
-
+++ /dev/null
-
-/* monot.c
- Floating point function test vectors.
-
- Arguments and function values are synthesized for NPTS points in
- the vicinity of each given tabulated test point. The points are
- chosen to be near and on either side of the likely function algorithm
- domain boundaries. Since the function programs change their methods
- at these points, major coding errors or monotonicity failures might be
- detected.
-
- August, 1998
- S. L. Moshier */
-
-
-#include <stdio.h>
-
-/* Avoid including math.h. */
-double frexp (double, int *);
-double ldexp (double, int);
-
-/* Number of test points to generate on each side of tabulated point. */
-#define NPTS 100
-
-/* Functions of one variable. */
-double exp (double);
-double log (double);
-double sin (double);
-double cos (double);
-double tan (double);
-double atan (double);
-double asin (double);
-double acos (double);
-double sinh (double);
-double cosh (double);
-double tanh (double);
-double asinh (double);
-double acosh (double);
-double atanh (double);
-double gamma (double);
-double fabs (double);
-double floor (double);
-
-struct oneargument
- {
- char *name; /* Name of the function. */
- double (*func) (double);
- double arg1; /* Function argument, assumed exact. */
- double answer1; /* Exact, close to function value. */
- double answer2; /* answer1 + answer2 has extended precision. */
- double derivative; /* dy/dx evaluated at x = arg1. */
- int thresh; /* Error report threshold. 2 = 1 ULP approx. */
- };
-
-/* Add this to error threshold test[i].thresh. */
-#define OKERROR 0
-
-/* Unit of relative error in test[i].thresh. */
-static double MACHEP = 1.1102230246251565404e-16;
-/* extern double MACHEP; */
-
-
-struct oneargument test1[] =
-{
- {"exp", exp, 1.0, 2.7182769775390625,
- 4.85091998273536028747e-6, 2.71828182845904523536, 2},
- {"exp", exp, -1.0, 3.678741455078125e-1,
- 5.29566362982159552377e-6, 3.678794411714423215955e-1, 2},
- {"exp", exp, 0.5, 1.648712158203125,
- 9.1124970031468486507878e-6, 1.64872127070012814684865, 2},
- {"exp", exp, -0.5, 6.065216064453125e-1,
- 9.0532673209236037995e-6, 6.0653065971263342360e-1, 2},
- {"exp", exp, 2.0, 7.3890533447265625,
- 2.75420408772723042746e-6, 7.38905609893065022723, 2},
- {"exp", exp, -2.0, 1.353302001953125e-1,
- 5.08304130019189399949e-6, 1.3533528323661269189e-1, 2},
- {"log", log, 1.41421356237309492343, 3.465728759765625e-1,
- 7.1430341006605745676897e-7, 7.0710678118654758708668e-1, 2},
- {"log", log, 7.07106781186547461715e-1, -3.46588134765625e-1,
- 1.45444856522566402246e-5, 1.41421356237309517417, 2},
- {"sin", sin, 7.85398163397448278999e-1, 7.0709228515625e-1,
- 1.4496030297502751942956e-5, 7.071067811865475460497e-1, 2},
- {"sin", sin, -7.85398163397448501044e-1, -7.071075439453125e-1,
- 7.62758764840238811175e-7, 7.07106781186547389040e-1, 2},
- {"sin", sin, 1.570796326794896558, 9.999847412109375e-1,
- 1.52587890625e-5, 6.12323399573676588613e-17, 2},
- {"sin", sin, -1.57079632679489678004, -1.0,
- 1.29302922820150306903e-32, -1.60812264967663649223e-16, 2},
- {"sin", sin, 4.712388980384689674, -1.0,
- 1.68722975549458979398e-32, -1.83697019872102976584e-16, 2},
- {"sin", sin, -4.71238898038468989604, 9.999847412109375e-1,
- 1.52587890625e-5, 3.83475850529283315008e-17, 2},
- {"cos", cos, 3.92699081698724139500E-1, 9.23873901367187500000E-1,
- 5.63114409926198633370E-6, -3.82683432365089757586E-1, 2},
- {"cos", cos, 7.85398163397448278999E-1, 7.07092285156250000000E-1,
- 1.44960302975460497458E-5, -7.07106781186547502752E-1, 2},
- {"cos", cos, 1.17809724509617241850E0, 3.82675170898437500000E-1,
- 8.26146665231415693919E-6, -9.23879532511286738554E-1, 2},
- {"cos", cos, 1.96349540849362069750E0, -3.82690429687500000000E-1,
- 6.99732241029898567203E-6, -9.23879532511286785419E-1, 2},
- {"cos", cos, 2.35619449019234483700E0, -7.07107543945312500000E-1,
- 7.62758765040545859856E-7, -7.07106781186547589348E-1, 2},
- {"cos", cos, 2.74889357189106897650E0, -9.23889160156250000000E-1,
- 9.62764496328487887036E-6, -3.82683432365089870728E-1, 2},
- {"cos", cos, 3.14159265358979311600E0, -1.00000000000000000000E0,
- 7.49879891330928797323E-33, -1.22464679914735317723E-16, 2},
- {"tan", tan, 7.85398163397448278999E-1, 9.999847412109375e-1,
- 1.52587890624387676600E-5, 1.99999999999999987754E0, 2},
- {"tan", tan, 1.17809724509617241850E0, 2.41419982910156250000E0,
- 1.37332715322352112604E-5, 6.82842712474618858345E0, 2},
- {"tan", tan, 1.96349540849362069750E0, -2.41421508789062500000E0,
- 1.52551752942854759743E-6, 6.82842712474619262118E0, 2},
- {"tan", tan, 2.35619449019234483700E0, -1.00001525878906250000E0,
- 1.52587890623163029801E-5, 2.00000000000000036739E0, 2},
- {"tan", tan, 2.74889357189106897650E0, -4.14215087890625000000E-1,
- 1.52551752982565655126E-6, 1.17157287525381000640E0, 2},
- {"atan", atan, 4.14213562373094923430E-1, 3.92684936523437500000E-1,
- 1.41451752865477964149E-5, 8.53553390593273837869E-1, 2},
- {"atan", atan, 1.0, 7.85385131835937500000E-1,
- 1.30315615108096156608E-5, 0.5, 2},
- {"atan", atan, 2.41421356237309492343E0, 1.17808532714843750000E0,
- 1.19179477349460632350E-5, 1.46446609406726250782E-1, 2},
- {"atan", atan, -2.41421356237309514547E0, -1.17810058593750000000E0,
- 3.34084132752141908545E-6, 1.46446609406726227789E-1, 2},
- {"atan", atan, -1.0, -7.85400390625000000000E-1,
- 2.22722755169038433915E-6, 0.5, 2},
- {"atan", atan, -4.14213562373095145475E-1, -3.92700195312500000000E-1,
- 1.11361377576267665972E-6, 8.53553390593273703853E-1, 2},
- {"asin", asin, 3.82683432365089615246E-1, 3.92684936523437500000E-1,
- 1.41451752864854321970E-5, 1.08239220029239389286E0, 2},
- {"asin", asin, 0.5, 5.23590087890625000000E-1,
- 8.68770767387307710723E-6, 1.15470053837925152902E0, 2},
- {"asin", asin, 7.07106781186547461715E-1, 7.85385131835937500000E-1,
- 1.30315615107209645016E-5, 1.41421356237309492343E0, 2},
- {"asin", asin, 9.23879532511286738483E-1, 1.17808532714843750000E0,
- 1.19179477349183147612E-5, 2.61312592975275276483E0, 2},
- {"asin", asin, -0.5, -5.23605346679687500000E-1,
- 6.57108138862692289277E-6, 1.15470053837925152902E0, 2},
- {"acos", acos, 1.95090322016128192573E-1, 1.37443542480468750000E0,
- 1.13611408471185777914E-5, -1.01959115820831832232E0, 2},
- {"acos", acos, 3.82683432365089615246E-1, 1.17808532714843750000E0,
- 1.19179477351337991247E-5, -1.08239220029239389286E0, 2},
- {"acos", acos, 0.5, 1.04719543457031250000E0,
- 2.11662628524615421446E-6, -1.15470053837925152902E0, 2},
- {"acos", acos, 7.07106781186547461715E-1, 7.85385131835937500000E-1,
- 1.30315615108982668201E-5, -1.41421356237309492343E0, 2},
- {"acos", acos, 9.23879532511286738483E-1, 3.92684936523437500000E-1,
- 1.41451752867009165605E-5, -2.61312592975275276483E0, 2},
- {"acos", acos, 9.80785280403230430579E-1, 1.96334838867187500000E-1,
- 1.47019821746724723933E-5, -5.12583089548300990774E0, 2},
- {"acos", acos, -0.5, 2.09439086914062500000E0,
- 4.23325257049230842892E-6, -1.15470053837925152902E0, 2},
- {"sinh", sinh, 1.0, 1.17518615722656250000E0,
- 1.50364172389568823819E-5, 1.54308063481524377848E0, 2},
- {"sinh", sinh, 7.09089565712818057364E2, 4.49423283712885057274E307,
- 4.25947714184369757620E208, 4.49423283712885057274E307, 2},
- {"sinh", sinh, 2.22044604925031308085E-16, 0.00000000000000000000E0,
- 2.22044604925031308085E-16, 1.00000000000000000000E0, 2},
- {"cosh", cosh, 7.09089565712818057364E2, 4.49423283712885057274E307,
- 4.25947714184369757620E208, 4.49423283712885057274E307, 2},
- {"cosh", cosh, 1.0, 1.54307556152343750000E0,
- 5.07329180627847790562E-6, 1.17520119364380145688E0, 2},
- {"cosh", cosh, 0.5, 1.12762451171875000000E0,
- 1.45348763078522622516E-6, 5.21095305493747361622E-1, 2},
- {"tanh", tanh, 0.5, 4.62112426757812500000E-1,
- 4.73050219725850231848E-6, 7.86447732965927410150E-1, 2},
- {"tanh", tanh, 5.49306144334054780032E-1, 4.99984741210937500000E-1,
- 1.52587890624507506378E-5, 7.50000000000000049249E-1, 2},
- {"tanh", tanh, 0.625, 5.54595947265625000000E-1,
- 3.77508375729399903910E-6, 6.92419147969988069631E-1, 2},
- {"asinh", asinh, 0.5, 4.81201171875000000000E-1,
- 1.06531846034474977589E-5, 8.94427190999915878564E-1, 2},
- {"asinh", asinh, 1.0, 8.81362915039062500000E-1,
- 1.06719804805252326093E-5, 7.07106781186547524401E-1, 2},
- {"asinh", asinh, 2.0, 1.44363403320312500000E0,
- 1.44197568534249327674E-6, 4.47213595499957939282E-1, 2},
- {"acosh", acosh, 2.0, 1.31695556640625000000E0,
- 2.33051856670862504635E-6, 5.77350269189625764509E-1, 2},
- {"acosh", acosh, 1.5, 9.62417602539062500000E-1,
- 6.04758014439499551783E-6, 8.94427190999915878564E-1, 2},
- {"acosh", acosh, 1.03125, 2.49343872070312500000E-1,
- 9.62177257298785143908E-6, 3.96911150685467059809E0, 2},
- {"atanh", atanh, 0.5, 5.49301147460937500000E-1,
- 4.99687311734569762262E-6, 1.33333333333333333333E0, 2},
-#if 0
- {"gamma", gamma, 1.0, 1.0,
- 0.0, -5.772156649015328606e-1, 2},
- {"gamma", gamma, 2.0, 1.0,
- 0.0, 4.2278433509846713939e-1, 2},
- {"gamma", gamma, 3.0, 2.0,
- 0.0, 1.845568670196934279, 2},
- {"gamma", gamma, 4.0, 6.0,
- 0.0, 7.536706010590802836, 2},
-#endif
- {"null", NULL, 0.0, 0.0, 0.0, 2},
-};
-
-/* These take care of extra-precise floating point register problems. */
-volatile double volat1;
-volatile double volat2;
-
-
-/* Return the next nearest floating point value to X
- in the direction of UPDOWN (+1 or -1).
- (Fails if X is denormalized.) */
-
-double
-nextval (x, updown)
- double x;
- int updown;
-{
- double m;
- int i;
-
- volat1 = x;
- m = 0.25 * MACHEP * volat1 * updown;
- volat2 = volat1 + m;
- if (volat2 != volat1)
- printf ("successor failed\n");
-
- for (i = 2; i < 10; i++)
- {
- volat2 = volat1 + i * m;
- if (volat1 != volat2)
- return volat2;
- }
-
- printf ("nextval failed\n");
- return volat1;
-}
-
-
-
-
-int
-main ()
-{
- double (*fun1) (double);
- int i, j, errs, tests;
- double x, x0, y, dy, err;
-
- /* Set math coprocessor to double precision. */
- /* dprec (); */
- errs = 0;
- tests = 0;
- i = 0;
-
- for (;;)
- {
- fun1 = test1[i].func;
- if (fun1 == NULL)
- break;
- volat1 = test1[i].arg1;
- x0 = volat1;
- x = volat1;
- for (j = 0; j <= NPTS; j++)
- {
- volat1 = x - x0;
- dy = volat1 * test1[i].derivative;
- dy = test1[i].answer2 + dy;
- volat1 = test1[i].answer1 + dy;
- volat2 = (*(fun1)) (x);
- if (volat2 != volat1)
- {
- /* Report difference between program result
- and extended precision function value. */
- err = volat2 - test1[i].answer1;
- err = err - dy;
- err = err / volat1;
- if (fabs (err) > ((OKERROR + test1[i].thresh) * MACHEP))
- {
- printf ("%d %s(%.16e) = %.16e, rel err = %.3e\n",
- j, test1[i].name, x, volat2, err);
- errs += 1;
- }
- }
- x = nextval (x, 1);
- tests += 1;
- }
-
- x = x0;
- x = nextval (x, -1);
- for (j = 1; j < NPTS; j++)
- {
- volat1 = x - x0;
- dy = volat1 * test1[i].derivative;
- dy = test1[i].answer2 + dy;
- volat1 = test1[i].answer1 + dy;
- volat2 = (*(fun1)) (x);
- if (volat2 != volat1)
- {
- err = volat2 - test1[i].answer1;
- err = err - dy;
- err = err / volat1;
- if (fabs (err) > ((OKERROR + test1[i].thresh) * MACHEP))
- {
- printf ("%d %s(%.16e) = %.16e, rel err = %.3e\n",
- j, test1[i].name, x, volat2, err);
- errs += 1;
- }
- }
- x = nextval (x, -1);
- tests += 1;
- }
- i += 1;
- }
- printf ("%d errors in %d tests\n", errs, tests);
-}
+++ /dev/null
-/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * int mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file math.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * math.h
- *
- */
-\f
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <stdio.h>
-#include <math.h>
-
-int merror = 0;
-
-/* Notice: the order of appearance of the following
- * messages is bound to the error codes defined
- * in math.h.
- */
-static char *ermsg[7] = {
-"unknown", /* error code 0 */
-"domain", /* error code 1 */
-"singularity", /* et seq. */
-"overflow",
-"underflow",
-"total loss of precision",
-"partial loss of precision"
-};
-
-
-int mtherr( name, code )
-char *name;
-int code;
-{
-
-/* Display string passed by calling program,
- * which is supposed to be the name of the
- * function in which the error occurred:
- */
-printf( "\n%s ", name );
-
-/* Set global error message word */
-merror = code;
-
-/* Display error message defined
- * by the code argument.
- */
-if( (code <= 0) || (code >= 7) )
- code = 0;
-printf( "%s error\n", ermsg[code] );
-
-/* Return to calling
- * program
- */
-return( 0 );
-}
+++ /dev/null
-/* mtransp.c
- *
- * Matrix transpose
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * double A[n*n], T[n*n];
- *
- * mtransp( n, A, T );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * T[r][c] = A[c][r]
- *
- *
- * Transposes the n by n square matrix A and puts the result in T.
- * The output, T, may occupy the same storage as A.
- *
- *
- *
- */
-\f
-
-mtransp( n, A, T )
-int n;
-double *A, *T;
-{
-int i, j, np1;
-double *pAc, *pAr, *pTc, *pTr, *pA0, *pT0;
-double x, y;
-
-np1 = n+1;
-pA0 = A;
-pT0 = T;
-for( i=0; i<n-1; i++ ) /* row index */
- {
- pAc = pA0; /* next diagonal element of input */
- pAr = pAc + n; /* next row down underneath the diagonal element */
- pTc = pT0; /* next diagonal element of the output */
- pTr = pTc + n; /* next row underneath */
- *pTc++ = *pAc++; /* copy the diagonal element */
- for( j=i+1; j<n; j++ ) /* column index */
- {
- x = *pAr;
- *pTr = *pAc++;
- *pTc++ = x;
- pAr += n;
- pTr += n;
- }
- pA0 += np1; /* &A[n*i+i] for next i */
- pT0 += np1; /* &T[n*i+i] for next i */
- }
-*pT0 = *pA0; /* copy the diagonal element */
-}
-
+++ /dev/null
-/* mtst.c
- Consistency tests for math functions.
- To get strict rounding rules on a 386 or 68000 computer,
- define SETPREC to 1.
-
- With NTRIALS=10000, the following are typical results for
- IEEE double precision arithmetic.
-
-Consistency test of math functions.
-Max and rms relative errors for 10000 random arguments.
-x = cbrt( cube(x) ): max = 0.00E+00 rms = 0.00E+00
-x = atan( tan(x) ): max = 2.21E-16 rms = 3.27E-17
-x = sin( asin(x) ): max = 2.13E-16 rms = 2.95E-17
-x = sqrt( square(x) ): max = 0.00E+00 rms = 0.00E+00
-x = log( exp(x) ): max = 1.11E-16 A rms = 4.35E-18 A
-x = tanh( atanh(x) ): max = 2.22E-16 rms = 2.43E-17
-x = asinh( sinh(x) ): max = 2.05E-16 rms = 3.49E-18
-x = acosh( cosh(x) ): max = 1.43E-15 A rms = 1.54E-17 A
-x = log10( exp10(x) ): max = 5.55E-17 A rms = 1.27E-18 A
-x = pow( pow(x,a),1/a ): max = 7.60E-14 rms = 1.05E-15
-x = cos( acos(x) ): max = 2.22E-16 A rms = 6.90E-17 A
-*/
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
-*/
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <math.h>
-
-#ifndef NTRIALS
-#define NTRIALS 10000
-#endif
-
-#define SETPREC 1
-#define STRTST 0
-
-#define WTRIALS (NTRIALS/5)
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double sqrt ( double );
-extern double cbrt ( double );
-extern double exp ( double );
-extern double log ( double );
-extern double exp10 ( double );
-extern double log10 ( double );
-extern double tan ( double );
-extern double atan ( double );
-extern double sin ( double );
-extern double asin ( double );
-extern double cos ( double );
-extern double acos ( double );
-extern double pow ( double, double );
-extern double tanh ( double );
-extern double atanh ( double );
-extern double sinh ( double );
-extern double asinh ( double x );
-extern double cosh ( double );
-extern double acosh ( double );
-extern double gamma ( double );
-extern double lgam ( double );
-#else
-double fabs(), sqrt(), cbrt(), exp(), log();
-double exp10(), log10(), tan(), atan();
-double sin(), asin(), cos(), acos(), pow();
-double tanh(), atanh(), sinh(), asinh(), cosh(), acosh();
-double gamma(), lgam();
-#endif
-
-/* C9X spells lgam lgamma. */
-#define GLIBC2 0
-#if GLIBC2
-double lgamma (double);
-#endif
-
-#if SETPREC
-int dprec();
-#endif
-
-int drand();
-/* void exit(); */
-/* int printf(); */
-
-
-/* Provide inverses for square root and cube root: */
-double square(x)
-double x;
-{
-return( x * x );
-}
-
-double cube(x)
-double x;
-{
-return( x * x * x );
-}
-
-/* lookup table for each function */
-struct fundef
- {
- char *nam1; /* the function */
- double (*name )();
- char *nam2; /* its inverse */
- double (*inv )();
- int nargs; /* number of function arguments */
- int tstyp; /* type code of the function */
- long ctrl; /* relative error flag */
- double arg1w; /* width of domain for 1st arg */
- double arg1l; /* lower bound domain 1st arg */
- long arg1f; /* flags, e.g. integer arg */
- double arg2w; /* same info for args 2, 3, 4 */
- double arg2l;
- long arg2f;
-/*
- double arg3w;
- double arg3l;
- long arg3f;
- double arg4w;
- double arg4l;
- long arg4f;
-*/
- };
-
-
-/* fundef.ctrl bits: */
-#define RELERR 1
-
-/* fundef.tstyp test types: */
-#define POWER 1
-#define ELLIP 2
-#define GAMMA 3
-#define WRONK1 4
-#define WRONK2 5
-#define WRONK3 6
-
-/* fundef.argNf argument flag bits: */
-#define INT 2
-#define EXPSCAL 4
-
-extern double MINLOG;
-extern double MAXLOG;
-extern double PI;
-extern double PIO2;
-/*
-define MINLOG -170.0
-define MAXLOG +170.0
-define PI 3.14159265358979323846
-define PIO2 1.570796326794896619
-*/
-
-#define NTESTS 12
-struct fundef defs[NTESTS] = {
-{" cube", cube, " cbrt", cbrt, 1, 0, 1, 2002.0, -1001.0, 0,
-0.0, 0.0, 0},
-{" tan", tan, " atan", atan, 1, 0, 1, 0.0, 0.0, 0,
-0.0, 0.0, 0},
-{" asin", asin, " sin", sin, 1, 0, 1, 2.0, -1.0, 0,
-0.0, 0.0, 0},
-{"square", square, " sqrt", sqrt, 1, 0, 1, 170.0, -85.0, EXPSCAL,
-0.0, 0.0, 0},
-{" exp", exp, " log", log, 1, 0, 0, 340.0, -170.0, 0,
-0.0, 0.0, 0},
-{" atanh", atanh, " tanh", tanh, 1, 0, 1, 2.0, -1.0, 0,
-0.0, 0.0, 0},
-{" sinh", sinh, " asinh", asinh, 1, 0, 1, 340.0, 0.0, 0,
-0.0, 0.0, 0},
-{" cosh", cosh, " acosh", acosh, 1, 0, 0, 340.0, 0.0, 0,
-0.0, 0.0, 0},
-{" exp10", exp10, " log10", log10, 1, 0, 0, 340.0, -170.0, 0,
-0.0, 0.0, 0},
-{"pow", pow, "pow", pow, 2, POWER, 1, 21.0, 0.0, 0,
-42.0, -21.0, 0},
-{" acos", acos, " cos", cos, 1, 0, 0, 2.0, -1.0, 0,
-0.0, 0.0, 0},
-#if GLIBC2
-{ "gamma", gamma, "lgamma", lgamma, 1, GAMMA, 0, 34.0, 0.0, 0,
-0.0, 0.0, 0},
-#else
-{ "gamma", gamma, "lgam", lgam, 1, GAMMA, 0, 34.0, 0.0, 0,
-0.0, 0.0, 0},
-#endif
-};
-
-static char *headrs[] = {
-"x = %s( %s(x) ): ",
-"x = %s( %s(x,a),1/a ): ", /* power */
-"Legendre %s, %s: ", /* ellip */
-"%s(x) = log(%s(x)): ", /* gamma */
-"Wronksian of %s, %s: ",
-"Wronksian of %s, %s: ",
-"Wronksian of %s, %s: "
-};
-
-static double yy1 = 0.0;
-static double y2 = 0.0;
-static double y3 = 0.0;
-static double y4 = 0.0;
-static double a = 0.0;
-static double x = 0.0;
-static double y = 0.0;
-static double z = 0.0;
-static double e = 0.0;
-static double max = 0.0;
-static double rmsa = 0.0;
-static double rms = 0.0;
-static double ave = 0.0;
-
-
-int main()
-{
-double (*fun )();
-double (*ifun )();
-struct fundef *d;
-int i, k, itst;
-int m, ntr;
-
-#if SETPREC
-dprec(); /* set coprocessor precision */
-#endif
-ntr = NTRIALS;
-printf( "Consistency test of math functions.\n" );
-printf( "Max and rms relative errors for %d random arguments.\n",
- ntr );
-
-/* Initialize machine dependent parameters: */
-defs[1].arg1w = PI;
-defs[1].arg1l = -PI/2.0;
-/* Microsoft C has trouble with denormal numbers. */
-#if 0
-defs[3].arg1w = MAXLOG;
-defs[3].arg1l = -MAXLOG/2.0;
-defs[4].arg1w = 2*MAXLOG;
-defs[4].arg1l = -MAXLOG;
-#endif
-defs[6].arg1w = 2.0*MAXLOG;
-defs[6].arg1l = -MAXLOG;
-defs[7].arg1w = MAXLOG;
-defs[7].arg1l = 0.0;
-
-
-/* Outer loop, on the test number: */
-
-for( itst=STRTST; itst<NTESTS; itst++ )
-{
-d = &defs[itst];
-k = 0;
-m = 0;
-max = 0.0;
-rmsa = 0.0;
-ave = 0.0;
-fun = d->name;
-ifun = d->inv;
-
-/* Absolute error criterion starts with gamma function
- * (put all such at end of table)
- */
-if( d->tstyp == GAMMA )
- printf( "Absolute error criterion (but relative if >1):\n" );
-
-/* Smaller number of trials for Wronksians
- * (put them at end of list)
- */
-if( d->tstyp == WRONK1 )
- {
- ntr = WTRIALS;
- printf( "Absolute error and only %d trials:\n", ntr );
- }
-
-printf( headrs[d->tstyp], d->nam2, d->nam1 );
-
-for( i=0; i<ntr; i++ )
-{
-m++;
-
-/* make random number(s) in desired range(s) */
-switch( d->nargs )
-{
-
-default:
-goto illegn;
-
-case 2:
-drand( &a );
-a = d->arg2w * ( a - 1.0 ) + d->arg2l;
-if( d->arg2f & EXPSCAL )
- {
- a = exp(a);
- drand( &y2 );
- a -= 1.0e-13 * a * y2;
- }
-if( d->arg2f & INT )
- {
- k = a + 0.25;
- a = k;
- }
-
-case 1:
-drand( &x );
-x = d->arg1w * ( x - 1.0 ) + d->arg1l;
-if( d->arg1f & EXPSCAL )
- {
- x = exp(x);
- drand( &a );
- x += 1.0e-13 * x * a;
- }
-}
-
-
-/* compute function under test */
-switch( d->nargs )
- {
- case 1:
- switch( d->tstyp )
- {
- case ELLIP:
- yy1 = ( *(fun) )(x);
- y2 = ( *(fun) )(1.0-x);
- y3 = ( *(ifun) )(x);
- y4 = ( *(ifun) )(1.0-x);
- break;
-
-#if 1
- case GAMMA:
-#if GLIBC2
- y = lgamma(x);
-#else
- y = lgam(x);
-#endif
- x = log( gamma(x) );
- break;
-#endif
- default:
- z = ( *(fun) )(x);
- y = ( *(ifun) )(z);
- }
- break;
-
- case 2:
- if( d->arg2f & INT )
- {
- switch( d->tstyp )
- {
- case WRONK1:
- yy1 = (*fun)( k, x ); /* jn */
- y2 = (*fun)( k+1, x );
- y3 = (*ifun)( k, x ); /* yn */
- y4 = (*ifun)( k+1, x );
- break;
-
- case WRONK2:
- yy1 = (*fun)( a, x ); /* iv */
- y2 = (*fun)( a+1.0, x );
- y3 = (*ifun)( k, x ); /* kn */
- y4 = (*ifun)( k+1, x );
- break;
-
- default:
- z = (*fun)( k, x );
- y = (*ifun)( k, z );
- }
- }
- else
- {
- if( d->tstyp == POWER )
- {
- z = (*fun)( x, a );
- y = (*ifun)( z, 1.0/a );
- }
- else
- {
- z = (*fun)( a, x );
- y = (*ifun)( a, z );
- }
- }
- break;
-
-
- default:
-illegn:
- printf( "Illegal nargs= %d", d->nargs );
- exit(1);
- }
-
-switch( d->tstyp )
- {
- case WRONK1:
- e = (y2*y3 - yy1*y4) - 2.0/(PI*x); /* Jn, Yn */
- break;
-
- case WRONK2:
- e = (y2*y3 + yy1*y4) - 1.0/x; /* In, Kn */
- break;
-
- case ELLIP:
- e = (yy1-y3)*y4 + y3*y2 - PIO2;
- break;
-
- default:
- e = y - x;
- break;
- }
-
-if( d->ctrl & RELERR )
- e /= x;
-else
- {
- if( fabs(x) > 1.0 )
- e /= x;
- }
-
-ave += e;
-/* absolute value of error */
-if( e < 0 )
- e = -e;
-
-/* peak detect the error */
-if( e > max )
- {
- max = e;
-
- if( e > 1.0e-10 )
- {
- printf("x %.6E z %.6E y %.6E max %.4E\n",
- x, z, y, max);
- if( d->tstyp == POWER )
- {
- printf( "a %.6E\n", a );
- }
- if( d->tstyp >= WRONK1 )
- {
- printf( "yy1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
- yy1, y2, y3, y4, k, x );
- }
- }
-
-/*
- printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
- printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
- printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
- printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
- printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
- a, b, c, x, y, max, n);
-*/
- }
-
-/* accumulate rms error */
-e *= 1.0e16; /* adjust range */
-rmsa += e * e; /* accumulate the square of the error */
-}
-
-/* report after NTRIALS trials */
-rms = 1.0e-16 * sqrt( rmsa/m );
-if(d->ctrl & RELERR)
- printf(" max = %.2E rms = %.2E\n", max, rms );
-else
- printf(" max = %.2E A rms = %.2E A\n", max, rms );
-} /* loop on itst */
-
-exit(0);
-}
+++ /dev/null
-/* nbdtr.c
- *
- * Negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtr();
- *
- * y = nbdtr( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the negative
- * binomial distribution:
- *
- * k
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * In a sequence of Bernoulli trials, this is the probability
- * that k or fewer failures precede the nth success.
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p), with p between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 100000 1.7e-13 8.8e-15
- * See also incbet.c.
- *
- */
-\f/* nbdtrc.c
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtrc();
- *
- * y = nbdtrc( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,p), with p between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 100000 1.7e-13 8.8e-15
- * See also incbet.c.
- */
-\f
-/* nbdtrc
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtrc();
- *
- * y = nbdtrc( k, n, p );
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- * ACCURACY:
- *
- * See incbet.c.
- */
-\f/* nbdtri
- *
- * Functional inverse of negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * double p, y, nbdtri();
- *
- * p = nbdtri( k, n, y );
- *
- * DESCRIPTION:
- *
- * Finds the argument p such that nbdtr(k,n,p) is equal to y.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,y), with y between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 100000 1.5e-14 8.5e-16
- * See also incbi.c.
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double incbet ( double, double, double );
-extern double incbi ( double, double, double );
-#else
-double incbet(), incbi();
-#endif
-
-double nbdtrc( k, n, p )
-int k, n;
-double p;
-{
-double dk, dn;
-
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtr", DOMAIN );
- return( 0.0 );
- }
-
-dk = k+1;
-dn = n;
-return( incbet( dk, dn, 1.0 - p ) );
-}
-
-
-
-double nbdtr( k, n, p )
-int k, n;
-double p;
-{
-double dk, dn;
-
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtr", DOMAIN );
- return( 0.0 );
- }
-dk = k+1;
-dn = n;
-return( incbet( dn, dk, p ) );
-}
-
-
-
-double nbdtri( k, n, p )
-int k, n;
-double p;
-{
-double dk, dn, w;
-
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtri", DOMAIN );
- return( 0.0 );
- }
-dk = k+1;
-dn = n;
-w = incbi( dn, dk, p );
-return( w );
-}
+++ /dev/null
-/* ndtr.c
- *
- * Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, ndtr();
- *
- * y = ndtr( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the Gaussian probability density
- * function, integrated from minus infinity to x:
- *
- * x
- * -
- * 1 | | 2
- * ndtr(x) = --------- | exp( - t /2 ) dt
- * sqrt(2pi) | |
- * -
- * -inf.
- *
- * = ( 1 + erf(z) ) / 2
- * = erfc(z) / 2
- *
- * where z = x/sqrt(2). Computation is via the functions
- * erf and erfc.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -13,0 8000 2.1e-15 4.8e-16
- * IEEE -13,0 30000 3.4e-14 6.7e-15
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfc underflow x > 37.519379347 0.0
- *
- */
-\f/* erf.c
- *
- * Error function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, erf();
- *
- * y = erf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The integral is
- *
- * x
- * -
- * 2 | | 2
- * erf(x) = -------- | exp( - t ) dt.
- * sqrt(pi) | |
- * -
- * 0
- *
- * The magnitude of x is limited to 9.231948545 for DEC
- * arithmetic; 1 or -1 is returned outside this range.
- *
- * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
- * erf(x) = 1 - erfc(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,1 14000 4.7e-17 1.5e-17
- * IEEE 0,1 30000 3.7e-16 1.0e-16
- *
- */
-\f/* erfc.c
- *
- * Complementary error function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, erfc();
- *
- * y = erfc( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * 1 - erf(x) =
- *
- * inf.
- * -
- * 2 | | 2
- * erfc(x) = -------- | exp( - t ) dt
- * sqrt(pi) | |
- * -
- * x
- *
- *
- * For small x, erfc(x) = 1 - erf(x); otherwise rational
- * approximations are computed.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 9.2319 12000 5.1e-16 1.2e-16
- * IEEE 0,26.6417 30000 5.7e-14 1.5e-14
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfc underflow x > 9.231948545 (DEC) 0.0
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-extern double SQRTH;
-extern double MAXLOG;
-
-
-#ifdef UNK
-static double P[] = {
- 2.46196981473530512524E-10,
- 5.64189564831068821977E-1,
- 7.46321056442269912687E0,
- 4.86371970985681366614E1,
- 1.96520832956077098242E2,
- 5.26445194995477358631E2,
- 9.34528527171957607540E2,
- 1.02755188689515710272E3,
- 5.57535335369399327526E2
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 1.32281951154744992508E1,
- 8.67072140885989742329E1,
- 3.54937778887819891062E2,
- 9.75708501743205489753E2,
- 1.82390916687909736289E3,
- 2.24633760818710981792E3,
- 1.65666309194161350182E3,
- 5.57535340817727675546E2
-};
-static double R[] = {
- 5.64189583547755073984E-1,
- 1.27536670759978104416E0,
- 5.01905042251180477414E0,
- 6.16021097993053585195E0,
- 7.40974269950448939160E0,
- 2.97886665372100240670E0
-};
-static double S[] = {
-/* 1.00000000000000000000E0,*/
- 2.26052863220117276590E0,
- 9.39603524938001434673E0,
- 1.20489539808096656605E1,
- 1.70814450747565897222E1,
- 9.60896809063285878198E0,
- 3.36907645100081516050E0
-};
-static double T[] = {
- 9.60497373987051638749E0,
- 9.00260197203842689217E1,
- 2.23200534594684319226E3,
- 7.00332514112805075473E3,
- 5.55923013010394962768E4
-};
-static double U[] = {
-/* 1.00000000000000000000E0,*/
- 3.35617141647503099647E1,
- 5.21357949780152679795E2,
- 4.59432382970980127987E3,
- 2.26290000613890934246E4,
- 4.92673942608635921086E4
-};
-
-#define UTHRESH 37.519379347
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0030207,0054445,0011173,0021706,
-0040020,0067272,0030661,0122075,
-0040756,0151236,0173053,0067042,
-0041502,0106175,0062555,0151457,
-0042104,0102525,0047401,0003667,
-0042403,0116176,0011446,0075303,
-0042551,0120723,0061641,0123275,
-0042600,0070651,0007264,0134516,
-0042413,0061102,0167507,0176625
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041123,0123257,0165741,0017142,
-0041655,0065027,0173413,0115450,
-0042261,0074011,0021573,0004150,
-0042563,0166530,0013662,0007200,
-0042743,0176427,0162443,0105214,
-0043014,0062546,0153727,0123772,
-0042717,0012470,0006227,0067424,
-0042413,0061103,0003042,0013254
-};
-static unsigned short R[] = {
-0040020,0067272,0101024,0155421,
-0040243,0037467,0056706,0026462,
-0040640,0116017,0120665,0034315,
-0040705,0020162,0143350,0060137,
-0040755,0016234,0134304,0130157,
-0040476,0122700,0051070,0015473
-};
-static unsigned short S[] = {
-/*0040200,0000000,0000000,0000000,*/
-0040420,0126200,0044276,0070413,
-0041026,0053051,0007302,0063746,
-0041100,0144203,0174051,0061151,
-0041210,0123314,0126343,0177646,
-0041031,0137125,0051431,0033011,
-0040527,0117362,0152661,0066201
-};
-static unsigned short T[] = {
-0041031,0126770,0170672,0166101,
-0041664,0006522,0072360,0031770,
-0043013,0100025,0162641,0126671,
-0043332,0155231,0161627,0076200,
-0044131,0024115,0021020,0117343
-};
-static unsigned short U[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041406,0037461,0177575,0032714,
-0042402,0053350,0123061,0153557,
-0043217,0111227,0032007,0164217,
-0043660,0145000,0004013,0160114,
-0044100,0071544,0167107,0125471
-};
-#define UTHRESH 14.0
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x6479,0xa24f,0xeb24,0x3df0,
-0x3488,0x4636,0x0dd7,0x3fe2,
-0x6dc4,0xdec5,0xda53,0x401d,
-0xba66,0xacad,0x518f,0x4048,
-0x20f7,0xa9e0,0x90aa,0x4068,
-0xcf58,0xc264,0x738f,0x4080,
-0x34d8,0x6c74,0x343a,0x408d,
-0x972a,0x21d6,0x0e35,0x4090,
-0xffb3,0x5de8,0x6c48,0x4081
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x23cc,0xfd7c,0x74d5,0x402a,
-0x7365,0xfee1,0xad42,0x4055,
-0x610d,0x246f,0x2f01,0x4076,
-0x41d0,0x02f6,0x7dab,0x408e,
-0x7151,0xfca4,0x7fa2,0x409c,
-0xf4ff,0xdafa,0x8cac,0x40a1,
-0xede2,0x0192,0xe2a7,0x4099,
-0x42d6,0x60c4,0x6c48,0x4081
-};
-static unsigned short R[] = {
-0x9b62,0x5042,0x0dd7,0x3fe2,
-0xc5a6,0xebb8,0x67e6,0x3ff4,
-0xa71a,0xf436,0x1381,0x4014,
-0x0c0c,0x58dd,0xa40e,0x4018,
-0x960e,0x9718,0xa393,0x401d,
-0x0367,0x0a47,0xd4b8,0x4007
-};
-static unsigned short S[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xce21,0x0917,0x1590,0x4002,
-0x4cfd,0x21d8,0xcac5,0x4022,
-0x2c4d,0x7f05,0x1910,0x4028,
-0x7ff5,0x959c,0x14d9,0x4031,
-0x26c1,0xaa63,0x37ca,0x4023,
-0x2d90,0x5ab6,0xf3de,0x400a
-};
-static unsigned short T[] = {
-0x5d88,0x1e37,0x35bf,0x4023,
-0x067f,0x4e9e,0x81aa,0x4056,
-0x35b7,0xbcb4,0x7002,0x40a1,
-0xef90,0x3c72,0x5b53,0x40bb,
-0x13dc,0xa442,0x2509,0x40eb
-};
-static unsigned short U[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xa6ba,0x3fef,0xc7e6,0x4040,
-0x3aee,0x14c6,0x4add,0x4080,
-0xfd12,0xe680,0xf252,0x40b1,
-0x7c0a,0x0101,0x1940,0x40d6,
-0xf567,0x9dc8,0x0e6c,0x40e8
-};
-#define UTHRESH 37.519379347
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3df0,0xeb24,0xa24f,0x6479,
-0x3fe2,0x0dd7,0x4636,0x3488,
-0x401d,0xda53,0xdec5,0x6dc4,
-0x4048,0x518f,0xacad,0xba66,
-0x4068,0x90aa,0xa9e0,0x20f7,
-0x4080,0x738f,0xc264,0xcf58,
-0x408d,0x343a,0x6c74,0x34d8,
-0x4090,0x0e35,0x21d6,0x972a,
-0x4081,0x6c48,0x5de8,0xffb3
-};
-static unsigned short Q[] = {
-0x402a,0x74d5,0xfd7c,0x23cc,
-0x4055,0xad42,0xfee1,0x7365,
-0x4076,0x2f01,0x246f,0x610d,
-0x408e,0x7dab,0x02f6,0x41d0,
-0x409c,0x7fa2,0xfca4,0x7151,
-0x40a1,0x8cac,0xdafa,0xf4ff,
-0x4099,0xe2a7,0x0192,0xede2,
-0x4081,0x6c48,0x60c4,0x42d6
-};
-static unsigned short R[] = {
-0x3fe2,0x0dd7,0x5042,0x9b62,
-0x3ff4,0x67e6,0xebb8,0xc5a6,
-0x4014,0x1381,0xf436,0xa71a,
-0x4018,0xa40e,0x58dd,0x0c0c,
-0x401d,0xa393,0x9718,0x960e,
-0x4007,0xd4b8,0x0a47,0x0367
-};
-static unsigned short S[] = {
-0x4002,0x1590,0x0917,0xce21,
-0x4022,0xcac5,0x21d8,0x4cfd,
-0x4028,0x1910,0x7f05,0x2c4d,
-0x4031,0x14d9,0x959c,0x7ff5,
-0x4023,0x37ca,0xaa63,0x26c1,
-0x400a,0xf3de,0x5ab6,0x2d90
-};
-static unsigned short T[] = {
-0x4023,0x35bf,0x1e37,0x5d88,
-0x4056,0x81aa,0x4e9e,0x067f,
-0x40a1,0x7002,0xbcb4,0x35b7,
-0x40bb,0x5b53,0x3c72,0xef90,
-0x40eb,0x2509,0xa442,0x13dc
-};
-static unsigned short U[] = {
-0x4040,0xc7e6,0x3fef,0xa6ba,
-0x4080,0x4add,0x14c6,0x3aee,
-0x40b1,0xf252,0xe680,0xfd12,
-0x40d6,0x1940,0x0101,0x7c0a,
-0x40e8,0x0e6c,0x9dc8,0xf567
-};
-#define UTHRESH 37.519379347
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double exp ( double );
-extern double log ( double );
-extern double fabs ( double );
-double erf ( double );
-double erfc ( double );
-#else
-double polevl(), p1evl(), exp(), log(), fabs();
-double erf(), erfc();
-#endif
-
-double ndtr(a)
-double a;
-{
-double x, y, z;
-
-x = a * SQRTH;
-z = fabs(x);
-
-if( z < SQRTH )
- y = 0.5 + 0.5 * erf(x);
-
-else
- {
- y = 0.5 * erfc(z);
-
- if( x > 0 )
- y = 1.0 - y;
- }
-
-return(y);
-}
-
-
-double erfc(a)
-double a;
-{
-double p,q,x,y,z;
-
-
-if( a < 0.0 )
- x = -a;
-else
- x = a;
-
-if( x < 1.0 )
- return( 1.0 - erf(a) );
-
-z = -a * a;
-
-if( z < -MAXLOG )
- {
-under:
- mtherr( "erfc", UNDERFLOW );
- if( a < 0 )
- return( 2.0 );
- else
- return( 0.0 );
- }
-
-z = exp(z);
-
-if( x < 8.0 )
- {
- p = polevl( x, P, 8 );
- q = p1evl( x, Q, 8 );
- }
-else
- {
- p = polevl( x, R, 5 );
- q = p1evl( x, S, 6 );
- }
-y = (z * p)/q;
-
-if( a < 0 )
- y = 2.0 - y;
-
-if( y == 0.0 )
- goto under;
-
-return(y);
-}
-
-
-
-double erf(x)
-double x;
-{
-double y, z;
-
-if( fabs(x) > 1.0 )
- return( 1.0 - erfc(x) );
-z = x * x;
-y = x * polevl( z, T, 4 ) / p1evl( z, U, 5 );
-return( y );
-
-}
+++ /dev/null
-/* ndtri.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, ndtri();
- *
- * x = ndtri( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2.0 * log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
- * There are two rational functions P/Q, one for 0 < y < exp(-32)
- * and the other for y up to exp(-2). For larger arguments,
- * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0.125, 1 5500 9.5e-17 2.1e-17
- * DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
- * IEEE 0.125, 1 20000 7.2e-16 1.3e-16
- * IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtri domain x <= 0 -MAXNUM
- * ndtri domain x >= 1 MAXNUM
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-extern double MAXNUM;
-
-#ifdef UNK
-/* sqrt(2pi) */
-static double s2pi = 2.50662827463100050242E0;
-#endif
-
-#ifdef DEC
-static unsigned short s2p[] = {0040440,0066230,0177661,0034055};
-#define s2pi *(double *)s2p
-#endif
-
-#ifdef IBMPC
-static unsigned short s2p[] = {0x2706,0x1ff6,0x0d93,0x4004};
-#define s2pi *(double *)s2p
-#endif
-
-#ifdef MIEEE
-static unsigned short s2p[] = {
-0x4004,0x0d93,0x1ff6,0x2706
-};
-#define s2pi *(double *)s2p
-#endif
-
-/* approximation for 0 <= |y - 0.5| <= 3/8 */
-#ifdef UNK
-static double P0[5] = {
--5.99633501014107895267E1,
- 9.80010754185999661536E1,
--5.66762857469070293439E1,
- 1.39312609387279679503E1,
--1.23916583867381258016E0,
-};
-static double Q0[8] = {
-/* 1.00000000000000000000E0,*/
- 1.95448858338141759834E0,
- 4.67627912898881538453E0,
- 8.63602421390890590575E1,
--2.25462687854119370527E2,
- 2.00260212380060660359E2,
--8.20372256168333339912E1,
- 1.59056225126211695515E1,
--1.18331621121330003142E0,
-};
-#endif
-#ifdef DEC
-static unsigned short P0[20] = {
-0141557,0155170,0071360,0120550,
-0041704,0000214,0172417,0067307,
-0141542,0132204,0040066,0156723,
-0041136,0163161,0157276,0007747,
-0140236,0116374,0073666,0051764,
-};
-static unsigned short Q0[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0040372,0026256,0110403,0123707,
-0040625,0122024,0020277,0026661,
-0041654,0134161,0124134,0007244,
-0142141,0073162,0133021,0131371,
-0042110,0041235,0043516,0057767,
-0141644,0011417,0036155,0137305,
-0041176,0076556,0004043,0125430,
-0140227,0073347,0152776,0067251,
-};
-#endif
-#ifdef IBMPC
-static unsigned short P0[20] = {
-0x142d,0x0e5e,0xfb4f,0xc04d,
-0xedd9,0x9ea1,0x8011,0x4058,
-0xdbba,0x8806,0x5690,0xc04c,
-0xc1fd,0x3bd7,0xdcce,0x402b,
-0xca7e,0x8ef6,0xd39f,0xbff3,
-};
-static unsigned short Q0[36] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x74f9,0xd220,0x4595,0x3fff,
-0xe5b6,0x8417,0xb482,0x4012,
-0x81d4,0x350b,0x970e,0x4055,
-0x365f,0x56c2,0x2ece,0xc06c,
-0xcbff,0xa8e9,0x0853,0x4069,
-0xb7d9,0xe78d,0x8261,0xc054,
-0x7563,0xc104,0xcfad,0x402f,
-0xcdd5,0xfabf,0xeedc,0xbff2,
-};
-#endif
-#ifdef MIEEE
-static unsigned short P0[20] = {
-0xc04d,0xfb4f,0x0e5e,0x142d,
-0x4058,0x8011,0x9ea1,0xedd9,
-0xc04c,0x5690,0x8806,0xdbba,
-0x402b,0xdcce,0x3bd7,0xc1fd,
-0xbff3,0xd39f,0x8ef6,0xca7e,
-};
-static unsigned short Q0[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3fff,0x4595,0xd220,0x74f9,
-0x4012,0xb482,0x8417,0xe5b6,
-0x4055,0x970e,0x350b,0x81d4,
-0xc06c,0x2ece,0x56c2,0x365f,
-0x4069,0x0853,0xa8e9,0xcbff,
-0xc054,0x8261,0xe78d,0xb7d9,
-0x402f,0xcfad,0xc104,0x7563,
-0xbff2,0xeedc,0xfabf,0xcdd5,
-};
-#endif
-
-
-/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
- * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
- */
-#ifdef UNK
-static double P1[9] = {
- 4.05544892305962419923E0,
- 3.15251094599893866154E1,
- 5.71628192246421288162E1,
- 4.40805073893200834700E1,
- 1.46849561928858024014E1,
- 2.18663306850790267539E0,
--1.40256079171354495875E-1,
--3.50424626827848203418E-2,
--8.57456785154685413611E-4,
-};
-static double Q1[8] = {
-/* 1.00000000000000000000E0,*/
- 1.57799883256466749731E1,
- 4.53907635128879210584E1,
- 4.13172038254672030440E1,
- 1.50425385692907503408E1,
- 2.50464946208309415979E0,
--1.42182922854787788574E-1,
--3.80806407691578277194E-2,
--9.33259480895457427372E-4,
-};
-#endif
-#ifdef DEC
-static unsigned short P1[36] = {
-0040601,0143074,0150744,0073326,
-0041374,0031554,0113253,0146016,
-0041544,0123272,0012463,0176771,
-0041460,0051160,0103560,0156511,
-0041152,0172624,0117772,0030755,
-0040413,0170713,0151545,0176413,
-0137417,0117512,0022154,0131671,
-0137017,0104257,0071432,0007072,
-0135540,0143363,0063137,0036166,
-};
-static unsigned short Q1[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0041174,0075325,0004736,0120326,
-0041465,0110044,0047561,0045567,
-0041445,0042321,0012142,0030340,
-0041160,0127074,0166076,0141051,
-0040440,0046055,0040745,0150400,
-0137421,0114146,0067330,0010621,
-0137033,0175162,0025555,0114351,
-0135564,0122773,0145750,0030357,
-};
-#endif
-#ifdef IBMPC
-static unsigned short P1[36] = {
-0x8edb,0x9a3c,0x38c7,0x4010,
-0x7982,0x92d5,0x866d,0x403f,
-0x7fbf,0x42a6,0x94d7,0x404c,
-0x1ba9,0x10ee,0x0a4e,0x4046,
-0x463e,0x93ff,0x5eb2,0x402d,
-0xbfa1,0x7a6c,0x7e39,0x4001,
-0x9677,0x448d,0xf3e9,0xbfc1,
-0x41c7,0xee63,0xf115,0xbfa1,
-0xe78f,0x6ccb,0x18de,0xbf4c,
-};
-static unsigned short Q1[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xd41b,0xa13b,0x8f5a,0x402f,
-0x296f,0x89ee,0xb204,0x4046,
-0x461c,0x228c,0xa89a,0x4044,
-0xd845,0x9d87,0x15c7,0x402e,
-0xba20,0xa83c,0x0985,0x4004,
-0x0232,0xcddb,0x330c,0xbfc2,
-0xb31d,0x456d,0x7f4e,0xbfa3,
-0x061e,0x797d,0x94bf,0xbf4e,
-};
-#endif
-#ifdef MIEEE
-static unsigned short P1[36] = {
-0x4010,0x38c7,0x9a3c,0x8edb,
-0x403f,0x866d,0x92d5,0x7982,
-0x404c,0x94d7,0x42a6,0x7fbf,
-0x4046,0x0a4e,0x10ee,0x1ba9,
-0x402d,0x5eb2,0x93ff,0x463e,
-0x4001,0x7e39,0x7a6c,0xbfa1,
-0xbfc1,0xf3e9,0x448d,0x9677,
-0xbfa1,0xf115,0xee63,0x41c7,
-0xbf4c,0x18de,0x6ccb,0xe78f,
-};
-static unsigned short Q1[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x402f,0x8f5a,0xa13b,0xd41b,
-0x4046,0xb204,0x89ee,0x296f,
-0x4044,0xa89a,0x228c,0x461c,
-0x402e,0x15c7,0x9d87,0xd845,
-0x4004,0x0985,0xa83c,0xba20,
-0xbfc2,0x330c,0xcddb,0x0232,
-0xbfa3,0x7f4e,0x456d,0xb31d,
-0xbf4e,0x94bf,0x797d,0x061e,
-};
-#endif
-
-/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
- * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
- */
-
-#ifdef UNK
-static double P2[9] = {
- 3.23774891776946035970E0,
- 6.91522889068984211695E0,
- 3.93881025292474443415E0,
- 1.33303460815807542389E0,
- 2.01485389549179081538E-1,
- 1.23716634817820021358E-2,
- 3.01581553508235416007E-4,
- 2.65806974686737550832E-6,
- 6.23974539184983293730E-9,
-};
-static double Q2[8] = {
-/* 1.00000000000000000000E0,*/
- 6.02427039364742014255E0,
- 3.67983563856160859403E0,
- 1.37702099489081330271E0,
- 2.16236993594496635890E-1,
- 1.34204006088543189037E-2,
- 3.28014464682127739104E-4,
- 2.89247864745380683936E-6,
- 6.79019408009981274425E-9,
-};
-#endif
-#ifdef DEC
-static unsigned short P2[36] = {
-0040517,0033507,0036236,0125641,
-0040735,0044616,0014473,0140133,
-0040574,0012567,0114535,0102541,
-0040252,0120340,0143474,0150135,
-0037516,0051057,0115361,0031211,
-0036512,0131204,0101511,0125144,
-0035236,0016627,0043160,0140216,
-0033462,0060512,0060141,0010641,
-0031326,0062541,0101304,0077706,
-};
-static unsigned short Q2[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0040700,0143322,0132137,0040501,
-0040553,0101155,0053221,0140257,
-0040260,0041071,0052573,0010004,
-0037535,0066472,0177261,0162330,
-0036533,0160475,0066666,0036132,
-0035253,0174533,0027771,0044027,
-0033502,0016147,0117666,0063671,
-0031351,0047455,0141663,0054751,
-};
-#endif
-#ifdef IBMPC
-static unsigned short P2[36] = {
-0xd574,0xe793,0xe6e8,0x4009,
-0x780b,0xc327,0xa931,0x401b,
-0xb0ac,0xf32b,0x82ae,0x400f,
-0x9a0c,0x18e7,0x541c,0x3ff5,
-0x2651,0xf35e,0xca45,0x3fc9,
-0x354d,0x9069,0x5650,0x3f89,
-0x1812,0xe8ce,0xc3b2,0x3f33,
-0x2234,0x4c0c,0x4c29,0x3ec6,
-0x8ff9,0x3058,0xccac,0x3e3a,
-};
-static unsigned short Q2[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xe828,0x568b,0x18da,0x4018,
-0x3816,0xaad2,0x704d,0x400d,
-0x6200,0x2aaf,0x0847,0x3ff6,
-0x3c9b,0x5fd6,0xada7,0x3fcb,
-0xc78b,0xadb6,0x7c27,0x3f8b,
-0x2903,0x65ff,0x7f2b,0x3f35,
-0xccf7,0xf3f6,0x438c,0x3ec8,
-0x6b3d,0xb876,0x29e5,0x3e3d,
-};
-#endif
-#ifdef MIEEE
-static unsigned short P2[36] = {
-0x4009,0xe6e8,0xe793,0xd574,
-0x401b,0xa931,0xc327,0x780b,
-0x400f,0x82ae,0xf32b,0xb0ac,
-0x3ff5,0x541c,0x18e7,0x9a0c,
-0x3fc9,0xca45,0xf35e,0x2651,
-0x3f89,0x5650,0x9069,0x354d,
-0x3f33,0xc3b2,0xe8ce,0x1812,
-0x3ec6,0x4c29,0x4c0c,0x2234,
-0x3e3a,0xccac,0x3058,0x8ff9,
-};
-static unsigned short Q2[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4018,0x18da,0x568b,0xe828,
-0x400d,0x704d,0xaad2,0x3816,
-0x3ff6,0x0847,0x2aaf,0x6200,
-0x3fcb,0xada7,0x5fd6,0x3c9b,
-0x3f8b,0x7c27,0xadb6,0xc78b,
-0x3f35,0x7f2b,0x65ff,0x2903,
-0x3ec8,0x438c,0xf3f6,0xccf7,
-0x3e3d,0x29e5,0xb876,0x6b3d,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-extern double sqrt ( double );
-#else
-double polevl(), p1evl(), log(), sqrt();
-#endif
-
-double ndtri(y0)
-double y0;
-{
-double x, y, z, y2, x0, x1;
-int code;
-
-if( y0 <= 0.0 )
- {
- mtherr( "ndtri", DOMAIN );
- return( -MAXNUM );
- }
-if( y0 >= 1.0 )
- {
- mtherr( "ndtri", DOMAIN );
- return( MAXNUM );
- }
-code = 1;
-y = y0;
-if( y > (1.0 - 0.13533528323661269189) ) /* 0.135... = exp(-2) */
- {
- y = 1.0 - y;
- code = 0;
- }
-
-if( y > 0.13533528323661269189 )
- {
- y = y - 0.5;
- y2 = y * y;
- x = y + y * (y2 * polevl( y2, P0, 4)/p1evl( y2, Q0, 8 ));
- x = x * s2pi;
- return(x);
- }
-
-x = sqrt( -2.0 * log(y) );
-x0 = x - log(x)/x;
-
-z = 1.0/x;
-if( x < 8.0 ) /* y > exp(-32) = 1.2664165549e-14 */
- x1 = z * polevl( z, P1, 8 )/p1evl( z, Q1, 8 );
-else
- x1 = z * polevl( z, P2, 8 )/p1evl( z, Q2, 8 );
-x = x0 - x1;
-if( code != 0 )
- x = -x;
-return( x );
-}
+++ /dev/null
-/*
- * This file contains math functions missing from the Cephes library.
- *
- * May 22, 2001 Manuel Novoa III
- *
- * Added modf and fmod.
- *
- * TODO:
- * Break out functions into seperate object files as is done
- * by (for example) stdio. Also do this with cephes files.
- */
-
-#include <math.h>
-#include <errno.h>
-
-#undef UNK
-
-/* Set this to nonzero to enable a couple of shortcut tests in fmod. */
-#define SPEED_OVER_SIZE 0
-
-/**********************************************************************/
-
-double modf(double x, double *iptr)
-{
- double y;
-
-#ifdef UNK
- mtherr( "modf", DOMAIN );
- *iptr = NAN;
- return NAN;
-#endif
-
-#ifdef NANS
- if( isnan(x) ) {
- *iptr = x;
- return x;
- }
-#endif
-
-#ifdef INFINITIES
- if(!isfinite(x)) {
- *iptr = x; /* Matches glibc, but returning NAN */
- return 0; /* makes more sense to me... */
- }
-#endif
-
- if (x < 0) { /* Round towards 0. */
- y = ceil(x);
- } else {
- y = floor(x);
- }
-
- *iptr = y;
- return x - y;
-}
-
-/**********************************************************************/
-
-extern double NAN;
-
-double fmod(double x, double y)
-{
- double z;
- int negative, ex, ey;
-
-#ifdef UNK
- mtherr( "fmod", DOMAIN );
- return NAN;
-#endif
-
-#ifdef NANS
- if( isnan(x) || isnan(y) ) {
- errno = EDOM;
- return NAN;
- }
-#endif
-
- if (y == 0) {
- errno = EDOM;
- return NAN;
- }
-
-#ifdef INFINITIES
- if(!isfinite(x)) {
- errno = EDOM;
- return NAN;
- }
-
-#if SPEED_OVER_SIZE
- if(!isfinite(y)) {
- return x;
- }
-#endif
-#endif
-
-#if SPEED_OVER_SIZE
- if (x == 0) {
- return 0;
- }
-#endif
-
- negative = 0;
- if (x < 0) {
- negative = 1;
- x = -x;
- }
-
- if (y < 0) {
- y = -y;
- }
-
- frexp(y,&ey);
- while (x >= y) {
- frexp(x,&ex);
- z = ldexp(y,ex-ey);
- if (z > x) {
- z /= 2;
- }
- x -= z;
- }
-
- if (negative) {
- return -x;
- } else {
- return x;
- }
-}
+++ /dev/null
-/* A C version of Kahan's Floating Point Test "Paranoia"
-
- Thos Sumner, UCSF, Feb. 1985
- David Gay, BTL, Jan. 1986
-
- This is a rewrite from the Pascal version by
-
- B. A. Wichmann, 18 Jan. 1985
-
- (and does NOT exhibit good C programming style).
-
-(C) Apr 19 1983 in BASIC version by:
- Professor W. M. Kahan,
- 567 Evans Hall
- Electrical Engineering & Computer Science Dept.
- University of California
- Berkeley, California 94720
- USA
-
-converted to Pascal by:
- B. A. Wichmann
- National Physical Laboratory
- Teddington Middx
- TW11 OLW
- UK
-
-converted to C by:
-
- David M. Gay and Thos Sumner
- AT&T Bell Labs Computer Center, Rm. U-76
- 600 Mountainn Avenue University of California
- Murray Hill, NJ 07974 San Francisco, CA 94143
- USA USA
-
-with simultaneous corrections to the Pascal source (reflected
-in the Pascal source available over netlib).
-
-Reports of results on various systems from all the versions
-of Paranoia are being collected by Richard Karpinski at the
-same address as Thos Sumner. This includes sample outputs,
-bug reports, and criticisms.
-
-You may copy this program freely if you acknowledge its source.
-Comments on the Pascal version to NPL, please.
-
-
-The C version catches signals from floating-point exceptions.
-If signal(SIGFPE,...) is unavailable in your environment, you may
-#define NOSIGNAL to comment out the invocations of signal.
-
-This source file is too big for some C compilers, but may be split
-into pieces. Comments containing "SPLIT" suggest convenient places
-for this splitting. At the end of these comments is an "ed script"
-(for the UNIX(tm) editor ed) that will do this splitting.
-
-By #defining Single when you compile this source, you may obtain
-a single-precision C version of Paranoia.
-
-
-The following is from the introductory commentary from Wichmann's work:
-
-The BASIC program of Kahan is written in Microsoft BASIC using many
-facilities which have no exact analogy in Pascal. The Pascal
-version below cannot therefore be exactly the same. Rather than be
-a minimal transcription of the BASIC program, the Pascal coding
-follows the conventional style of block-structured languages. Hence
-the Pascal version could be useful in producing versions in other
-structured languages.
-
-Rather than use identifiers of minimal length (which therefore have
-little mnemonic significance), the Pascal version uses meaningful
-identifiers as follows [Note: A few changes have been made for C]:
-
-
-BASIC C BASIC C BASIC C
-
- A J S StickyBit
- A1 AInverse J0 NoErrors T
- B Radix [Failure] T0 Underflow
- B1 BInverse J1 NoErrors T2 ThirtyTwo
- B2 RadixD2 [SeriousDefect] T5 OneAndHalf
- B9 BMinusU2 J2 NoErrors T7 TwentySeven
- C [Defect] T8 TwoForty
- C1 CInverse J3 NoErrors U OneUlp
- D [Flaw] U0 UnderflowThreshold
- D4 FourD K PageNo U1
- E0 L Milestone U2
- E1 M V
- E2 Exp2 N V0
- E3 N1 V8
- E5 MinSqEr O Zero V9
- E6 SqEr O1 One W
- E7 MaxSqEr O2 Two X
- E8 O3 Three X1
- E9 O4 Four X8
- F1 MinusOne O5 Five X9 Random1
- F2 Half O8 Eight Y
- F3 Third O9 Nine Y1
- F6 P Precision Y2
- F9 Q Y9 Random2
- G1 GMult Q8 Z
- G2 GDiv Q9 Z0 PseudoZero
- G3 GAddSub R Z1
- H R1 RMult Z2
- H1 HInverse R2 RDiv Z9
- I R3 RAddSub
- IO NoTrials R4 RSqrt
- I3 IEEE R9 Random9
-
- SqRWrng
-
-All the variables in BASIC are true variables and in consequence,
-the program is more difficult to follow since the "constants" must
-be determined (the glossary is very helpful). The Pascal version
-uses Real constants, but checks are added to ensure that the values
-are correctly converted by the compiler.
-
-The major textual change to the Pascal version apart from the
-identifiersis that named procedures are used, inserting parameters
-wherehelpful. New procedures are also introduced. The
-correspondence is as follows:
-
-
-BASIC Pascal
-lines
-
- 90- 140 Pause
- 170- 250 Instructions
- 380- 460 Heading
- 480- 670 Characteristics
- 690- 870 History
-2940-2950 Random
-3710-3740 NewD
-4040-4080 DoesYequalX
-4090-4110 PrintIfNPositive
-4640-4850 TestPartialUnderflow
-
-=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
-
-Below is an "ed script" that splits para.c into 10 files
-of the form part[1-8].c, subs.c, and msgs.c, plus a header
-file, paranoia.h, that these files require.
-r paranoia.c
-$
-?SPLIT
-+,$w msgs.c
-.,$d
-?SPLIT
-.d
-+d
--,$w subs.c
--,$d
-?part8
-+d
-?include
-.,$w part8.c
-.,$d
--d
-?part7
-+d
-?include
-.,$w part7.c
-.,$d
--d
-?part6
-+d
-?include
-.,$w part6.c
-.,$d
--d
-?part5
-+d
-?include
-.,$w part5.c
-.,$d
--d
-?part4
-+d
-?include
-.,$w part4.c
-.,$d
--d
-?part3
-+d
-?include
-.,$w part3.c
-.,$d
--d
-?part2
-+d
-?include
-.,$w part2.c
-.,$d
-?SPLIT
-.d
-1,/^#include/-1d
-1,$w part1.c
-/Computed constants/,$d
-1,$s/^int/extern &/
-1,$s/^FLOAT/extern &/
-1,$s! = .*!;!
-/^Guard/,/^Round/s/^/extern /
-/^jmp_buf/s/^/extern /
-/^Sig_type/s/^/extern /
-a
-extern int sigfpe();
-.
-w paranoia.h
-q
-
-*/
-
-#include <stdio.h>
-#ifndef NOSIGNAL
-#include <signal.h>
-#endif
-#include <setjmp.h>
-
-extern double fabs(), floor(), log(), pow(), sqrt();
-
-#ifdef Single
-#define FLOAT float
-#define FABS(x) (float)fabs((double)(x))
-#define FLOOR(x) (float)floor((double)(x))
-#define LOG(x) (float)log((double)(x))
-#define POW(x,y) (float)pow((double)(x),(double)(y))
-#define SQRT(x) (float)sqrt((double)(x))
-#else
-#define FLOAT double
-#define FABS(x) fabs(x)
-#define FLOOR(x) floor(x)
-#define LOG(x) log(x)
-#define POW(x,y) pow(x,y)
-#define SQRT(x) sqrt(x)
-#endif
-
-jmp_buf ovfl_buf;
-typedef int (*Sig_type)();
-Sig_type sigsave;
-
-#define KEYBOARD 0
-
-FLOAT Radix, BInvrse, RadixD2, BMinusU2;
-FLOAT Sign(), Random();
-
-/*Small floating point constants.*/
-FLOAT Zero = 0.0;
-FLOAT Half = 0.5;
-FLOAT One = 1.0;
-FLOAT Two = 2.0;
-FLOAT Three = 3.0;
-FLOAT Four = 4.0;
-FLOAT Five = 5.0;
-FLOAT Eight = 8.0;
-FLOAT Nine = 9.0;
-FLOAT TwentySeven = 27.0;
-FLOAT ThirtyTwo = 32.0;
-FLOAT TwoForty = 240.0;
-FLOAT MinusOne = -1.0;
-FLOAT OneAndHalf = 1.5;
-/*Integer constants*/
-int NoTrials = 20; /*Number of tests for commutativity. */
-#define False 0
-#define True 1
-
-/* Definitions for declared types
- Guard == (Yes, No);
- Rounding == (Chopped, Rounded, Other);
- Message == packed array [1..40] of char;
- Class == (Flaw, Defect, Serious, Failure);
- */
-#define Yes 1
-#define No 0
-#define Chopped 2
-#define Rounded 1
-#define Other 0
-#define Flaw 3
-#define Defect 2
-#define Serious 1
-#define Failure 0
-typedef int Guard, Rounding, Class;
-typedef char Message;
-
-/* Declarations of Variables */
-int Indx;
-char ch[8];
-FLOAT AInvrse, A1;
-FLOAT C, CInvrse;
-FLOAT D, FourD;
-FLOAT E0, E1, Exp2, E3, MinSqEr;
-FLOAT SqEr, MaxSqEr, E9;
-FLOAT Third;
-FLOAT F6, F9;
-FLOAT H, HInvrse;
-int I;
-FLOAT StickyBit, J;
-FLOAT MyZero;
-FLOAT Precision;
-FLOAT Q, Q9;
-FLOAT R, Random9;
-FLOAT T, Underflow, S;
-FLOAT OneUlp, UfThold, U1, U2;
-FLOAT V, V0, V9;
-FLOAT W;
-FLOAT X, X1, X2, X8, Random1;
-FLOAT Y, Y1, Y2, Random2;
-FLOAT Z, PseudoZero, Z1, Z2, Z9;
-volatile FLOAT VV;
-int ErrCnt[4];
-int fpecount;
-int Milestone;
-int PageNo;
-int M, N, N1;
-Guard GMult, GDiv, GAddSub;
-Rounding RMult, RDiv, RAddSub, RSqrt;
-int Break, Done, NotMonot, Monot, Anomaly, IEEE,
- SqRWrng, UfNGrad;
-/* Computed constants. */
-/*U1 gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */
-/*U2 gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */
-
-/* floating point exception receiver */
-sigfpe()
-{
- fpecount++;
- printf("\n* * * FLOATING-POINT ERROR * * *\n");
- fflush(stdout);
- if (sigsave) {
-#ifndef NOSIGNAL
- signal(SIGFPE, sigsave);
-#endif
- sigsave = 0;
- longjmp(ovfl_buf, 1);
- }
- abort();
-}
-
-main()
-{
- /* Set coprocessor to double precision, no arith traps. */
- /* __setfpucw(0x127f);*/
- dprec();
- /* First two assignments use integer right-hand sides. */
- Zero = 0;
- One = 1;
- Two = One + One;
- Three = Two + One;
- Four = Three + One;
- Five = Four + One;
- Eight = Four + Four;
- Nine = Three * Three;
- TwentySeven = Nine * Three;
- ThirtyTwo = Four * Eight;
- TwoForty = Four * Five * Three * Four;
- MinusOne = -One;
- Half = One / Two;
- OneAndHalf = One + Half;
- ErrCnt[Failure] = 0;
- ErrCnt[Serious] = 0;
- ErrCnt[Defect] = 0;
- ErrCnt[Flaw] = 0;
- PageNo = 1;
- /*=============================================*/
- Milestone = 0;
- /*=============================================*/
-#ifndef NOSIGNAL
- signal(SIGFPE, sigfpe);
-#endif
- Instructions();
- Pause();
- Heading();
- Pause();
- Characteristics();
- Pause();
- History();
- Pause();
- /*=============================================*/
- Milestone = 7;
- /*=============================================*/
- printf("Program is now RUNNING tests on small integers:\n");
-
- TstCond (Failure, (Zero + Zero == Zero) && (One - One == Zero)
- && (One > Zero) && (One + One == Two),
- "0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2");
- Z = - Zero;
- if (Z == 0.0) {
- U1 = 0.001;
- Radix = 1;
- TstPtUf();
- }
- else {
- ErrCnt[Failure] = ErrCnt[Failure] + 1;
- printf("Comparison alleges that -0.0 is Non-zero!\n");
- }
- TstCond (Failure, (Three == Two + One) && (Four == Three + One)
- && (Four + Two * (- Two) == Zero)
- && (Four - Three - One == Zero),
- "3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0");
- TstCond (Failure, (MinusOne == (0 - One))
- && (MinusOne + One == Zero ) && (One + MinusOne == Zero)
- && (MinusOne + FABS(One) == Zero)
- && (MinusOne + MinusOne * MinusOne == Zero),
- "-1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0");
- TstCond (Failure, Half + MinusOne + Half == Zero,
- "1/2 + (-1) + 1/2 != 0");
- /*=============================================*/
- /*SPLIT
- part2();
- part3();
- part4();
- part5();
- part6();
- part7();
- part8();
- }
-#include "paranoia.h"
-part2(){
-*/
- Milestone = 10;
- /*=============================================*/
- TstCond (Failure, (Nine == Three * Three)
- && (TwentySeven == Nine * Three) && (Eight == Four + Four)
- && (ThirtyTwo == Eight * Four)
- && (ThirtyTwo - TwentySeven - Four - One == Zero),
- "9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0");
- TstCond (Failure, (Five == Four + One) &&
- (TwoForty == Four * Five * Three * Four)
- && (TwoForty / Three - Four * Four * Five == Zero)
- && ( TwoForty / Four - Five * Three * Four == Zero)
- && ( TwoForty / Five - Four * Three * Four == Zero),
- "5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48");
- if (ErrCnt[Failure] == 0) {
- printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n");
- printf("\n");
- }
- printf("Searching for Radix and Precision.\n");
- W = One;
- do {
- W = W + W;
- Y = W + One;
- Z = Y - W;
- Y = Z - One;
- } while (MinusOne + FABS(Y) < Zero);
- /*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
- Precision = Zero;
- Y = One;
- do {
- Radix = W + Y;
- Y = Y + Y;
- Radix = Radix - W;
- } while ( Radix == Zero);
- if (Radix < Two) Radix = One;
- printf("Radix = %f .\n", Radix);
- if (Radix != 1) {
- W = One;
- do {
- Precision = Precision + One;
- W = W * Radix;
- Y = W + One;
- } while ((Y - W) == One);
- }
- /*... now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1
- ...*/
- U1 = One / W;
- U2 = Radix * U1;
- printf("Closest relative separation found is U1 = %.7e .\n\n", U1);
- printf("Recalculating radix and precision.");
-
- /*save old values*/
- E0 = Radix;
- E1 = U1;
- E9 = U2;
- E3 = Precision;
-
- X = Four / Three;
- Third = X - One;
- F6 = Half - Third;
- X = F6 + F6;
- X = FABS(X - Third);
- if (X < U2) X = U2;
-
- /*... now X = (unknown no.) ulps of 1+...*/
- do {
- U2 = X;
- Y = Half * U2 + ThirtyTwo * U2 * U2;
- Y = One + Y;
- X = Y - One;
- } while ( ! ((U2 <= X) || (X <= Zero)));
-
- /*... now U2 == 1 ulp of 1 + ... */
- X = Two / Three;
- F6 = X - Half;
- Third = F6 + F6;
- X = Third - Half;
- X = FABS(X + F6);
- if (X < U1) X = U1;
-
- /*... now X == (unknown no.) ulps of 1 -... */
- do {
- U1 = X;
- Y = Half * U1 + ThirtyTwo * U1 * U1;
- Y = Half - Y;
- X = Half + Y;
- Y = Half - X;
- X = Half + Y;
- } while ( ! ((U1 <= X) || (X <= Zero)));
- /*... now U1 == 1 ulp of 1 - ... */
- if (U1 == E1) printf("confirms closest relative separation U1 .\n");
- else printf("gets better closest relative separation U1 = %.7e .\n", U1);
- W = One / U1;
- F9 = (Half - U1) + Half;
- Radix = FLOOR(0.01 + U2 / U1);
- if (Radix == E0) printf("Radix confirmed.\n");
- else printf("MYSTERY: recalculated Radix = %.7e .\n", Radix);
- TstCond (Defect, Radix <= Eight + Eight,
- "Radix is too big: roundoff problems");
- TstCond (Flaw, (Radix == Two) || (Radix == 10)
- || (Radix == One), "Radix is not as good as 2 or 10");
- /*=============================================*/
- Milestone = 20;
- /*=============================================*/
- TstCond (Failure, F9 - Half < Half,
- "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?");
- X = F9;
- I = 1;
- Y = X - Half;
- Z = Y - Half;
- TstCond (Failure, (X != One)
- || (Z == Zero), "Comparison is fuzzy,X=1 but X-1/2-1/2 != 0");
- X = One + U2;
- I = 0;
- /*=============================================*/
- Milestone = 25;
- /*=============================================*/
- /*... BMinusU2 = nextafter(Radix, 0) */
- BMinusU2 = Radix - One;
- BMinusU2 = (BMinusU2 - U2) + One;
- /* Purify Integers */
- if (Radix != One) {
- X = - TwoForty * LOG(U1) / LOG(Radix);
- Y = FLOOR(Half + X);
- if (FABS(X - Y) * Four < One) X = Y;
- Precision = X / TwoForty;
- Y = FLOOR(Half + Precision);
- if (FABS(Precision - Y) * TwoForty < Half) Precision = Y;
- }
- if ((Precision != FLOOR(Precision)) || (Radix == One)) {
- printf("Precision cannot be characterized by an Integer number\n");
- printf("of significant digits but, by itself, this is a minor flaw.\n");
- }
- if (Radix == One)
- printf("logarithmic encoding has precision characterized solely by U1.\n");
- else printf("The number of significant digits of the Radix is %f .\n",
- Precision);
- TstCond (Serious, U2 * Nine * Nine * TwoForty < One,
- "Precision worse than 5 decimal figures ");
- /*=============================================*/
- Milestone = 30;
- /*=============================================*/
- /* Test for extra-precise subepressions */
- X = FABS(((Four / Three - One) - One / Four) * Three - One / Four);
- do {
- Z2 = X;
- X = (One + (Half * Z2 + ThirtyTwo * Z2 * Z2)) - One;
- } while ( ! ((Z2 <= X) || (X <= Zero)));
- X = Y = Z = FABS((Three / Four - Two / Three) * Three - One / Four);
- do {
- Z1 = Z;
- Z = (One / Two - ((One / Two - (Half * Z1 + ThirtyTwo * Z1 * Z1))
- + One / Two)) + One / Two;
- } while ( ! ((Z1 <= Z) || (Z <= Zero)));
- do {
- do {
- Y1 = Y;
- Y = (Half - ((Half - (Half * Y1 + ThirtyTwo * Y1 * Y1)) + Half
- )) + Half;
- } while ( ! ((Y1 <= Y) || (Y <= Zero)));
- X1 = X;
- X = ((Half * X1 + ThirtyTwo * X1 * X1) - F9) + F9;
- } while ( ! ((X1 <= X) || (X <= Zero)));
- if ((X1 != Y1) || (X1 != Z1)) {
- BadCond(Serious, "Disagreements among the values X1, Y1, Z1,\n");
- printf("respectively %.7e, %.7e, %.7e,\n", X1, Y1, Z1);
- printf("are symptoms of inconsistencies introduced\n");
- printf("by extra-precise evaluation of arithmetic subexpressions.\n");
- notify("Possibly some part of this");
- if ((X1 == U1) || (Y1 == U1) || (Z1 == U1)) printf(
- "That feature is not tested further by this program.\n") ;
- }
- else {
- if ((Z1 != U1) || (Z2 != U2)) {
- if ((Z1 >= U1) || (Z2 >= U2)) {
- BadCond(Failure, "");
- notify("Precision");
- printf("\tU1 = %.7e, Z1 - U1 = %.7e\n",U1,Z1-U1);
- printf("\tU2 = %.7e, Z2 - U2 = %.7e\n",U2,Z2-U2);
- }
- else {
- if ((Z1 <= Zero) || (Z2 <= Zero)) {
- printf("Because of unusual Radix = %f", Radix);
- printf(", or exact rational arithmetic a result\n");
- printf("Z1 = %.7e, or Z2 = %.7e ", Z1, Z2);
- notify("of an\nextra-precision");
- }
- if (Z1 != Z2 || Z1 > Zero) {
- X = Z1 / U1;
- Y = Z2 / U2;
- if (Y > X) X = Y;
- Q = - LOG(X);
- printf("Some subexpressions appear to be calculated extra\n");
- printf("precisely with about %g extra B-digits, i.e.\n",
- (Q / LOG(Radix)));
- printf("roughly %g extra significant decimals.\n",
- Q / LOG(10.));
- }
- printf("That feature is not tested further by this program.\n");
- }
- }
- }
- Pause();
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part3(){
-*/
- Milestone = 35;
- /*=============================================*/
- if (Radix >= Two) {
- X = W / (Radix * Radix);
- Y = X + One;
- Z = Y - X;
- T = Z + U2;
- X = T - Z;
- TstCond (Failure, X == U2,
- "Subtraction is not normalized X=Y,X+Z != Y+Z!");
- if (X == U2) printf(
- "Subtraction appears to be normalized, as it should be.");
- }
- printf("\nChecking for guard digit in *, /, and -.\n");
- Y = F9 * One;
- Z = One * F9;
- X = F9 - Half;
- Y = (Y - Half) - X;
- Z = (Z - Half) - X;
- X = One + U2;
- T = X * Radix;
- R = Radix * X;
- X = T - Radix;
- X = X - Radix * U2;
- T = R - Radix;
- T = T - Radix * U2;
- X = X * (Radix - One);
- T = T * (Radix - One);
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)) GMult = Yes;
- else {
- GMult = No;
- TstCond (Serious, False,
- "* lacks a Guard Digit, so 1*X != X");
- }
- Z = Radix * U2;
- X = One + Z;
- Y = FABS((X + Z) - X * X) - U2;
- X = One - U2;
- Z = FABS((X - U2) - X * X) - U1;
- TstCond (Failure, (Y <= Zero)
- && (Z <= Zero), "* gets too many final digits wrong.\n");
- Y = One - U2;
- X = One + U2;
- Z = One / Y;
- Y = Z - X;
- X = One / Three;
- Z = Three / Nine;
- X = X - Z;
- T = Nine / TwentySeven;
- Z = Z - T;
- TstCond(Defect, X == Zero && Y == Zero && Z == Zero,
- "Division lacks a Guard Digit, so error can exceed 1 ulp\n\
-or 1/3 and 3/9 and 9/27 may disagree");
- Y = F9 / One;
- X = F9 - Half;
- Y = (Y - Half) - X;
- X = One + U2;
- T = X / One;
- X = T - X;
- if ((X == Zero) && (Y == Zero) && (Z == Zero)) GDiv = Yes;
- else {
- GDiv = No;
- TstCond (Serious, False,
- "Division lacks a Guard Digit, so X/1 != X");
- }
- X = One / (One + U2);
- Y = X - Half - Half;
- TstCond (Serious, Y < Zero,
- "Computed value of 1/1.000..1 >= 1");
- X = One - U2;
- Y = One + Radix * U2;
- Z = X * Radix;
- T = Y * Radix;
- R = Z / Radix;
- StickyBit = T / Radix;
- X = R - X;
- Y = StickyBit - Y;
- TstCond (Failure, X == Zero && Y == Zero,
- "* and/or / gets too many last digits wrong");
- Y = One - U1;
- X = One - F9;
- Y = One - Y;
- T = Radix - U2;
- Z = Radix - BMinusU2;
- T = Radix - T;
- if ((X == U1) && (Y == U1) && (Z == U2) && (T == U2)) GAddSub = Yes;
- else {
- GAddSub = No;
- TstCond (Serious, False,
- "- lacks Guard Digit, so cancellation is obscured");
- }
- if (F9 != One && F9 - One >= Zero) {
- BadCond(Serious, "comparison alleges (1-U1) < 1 although\n");
- printf(" subtration yields (1-U1) - 1 = 0 , thereby vitiating\n");
- printf(" such precautions against division by zero as\n");
- printf(" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
- }
- if (GMult == Yes && GDiv == Yes && GAddSub == Yes) printf(
- " *, /, and - appear to have guard digits, as they should.\n");
- /*=============================================*/
- Milestone = 40;
- /*=============================================*/
- Pause();
- printf("Checking rounding on multiply, divide and add/subtract.\n");
- RMult = Other;
- RDiv = Other;
- RAddSub = Other;
- RadixD2 = Radix / Two;
- A1 = Two;
- Done = False;
- do {
- AInvrse = Radix;
- do {
- X = AInvrse;
- AInvrse = AInvrse / A1;
- } while ( ! (FLOOR(AInvrse) != AInvrse));
- Done = (X == One) || (A1 > Three);
- if (! Done) A1 = Nine + One;
- } while ( ! (Done));
- if (X == One) A1 = Radix;
- AInvrse = One / A1;
- X = A1;
- Y = AInvrse;
- Done = False;
- do {
- Z = X * Y - Half;
- TstCond (Failure, Z == Half,
- "X * (1/X) differs from 1");
- Done = X == Radix;
- X = Radix;
- Y = One / X;
- } while ( ! (Done));
- Y2 = One + U2;
- Y1 = One - U2;
- X = OneAndHalf - U2;
- Y = OneAndHalf + U2;
- Z = (X - U2) * Y2;
- T = Y * Y1;
- Z = Z - X;
- T = T - X;
- X = X * Y2;
- Y = (Y + U2) * Y1;
- X = X - OneAndHalf;
- Y = Y - OneAndHalf;
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T <= Zero)) {
- X = (OneAndHalf + U2) * Y2;
- Y = OneAndHalf - U2 - U2;
- Z = OneAndHalf + U2 + U2;
- T = (OneAndHalf - U2) * Y1;
- X = X - (Z + U2);
- StickyBit = Y * Y1;
- S = Z * Y2;
- T = T - Y;
- Y = (U2 - Y) + StickyBit;
- Z = S - (Z + U2 + U2);
- StickyBit = (Y2 + U2) * Y1;
- Y1 = Y2 * Y1;
- StickyBit = StickyBit - Y2;
- Y1 = Y1 - Half;
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
- && ( StickyBit == Zero) && (Y1 == Half)) {
- RMult = Rounded;
- printf("Multiplication appears to round correctly.\n");
- }
- else if ((X + U2 == Zero) && (Y < Zero) && (Z + U2 == Zero)
- && (T < Zero) && (StickyBit + U2 == Zero)
- && (Y1 < Half)) {
- RMult = Chopped;
- printf("Multiplication appears to chop.\n");
- }
- else printf("* is neither chopped nor correctly rounded.\n");
- if ((RMult == Rounded) && (GMult == No)) notify("Multiplication");
- }
- else printf("* is neither chopped nor correctly rounded.\n");
- /*=============================================*/
- Milestone = 45;
- /*=============================================*/
- Y2 = One + U2;
- Y1 = One - U2;
- Z = OneAndHalf + U2 + U2;
- X = Z / Y2;
- T = OneAndHalf - U2 - U2;
- Y = (T - U2) / Y1;
- Z = (Z + U2) / Y2;
- X = X - OneAndHalf;
- Y = Y - T;
- T = T / Y1;
- Z = Z - (OneAndHalf + U2);
- T = (U2 - OneAndHalf) + T;
- if (! ((X > Zero) || (Y > Zero) || (Z > Zero) || (T > Zero))) {
- X = OneAndHalf / Y2;
- Y = OneAndHalf - U2;
- Z = OneAndHalf + U2;
- X = X - Y;
- T = OneAndHalf / Y1;
- Y = Y / Y1;
- T = T - (Z + U2);
- Y = Y - Z;
- Z = Z / Y2;
- Y1 = (Y2 + U2) / Y2;
- Z = Z - OneAndHalf;
- Y2 = Y1 - Y2;
- Y1 = (F9 - U1) / F9;
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
- && (Y2 == Zero) && (Y2 == Zero)
- && (Y1 - Half == F9 - Half )) {
- RDiv = Rounded;
- printf("Division appears to round correctly.\n");
- if (GDiv == No) notify("Division");
- }
- else if ((X < Zero) && (Y < Zero) && (Z < Zero) && (T < Zero)
- && (Y2 < Zero) && (Y1 - Half < F9 - Half)) {
- RDiv = Chopped;
- printf("Division appears to chop.\n");
- }
- }
- if (RDiv == Other) printf("/ is neither chopped nor correctly rounded.\n");
- BInvrse = One / Radix;
- TstCond (Failure, (BInvrse * Radix - Half == Half),
- "Radix * ( 1 / Radix ) differs from 1");
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part4(){
-*/
- Milestone = 50;
- /*=============================================*/
- TstCond (Failure, ((F9 + U1) - Half == Half)
- && ((BMinusU2 + U2 ) - One == Radix - One),
- "Incomplete carry-propagation in Addition");
- X = One - U1 * U1;
- Y = One + U2 * (One - U2);
- Z = F9 - Half;
- X = (X - Half) - Z;
- Y = Y - One;
- if ((X == Zero) && (Y == Zero)) {
- RAddSub = Chopped;
- printf("Add/Subtract appears to be chopped.\n");
- }
- if (GAddSub == Yes) {
- X = (Half + U2) * U2;
- Y = (Half - U2) * U2;
- X = One + X;
- Y = One + Y;
- X = (One + U2) - X;
- Y = One - Y;
- if ((X == Zero) && (Y == Zero)) {
- X = (Half + U2) * U1;
- Y = (Half - U2) * U1;
- X = One - X;
- Y = One - Y;
- X = F9 - X;
- Y = One - Y;
- if ((X == Zero) && (Y == Zero)) {
- RAddSub = Rounded;
- printf("Addition/Subtraction appears to round correctly.\n");
- if (GAddSub == No) notify("Add/Subtract");
- }
- else printf("Addition/Subtraction neither rounds nor chops.\n");
- }
- else printf("Addition/Subtraction neither rounds nor chops.\n");
- }
- else printf("Addition/Subtraction neither rounds nor chops.\n");
- S = One;
- X = One + Half * (One + Half);
- Y = (One + U2) * Half;
- Z = X - Y;
- T = Y - X;
- StickyBit = Z + T;
- if (StickyBit != Zero) {
- S = Zero;
- BadCond(Flaw, "(X - Y) + (Y - X) is non zero!\n");
- }
- StickyBit = Zero;
- if ((GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
- && (RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (FLOOR(RadixD2) == RadixD2)) {
- printf("Checking for sticky bit.\n");
- X = (Half + U1) * U2;
- Y = Half * U2;
- Z = One + Y;
- T = One + X;
- if ((Z - One <= Zero) && (T - One >= U2)) {
- Z = T + Y;
- Y = Z - X;
- if ((Z - T >= U2) && (Y - T == Zero)) {
- X = (Half + U1) * U1;
- Y = Half * U1;
- Z = One - Y;
- T = One - X;
- if ((Z - One == Zero) && (T - F9 == Zero)) {
- Z = (Half - U1) * U1;
- T = F9 - Z;
- Q = F9 - Y;
- if ((T - F9 == Zero) && (F9 - U1 - Q == Zero)) {
- Z = (One + U2) * OneAndHalf;
- T = (OneAndHalf + U2) - Z + U2;
- X = One + Half / Radix;
- Y = One + Radix * U2;
- Z = X * Y;
- if (T == Zero && X + Radix * U2 - Z == Zero) {
- if (Radix != Two) {
- X = Two + U2;
- Y = X / Two;
- if ((Y - One == Zero)) StickyBit = S;
- }
- else StickyBit = S;
- }
- }
- }
- }
- }
- }
- if (StickyBit == One) printf("Sticky bit apparently used correctly.\n");
- else printf("Sticky bit used incorrectly or not at all.\n");
- TstCond (Flaw, !(GMult == No || GDiv == No || GAddSub == No ||
- RMult == Other || RDiv == Other || RAddSub == Other),
- "lack(s) of guard digits or failure(s) to correctly round or chop\n\
-(noted above) count as one flaw in the final tally below");
- /*=============================================*/
- Milestone = 60;
- /*=============================================*/
- printf("\n");
- printf("Does Multiplication commute? ");
- printf("Testing on %d random pairs.\n", NoTrials);
- Random9 = SQRT(3.0);
- Random1 = Third;
- I = 1;
- do {
- X = Random();
- Y = Random();
- Z9 = Y * X;
- Z = X * Y;
- Z9 = Z - Z9;
- I = I + 1;
- } while ( ! ((I > NoTrials) || (Z9 != Zero)));
- if (I == NoTrials) {
- Random1 = One + Half / Three;
- Random2 = (U2 + U1) + One;
- Z = Random1 * Random2;
- Y = Random2 * Random1;
- Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
- Three) * ((U2 + U1) + One);
- }
- if (! ((I == NoTrials) || (Z9 == Zero)))
- BadCond(Defect, "X * Y == Y * X trial fails.\n");
- else printf(" No failures found in %d integer pairs.\n", NoTrials);
- /*=============================================*/
- Milestone = 70;
- /*=============================================*/
- printf("\nRunning test of square root(x).\n");
- TstCond (Failure, (Zero == SQRT(Zero))
- && (- Zero == SQRT(- Zero))
- && (One == SQRT(One)), "Square root of 0.0, -0.0 or 1.0 wrong");
- MinSqEr = Zero;
- MaxSqEr = Zero;
- J = Zero;
- X = Radix;
- OneUlp = U2;
- SqXMinX (Serious);
- X = BInvrse;
- OneUlp = BInvrse * U1;
- SqXMinX (Serious);
- X = U1;
- OneUlp = U1 * U1;
- SqXMinX (Serious);
- if (J != Zero) Pause();
- printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
- J = Zero;
- X = Two;
- Y = Radix;
- if ((Radix != One)) do {
- X = Y;
- Y = Radix * Y;
- } while ( ! ((Y - X >= NoTrials)));
- OneUlp = X * U2;
- I = 1;
- while (I < 10) {
- X = X + One;
- SqXMinX (Defect);
- if (J > Zero) break;
- I = I + 1;
- }
- printf("Test for sqrt monotonicity.\n");
- I = - 1;
- X = BMinusU2;
- Y = Radix;
- Z = Radix + Radix * U2;
- NotMonot = False;
- Monot = False;
- while ( ! (NotMonot || Monot)) {
- I = I + 1;
- X = SQRT(X);
- Q = SQRT(Y);
- Z = SQRT(Z);
- if ((X > Q) || (Q > Z)) NotMonot = True;
- else {
- Q = FLOOR(Q + Half);
- if ((I > 0) || (Radix == Q * Q)) Monot = True;
- else if (I > 0) {
- if (I > 1) Monot = True;
- else {
- Y = Y * BInvrse;
- X = Y - U1;
- Z = Y + U1;
- }
- }
- else {
- Y = Q;
- X = Y - U2;
- Z = Y + U2;
- }
- }
- }
- if (Monot) printf("sqrt has passed a test for Monotonicity.\n");
- else {
- BadCond(Defect, "");
- printf("sqrt(X) is non-monotonic for X near %.7e .\n", Y);
- }
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part5(){
-*/
- Milestone = 80;
- /*=============================================*/
- MinSqEr = MinSqEr + Half;
- MaxSqEr = MaxSqEr - Half;
- Y = (SQRT(One + U2) - One) / U2;
- SqEr = (Y - One) + U2 / Eight;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- SqEr = Y + U2 / Eight;
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- Y = ((SQRT(F9) - U2) - (One - U2)) / U1;
- SqEr = Y + U1 / Eight;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- SqEr = (Y + One) + U1 / Eight;
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- OneUlp = U2;
- X = OneUlp;
- for( Indx = 1; Indx <= 3; ++Indx) {
- Y = SQRT((X + U1 + X) + F9);
- Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;
- Z = ((U1 - X) + F9) * Half * X * X / OneUlp;
- SqEr = (Y + Half) + Z;
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- SqEr = (Y - Half) + Z;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- if (((Indx == 1) || (Indx == 3)))
- X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));
- else {
- OneUlp = U1;
- X = - OneUlp;
- }
- }
- /*=============================================*/
- Milestone = 85;
- /*=============================================*/
- SqRWrng = False;
- Anomaly = False;
- if (Radix != One) {
- printf("Testing whether sqrt is rounded or chopped.\n");
- D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));
- /* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
- X = D / Radix;
- Y = D / A1;
- if ((X != FLOOR(X)) || (Y != FLOOR(Y))) {
- Anomaly = True;
- }
- else {
- X = Zero;
- Z2 = X;
- Y = One;
- Y2 = Y;
- Z1 = Radix - One;
- FourD = Four * D;
- do {
- if (Y2 > Z2) {
- Q = Radix;
- Y1 = Y;
- do {
- X1 = FABS(Q + FLOOR(Half - Q / Y1) * Y1);
- Q = Y1;
- Y1 = X1;
- } while ( ! (X1 <= Zero));
- if (Q <= One) {
- Z2 = Y2;
- Z = Y;
- }
- }
- Y = Y + Two;
- X = X + Eight;
- Y2 = Y2 + X;
- if (Y2 >= FourD) Y2 = Y2 - FourD;
- } while ( ! (Y >= D));
- X8 = FourD - Z2;
- Q = (X8 + Z * Z) / FourD;
- X8 = X8 / Eight;
- if (Q != FLOOR(Q)) Anomaly = True;
- else {
- Break = False;
- do {
- X = Z1 * Z;
- X = X - FLOOR(X / Radix) * Radix;
- if (X == One)
- Break = True;
- else
- Z1 = Z1 - One;
- } while ( ! (Break || (Z1 <= Zero)));
- if ((Z1 <= Zero) && (! Break)) Anomaly = True;
- else {
- if (Z1 > RadixD2) Z1 = Z1 - Radix;
- do {
- NewD();
- } while ( ! (U2 * D >= F9));
- if (D * Radix - D != W - D) Anomaly = True;
- else {
- Z2 = D;
- I = 0;
- Y = D + (One + Z) * Half;
- X = D + Z + Q;
- SR3750();
- Y = D + (One - Z) * Half + D;
- X = D - Z + D;
- X = X + Q + X;
- SR3750();
- NewD();
- if (D - Z2 != W - Z2) Anomaly = True;
- else {
- Y = (D - Z2) + (Z2 + (One - Z) * Half);
- X = (D - Z2) + (Z2 - Z + Q);
- SR3750();
- Y = (One + Z) * Half;
- X = Q;
- SR3750();
- if (I == 0) Anomaly = True;
- }
- }
- }
- }
- }
- if ((I == 0) || Anomaly) {
- BadCond(Failure, "Anomalous arithmetic with Integer < ");
- printf("Radix^Precision = %.7e\n", W);
- printf(" fails test whether sqrt rounds or chops.\n");
- SqRWrng = True;
- }
- }
- if (! Anomaly) {
- if (! ((MinSqEr < Zero) || (MaxSqEr > Zero))) {
- RSqrt = Rounded;
- printf("Square root appears to be correctly rounded.\n");
- }
- else {
- if ((MaxSqEr + U2 > U2 - Half) || (MinSqEr > Half)
- || (MinSqEr + Radix < Half)) SqRWrng = True;
- else {
- RSqrt = Chopped;
- printf("Square root appears to be chopped.\n");
- }
- }
- }
- if (SqRWrng) {
- printf("Square root is neither chopped nor correctly rounded.\n");
- printf("Observed errors run from %.7e ", MinSqEr - Half);
- printf("to %.7e ulps.\n", Half + MaxSqEr);
- TstCond (Serious, MaxSqEr - MinSqEr < Radix * Radix,
- "sqrt gets too many last digits wrong");
- }
- /*=============================================*/
- Milestone = 90;
- /*=============================================*/
- Pause();
- printf("Testing powers Z^i for small Integers Z and i.\n");
- N = 0;
- /* ... test powers of zero. */
- I = 0;
- Z = -Zero;
- M = 3.0;
- Break = False;
- do {
- X = One;
- SR3980();
- if (I <= 10) {
- I = 1023;
- SR3980();
- }
- if (Z == MinusOne) Break = True;
- else {
- Z = MinusOne;
- PrintIfNPositive();
- N = 0;
- /* .. if(-1)^N is invalid, replace MinusOne by One. */
- I = - 4;
- }
- } while ( ! Break);
- PrintIfNPositive();
- N1 = N;
- N = 0;
- Z = A1;
- M = FLOOR(Two * LOG(W) / LOG(A1));
- Break = False;
- do {
- X = Z;
- I = 1;
- SR3980();
- if (Z == AInvrse) Break = True;
- else Z = AInvrse;
- } while ( ! (Break));
- /*=============================================*/
- Milestone = 100;
- /*=============================================*/
- /* Powers of Radix have been tested, */
- /* next try a few primes */
- M = NoTrials;
- Z = Three;
- do {
- X = Z;
- I = 1;
- SR3980();
- do {
- Z = Z + Two;
- } while ( Three * FLOOR(Z / Three) == Z );
- } while ( Z < Eight * Three );
- if (N > 0) {
- printf("Errors like this may invalidate financial calculations\n");
- printf("\tinvolving interest rates.\n");
- }
- PrintIfNPositive();
- N += N1;
- if (N == 0) printf("... no discrepancis found.\n");
- if (N > 0) Pause();
- else printf("\n");
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part6(){
-*/
- Milestone = 110;
- /*=============================================*/
- printf("Seeking Underflow thresholds UfThold and E0.\n");
- D = U1;
- if (Precision != FLOOR(Precision)) {
- D = BInvrse;
- X = Precision;
- do {
- D = D * BInvrse;
- X = X - One;
- } while ( X > Zero);
- }
- Y = One;
- Z = D;
- /* ... D is power of 1/Radix < 1. */
- do {
- C = Y;
- Y = Z;
- Z = Y * Y;
- VV = Z;
- } while ((Y > Z) && (VV + VV > VV));
- Y = C;
- Z = Y * D;
- do {
- C = Y;
- Y = Z;
- Z = Y * D;
- VV = Z;
- } while ((Y > Z) && (VV + VV > VV));
- if (Radix < Two) HInvrse = Two;
- else HInvrse = Radix;
- H = One / HInvrse;
- /* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
- CInvrse = One / C;
- E0 = C;
- Z = E0 * H;
- /* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
- do {
- Y = E0;
- E0 = Z;
- Z = E0 * H;
- VV = Z;
- } while ((E0 > VV) && (VV + VV > VV));
- UfThold = E0;
- E1 = Zero;
- Q = Zero;
- E9 = U2;
- S = One + E9;
- D = C * S;
- if (D <= C) {
- E9 = Radix * U2;
- S = One + E9;
- D = C * S;
- if (D <= C) {
- BadCond(Failure, "multiplication gets too many last digits wrong.\n");
- Underflow = E0;
- Y1 = Zero;
- PseudoZero = Z;
- Pause();
- }
- }
- else {
- Underflow = D;
- PseudoZero = Underflow * H;
- UfThold = Zero;
- do {
- Y1 = Underflow;
- Underflow = PseudoZero;
- if (E1 + E1 <= E1) {
- Y2 = Underflow * HInvrse;
- E1 = FABS(Y1 - Y2);
- Q = Y1;
- if ((UfThold == Zero) && (Y1 != Y2)) UfThold = Y1;
- }
- PseudoZero = PseudoZero * H;
- VV = PseudoZero;
- } while ((Underflow > VV)
- && (VV + VV > VV));
- }
- /* Comment line 4530 .. 4560 */
- if (PseudoZero != Zero) {
- printf("\n");
- Z = PseudoZero;
- /* ... Test PseudoZero for "phoney- zero" violates */
- /* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
- ... */
- if (PseudoZero <= Zero) {
- BadCond(Failure, "Positive expressions can underflow to an\n");
- printf("allegedly negative value\n");
- printf("PseudoZero that prints out as: %g .\n", PseudoZero);
- X = - PseudoZero;
- if (X <= Zero) {
- printf("But -PseudoZero, which should be\n");
- printf("positive, isn't; it prints out as %g .\n", X);
- }
- }
- else {
- BadCond(Flaw, "Underflow can stick at an allegedly positive\n");
- printf("value PseudoZero that prints out as %g .\n", PseudoZero);
- }
- TstPtUf();
- }
- /*=============================================*/
- Milestone = 120;
- /*=============================================*/
- if (CInvrse * Y > CInvrse * Y1) {
- S = H * S;
- E0 = Underflow;
- }
- if (! ((E1 == Zero) || (E1 == E0))) {
- BadCond(Defect, "");
- if (E1 < E0) {
- printf("Products underflow at a higher");
- printf(" threshold than differences.\n");
- if (PseudoZero == Zero)
- E0 = E1;
- }
- else {
- printf("Difference underflows at a higher");
- printf(" threshold than products.\n");
- }
- }
- printf("Smallest strictly positive number found is E0 = %g .\n", E0);
- Z = E0;
- TstPtUf();
- Underflow = E0;
- if (N == 1) Underflow = Y;
- I = 4;
- if (E1 == Zero) I = 3;
- if (UfThold == Zero) I = I - 2;
- UfNGrad = True;
- switch (I) {
- case 1:
- UfThold = Underflow;
- if ((CInvrse * Q) != ((CInvrse * Y) * S)) {
- UfThold = Y;
- BadCond(Failure, "Either accuracy deteriorates as numbers\n");
- printf("approach a threshold = %.17e\n", UfThold);;
- printf(" coming down from %.17e\n", C);
- printf(" or else multiplication gets too many last digits wrong.\n");
- }
- Pause();
- break;
-
- case 2:
- BadCond(Failure, "Underflow confuses Comparison which alleges that\n");
- printf("Q == Y while denying that |Q - Y| == 0; these values\n");
- printf("print out as Q = %.17e, Y = %.17e .\n", Q, Y);
- printf ("|Q - Y| = %.17e .\n" , FABS(Q - Y2));
- UfThold = Q;
- break;
-
- case 3:
- X = X;
- break;
-
- case 4:
- if ((Q == UfThold) && (E1 == E0)
- && (FABS( UfThold - E1 / E9) <= E1)) {
- UfNGrad = False;
- printf("Underflow is gradual; it incurs Absolute Error =\n");
- printf("(roundoff in UfThold) < E0.\n");
- Y = E0 * CInvrse;
- Y = Y * (OneAndHalf + U2);
- X = CInvrse * (One + U2);
- Y = Y / X;
- IEEE = (Y == E0);
- }
- }
- if (UfNGrad) {
- printf("\n");
- R = SQRT(Underflow / UfThold);
- if (R <= H) {
- Z = R * UfThold;
- X = Z * (One + R * H * (One + H));
- }
- else {
- Z = UfThold;
- X = Z * (One + H * H * (One + H));
- }
- if (! ((X == Z) || (X - Z != Zero))) {
- BadCond(Flaw, "");
- printf("X = %.17e\n\tis not equal to Z = %.17e .\n", X, Z);
- Z9 = X - Z;
- printf("yet X - Z yields %.17e .\n", Z9);
- printf(" Should this NOT signal Underflow, ");
- printf("this is a SERIOUS DEFECT\nthat causes ");
- printf("confusion when innocent statements like\n");;
- printf(" if (X == Z) ... else");
- printf(" ... (f(X) - f(Z)) / (X - Z) ...\n");
- printf("encounter Division by Zero although actually\n");
- printf("X / Z = 1 + %g .\n", (X / Z - Half) - Half);
- }
- }
- printf("The Underflow threshold is %.17e, %s\n", UfThold,
- " below which");
- printf("calculation may suffer larger Relative error than ");
- printf("merely roundoff.\n");
- Y2 = U1 * U1;
- Y = Y2 * Y2;
- Y2 = Y * U1;
- if (Y2 <= UfThold) {
- if (Y > E0) {
- BadCond(Defect, "");
- I = 5;
- }
- else {
- BadCond(Serious, "");
- I = 4;
- }
- printf("Range is too narrow; U1^%d Underflows.\n", I);
- }
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part7(){
-*/
- Milestone = 130;
- /*=============================================*/
- Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;
- Y2 = Y + Y;
- printf("Since underflow occurs below the threshold\n");
- printf("UfThold = (%.17e) ^ (%.17e)\nonly underflow ", HInvrse, Y);
- printf("should afflict the expression\n\t(%.17e) ^ (%.17e);\n", HInvrse, Y);
- V9 = POW(HInvrse, Y2);
- printf("actually calculating yields: %.17e .\n", V9);
- if (! ((V9 >= Zero) && (V9 <= (Radix + Radix + E9) * UfThold))) {
- BadCond(Serious, "this is not between 0 and underflow\n");
- printf(" threshold = %.17e .\n", UfThold);
- }
- else if (! (V9 > UfThold * (One + E9)))
- printf("This computed value is O.K.\n");
- else {
- BadCond(Defect, "this is not between 0 and underflow\n");
- printf(" threshold = %.17e .\n", UfThold);
- }
- /*=============================================*/
- Milestone = 140;
- /*=============================================*/
- printf("\n");
- /* ...calculate Exp2 == exp(2) == 7.389056099... */
- X = Zero;
- I = 2;
- Y = Two * Three;
- Q = Zero;
- N = 0;
- do {
- Z = X;
- I = I + 1;
- Y = Y / (I + I);
- R = Y + Q;
- X = Z + R;
- Q = (Z - X) + R;
- } while(X > Z);
- Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);
- X = Z * Z;
- Exp2 = X * X;
- X = F9;
- Y = X - U1;
- printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = %.17e as X -> 1.\n",
- Exp2);
- for(I = 1;;) {
- Z = X - BInvrse;
- Z = (X + One) / (Z - (One - BInvrse));
- Q = POW(X, Z) - Exp2;
- if (FABS(Q) > TwoForty * U2) {
- N = 1;
- V9 = (X - BInvrse) - (One - BInvrse);
- BadCond(Defect, "Calculated");
- printf(" %.17e for\n", POW(X,Z));
- printf("\t(1 + (%.17e) ^ (%.17e);\n", V9, Z);
- printf("\tdiffers from correct value by %.17e .\n", Q);
- printf("\tThis much error may spoil financial\n");
- printf("\tcalculations involving tiny interest rates.\n");
- break;
- }
- else {
- Z = (Y - X) * Two + Y;
- X = Y;
- Y = Z;
- Z = One + (X - F9)*(X - F9);
- if (Z > One && I < NoTrials) I++;
- else {
- if (X > One) {
- if (N == 0)
- printf("Accuracy seems adequate.\n");
- break;
- }
- else {
- X = One + U2;
- Y = U2 + U2;
- Y += X;
- I = 1;
- }
- }
- }
- }
- /*=============================================*/
- Milestone = 150;
- /*=============================================*/
- printf("Testing powers Z^Q at four nearly extreme values.\n");
- N = 0;
- Z = A1;
- Q = FLOOR(Half - LOG(C) / LOG(A1));
- Break = False;
- do {
- X = CInvrse;
- Y = POW(Z, Q);
- IsYeqX();
- Q = - Q;
- X = C;
- Y = POW(Z, Q);
- IsYeqX();
- if (Z < One) Break = True;
- else Z = AInvrse;
- } while ( ! (Break));
- PrintIfNPositive();
- if (N == 0) printf(" ... no discrepancies found.\n");
- printf("\n");
-
- /*=============================================*/
- Milestone = 160;
- /*=============================================*/
- Pause();
- printf("Searching for Overflow threshold:\n");
- printf("This may generate an error.\n");
- sigsave = sigfpe;
- I = 0;
- Y = - CInvrse;
- V9 = HInvrse * Y;
- if (setjmp(ovfl_buf)) goto overflow;
- do {
- V = Y;
- Y = V9;
- V9 = HInvrse * Y;
- } while(V9 < Y);
- I = 1;
-overflow:
- Z = V9;
- printf("Can `Z = -Y' overflow?\n");
- printf("Trying it on Y = %.17e .\n", Y);
- V9 = - Y;
- V0 = V9;
- if (V - Y == V + V0) printf("Seems O.K.\n");
- else {
- printf("finds a ");
- BadCond(Flaw, "-(-Y) differs from Y.\n");
- }
- if (Z != Y) {
- BadCond(Serious, "");
- printf("overflow past %.17e\n\tshrinks to %.17e .\n", Y, Z);
- }
- Y = V * (HInvrse * U2 - HInvrse);
- Z = Y + ((One - HInvrse) * U2) * V;
- if (Z < V0) Y = Z;
- if (Y < V0) V = Y;
- if (V0 - V < V0) V = V0;
- printf("Overflow threshold is V = %.17e .\n", V);
- if (I) printf("Overflow saturates at V0 = %.17e .\n", V0);
- else printf("There is no saturation value because \
-the system traps on overflow.\n");
- V9 = V * One;
- printf("No Overflow should be signaled for V * 1 = %.17e\n", V9);
- V9 = V / One;
- printf(" nor for V / 1 = %.17e .\n", V9);
- printf("Any overflow signal separating this * from the one\n");
- printf("above is a DEFECT.\n");
- /*=============================================*/
- Milestone = 170;
- /*=============================================*/
- if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
- BadCond(Failure, "Comparisons involving ");
- printf("+-%g, +-%g\nand +-%g are confused by Overflow.",
- V, V0, UfThold);
- }
- /*=============================================*/
- Milestone = 175;
- /*=============================================*/
- printf("\n");
- for(Indx = 1; Indx <= 3; ++Indx) {
- switch (Indx) {
- case 1: Z = UfThold; break;
- case 2: Z = E0; break;
- case 3: Z = PseudoZero; break;
- }
- if (Z != Zero) {
- V9 = SQRT(Z);
- Y = V9 * V9;
- if (Y / (One - Radix * E9) < Z
- || Y > (One + Radix + E9) * Z) {
- if (V9 > U1) BadCond(Serious, "");
- else BadCond(Defect, "");
- printf("Comparison alleges that what prints as Z = %.17e\n", Z);
- printf(" is too far from sqrt(Z) ^ 2 = %.17e .\n", Y);
- }
- }
- }
- /*=============================================*/
- Milestone = 180;
- /*=============================================*/
- for(Indx = 1; Indx <= 2; ++Indx) {
- if (Indx == 1) Z = V;
- else Z = V0;
- V9 = SQRT(Z);
- X = (One - Radix * E9) * V9;
- V9 = V9 * X;
- if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
- Y = V9;
- if (X < W) BadCond(Serious, "");
- else BadCond(Defect, "");
- printf("Comparison alleges that Z = %17e\n", Z);
- printf(" is too far from sqrt(Z) ^ 2 (%.17e) .\n", Y);
- }
- }
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part8(){
-*/
- Milestone = 190;
- /*=============================================*/
- Pause();
- X = UfThold * V;
- Y = Radix * Radix;
- if (X*Y < One || X > Y) {
- if (X * Y < U1 || X > Y/U1) BadCond(Defect, "Badly");
- else BadCond(Flaw, "");
-
- printf(" unbalanced range; UfThold * V = %.17e\n\t%s\n",
- X, "is too far from 1.\n");
- }
- /*=============================================*/
- Milestone = 200;
- /*=============================================*/
- for (Indx = 1; Indx <= 5; ++Indx) {
- X = F9;
- switch (Indx) {
- case 2: X = One + U2; break;
- case 3: X = V; break;
- case 4: X = UfThold; break;
- case 5: X = Radix;
- }
- Y = X;
- sigsave = sigfpe;
- if (setjmp(ovfl_buf))
- printf(" X / X traps when X = %g\n", X);
- else {
- V9 = (Y / X - Half) - Half;
- if (V9 == Zero) continue;
- if (V9 == - U1 && Indx < 5) BadCond(Flaw, "");
- else BadCond(Serious, "");
- printf(" X / X differs from 1 when X = %.17e\n", X);
- printf(" instead, X / X - 1/2 - 1/2 = %.17e .\n", V9);
- }
- }
- /*=============================================*/
- Milestone = 210;
- /*=============================================*/
- MyZero = Zero;
- printf("\n");
- printf("What message and/or values does Division by Zero produce?\n") ;
-#ifndef NOPAUSE
- printf("This can interupt your program. You can ");
- printf("skip this part if you wish.\n");
- printf("Do you wish to compute 1 / 0? ");
- fflush(stdout);
- read (KEYBOARD, ch, 8);
- if ((ch[0] == 'Y') || (ch[0] == 'y')) {
-#endif
- sigsave = sigfpe;
- printf(" Trying to compute 1 / 0 produces ...");
- if (!setjmp(ovfl_buf)) printf(" %.7e .\n", One / MyZero);
-#ifndef NOPAUSE
- }
- else printf("O.K.\n");
- printf("\nDo you wish to compute 0 / 0? ");
- fflush(stdout);
- read (KEYBOARD, ch, 80);
- if ((ch[0] == 'Y') || (ch[0] == 'y')) {
-#endif
- sigsave = sigfpe;
- printf("\n Trying to compute 0 / 0 produces ...");
- if (!setjmp(ovfl_buf)) printf(" %.7e .\n", Zero / MyZero);
-#ifndef NOPAUSE
- }
- else printf("O.K.\n");
-#endif
- /*=============================================*/
- Milestone = 220;
- /*=============================================*/
- Pause();
- printf("\n");
- {
- static char *msg[] = {
- "FAILUREs encountered =",
- "SERIOUS DEFECTs discovered =",
- "DEFECTs discovered =",
- "FLAWs discovered =" };
- int i;
- for(i = 0; i < 4; i++) if (ErrCnt[i])
- printf("The number of %-29s %d.\n",
- msg[i], ErrCnt[i]);
- }
- printf("\n");
- if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
- + ErrCnt[Flaw]) > 0) {
- if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
- Defect] == 0) && (ErrCnt[Flaw] > 0)) {
- printf("The arithmetic diagnosed seems ");
- printf("satisfactory though flawed.\n");
- }
- if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
- && ( ErrCnt[Defect] > 0)) {
- printf("The arithmetic diagnosed may be acceptable\n");
- printf("despite inconvenient Defects.\n");
- }
- if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
- printf("The arithmetic diagnosed has ");
- printf("unacceptable serious defects.\n");
- }
- if (ErrCnt[Failure] > 0) {
- printf("Fatal FAILURE may have spoiled this");
- printf(" program's subsequent diagnoses.\n");
- }
- }
- else {
- printf("No failures, defects nor flaws have been discovered.\n");
- if (! ((RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (RSqrt == Rounded)))
- printf("The arithmetic diagnosed seems satisfactory.\n");
- else {
- if (StickyBit >= One &&
- (Radix - Two) * (Radix - Nine - One) == Zero) {
- printf("Rounding appears to conform to ");
- printf("the proposed IEEE standard P");
- if ((Radix == Two) &&
- ((Precision - Four * Three * Two) *
- ( Precision - TwentySeven -
- TwentySeven + One) == Zero))
- printf("754");
- else printf("854");
- if (IEEE) printf(".\n");
- else {
- printf(",\nexcept for possibly Double Rounding");
- printf(" during Gradual Underflow.\n");
- }
- }
- printf("The arithmetic diagnosed appears to be excellent!\n");
- }
- }
- if (fpecount)
- printf("\nA total of %d floating point exceptions were registered.\n",
- fpecount);
- printf("END OF TEST.\n");
- }
-
-/*SPLIT subs.c
-#include "paranoia.h"
-*/
-
-/* Sign */
-
-FLOAT Sign (X)
-FLOAT X;
-{ return X >= 0. ? 1.0 : -1.0; }
-
-/* Pause */
-
-Pause()
-{
- char ch[8];
-
-#ifndef NOPAUSE
- printf("\nTo continue, press RETURN");
- fflush(stdout);
- read(KEYBOARD, ch, 8);
-#endif
- printf("\nDiagnosis resumes after milestone Number %d", Milestone);
- printf(" Page: %d\n\n", PageNo);
- ++Milestone;
- ++PageNo;
- }
-
- /* TstCond */
-
-TstCond (K, Valid, T)
-int K, Valid;
-char *T;
-{ if (! Valid) { BadCond(K,T); printf(".\n"); } }
-
-BadCond(K, T)
-int K;
-char *T;
-{
- static char *msg[] = { "FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW" };
-
- ErrCnt [K] = ErrCnt [K] + 1;
- printf("%s: %s", msg[K], T);
- }
-
-/* Random */
-/* Random computes
- X = (Random1 + Random9)^5
- Random1 = X - FLOOR(X) + 0.000005 * X;
- and returns the new value of Random1
-*/
-
-FLOAT Random()
-{
- FLOAT X, Y;
-
- X = Random1 + Random9;
- Y = X * X;
- Y = Y * Y;
- X = X * Y;
- Y = X - FLOOR(X);
- Random1 = Y + X * 0.000005;
- return(Random1);
- }
-
-/* SqXMinX */
-
-SqXMinX (ErrKind)
-int ErrKind;
-{
- FLOAT XA, XB;
-
- XB = X * BInvrse;
- XA = X - XB;
- SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;
- if (SqEr != Zero) {
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- J = J + 1.0;
- BadCond(ErrKind, "\n");
- printf("sqrt( %.17e) - %.17e = %.17e\n", X * X, X, OneUlp * SqEr);
- printf("\tinstead of correct value 0 .\n");
- }
- }
-
-/* NewD */
-
-NewD()
-{
- X = Z1 * Q;
- X = FLOOR(Half - X / Radix) * Radix + X;
- Q = (Q - X * Z) / Radix + X * X * (D / Radix);
- Z = Z - Two * X * D;
- if (Z <= Zero) {
- Z = - Z;
- Z1 = - Z1;
- }
- D = Radix * D;
- }
-
-/* SR3750 */
-
-SR3750()
-{
- if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {
- I = I + 1;
- X2 = SQRT(X * D);
- Y2 = (X2 - Z2) - (Y - Z2);
- X2 = X8 / (Y - Half);
- X2 = X2 - Half * X2 * X2;
- SqEr = (Y2 + Half) + (Half - X2);
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- SqEr = Y2 - X2;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- }
- }
-
-/* IsYeqX */
-
-IsYeqX()
-{
- if (Y != X) {
- if (N <= 0) {
- if (Z == Zero && Q <= Zero)
- printf("WARNING: computing\n");
- else BadCond(Defect, "computing\n");
- printf("\t(%.17e) ^ (%.17e)\n", Z, Q);
- printf("\tyielded %.17e;\n", Y);
- printf("\twhich compared unequal to correct %.17e ;\n",
- X);
- printf("\t\tthey differ by %.17e .\n", Y - X);
- }
- N = N + 1; /* ... count discrepancies. */
- }
- }
-
-/* SR3980 */
-
-SR3980()
-{
- do {
- Q = (FLOAT) I;
- Y = POW(Z, Q);
- IsYeqX();
- if (++I > M) break;
- X = Z * X;
- } while ( X < W );
- }
-
-/* PrintIfNPositive */
-
-PrintIfNPositive()
-{
- if (N > 0) printf("Similar discrepancies have occurred %d times.\n", N);
- }
-
-/* TstPtUf */
-
-TstPtUf()
-{
- N = 0;
- if (Z != Zero) {
- printf("Since comparison denies Z = 0, evaluating ");
- printf("(Z + Z) / Z should be safe.\n");
- sigsave = sigfpe;
- if (setjmp(ovfl_buf)) goto very_serious;
- Q9 = (Z + Z) / Z;
- printf("What the machine gets for (Z + Z) / Z is %.17e .\n",
- Q9);
- if (FABS(Q9 - Two) < Radix * U2) {
- printf("This is O.K., provided Over/Underflow");
- printf(" has NOT just been signaled.\n");
- }
- else {
- if ((Q9 < One) || (Q9 > Two)) {
-very_serious:
- N = 1;
- ErrCnt [Serious] = ErrCnt [Serious] + 1;
- printf("This is a VERY SERIOUS DEFECT!\n");
- }
- else {
- N = 1;
- ErrCnt [Defect] = ErrCnt [Defect] + 1;
- printf("This is a DEFECT!\n");
- }
- }
- V9 = Z * One;
- Random1 = V9;
- V9 = One * Z;
- Random2 = V9;
- V9 = Z / One;
- if ((Z == Random1) && (Z == Random2) && (Z == V9)) {
- if (N > 0) Pause();
- }
- else {
- N = 1;
- BadCond(Defect, "What prints as Z = ");
- printf("%.17e\n\tcompares different from ", Z);
- if (Z != Random1) printf("Z * 1 = %.17e ", Random1);
- if (! ((Z == Random2)
- || (Random2 == Random1)))
- printf("1 * Z == %g\n", Random2);
- if (! (Z == V9)) printf("Z / 1 = %.17e\n", V9);
- if (Random2 != Random1) {
- ErrCnt [Defect] = ErrCnt [Defect] + 1;
- BadCond(Defect, "Multiplication does not commute!\n");
- printf("\tComparison alleges that 1 * Z = %.17e\n",
- Random2);
- printf("\tdiffers from Z * 1 = %.17e\n", Random1);
- }
- Pause();
- }
- }
- }
-
-notify(s)
-char *s;
-{
- printf("%s test appears to be inconsistent...\n", s);
- printf(" PLEASE NOTIFY KARPINKSI!\n");
- }
-
-/*SPLIT msgs.c */
-
-/* Instructions */
-
-msglist(s)
-char **s;
-{ while(*s) printf("%s\n", *s++); }
-
-Instructions()
-{
- static char *instr[] = {
- "Lest this program stop prematurely, i.e. before displaying\n",
- " `END OF TEST',\n",
- "try to persuade the computer NOT to terminate execution when an",
- "error like Over/Underflow or Division by Zero occurs, but rather",
- "to persevere with a surrogate value after, perhaps, displaying some",
- "warning. If persuasion avails naught, don't despair but run this",
- "program anyway to see how many milestones it passes, and then",
- "amend it to make further progress.\n",
- "Answer questions with Y, y, N or n (unless otherwise indicated).\n",
- 0};
-
- msglist(instr);
- }
-
-/* Heading */
-
-Heading()
-{
- static char *head[] = {
- "Users are invited to help debug and augment this program so it will",
- "cope with unanticipated and newly uncovered arithmetic pathologies.\n",
- "Please send suggestions and interesting results to",
- "\tRichard Karpinski",
- "\tComputer Center U-76",
- "\tUniversity of California",
- "\tSan Francisco, CA 94143-0704, USA\n",
- "In doing so, please include the following information:",
-#ifdef Single
- "\tPrecision:\tsingle;",
-#else
- "\tPrecision:\tdouble;",
-#endif
- "\tVersion:\t27 January 1986;",
- "\tComputer:\n",
- "\tCompiler:\n",
- "\tOptimization level:\n",
- "\tOther relevant compiler options:",
- 0};
-
- msglist(head);
- }
-
-/* Characteristics */
-
-Characteristics()
-{
- static char *chars[] = {
- "Running this program should reveal these characteristics:",
- " Radix = 1, 2, 4, 8, 10, 16, 100, 256 ...",
- " Precision = number of significant digits carried.",
- " U2 = Radix/Radix^Precision = One Ulp",
- "\t(OneUlpnit in the Last Place) of 1.000xxx .",
- " U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 .",
- " Adequacy of guard digits for Mult., Div. and Subt.",
- " Whether arithmetic is chopped, correctly rounded, or something else",
- "\tfor Mult., Div., Add/Subt. and Sqrt.",
- " Whether a Sticky Bit used correctly for rounding.",
- " UnderflowThreshold = an underflow threshold.",
- " E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy.",
- " V = an overflow threshold, roughly.",
- " V0 tells, roughly, whether Infinity is represented.",
- " Comparisions are checked for consistency with subtraction",
- "\tand for contamination with pseudo-zeros.",
- " Sqrt is tested. Y^X is not tested.",
- " Extra-precise subexpressions are revealed but NOT YET tested.",
- " Decimal-Binary conversion is NOT YET tested for accuracy.",
- 0};
-
- msglist(chars);
- }
-
-History()
-
-{ /* History */
- /* Converted from Brian Wichmann's Pascal version to C by Thos Sumner,
- with further massaging by David M. Gay. */
-
- static char *hist[] = {
- "The program attempts to discriminate among",
- " FLAWs, like lack of a sticky bit,",
- " Serious DEFECTs, like lack of a guard digit, and",
- " FAILUREs, like 2+2 == 5 .",
- "Failures may confound subsequent diagnoses.\n",
- "The diagnostic capabilities of this program go beyond an earlier",
- "program called `MACHAR', which can be found at the end of the",
- "book `Software Manual for the Elementary Functions' (1980) by",
- "W. J. Cody and W. Waite. Although both programs try to discover",
- "the Radix, Precision and range (over/underflow thresholds)",
- "of the arithmetic, this program tries to cope with a wider variety",
- "of pathologies, and to say how well the arithmetic is implemented.",
- "\nThe program is based upon a conventional radix representation for",
- "floating-point numbers, but also allows logarithmic encoding",
- "as used by certain early WANG machines.\n",
- "BASIC version of this program (C) 1983 by Prof. W. M. Kahan;",
- "see source comments for more history.",
- 0};
-
- msglist(hist);
- }
+++ /dev/null
-/* pdtr.c
- *
- * Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * double m, y, pdtr();
- *
- * y = pdtr( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the first k terms of the Poisson
- * distribution:
- *
- * k j
- * -- -m m
- * > e --
- * -- j!
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the relation
- *
- * y = pdtr( k, m ) = igamc( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- */
-\f/* pdtrc()
- *
- * Complemented poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * double m, y, pdtrc();
- *
- * y = pdtrc( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the Poisson
- * distribution:
- *
- * inf. j
- * -- -m m
- * > e --
- * -- j!
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the formula
- *
- * y = pdtrc( k, m ) = igam( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam.c.
- *
- */
-\f/* pdtri()
- *
- * Inverse Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * double m, y, pdtr();
- *
- * m = pdtri( k, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Poisson variable x such that the integral
- * from 0 to x of the Poisson density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * m = igami( k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pdtri domain y < 0 or y >= 1 0.0
- * k < 0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double igam ( double, double );
-extern double igamc ( double, double );
-extern double igami ( double, double );
-#else
-double igam(), igamc(), igami();
-#endif
-
-double pdtrc( k, m )
-int k;
-double m;
-{
-double v;
-
-if( (k < 0) || (m <= 0.0) )
- {
- mtherr( "pdtrc", DOMAIN );
- return( 0.0 );
- }
-v = k+1;
-return( igam( v, m ) );
-}
-
-
-
-double pdtr( k, m )
-int k;
-double m;
-{
-double v;
-
-if( (k < 0) || (m <= 0.0) )
- {
- mtherr( "pdtr", DOMAIN );
- return( 0.0 );
- }
-v = k+1;
-return( igamc( v, m ) );
-}
-
-
-double pdtri( k, y )
-int k;
-double y;
-{
-double v;
-
-if( (k < 0) || (y < 0.0) || (y >= 1.0) )
- {
- mtherr( "pdtri", DOMAIN );
- return( 0.0 );
- }
-v = k+1;
-v = igami( v, y );
-return( v );
-}
+++ /dev/null
-/* planck.c
- *
- * Integral of Planck's black body radiation formula
- *
- *
- *
- * SYNOPSIS:
- *
- * double lambda, T, y, plancki();
- *
- * y = plancki( lambda, T );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the definite integral, from wavelength 0 to lambda,
- * of Planck's radiation formula
- * -5
- * c1 lambda
- * E = ------------------
- * c2/(lambda T)
- * e - 1
- *
- * Physical constants c1 = 3.7417749e-16 and c2 = 0.01438769 are built in
- * to the function program. They are scaled to provide a result
- * in watts per square meter. Argument T represents temperature in degrees
- * Kelvin; lambda is wavelength in meters.
- *
- * The integral is expressed in closed form, in terms of polylogarithms
- * (see polylog.c).
- *
- * The total area under the curve is
- * (-1/8) (42 zeta(4) - 12 pi^2 zeta(2) + pi^4 ) c1 (T/c2)^4
- * = (pi^4 / 15) c1 (T/c2)^4
- * = 5.6705032e-8 T^4
- * where sigma = 5.6705032e-8 W m^2 K^-4 is the Stefan-Boltzmann constant.
- *
- *
- * ACCURACY:
- *
- * The left tail of the function experiences some relative error
- * amplification in computing the dominant term exp(-c2/(lambda T)).
- * For the right-hand tail see planckc, below.
- *
- * Relative error.
- * The domain refers to lambda T / c2.
- * arithmetic domain # trials peak rms
- * IEEE 0.1, 10 50000 7.1e-15 5.4e-16
- *
- */
-
-
-/*
-Cephes Math Library Release 2.8: July, 1999
-Copyright 1999 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double polylog (int, double);
-extern double exp (double);
-extern double log1p (double); /* log(1+x) */
-extern double expm1 (double); /* exp(x) - 1 */
-double planckc(double, double);
-double plancki(double, double);
-#else
-double polylog(), exp(), log1p(), expm1();
-double planckc(), plancki();
-#endif
-
-/* NIST value (1999): 2 pi h c^2 = 3.741 7749(22) \81× 10-16 W m2 */
-double planck_c1 = 3.7417749e-16;
-/* NIST value (1999): h c / k = 0.014 387 69 m K */
-double planck_c2 = 0.01438769;
-
-
-double
-plancki(w, T)
- double w, T;
-{
- double b, h, y, bw;
-
- b = T / planck_c2;
- bw = b * w;
-
- if (bw > 0.59375)
- {
- y = b * b;
- h = y * y;
- /* Right tail. */
- y = planckc (w, T);
- /* pi^4 / 15 */
- y = 6.493939402266829149096 * planck_c1 * h - y;
- return y;
- }
-
- h = exp(-planck_c2/(w*T));
- y = 6. * polylog (4, h) * bw;
- y = (y + 6. * polylog (3, h)) * bw;
- y = (y + 3. * polylog (2, h)) * bw;
- y = (y - log1p (-h)) * bw;
- h = w * w;
- h = h * h;
- y = y * (planck_c1 / h);
- return y;
-}
-
-/* planckc
- *
- * Complemented Planck radiation integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double lambda, T, y, planckc();
- *
- * y = planckc( lambda, T );
- *
- *
- *
- * DESCRIPTION:
- *
- * Integral from w to infinity (area under right hand tail)
- * of Planck's radiation formula.
- *
- * The program for large lambda uses an asymptotic series in inverse
- * powers of the wavelength.
- *
- * ACCURACY:
- *
- * Relative error.
- * The domain refers to lambda T / c2.
- * arithmetic domain # trials peak rms
- * IEEE 0.6, 10 50000 1.1e-15 2.2e-16
- *
- */
-
-double
-planckc (w, T)
- double w;
- double T;
-{
- double b, d, p, u, y;
-
- b = T / planck_c2;
- d = b*w;
- if (d <= 0.59375)
- {
- y = 6.493939402266829149096 * planck_c1 * b*b*b*b;
- return (y - plancki(w,T));
- }
- u = 1.0/d;
- p = u * u;
-#if 0
- y = 236364091.*p/365866013534056632601804800000.;
- y = (y - 15458917./475677107995483570176000000.)*p;
- y = (y + 174611./123104841613737984000000.)*p;
- y = (y - 43867./643745871363538944000.)*p;
- y = ((y + 3617./1081289781411840000.)*p - 1./5928123801600.)*p;
- y = ((y + 691./78460462080000.)*p - 1./2075673600.)*p;
- y = ((((y + 1./35481600.)*p - 1.0/544320.)*p + 1.0/6720.)*p - 1./40.)*p;
- y = y + log(d * expm1(u));
- y = y - 5.*u/8. + 1./3.;
-#else
- y = -236364091.*p/45733251691757079075225600000.;
- y = (y + 77683./352527500984795136000000.)*p;
- y = (y - 174611./18465726242060697600000.)*p;
- y = (y + 43867./107290978560589824000.)*p;
- y = ((y - 3617./202741834014720000.)*p + 1./1270312243200.)*p;
- y = ((y - 691./19615115520000.)*p + 1./622702080.)*p;
- y = ((((y - 1./13305600.)*p + 1./272160.)*p - 1./5040.)*p + 1./60.)*p;
- y = y - 0.125*u + 1./3.;
-#endif
- y = y * planck_c1 * b / (w*w*w);
- return y;
-}
-
-
-/* planckd
- *
- * Planck's black body radiation formula
- *
- *
- *
- * SYNOPSIS:
- *
- * double lambda, T, y, planckd();
- *
- * y = planckd( lambda, T );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates Planck's radiation formula
- * -5
- * c1 lambda
- * E = ------------------
- * c2/(lambda T)
- * e - 1
- *
- */
-
-double
-planckd(w, T)
- double w, T;
-{
- return (planck_c2 / ((w*w*w*w*w) * (exp(planck_c2/(w*T)) - 1.0)));
-}
-
-
-/* Wavelength, w, of maximum radiation at given temperature T.
- c2/wT = constant
- Wein displacement law.
- */
-double
-planckw(T)
- double T;
-{
- return (planck_c2 / (4.96511423174427630 * T));
-}
+++ /dev/null
-/* polevl.c
- * p1evl.c
- *
- * Evaluate polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * double x, y, coef[N+1], polevl[];
- *
- * y = polevl( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates polynomial of degree N:
- *
- * 2 N
- * y = C + C x + C x +...+ C x
- * 0 1 2 N
- *
- * Coefficients are stored in reverse order:
- *
- * coef[0] = C , ..., coef[N] = C .
- * N 0
- *
- * The function p1evl() assumes that coef[N] = 1.0 and is
- * omitted from the array. Its calling arguments are
- * otherwise the same as polevl().
- *
- *
- * SPEED:
- *
- * In the interest of speed, there are no checks for out
- * of bounds arithmetic. This routine is used by most of
- * the functions in the library. Depending on available
- * equipment features, the user may wish to rewrite the
- * program in microcode or assembly language.
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-double polevl( x, coef, N )
-double x;
-double coef[];
-int N;
-{
-double ans;
-int i;
-double *p;
-
-p = coef;
-ans = *p++;
-i = N;
-
-do
- ans = ans * x + *p++;
-while( --i );
-
-return( ans );
-}
-
-/* p1evl() */
-/* N
- * Evaluate polynomial when coefficient of x is 1.0.
- * Otherwise same as polevl.
- */
-
-double p1evl( x, coef, N )
-double x;
-double coef[];
-int N;
-{
-double ans;
-double *p;
-int i;
-
-p = coef;
-ans = x + *p++;
-i = N-1;
-
-do
- ans = ans * x + *p++;
-while( --i );
-
-return( ans );
-}
+++ /dev/null
-
-/* Square root, sine, cosine, and arctangent of polynomial.
- * See polyn.c for data structures and discussion.
- */
-
-#include <stdio.h>
-#include <math.h>
-#ifdef ANSIPROT
-extern double atan2 ( double, double );
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern void polclr ( double *a, int n );
-extern void polmov ( double *a, int na, double *b );
-extern void polmul ( double a[], int na, double b[], int nb, double c[] );
-extern void poladd ( double a[], int na, double b[], int nb, double c[] );
-extern void polsub ( double a[], int na, double b[], int nb, double c[] );
-extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
-extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
-extern void * malloc ( long );
-extern void free ( void * );
-#else
-double atan2(), sqrt(), fabs(), sin(), cos();
-void polclr(), polmov(), polsbt(), poladd(), polsub(), polmul();
-int poldiv();
-void * malloc();
-void free ();
-#endif
-
-/* Highest degree of polynomial to be handled
- by the polyn.c subroutine package. */
-#define N 16
-/* Highest degree actually initialized at runtime. */
-extern int MAXPOL;
-
-/* Taylor series coefficients for various functions
- */
-double patan[N+1] = {
- 0.0, 1.0, 0.0, -1.0/3.0, 0.0,
- 1.0/5.0, 0.0, -1.0/7.0, 0.0, 1.0/9.0, 0.0, -1.0/11.0,
- 0.0, 1.0/13.0, 0.0, -1.0/15.0, 0.0 };
-
-double psin[N+1] = {
- 0.0, 1.0, 0.0, -1.0/6.0, 0.0, 1.0/120.0, 0.0,
- -1.0/5040.0, 0.0, 1.0/362880.0, 0.0, -1.0/39916800.0,
- 0.0, 1.0/6227020800.0, 0.0, -1.0/1.307674368e12, 0.0};
-
-double pcos[N+1] = {
- 1.0, 0.0, -1.0/2.0, 0.0, 1.0/24.0, 0.0,
- -1.0/720.0, 0.0, 1.0/40320.0, 0.0, -1.0/3628800.0, 0.0,
- 1.0/479001600.0, 0.0, -1.0/8.7179291e10, 0.0, 1.0/2.0922789888e13};
-
-double pasin[N+1] = {
- 0.0, 1.0, 0.0, 1.0/6.0, 0.0,
- 3.0/40.0, 0.0, 15.0/336.0, 0.0, 105.0/3456.0, 0.0, 945.0/42240.0,
- 0.0, 10395.0/599040.0 , 0.0, 135135.0/9676800.0 , 0.0
-};
-
-/* Square root of 1 + x. */
-double psqrt[N+1] = {
- 1.0, 1./2., -1./8., 1./16., -5./128., 7./256., -21./1024., 33./2048.,
- -429./32768., 715./65536., -2431./262144., 4199./524288., -29393./4194304.,
- 52003./8388608., -185725./33554432., 334305./67108864.,
- -9694845./2147483648.};
-
-/* Arctangent of the ratio num/den of two polynomials.
- */
-void
-polatn( num, den, ans, nn )
- double num[], den[], ans[];
- int nn;
-{
- double a, t;
- double *polq, *polu, *polt;
- int i;
-
- if (nn > N)
- {
- mtherr ("polatn", OVERFLOW);
- return;
- }
- /* arctan( a + b ) = arctan(a) + arctan( b/(1 + ab + a**2) ) */
- t = num[0];
- a = den[0];
- if( (t == 0.0) && (a == 0.0 ) )
- {
- t = num[1];
- a = den[1];
- }
- t = atan2( t, a ); /* arctan(num/den), the ANSI argument order */
- polq = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- polu = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- polt = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- polclr( polq, MAXPOL );
- i = poldiv( den, nn, num, nn, polq );
- a = polq[0]; /* a */
- polq[0] = 0.0; /* b */
- polmov( polq, nn, polu ); /* b */
- /* Form the polynomial
- 1 + ab + a**2
- where a is a scalar. */
- for( i=0; i<=nn; i++ )
- polu[i] *= a;
- polu[0] += 1.0 + a * a;
- poldiv( polu, nn, polq, nn, polt ); /* divide into b */
- polsbt( polt, nn, patan, nn, polu ); /* arctan(b) */
- polu[0] += t; /* plus arctan(a) */
- polmov( polu, nn, ans );
- free( polt );
- free( polu );
- free( polq );
-}
-
-
-
-/* Square root of a polynomial.
- * Assumes the lowest degree nonzero term is dominant
- * and of even degree. An error message is given
- * if the Newton iteration does not converge.
- */
-void
-polsqt( pol, ans, nn )
- double pol[], ans[];
- int nn;
-{
- double t;
- double *x, *y;
- int i, n;
-#if 0
- double z[N+1];
- double u;
-#endif
-
- if (nn > N)
- {
- mtherr ("polatn", OVERFLOW);
- return;
- }
- x = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- y = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- polmov( pol, nn, x );
- polclr( y, MAXPOL );
-
- /* Find lowest degree nonzero term. */
- t = 0.0;
- for( n=0; n<nn; n++ )
- {
- if( x[n] != 0.0 )
- goto nzero;
- }
- polmov( y, nn, ans );
- return;
-
-nzero:
-
- if( n > 0 )
- {
- if (n & 1)
- {
- printf("error, sqrt of odd polynomial\n");
- return;
- }
- /* Divide by x^n. */
- y[n] = x[n];
- poldiv (y, nn, pol, N, x);
- }
-
- t = x[0];
- for( i=1; i<=nn; i++ )
- x[i] /= t;
- x[0] = 0.0;
- /* series development sqrt(1+x) = 1 + x / 2 - x**2 / 8 + x**3 / 16
- hopes that first (constant) term is greater than what follows */
- polsbt( x, nn, psqrt, nn, y);
- t = sqrt( t );
- for( i=0; i<=nn; i++ )
- y[i] *= t;
-
- /* If first nonzero coefficient was at degree n > 0, multiply by
- x^(n/2). */
- if (n > 0)
- {
- polclr (x, MAXPOL);
- x[n/2] = 1.0;
- polmul (x, nn, y, nn, y);
- }
-#if 0
-/* Newton iterations */
-for( n=0; n<10; n++ )
- {
- poldiv( y, nn, pol, nn, z );
- poladd( y, nn, z, nn, y );
- for( i=0; i<=nn; i++ )
- y[i] *= 0.5;
- for( i=0; i<=nn; i++ )
- {
- u = fabs( y[i] - z[i] );
- if( u > 1.0e-15 )
- goto more;
- }
- goto done;
-more: ;
- }
-printf( "square root did not converge\n" );
-done:
-#endif /* 0 */
-
-polmov( y, nn, ans );
-free( y );
-free( x );
-}
-
-
-
-/* Sine of a polynomial.
- * The computation uses
- * sin(a+b) = sin(a) cos(b) + cos(a) sin(b)
- * where a is the constant term of the polynomial and
- * b is the sum of the rest of the terms.
- * Since sin(b) and cos(b) are computed by series expansions,
- * the value of b should be small.
- */
-void
-polsin( x, y, nn )
- double x[], y[];
- int nn;
-{
- double a, sc;
- double *w, *c;
- int i;
-
- if (nn > N)
- {
- mtherr ("polatn", OVERFLOW);
- return;
- }
- w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- polmov( x, nn, w );
- polclr( c, MAXPOL );
- polclr( y, nn );
- /* a, in the description, is x[0]. b is the polynomial x - x[0]. */
- a = w[0];
- /* c = cos (b) */
- w[0] = 0.0;
- polsbt( w, nn, pcos, nn, c );
- sc = sin(a);
- /* sin(a) cos (b) */
- for( i=0; i<=nn; i++ )
- c[i] *= sc;
- /* y = sin (b) */
- polsbt( w, nn, psin, nn, y );
- sc = cos(a);
- /* cos(a) sin(b) */
- for( i=0; i<=nn; i++ )
- y[i] *= sc;
- poladd( c, nn, y, nn, y );
- free( c );
- free( w );
-}
-
-
-/* Cosine of a polynomial.
- * The computation uses
- * cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
- * where a is the constant term of the polynomial and
- * b is the sum of the rest of the terms.
- * Since sin(b) and cos(b) are computed by series expansions,
- * the value of b should be small.
- */
-void
-polcos( x, y, nn )
- double x[], y[];
- int nn;
-{
- double a, sc;
- double *w, *c;
- int i;
- double sin(), cos();
-
- if (nn > N)
- {
- mtherr ("polatn", OVERFLOW);
- return;
- }
- w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
- polmov( x, nn, w );
- polclr( c, MAXPOL );
- polclr( y, nn );
- a = w[0];
- w[0] = 0.0;
- /* c = cos(b) */
- polsbt( w, nn, pcos, nn, c );
- sc = cos(a);
- /* cos(a) cos(b) */
- for( i=0; i<=nn; i++ )
- c[i] *= sc;
- /* y = sin(b) */
- polsbt( w, nn, psin, nn, y );
- sc = sin(a);
- /* sin(a) sin(b) */
- for( i=0; i<=nn; i++ )
- y[i] *= sc;
- polsub( y, nn, c, nn, y );
- free( c );
- free( w );
-}
+++ /dev/null
-/* polrt.c
- *
- * Find roots of a polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct
- * {
- * double r;
- * double i;
- * }cmplx;
- *
- * double xcof[], cof[];
- * int m;
- * cmplx root[];
- *
- * polrt( xcof, cof, m, root )
- *
- *
- *
- * DESCRIPTION:
- *
- * Iterative determination of the roots of a polynomial of
- * degree m whose coefficient vector is xcof[]. The
- * coefficients are arranged in ascending order; i.e., the
- * coefficient of x**m is xcof[m].
- *
- * The array cof[] is working storage the same size as xcof[].
- * root[] is the output array containing the complex roots.
- *
- *
- * ACCURACY:
- *
- * Termination depends on evaluation of the polynomial at
- * the trial values of the roots. The values of multiple roots
- * or of roots that are nearly equal may have poor relative
- * accuracy after the first root in the neighborhood has been
- * found.
- *
- */
-\f
-/* polrt */
-/* Complex roots of real polynomial */
-/* number of coefficients is m + 1 ( i.e., m is degree of polynomial) */
-
-#include <math.h>
-/*
-typedef struct
- {
- double r;
- double i;
- }cmplx;
-*/
-#ifdef ANSIPROT
-extern double fabs ( double );
-#else
-double fabs();
-#endif
-
-int polrt( xcof, cof, m, root )
-double xcof[], cof[];
-int m;
-cmplx root[];
-{
-register double *p, *q;
-int i, j, nsav, n, n1, n2, nroot, iter, retry;
-int final;
-double mag, cofj;
-cmplx x0, x, xsav, dx, t, t1, u, ud;
-
-final = 0;
-n = m;
-if( n <= 0 )
- return(1);
-if( n > 36 )
- return(2);
-if( xcof[m] == 0.0 )
- return(4);
-
-n1 = n;
-n2 = n;
-nroot = 0;
-nsav = n;
-q = &xcof[0];
-p = &cof[n];
-for( j=0; j<=nsav; j++ )
- *p-- = *q++; /* cof[ n-j ] = xcof[j];*/
-xsav.r = 0.0;
-xsav.i = 0.0;
-
-nxtrut:
-x0.r = 0.00500101;
-x0.i = 0.01000101;
-retry = 0;
-
-tryagn:
-retry += 1;
-x.r = x0.r;
-
-x0.r = -10.0 * x0.i;
-x0.i = -10.0 * x.r;
-
-x.r = x0.r;
-x.i = x0.i;
-
-finitr:
-iter = 0;
-
-while( iter < 500 )
-{
-u.r = cof[n];
-if( u.r == 0.0 )
- { /* this root is zero */
- x.r = 0;
- n1 -= 1;
- n2 -= 1;
- goto zerrut;
- }
-u.i = 0;
-ud.r = 0;
-ud.i = 0;
-t.r = 1.0;
-t.i = 0;
-p = &cof[n-1];
-for( i=0; i<n; i++ )
- {
- t1.r = x.r * t.r - x.i * t.i;
- t1.i = x.r * t.i + x.i * t.r;
- cofj = *p--; /* evaluate polynomial */
- u.r += cofj * t1.r;
- u.i += cofj * t1.i;
- cofj = cofj * (i+1); /* derivative */
- ud.r += cofj * t.r;
- ud.i -= cofj * t.i;
- t.r = t1.r;
- t.i = t1.i;
- }
-
-mag = ud.r * ud.r + ud.i * ud.i;
-if( mag == 0.0 )
- {
- if( !final )
- goto tryagn;
- x.r = xsav.r;
- x.i = xsav.i;
- goto findon;
- }
-dx.r = (u.i * ud.i - u.r * ud.r)/mag;
-x.r += dx.r;
-dx.i = -(u.r * ud.i + u.i * ud.r)/mag;
-x.i += dx.i;
-if( (fabs(dx.i) + fabs(dx.r)) < 1.0e-6 )
- goto lupdon;
-iter += 1;
-} /* while iter < 500 */
-
-if( final )
- goto lupdon;
-if( retry < 5 )
- goto tryagn;
-return(3);
-
-lupdon:
-/* Swap original and reduced polynomials */
-q = &xcof[nsav];
-p = &cof[0];
-for( j=0; j<=n2; j++ )
- {
- cofj = *q;
- *q-- = *p;
- *p++ = cofj;
- }
-i = n;
-n = n1;
-n1 = i;
-
-if( !final )
- {
- final = 1;
- if( fabs(x.i/x.r) < 1.0e-4 )
- x.i = 0.0;
- xsav.r = x.r;
- xsav.i = x.i;
- goto finitr; /* do final iteration on original polynomial */
- }
-
-findon:
-final = 0;
-if( fabs(x.i/x.r) >= 1.0e-5 )
- {
- cofj = x.r + x.r;
- mag = x.r * x.r + x.i * x.i;
- n -= 2;
- }
-else
- { /* root is real */
-zerrut:
- x.i = 0;
- cofj = x.r;
- mag = 0;
- n -= 1;
- }
-/* divide working polynomial cof(z) by z - x */
-p = &cof[1];
-*p += cofj * *(p-1);
-for( j=1; j<n; j++ )
- {
- *(p+1) += cofj * *p - mag * *(p-1);
- p++;
- }
-
-setrut:
-root[nroot].r = x.r;
-root[nroot].i = x.i;
-nroot += 1;
-if( mag != 0.0 )
- {
- x.i = -x.i;
- mag = 0;
- goto setrut; /* fill in the complex conjugate root */
- }
-if( n > 0 )
- goto nxtrut;
-return(0);
-}
+++ /dev/null
-/* polylog.c
- *
- * Polylogarithms
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, polylog();
- * int n;
- *
- * y = polylog( n, x );
- *
- *
- * The polylogarithm of order n is defined by the series
- *
- *
- * inf k
- * - x
- * Li (x) = > --- .
- * n - n
- * k=1 k
- *
- *
- * For x = 1,
- *
- * inf
- * - 1
- * Li (1) = > --- = Riemann zeta function (n) .
- * n - n
- * k=1 k
- *
- *
- * When n = 2, the function is the dilogarithm, related to Spence's integral:
- *
- * x 1-x
- * - -
- * | | -ln(1-t) | | ln t
- * Li (x) = | -------- dt = | ------ dt = spence(1-x) .
- * 2 | | t | | 1 - t
- * - -
- * 0 1
- *
- *
- * See also the program cpolylog.c for the complex polylogarithm,
- * whose definition is extended to x > 1.
- *
- * References:
- *
- * Lewin, L., _Polylogarithms and Associated Functions_,
- * North Holland, 1981.
- *
- * Lewin, L., ed., _Structural Properties of Polylogarithms_,
- * American Mathematical Society, 1991.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain n # trials peak rms
- * IEEE 0, 1 2 50000 6.2e-16 8.0e-17
- * IEEE 0, 1 3 100000 2.5e-16 6.6e-17
- * IEEE 0, 1 4 30000 1.7e-16 4.9e-17
- * IEEE 0, 1 5 30000 5.1e-16 7.8e-17
- *
- */
-
-/*
-Cephes Math Library Release 2.8: July, 1999
-Copyright 1999 by Stephen L. Moshier
-*/
-
-#include <math.h>
-extern double PI;
-
-/* polylog(4, 1-x) = zeta(4) - x zeta(3) + x^2 A4(x)/B4(x)
- 0 <= x <= 0.125
- Theoretical peak absolute error 4.5e-18 */
-#if UNK
-static double A4[13] = {
- 3.056144922089490701751E-2,
- 3.243086484162581557457E-1,
- 2.877847281461875922565E-1,
- 7.091267785886180663385E-2,
- 6.466460072456621248630E-3,
- 2.450233019296542883275E-4,
- 4.031655364627704957049E-6,
- 2.884169163909467997099E-8,
- 8.680067002466594858347E-11,
- 1.025983405866370985438E-13,
- 4.233468313538272640380E-17,
- 4.959422035066206902317E-21,
- 1.059365867585275714599E-25,
-};
-static double B4[12] = {
- /* 1.000000000000000000000E0, */
- 2.821262403600310974875E0,
- 1.780221124881327022033E0,
- 3.778888211867875721773E-1,
- 3.193887040074337940323E-2,
- 1.161252418498096498304E-3,
- 1.867362374829870620091E-5,
- 1.319022779715294371091E-7,
- 3.942755256555603046095E-10,
- 4.644326968986396928092E-13,
- 1.913336021014307074861E-16,
- 2.240041814626069927477E-20,
- 4.784036597230791011855E-25,
-};
-#endif
-#if DEC
-static short A4[52] = {
-0036772,0056001,0016601,0164507,
-0037646,0005710,0076603,0176456,
-0037623,0054205,0013532,0026476,
-0037221,0035252,0101064,0065407,
-0036323,0162231,0042033,0107244,
-0035200,0073170,0106141,0136543,
-0033607,0043647,0163672,0055340,
-0031767,0137614,0173376,0072313,
-0027676,0160156,0161276,0034203,
-0025347,0003752,0123106,0064266,
-0022503,0035770,0160173,0177501,
-0017273,0056226,0033704,0132530,
-0013403,0022244,0175205,0052161,
-};
-static short B4[48] = {
- /*0040200,0000000,0000000,0000000, */
-0040464,0107620,0027471,0071672,
-0040343,0157111,0025601,0137255,
-0037701,0075244,0140412,0160220,
-0037002,0151125,0036572,0057163,
-0035630,0032452,0050727,0161653,
-0034234,0122515,0034323,0172615,
-0032415,0120405,0123660,0003160,
-0030330,0140530,0161045,0150177,
-0026002,0134747,0014542,0002510,
-0023134,0113666,0035730,0035732,
-0017723,0110343,0041217,0007764,
-0014024,0007412,0175575,0160230,
-};
-#endif
-#if IBMPC
-static short A4[52] = {
-0x3d29,0x23b0,0x4b80,0x3f9f,
-0x7fa6,0x0fb0,0xc179,0x3fd4,
-0x45a8,0xa2eb,0x6b10,0x3fd2,
-0x8d61,0x5046,0x2755,0x3fb2,
-0x71d4,0x2883,0x7c93,0x3f7a,
-0x37ac,0x118c,0x0ecf,0x3f30,
-0x4b5c,0xfcf7,0xe8f4,0x3ed0,
-0xce99,0x9edf,0xf7f1,0x3e5e,
-0xc710,0xdc57,0xdc0d,0x3dd7,
-0xcd17,0x54c8,0xe0fd,0x3d3c,
-0x7fe8,0x1c0f,0x677f,0x3c88,
-0x96ab,0xc6f8,0x6b92,0x3bb7,
-0xaa8e,0x9f50,0x6494,0x3ac0,
-};
-static short B4[48] = {
- /*0x0000,0x0000,0x0000,0x3ff0,*/
-0x2e77,0x05e7,0x91f2,0x4006,
-0x37d6,0x2570,0x7bc9,0x3ffc,
-0x5c12,0x9821,0x2f54,0x3fd8,
-0x4bce,0xa7af,0x5a4a,0x3fa0,
-0xfc75,0x4a3a,0x06a5,0x3f53,
-0x7eb2,0xa71a,0x94a9,0x3ef3,
-0x00ce,0xb4f6,0xb420,0x3e81,
-0xba10,0x1c44,0x182b,0x3dfb,
-0x40a9,0xe32c,0x573c,0x3d60,
-0x077b,0xc77b,0x92f6,0x3cab,
-0xe1fe,0x6851,0x721c,0x3bda,
-0xbc13,0x5f6f,0x81e1,0x3ae2,
-};
-#endif
-#if MIEEE
-static short A4[52] = {
-0x3f9f,0x4b80,0x23b0,0x3d29,
-0x3fd4,0xc179,0x0fb0,0x7fa6,
-0x3fd2,0x6b10,0xa2eb,0x45a8,
-0x3fb2,0x2755,0x5046,0x8d61,
-0x3f7a,0x7c93,0x2883,0x71d4,
-0x3f30,0x0ecf,0x118c,0x37ac,
-0x3ed0,0xe8f4,0xfcf7,0x4b5c,
-0x3e5e,0xf7f1,0x9edf,0xce99,
-0x3dd7,0xdc0d,0xdc57,0xc710,
-0x3d3c,0xe0fd,0x54c8,0xcd17,
-0x3c88,0x677f,0x1c0f,0x7fe8,
-0x3bb7,0x6b92,0xc6f8,0x96ab,
-0x3ac0,0x6494,0x9f50,0xaa8e,
-};
-static short B4[48] = {
- /*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4006,0x91f2,0x05e7,0x2e77,
-0x3ffc,0x7bc9,0x2570,0x37d6,
-0x3fd8,0x2f54,0x9821,0x5c12,
-0x3fa0,0x5a4a,0xa7af,0x4bce,
-0x3f53,0x06a5,0x4a3a,0xfc75,
-0x3ef3,0x94a9,0xa71a,0x7eb2,
-0x3e81,0xb420,0xb4f6,0x00ce,
-0x3dfb,0x182b,0x1c44,0xba10,
-0x3d60,0x573c,0xe32c,0x40a9,
-0x3cab,0x92f6,0xc77b,0x077b,
-0x3bda,0x721c,0x6851,0xe1fe,
-0x3ae2,0x81e1,0x5f6f,0xbc13,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double spence ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double zetac ( double );
-extern double pow ( double, double );
-extern double powi ( double, int );
-extern double log ( double );
-extern double fac ( int i );
-extern double fabs (double);
-double polylog (int, double);
-#else
-extern double spence(), polevl(), p1evl(), zetac();
-extern double pow(), powi(), log();
-extern double fac(); /* factorial */
-extern double fabs();
-double polylog();
-#endif
-extern double MACHEP;
-
-double
-polylog (n, x)
- int n;
- double x;
-{
- double h, k, p, s, t, u, xc, z;
- int i, j;
-
-/* This recurrence provides formulas for n < 2.
-
- d 1
- -- Li (x) = --- Li (x) .
- dx n x n-1
-
-*/
-
- if (n == -1)
- {
- p = 1.0 - x;
- u = x / p;
- s = u * u + u;
- return s;
- }
-
- if (n == 0)
- {
- s = x / (1.0 - x);
- return s;
- }
-
- /* Not implemented for n < -1.
- Not defined for x > 1. Use cpolylog if you need that. */
- if (x > 1.0 || n < -1)
- {
- mtherr("polylog", DOMAIN);
- return 0.0;
- }
-
- if (n == 1)
- {
- s = -log (1.0 - x);
- return s;
- }
-
- /* Argument +1 */
- if (x == 1.0 && n > 1)
- {
- s = zetac ((double) n) + 1.0;
- return s;
- }
-
- /* Argument -1.
- 1-n
- Li (-z) = - (1 - 2 ) Li (z)
- n n
- */
- if (x == -1.0 && n > 1)
- {
- /* Li_n(1) = zeta(n) */
- s = zetac ((double) n) + 1.0;
- s = s * (powi (2.0, 1 - n) - 1.0);
- return s;
- }
-
-/* Inversion formula:
- * [n/2] n-2r
- * n 1 n - log (z)
- * Li (-z) + (-1) Li (-1/z) = - --- log (z) + 2 > ----------- Li (-1)
- * n n n! - (n - 2r)! 2r
- * r=1
- */
- if (x < -1.0 && n > 1)
- {
- double q, w;
- int r;
-
- w = log (-x);
- s = 0.0;
- for (r = 1; r <= n / 2; r++)
- {
- j = 2 * r;
- p = polylog (j, -1.0);
- j = n - j;
- if (j == 0)
- {
- s = s + p;
- break;
- }
- q = (double) j;
- q = pow (w, q) * p / fac (j);
- s = s + q;
- }
- s = 2.0 * s;
- q = polylog (n, 1.0 / x);
- if (n & 1)
- q = -q;
- s = s - q;
- s = s - pow (w, (double) n) / fac (n);
- return s;
- }
-
- if (n == 2)
- {
- if (x < 0.0 || x > 1.0)
- return (spence (1.0 - x));
- }
-
-
-
- /* The power series converges slowly when x is near 1. For n = 3, this
- identity helps:
-
- Li (-x/(1-x)) + Li (1-x) + Li (x)
- 3 3 3
- 2 2 3
- = Li (1) + (pi /6) log(1-x) - (1/2) log(x) log (1-x) + (1/6) log (1-x)
- 3
- */
-
- if (n == 3)
- {
- p = x * x * x;
- if (x > 0.8)
- {
- u = log(x);
- s = p / 6.0;
- xc = 1.0 - x;
- s = s - 0.5 * u * u * log(xc);
- s = s + PI * PI * u / 6.0;
- s = s - polylog (3, -xc/x);
- s = s - polylog (3, xc);
- s = s + zetac(3.0);
- s = s + 1.0;
- return s;
- }
- /* Power series */
- t = p / 27.0;
- t = t + .125 * x * x;
- t = t + x;
-
- s = 0.0;
- k = 4.0;
- do
- {
- p = p * x;
- h = p / (k * k * k);
- s = s + h;
- k += 1.0;
- }
- while (fabs(h/s) > 1.1e-16);
- return (s + t);
- }
-
-if (n == 4)
- {
- if (x >= 0.875)
- {
- u = 1.0 - x;
- s = polevl(u, A4, 12) / p1evl(u, B4, 12);
- s = s * u * u - 1.202056903159594285400 * u;
- s += 1.0823232337111381915160;
- return s;
- }
- goto pseries;
- }
-
-
- if (x < 0.75)
- goto pseries;
-
-
-/* This expansion in powers of log(x) is especially useful when
- x is near 1.
-
- See also the pari gp calculator.
-
- inf j
- - z(n-j) (log(x))
- polylog(n,x) = > -----------------
- - j!
- j=0
-
- where
-
- z(j) = Riemann zeta function (j), j != 1
-
- n-1
- -
- z(1) = -log(-log(x)) + > 1/k
- -
- k=1
- */
-
- z = log(x);
- h = -log(-z);
- for (i = 1; i < n; i++)
- h = h + 1.0/i;
- p = 1.0;
- s = zetac((double)n) + 1.0;
- for (j=1; j<=n+1; j++)
- {
- p = p * z / j;
- if (j == n-1)
- s = s + h * p;
- else
- s = s + (zetac((double)(n-j)) + 1.0) * p;
- }
- j = n + 3;
- z = z * z;
- for(;;)
- {
- p = p * z / ((j-1)*j);
- h = (zetac((double)(n-j)) + 1.0);
- h = h * p;
- s = s + h;
- if (fabs(h/s) < MACHEP)
- break;
- j += 2;
- }
- return s;
-
-
-pseries:
-
- p = x * x * x;
- k = 3.0;
- s = 0.0;
- do
- {
- p = p * x;
- k += 1.0;
- h = p / powi(k, n);
- s = s + h;
- }
- while (fabs(h/s) > MACHEP);
- s += x * x * x / powi(3.0,n);
- s += x * x / powi(2.0,n);
- s += x;
- return s;
-}
+++ /dev/null
-/* polyn.c
- * polyr.c
- * Arithmetic operations on polynomials
- *
- * In the following descriptions a, b, c are polynomials of degree
- * na, nb, nc respectively. The degree of a polynomial cannot
- * exceed a run-time value MAXPOL. An operation that attempts
- * to use or generate a polynomial of higher degree may produce a
- * result that suffers truncation at degree MAXPOL. The value of
- * MAXPOL is set by calling the function
- *
- * polini( maxpol );
- *
- * where maxpol is the desired maximum degree. This must be
- * done prior to calling any of the other functions in this module.
- * Memory for internal temporary polynomial storage is allocated
- * by polini().
- *
- * Each polynomial is represented by an array containing its
- * coefficients, together with a separately declared integer equal
- * to the degree of the polynomial. The coefficients appear in
- * ascending order; that is,
- *
- * 2 na
- * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
- *
- *
- *
- * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
- * polprt( a, na, D ); Print the coefficients of a to D digits.
- * polclr( a, na ); Set a identically equal to zero, up to a[na].
- * polmov( a, na, b ); Set b = a.
- * poladd( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
- * polsub( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
- * polmul( a, na, b, nb, c ); c = b * a, nc = na+nb
- *
- *
- * Division:
- *
- * i = poldiv( a, na, b, nb, c ); c = b / a, nc = MAXPOL
- *
- * returns i = the degree of the first nonzero coefficient of a.
- * The computed quotient c must be divided by x^i. An error message
- * is printed if a is identically zero.
- *
- *
- * Change of variables:
- * If a and b are polynomials, and t = a(x), then
- * c(t) = b(a(x))
- * is a polynomial found by substituting a(x) for t. The
- * subroutine call for this is
- *
- * polsbt( a, na, b, nb, c );
- *
- *
- * Notes:
- * poldiv() is an integer routine; poleva() is double.
- * Any of the arguments a, b, c may refer to the same array.
- *
- */
-
-#include <stdio.h>
-#include <math.h>
-#if ANSIPROT
-void exit (int);
-extern void * malloc ( long );
-extern void free ( void * );
-void polclr ( double *, int );
-void polmov ( double *, int, double * );
-void polmul ( double *, int, double *, int, double * );
-int poldiv ( double *, int, double *, int, double * );
-#else
-void exit();
-void * malloc();
-void free ();
-void polclr(), polmov(), poldiv(), polmul();
-#endif
-#ifndef NULL
-#define NULL 0
-#endif
-
-/* near pointer version of malloc() */
-/*
-#define malloc _nmalloc
-#define free _nfree
-*/
-
-/* Pointers to internal arrays. Note poldiv() allocates
- * and deallocates some temporary arrays every time it is called.
- */
-static double *pt1 = 0;
-static double *pt2 = 0;
-static double *pt3 = 0;
-
-/* Maximum degree of polynomial. */
-int MAXPOL = 0;
-extern int MAXPOL;
-
-/* Number of bytes (chars) in maximum size polynomial. */
-static int psize = 0;
-
-
-/* Initialize max degree of polynomials
- * and allocate temporary storage.
- */
-void polini( maxdeg )
-int maxdeg;
-{
-
-MAXPOL = maxdeg;
-psize = (maxdeg + 1) * sizeof(double);
-
-/* Release previously allocated memory, if any. */
-if( pt3 )
- free(pt3);
-if( pt2 )
- free(pt2);
-if( pt1 )
- free(pt1);
-
-/* Allocate new arrays */
-pt1 = (double * )malloc(psize); /* used by polsbt */
-pt2 = (double * )malloc(psize); /* used by polsbt */
-pt3 = (double * )malloc(psize); /* used by polmul */
-
-/* Report if failure */
-if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
- {
- mtherr( "polini", ERANGE );
- exit(1);
- }
-}
-
-
-
-/* Print the coefficients of a, with d decimal precision.
- */
-static char *form = "abcdefghijk";
-
-void polprt( a, na, d )
-double a[];
-int na, d;
-{
-int i, j, d1;
-char *p;
-
-/* Create format descriptor string for the printout.
- * Do this partly by hand, since sprintf() may be too
- * bug-ridden to accomplish this feat by itself.
- */
-p = form;
-*p++ = '%';
-d1 = d + 8;
-sprintf( p, "%d ", d1 );
-p += 1;
-if( d1 >= 10 )
- p += 1;
-*p++ = '.';
-sprintf( p, "%d ", d );
-p += 1;
-if( d >= 10 )
- p += 1;
-*p++ = 'e';
-*p++ = ' ';
-*p++ = '\0';
-
-
-/* Now do the printing.
- */
-d1 += 1;
-j = 0;
-for( i=0; i<=na; i++ )
- {
-/* Detect end of available line */
- j += d1;
- if( j >= 78 )
- {
- printf( "\n" );
- j = d1;
- }
- printf( form, a[i] );
- }
-printf( "\n" );
-}
-
-
-
-/* Set a = 0.
- */
-void polclr( a, n )
-register double *a;
-int n;
-{
-int i;
-
-if( n > MAXPOL )
- n = MAXPOL;
-for( i=0; i<=n; i++ )
- *a++ = 0.0;
-}
-
-
-
-/* Set b = a.
- */
-void polmov( a, na, b )
-register double *a, *b;
-int na;
-{
-int i;
-
-if( na > MAXPOL )
- na = MAXPOL;
-
-for( i=0; i<= na; i++ )
- {
- *b++ = *a++;
- }
-}
-
-
-/* c = b * a.
- */
-void polmul( a, na, b, nb, c )
-double a[], b[], c[];
-int na, nb;
-{
-int i, j, k, nc;
-double x;
-
-nc = na + nb;
-polclr( pt3, MAXPOL );
-
-for( i=0; i<=na; i++ )
- {
- x = a[i];
- for( j=0; j<=nb; j++ )
- {
- k = i + j;
- if( k > MAXPOL )
- break;
- pt3[k] += x * b[j];
- }
- }
-
-if( nc > MAXPOL )
- nc = MAXPOL;
-for( i=0; i<=nc; i++ )
- c[i] = pt3[i];
-}
-
-
-
-
-/* c = b + a.
- */
-void poladd( a, na, b, nb, c )
-double a[], b[], c[];
-int na, nb;
-{
-int i, n;
-
-
-if( na > nb )
- n = na;
-else
- n = nb;
-
-if( n > MAXPOL )
- n = MAXPOL;
-
-for( i=0; i<=n; i++ )
- {
- if( i > na )
- c[i] = b[i];
- else if( i > nb )
- c[i] = a[i];
- else
- c[i] = b[i] + a[i];
- }
-}
-
-/* c = b - a.
- */
-void polsub( a, na, b, nb, c )
-double a[], b[], c[];
-int na, nb;
-{
-int i, n;
-
-
-if( na > nb )
- n = na;
-else
- n = nb;
-
-if( n > MAXPOL )
- n = MAXPOL;
-
-for( i=0; i<=n; i++ )
- {
- if( i > na )
- c[i] = b[i];
- else if( i > nb )
- c[i] = -a[i];
- else
- c[i] = b[i] - a[i];
- }
-}
-
-
-
-/* c = b/a
- */
-int poldiv( a, na, b, nb, c )
-double a[], b[], c[];
-int na, nb;
-{
-double quot;
-double *ta, *tb, *tq;
-int i, j, k, sing;
-
-sing = 0;
-
-/* Allocate temporary arrays. This would be quicker
- * if done automatically on the stack, but stack space
- * may be hard to obtain on a small computer.
- */
-ta = (double * )malloc( psize );
-polclr( ta, MAXPOL );
-polmov( a, na, ta );
-
-tb = (double * )malloc( psize );
-polclr( tb, MAXPOL );
-polmov( b, nb, tb );
-
-tq = (double * )malloc( psize );
-polclr( tq, MAXPOL );
-
-/* What to do if leading (constant) coefficient
- * of denominator is zero.
- */
-if( a[0] == 0.0 )
- {
- for( i=0; i<=na; i++ )
- {
- if( ta[i] != 0.0 )
- goto nzero;
- }
- mtherr( "poldiv", SING );
- goto done;
-
-nzero:
-/* Reduce the degree of the denominator. */
- for( i=0; i<na; i++ )
- ta[i] = ta[i+1];
- ta[na] = 0.0;
-
- if( b[0] != 0.0 )
- {
-/* Optional message:
- printf( "poldiv singularity, divide quotient by x\n" );
-*/
- sing += 1;
- }
- else
- {
-/* Reduce degree of numerator. */
- for( i=0; i<nb; i++ )
- tb[i] = tb[i+1];
- tb[nb] = 0.0;
- }
-/* Call self, using reduced polynomials. */
- sing += poldiv( ta, na, tb, nb, c );
- goto done;
- }
-
-/* Long division algorithm. ta[0] is nonzero.
- */
-for( i=0; i<=MAXPOL; i++ )
- {
- quot = tb[i]/ta[0];
- for( j=0; j<=MAXPOL; j++ )
- {
- k = j + i;
- if( k > MAXPOL )
- break;
- tb[k] -= quot * ta[j];
- }
- tq[i] = quot;
- }
-/* Send quotient to output array. */
-polmov( tq, MAXPOL, c );
-
-done:
-
-/* Restore allocated memory. */
-free(tq);
-free(tb);
-free(ta);
-return( sing );
-}
-
-
-
-
-/* Change of variables
- * Substitute a(y) for the variable x in b(x).
- * x = a(y)
- * c(x) = b(x) = b(a(y)).
- */
-
-void polsbt( a, na, b, nb, c )
-double a[], b[], c[];
-int na, nb;
-{
-int i, j, k, n2;
-double x;
-
-/* 0th degree term:
- */
-polclr( pt1, MAXPOL );
-pt1[0] = b[0];
-
-polclr( pt2, MAXPOL );
-pt2[0] = 1.0;
-n2 = 0;
-
-for( i=1; i<=nb; i++ )
- {
-/* Form ith power of a. */
- polmul( a, na, pt2, n2, pt2 );
- n2 += na;
- x = b[i];
-/* Add the ith coefficient of b times the ith power of a. */
- for( j=0; j<=n2; j++ )
- {
- if( j > MAXPOL )
- break;
- pt1[j] += x * pt2[j];
- }
- }
-
-k = n2 + nb;
-if( k > MAXPOL )
- k = MAXPOL;
-for( i=0; i<=k; i++ )
- c[i] = pt1[i];
-}
-
-
-
-
-/* Evaluate polynomial a(t) at t = x.
- */
-double poleva( a, na, x )
-double a[];
-int na;
-double x;
-{
-double s;
-int i;
-
-s = a[na];
-for( i=na-1; i>=0; i-- )
- {
- s = s * x + a[i];
- }
-return(s);
-}
-
+++ /dev/null
-
-/* Arithmetic operations on polynomials with rational coefficients
- *
- * In the following descriptions a, b, c are polynomials of degree
- * na, nb, nc respectively. The degree of a polynomial cannot
- * exceed a run-time value MAXPOL. An operation that attempts
- * to use or generate a polynomial of higher degree may produce a
- * result that suffers truncation at degree MAXPOL. The value of
- * MAXPOL is set by calling the function
- *
- * polini( maxpol );
- *
- * where maxpol is the desired maximum degree. This must be
- * done prior to calling any of the other functions in this module.
- * Memory for internal temporary polynomial storage is allocated
- * by polini().
- *
- * Each polynomial is represented by an array containing its
- * coefficients, together with a separately declared integer equal
- * to the degree of the polynomial. The coefficients appear in
- * ascending order; that is,
- *
- * 2 na
- * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
- *
- *
- *
- * `a', `b', `c' are arrays of fracts.
- * poleva( a, na, &x, &sum ); Evaluate polynomial a(t) at t = x.
- * polprt( a, na, D ); Print the coefficients of a to D digits.
- * polclr( a, na ); Set a identically equal to zero, up to a[na].
- * polmov( a, na, b ); Set b = a.
- * poladd( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
- * polsub( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
- * polmul( a, na, b, nb, c ); c = b * a, nc = na+nb
- *
- *
- * Division:
- *
- * i = poldiv( a, na, b, nb, c ); c = b / a, nc = MAXPOL
- *
- * returns i = the degree of the first nonzero coefficient of a.
- * The computed quotient c must be divided by x^i. An error message
- * is printed if a is identically zero.
- *
- *
- * Change of variables:
- * If a and b are polynomials, and t = a(x), then
- * c(t) = b(a(x))
- * is a polynomial found by substituting a(x) for t. The
- * subroutine call for this is
- *
- * polsbt( a, na, b, nb, c );
- *
- *
- * Notes:
- * poldiv() is an integer routine; poleva() is double.
- * Any of the arguments a, b, c may refer to the same array.
- *
- */
-
-#include <stdio.h>
-#include <math.h>
-#ifndef NULL
-#define NULL 0
-#endif
-typedef struct{
- double n;
- double d;
- }fract;
-
-#ifdef ANSIPROT
-extern void radd ( fract *, fract *, fract * );
-extern void rsub ( fract *, fract *, fract * );
-extern void rmul ( fract *, fract *, fract * );
-extern void rdiv ( fract *, fract *, fract * );
-void polmov ( fract *, int, fract * );
-void polmul ( fract *, int, fract *, int, fract * );
-int poldiv ( fract *, int, fract *, int, fract * );
-void * malloc ( long );
-void free ( void * );
-#else
-void radd(), rsub(), rmul(), rdiv();
-void polmov(), polmul();
-int poldiv();
-void * malloc();
-void free ();
-#endif
-
-/* near pointer version of malloc() */
-/*
-#define malloc _nmalloc
-#define free _nfree
-*/
-/* Pointers to internal arrays. Note poldiv() allocates
- * and deallocates some temporary arrays every time it is called.
- */
-static fract *pt1 = 0;
-static fract *pt2 = 0;
-static fract *pt3 = 0;
-
-/* Maximum degree of polynomial. */
-int MAXPOL = 0;
-extern int MAXPOL;
-
-/* Number of bytes (chars) in maximum size polynomial. */
-static int psize = 0;
-
-
-/* Initialize max degree of polynomials
- * and allocate temporary storage.
- */
-void polini( maxdeg )
-int maxdeg;
-{
-
-MAXPOL = maxdeg;
-psize = (maxdeg + 1) * sizeof(fract);
-
-/* Release previously allocated memory, if any. */
-if( pt3 )
- free(pt3);
-if( pt2 )
- free(pt2);
-if( pt1 )
- free(pt1);
-
-/* Allocate new arrays */
-pt1 = (fract * )malloc(psize); /* used by polsbt */
-pt2 = (fract * )malloc(psize); /* used by polsbt */
-pt3 = (fract * )malloc(psize); /* used by polmul */
-
-/* Report if failure */
-if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
- {
- mtherr( "polini", ERANGE );
- exit(1);
- }
-}
-
-
-
-/* Print the coefficients of a, with d decimal precision.
- */
-static char *form = "abcdefghijk";
-
-void polprt( a, na, d )
-fract a[];
-int na, d;
-{
-int i, j, d1;
-char *p;
-
-/* Create format descriptor string for the printout.
- * Do this partly by hand, since sprintf() may be too
- * bug-ridden to accomplish this feat by itself.
- */
-p = form;
-*p++ = '%';
-d1 = d + 8;
-sprintf( p, "%d ", d1 );
-p += 1;
-if( d1 >= 10 )
- p += 1;
-*p++ = '.';
-sprintf( p, "%d ", d );
-p += 1;
-if( d >= 10 )
- p += 1;
-*p++ = 'e';
-*p++ = ' ';
-*p++ = '\0';
-
-
-/* Now do the printing.
- */
-d1 += 1;
-j = 0;
-for( i=0; i<=na; i++ )
- {
-/* Detect end of available line */
- j += d1;
- if( j >= 78 )
- {
- printf( "\n" );
- j = d1;
- }
- printf( form, a[i].n );
- j += d1;
- if( j >= 78 )
- {
- printf( "\n" );
- j = d1;
- }
- printf( form, a[i].d );
- }
-printf( "\n" );
-}
-
-
-
-/* Set a = 0.
- */
-void polclr( a, n )
-fract a[];
-int n;
-{
-int i;
-
-if( n > MAXPOL )
- n = MAXPOL;
-for( i=0; i<=n; i++ )
- {
- a[i].n = 0.0;
- a[i].d = 1.0;
- }
-}
-
-
-
-/* Set b = a.
- */
-void polmov( a, na, b )
-fract a[], b[];
-int na;
-{
-int i;
-
-if( na > MAXPOL )
- na = MAXPOL;
-
-for( i=0; i<= na; i++ )
- {
- b[i].n = a[i].n;
- b[i].d = a[i].d;
- }
-}
-
-
-/* c = b * a.
- */
-void polmul( a, na, b, nb, c )
-fract a[], b[], c[];
-int na, nb;
-{
-int i, j, k, nc;
-fract temp;
-fract *p;
-
-nc = na + nb;
-polclr( pt3, MAXPOL );
-
-p = &a[0];
-for( i=0; i<=na; i++ )
- {
- for( j=0; j<=nb; j++ )
- {
- k = i + j;
- if( k > MAXPOL )
- break;
- rmul( p, &b[j], &temp ); /*pt3[k] += a[i] * b[j];*/
- radd( &temp, &pt3[k], &pt3[k] );
- }
- ++p;
- }
-
-if( nc > MAXPOL )
- nc = MAXPOL;
-for( i=0; i<=nc; i++ )
- {
- c[i].n = pt3[i].n;
- c[i].d = pt3[i].d;
- }
-}
-
-
-
-
-/* c = b + a.
- */
-void poladd( a, na, b, nb, c )
-fract a[], b[], c[];
-int na, nb;
-{
-int i, n;
-
-
-if( na > nb )
- n = na;
-else
- n = nb;
-
-if( n > MAXPOL )
- n = MAXPOL;
-
-for( i=0; i<=n; i++ )
- {
- if( i > na )
- {
- c[i].n = b[i].n;
- c[i].d = b[i].d;
- }
- else if( i > nb )
- {
- c[i].n = a[i].n;
- c[i].d = a[i].d;
- }
- else
- {
- radd( &a[i], &b[i], &c[i] ); /*c[i] = b[i] + a[i];*/
- }
- }
-}
-
-/* c = b - a.
- */
-void polsub( a, na, b, nb, c )
-fract a[], b[], c[];
-int na, nb;
-{
-int i, n;
-
-
-if( na > nb )
- n = na;
-else
- n = nb;
-
-if( n > MAXPOL )
- n = MAXPOL;
-
-for( i=0; i<=n; i++ )
- {
- if( i > na )
- {
- c[i].n = b[i].n;
- c[i].d = b[i].d;
- }
- else if( i > nb )
- {
- c[i].n = -a[i].n;
- c[i].d = a[i].d;
- }
- else
- {
- rsub( &a[i], &b[i], &c[i] ); /*c[i] = b[i] - a[i];*/
- }
- }
-}
-
-
-
-/* c = b/a
- */
-int poldiv( a, na, b, nb, c )
-fract a[], b[], c[];
-int na, nb;
-{
-fract *ta, *tb, *tq;
-fract quot;
-fract temp;
-int i, j, k, sing;
-
-sing = 0;
-
-/* Allocate temporary arrays. This would be quicker
- * if done automatically on the stack, but stack space
- * may be hard to obtain on a small computer.
- */
-ta = (fract * )malloc( psize );
-polclr( ta, MAXPOL );
-polmov( a, na, ta );
-
-tb = (fract * )malloc( psize );
-polclr( tb, MAXPOL );
-polmov( b, nb, tb );
-
-tq = (fract * )malloc( psize );
-polclr( tq, MAXPOL );
-
-/* What to do if leading (constant) coefficient
- * of denominator is zero.
- */
-if( a[0].n == 0.0 )
- {
- for( i=0; i<=na; i++ )
- {
- if( ta[i].n != 0.0 )
- goto nzero;
- }
- mtherr( "poldiv", SING );
- goto done;
-
-nzero:
-/* Reduce the degree of the denominator. */
- for( i=0; i<na; i++ )
- {
- ta[i].n = ta[i+1].n;
- ta[i].d = ta[i+1].d;
- }
- ta[na].n = 0.0;
- ta[na].d = 1.0;
-
- if( b[0].n != 0.0 )
- {
-/* Optional message:
- printf( "poldiv singularity, divide quotient by x\n" );
-*/
- sing += 1;
- }
- else
- {
-/* Reduce degree of numerator. */
- for( i=0; i<nb; i++ )
- {
- tb[i].n = tb[i+1].n;
- tb[i].d = tb[i+1].d;
- }
- tb[nb].n = 0.0;
- tb[nb].d = 1.0;
- }
-/* Call self, using reduced polynomials. */
- sing += poldiv( ta, na, tb, nb, c );
- goto done;
- }
-
-/* Long division algorithm. ta[0] is nonzero.
- */
-for( i=0; i<=MAXPOL; i++ )
- {
- rdiv( &ta[0], &tb[i], " ); /*quot = tb[i]/ta[0];*/
- for( j=0; j<=MAXPOL; j++ )
- {
- k = j + i;
- if( k > MAXPOL )
- break;
-
- rmul( &ta[j], ", &temp ); /*tb[k] -= quot * ta[j];*/
- rsub( &temp, &tb[k], &tb[k] );
- }
- tq[i].n = quot.n;
- tq[i].d = quot.d;
- }
-/* Send quotient to output array. */
-polmov( tq, MAXPOL, c );
-
-done:
-
-/* Restore allocated memory. */
-free(tq);
-free(tb);
-free(ta);
-return( sing );
-}
-
-
-
-
-/* Change of variables
- * Substitute a(y) for the variable x in b(x).
- * x = a(y)
- * c(x) = b(x) = b(a(y)).
- */
-
-void polsbt( a, na, b, nb, c )
-fract a[], b[], c[];
-int na, nb;
-{
-int i, j, k, n2;
-fract temp;
-fract *p;
-
-/* 0th degree term:
- */
-polclr( pt1, MAXPOL );
-pt1[0].n = b[0].n;
-pt1[0].d = b[0].d;
-
-polclr( pt2, MAXPOL );
-pt2[0].n = 1.0;
-pt2[0].d = 1.0;
-n2 = 0;
-p = &b[1];
-
-for( i=1; i<=nb; i++ )
- {
-/* Form ith power of a. */
- polmul( a, na, pt2, n2, pt2 );
- n2 += na;
-/* Add the ith coefficient of b times the ith power of a. */
- for( j=0; j<=n2; j++ )
- {
- if( j > MAXPOL )
- break;
- rmul( &pt2[j], p, &temp ); /*pt1[j] += b[i] * pt2[j];*/
- radd( &temp, &pt1[j], &pt1[j] );
- }
- ++p;
- }
-
-k = n2 + nb;
-if( k > MAXPOL )
- k = MAXPOL;
-for( i=0; i<=k; i++ )
- {
- c[i].n = pt1[i].n;
- c[i].d = pt1[i].d;
- }
-}
-
-
-
-
-/* Evaluate polynomial a(t) at t = x.
- */
-void poleva( a, na, x, s )
-fract a[];
-int na;
-fract *x;
-fract *s;
-{
-int i;
-fract temp;
-
-s->n = a[na].n;
-s->d = a[na].d;
-for( i=na-1; i>=0; i-- )
- {
- rmul( s, x, &temp ); /*s = s * x + a[i];*/
- radd( &a[i], &temp, s );
- }
-}
-
+++ /dev/null
-/* pow.c
- *
- * Power function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, z, pow();
- *
- * z = pow( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/16 and pseudo extended precision arithmetic to
- * obtain an extra three bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -26,26 30000 4.2e-16 7.7e-17
- * DEC -26,26 60000 4.8e-17 9.1e-18
- * 1/26 < x < 26, with log(x) uniformly distributed.
- * -26 < y < 26, y uniformly distributed.
- * IEEE 0,8700 30000 1.5e-14 2.1e-15
- * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pow overflow x**y > MAXNUM INFINITY
- * pow underflow x**y < 1/MAXNUM 0.0
- * pow domain x<0 and y noninteger 0.0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-static char fname[] = {"pow"};
-
-#define SQRTH 0.70710678118654752440
-
-#ifdef UNK
-static double P[] = {
- 4.97778295871696322025E-1,
- 3.73336776063286838734E0,
- 7.69994162726912503298E0,
- 4.66651806774358464979E0
-};
-static double Q[] = {
-/* 1.00000000000000000000E0, */
- 9.33340916416696166113E0,
- 2.79999886606328401649E1,
- 3.35994905342304405431E1,
- 1.39995542032307539578E1
-};
-/* 2^(-i/16), IEEE precision */
-static double A[] = {
- 1.00000000000000000000E0,
- 9.57603280698573700036E-1,
- 9.17004043204671215328E-1,
- 8.78126080186649726755E-1,
- 8.40896415253714502036E-1,
- 8.05245165974627141736E-1,
- 7.71105412703970372057E-1,
- 7.38413072969749673113E-1,
- 7.07106781186547572737E-1,
- 6.77127773468446325644E-1,
- 6.48419777325504820276E-1,
- 6.20928906036742001007E-1,
- 5.94603557501360513449E-1,
- 5.69394317378345782288E-1,
- 5.45253866332628844837E-1,
- 5.22136891213706877402E-1,
- 5.00000000000000000000E-1
-};
-static double B[] = {
- 0.00000000000000000000E0,
- 1.64155361212281360176E-17,
- 4.09950501029074826006E-17,
- 3.97491740484881042808E-17,
--4.83364665672645672553E-17,
- 1.26912513974441574796E-17,
- 1.99100761573282305549E-17,
--1.52339103990623557348E-17,
- 0.00000000000000000000E0
-};
-static double R[] = {
- 1.49664108433729301083E-5,
- 1.54010762792771901396E-4,
- 1.33335476964097721140E-3,
- 9.61812908476554225149E-3,
- 5.55041086645832347466E-2,
- 2.40226506959099779976E-1,
- 6.93147180559945308821E-1
-};
-
-#define douba(k) A[k]
-#define doubb(k) B[k]
-#define MEXP 16383.0
-#ifdef DENORMAL
-#define MNEXP -17183.0
-#else
-#define MNEXP -16383.0
-#endif
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0037776,0156313,0175332,0163602,
-0040556,0167577,0052366,0174245,
-0040766,0062753,0175707,0055564,
-0040625,0052035,0131344,0155636,
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041025,0052644,0154404,0105155,
-0041337,0177772,0007016,0047646,
-0041406,0062740,0154273,0020020,
-0041137,0177054,0106127,0044555,
-};
-static unsigned short A[] = {
-0040200,0000000,0000000,0000000,
-0040165,0022575,0012444,0103314,
-0040152,0140306,0163735,0022071,
-0040140,0146336,0166052,0112341,
-0040127,0042374,0145326,0116553,
-0040116,0022214,0012437,0102201,
-0040105,0063452,0010525,0003333,
-0040075,0004243,0117530,0006067,
-0040065,0002363,0031771,0157145,
-0040055,0054076,0165102,0120513,
-0040045,0177326,0124661,0050471,
-0040036,0172462,0060221,0120422,
-0040030,0033760,0050615,0134251,
-0040021,0141723,0071653,0010703,
-0040013,0112701,0161752,0105727,
-0040005,0125303,0063714,0044173,
-0040000,0000000,0000000,0000000
-};
-static unsigned short B[] = {
-0000000,0000000,0000000,0000000,
-0021473,0040265,0153315,0140671,
-0121074,0062627,0042146,0176454,
-0121413,0003524,0136332,0066212,
-0121767,0046404,0166231,0012553,
-0121257,0015024,0002357,0043574,
-0021736,0106532,0043060,0056206,
-0121310,0020334,0165705,0035326,
-0000000,0000000,0000000,0000000
-};
-
-static unsigned short R[] = {
-0034173,0014076,0137624,0115771,
-0035041,0076763,0003744,0111311,
-0035656,0141766,0041127,0074351,
-0036435,0112533,0073611,0116664,
-0037143,0054106,0134040,0152223,
-0037565,0176757,0176026,0025551,
-0040061,0071027,0173721,0147572
-};
-
-/*
-static double R[] = {
-0.14928852680595608186e-4,
-0.15400290440989764601e-3,
-0.13333541313585784703e-2,
-0.96181290595172416964e-2,
-0.55504108664085595326e-1,
-0.24022650695909537056e0,
-0.69314718055994529629e0
-};
-*/
-#define douba(k) (*(double *)&A[(k)<<2])
-#define doubb(k) (*(double *)&B[(k)<<2])
-#define MEXP 2031.0
-#define MNEXP -2031.0
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x5cf0,0x7f5b,0xdb99,0x3fdf,
-0xdf15,0xea9e,0xddef,0x400d,
-0xeb6f,0x7f78,0xccbd,0x401e,
-0x9b74,0xb65c,0xaa83,0x4012,
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x914e,0x9b20,0xaab4,0x4022,
-0xc9f5,0x41c1,0xffff,0x403b,
-0x6402,0x1b17,0xccbc,0x4040,
-0xe92e,0x918a,0xffc5,0x402b,
-};
-static unsigned short A[] = {
-0x0000,0x0000,0x0000,0x3ff0,
-0x90da,0xa2a4,0xa4af,0x3fee,
-0xa487,0xdcfb,0x5818,0x3fed,
-0x529c,0xdd85,0x199b,0x3fec,
-0xd3ad,0x995a,0xe89f,0x3fea,
-0xf090,0x82a3,0xc491,0x3fe9,
-0xa0db,0x422a,0xace5,0x3fe8,
-0x0187,0x73eb,0xa114,0x3fe7,
-0x3bcd,0x667f,0xa09e,0x3fe6,
-0x5429,0xdd48,0xab07,0x3fe5,
-0x2a27,0xd536,0xbfda,0x3fe4,
-0x3422,0x4c12,0xdea6,0x3fe3,
-0xb715,0x0a31,0x06fe,0x3fe3,
-0x6238,0x6e75,0x387a,0x3fe2,
-0x517b,0x3c7d,0x72b8,0x3fe1,
-0x890f,0x6cf9,0xb558,0x3fe0,
-0x0000,0x0000,0x0000,0x3fe0
-};
-static unsigned short B[] = {
-0x0000,0x0000,0x0000,0x0000,
-0x3707,0xd75b,0xed02,0x3c72,
-0xcc81,0x345d,0xa1cd,0x3c87,
-0x4b27,0x5686,0xe9f1,0x3c86,
-0x6456,0x13b2,0xdd34,0xbc8b,
-0x42e2,0xafec,0x4397,0x3c6d,
-0x82e4,0xd231,0xf46a,0x3c76,
-0x8a76,0xb9d7,0x9041,0xbc71,
-0x0000,0x0000,0x0000,0x0000
-};
-static unsigned short R[] = {
-0x937f,0xd7f2,0x6307,0x3eef,
-0x9259,0x60fc,0x2fbe,0x3f24,
-0xef1d,0xc84a,0xd87e,0x3f55,
-0x33b7,0x6ef1,0xb2ab,0x3f83,
-0x1a92,0xd704,0x6b08,0x3fac,
-0xc56d,0xff82,0xbfbd,0x3fce,
-0x39ef,0xfefa,0x2e42,0x3fe6
-};
-
-#define douba(k) (*(double *)&A[(k)<<2])
-#define doubb(k) (*(double *)&B[(k)<<2])
-#define MEXP 16383.0
-#ifdef DENORMAL
-#define MNEXP -17183.0
-#else
-#define MNEXP -16383.0
-#endif
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3fdf,0xdb99,0x7f5b,0x5cf0,
-0x400d,0xddef,0xea9e,0xdf15,
-0x401e,0xccbd,0x7f78,0xeb6f,
-0x4012,0xaa83,0xb65c,0x9b74
-};
-static unsigned short Q[] = {
-0x4022,0xaab4,0x9b20,0x914e,
-0x403b,0xffff,0x41c1,0xc9f5,
-0x4040,0xccbc,0x1b17,0x6402,
-0x402b,0xffc5,0x918a,0xe92e
-};
-static unsigned short A[] = {
-0x3ff0,0x0000,0x0000,0x0000,
-0x3fee,0xa4af,0xa2a4,0x90da,
-0x3fed,0x5818,0xdcfb,0xa487,
-0x3fec,0x199b,0xdd85,0x529c,
-0x3fea,0xe89f,0x995a,0xd3ad,
-0x3fe9,0xc491,0x82a3,0xf090,
-0x3fe8,0xace5,0x422a,0xa0db,
-0x3fe7,0xa114,0x73eb,0x0187,
-0x3fe6,0xa09e,0x667f,0x3bcd,
-0x3fe5,0xab07,0xdd48,0x5429,
-0x3fe4,0xbfda,0xd536,0x2a27,
-0x3fe3,0xdea6,0x4c12,0x3422,
-0x3fe3,0x06fe,0x0a31,0xb715,
-0x3fe2,0x387a,0x6e75,0x6238,
-0x3fe1,0x72b8,0x3c7d,0x517b,
-0x3fe0,0xb558,0x6cf9,0x890f,
-0x3fe0,0x0000,0x0000,0x0000
-};
-static unsigned short B[] = {
-0x0000,0x0000,0x0000,0x0000,
-0x3c72,0xed02,0xd75b,0x3707,
-0x3c87,0xa1cd,0x345d,0xcc81,
-0x3c86,0xe9f1,0x5686,0x4b27,
-0xbc8b,0xdd34,0x13b2,0x6456,
-0x3c6d,0x4397,0xafec,0x42e2,
-0x3c76,0xf46a,0xd231,0x82e4,
-0xbc71,0x9041,0xb9d7,0x8a76,
-0x0000,0x0000,0x0000,0x0000
-};
-static unsigned short R[] = {
-0x3eef,0x6307,0xd7f2,0x937f,
-0x3f24,0x2fbe,0x60fc,0x9259,
-0x3f55,0xd87e,0xc84a,0xef1d,
-0x3f83,0xb2ab,0x6ef1,0x33b7,
-0x3fac,0x6b08,0xd704,0x1a92,
-0x3fce,0xbfbd,0xff82,0xc56d,
-0x3fe6,0x2e42,0xfefa,0x39ef
-};
-
-#define douba(k) (*(double *)&A[(k)<<2])
-#define doubb(k) (*(double *)&B[(k)<<2])
-#define MEXP 16383.0
-#ifdef DENORMAL
-#define MNEXP -17183.0
-#else
-#define MNEXP -16383.0
-#endif
-#endif
-
-/* log2(e) - 1 */
-#define LOG2EA 0.44269504088896340736
-
-#define F W
-#define Fa Wa
-#define Fb Wb
-#define G W
-#define Ga Wa
-#define Gb u
-#define H W
-#define Ha Wb
-#define Hb Wb
-
-#ifdef ANSIPROT
-extern double floor ( double );
-extern double fabs ( double );
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double powi ( double, int );
-extern int signbit ( double );
-extern int isnan ( double );
-extern int isfinite ( double );
-static double reduc ( double );
-#else
-double floor(), fabs(), frexp(), ldexp();
-double polevl(), p1evl(), powi();
-int signbit(), isnan(), isfinite();
-static double reduc();
-#endif
-extern double MAXNUM;
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-#ifdef NANS
-extern double NAN;
-#endif
-#ifdef MINUSZERO
-extern double NEGZERO;
-#endif
-
-double pow( x, y )
-double x, y;
-{
-double w, z, W, Wa, Wb, ya, yb, u;
-/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
-double aw, ay, wy;
-int e, i, nflg, iyflg, yoddint;
-
-if( y == 0.0 )
- return( 1.0 );
-#ifdef NANS
-if( isnan(x) )
- return( x );
-if( isnan(y) )
- return( y );
-#endif
-if( y == 1.0 )
- return( x );
-
-
-#ifdef INFINITIES
-if( !isfinite(y) && (x == 1.0 || x == -1.0) )
- {
- mtherr( "pow", DOMAIN );
-#ifdef NANS
- return( NAN );
-#else
- return( INFINITY );
-#endif
- }
-#endif
-
-if( x == 1.0 )
- return( 1.0 );
-
-if( y >= MAXNUM )
- {
-#ifdef INFINITIES
- if( x > 1.0 )
- return( INFINITY );
-#else
- if( x > 1.0 )
- return( MAXNUM );
-#endif
- if( x > 0.0 && x < 1.0 )
- return( 0.0);
- if( x < -1.0 )
- {
-#ifdef INFINITIES
- return( INFINITY );
-#else
- return( MAXNUM );
-#endif
- }
- if( x > -1.0 && x < 0.0 )
- return( 0.0 );
- }
-if( y <= -MAXNUM )
- {
- if( x > 1.0 )
- return( 0.0 );
-#ifdef INFINITIES
- if( x > 0.0 && x < 1.0 )
- return( INFINITY );
-#else
- if( x > 0.0 && x < 1.0 )
- return( MAXNUM );
-#endif
- if( x < -1.0 )
- return( 0.0 );
-#ifdef INFINITIES
- if( x > -1.0 && x < 0.0 )
- return( INFINITY );
-#else
- if( x > -1.0 && x < 0.0 )
- return( MAXNUM );
-#endif
- }
-if( x >= MAXNUM )
- {
-#if INFINITIES
- if( y > 0.0 )
- return( INFINITY );
-#else
- if( y > 0.0 )
- return( MAXNUM );
-#endif
- return(0.0);
- }
-/* Set iyflg to 1 if y is an integer. */
-iyflg = 0;
-w = floor(y);
-if( w == y )
- iyflg = 1;
-
-/* Test for odd integer y. */
-yoddint = 0;
-if( iyflg )
- {
- ya = fabs(y);
- ya = floor(0.5 * ya);
- yb = 0.5 * fabs(w);
- if( ya != yb )
- yoddint = 1;
- }
-
-if( x <= -MAXNUM )
- {
- if( y > 0.0 )
- {
-#ifdef INFINITIES
- if( yoddint )
- return( -INFINITY );
- return( INFINITY );
-#else
- if( yoddint )
- return( -MAXNUM );
- return( MAXNUM );
-#endif
- }
- if( y < 0.0 )
- {
-#ifdef MINUSZERO
- if( yoddint )
- return( NEGZERO );
-#endif
- return( 0.0 );
- }
- }
-
-nflg = 0; /* flag = 1 if x<0 raised to integer power */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- {
- if( y < 0.0 )
- {
-#ifdef MINUSZERO
- if( signbit(x) && yoddint )
- return( -INFINITY );
-#endif
-#ifdef INFINITIES
- return( INFINITY );
-#else
- return( MAXNUM );
-#endif
- }
- if( y > 0.0 )
- {
-#ifdef MINUSZERO
- if( signbit(x) && yoddint )
- return( NEGZERO );
-#endif
- return( 0.0 );
- }
- return( 1.0 );
- }
- else
- {
- if( iyflg == 0 )
- { /* noninteger power of negative number */
- mtherr( fname, DOMAIN );
-#ifdef NANS
- return(NAN);
-#else
- return(0.0L);
-#endif
- }
- nflg = 1;
- }
- }
-
-/* Integer power of an integer. */
-
-if( iyflg )
- {
- i = w;
- w = floor(x);
- if( (w == x) && (fabs(y) < 32768.0) )
- {
- w = powi( x, (int) y );
- return( w );
- }
- }
-
-if( nflg )
- x = fabs(x);
-
-/* For results close to 1, use a series expansion. */
-w = x - 1.0;
-aw = fabs(w);
-ay = fabs(y);
-wy = w * y;
-ya = fabs(wy);
-if((aw <= 1.0e-3 && ay <= 1.0)
- || (ya <= 1.0e-3 && ay >= 1.0))
- {
- z = (((((w*(y-5.)/720. + 1./120.)*w*(y-4.) + 1./24.)*w*(y-3.)
- + 1./6.)*w*(y-2.) + 0.5)*w*(y-1.) )*wy + wy + 1.;
- goto done;
- }
-/* These are probably too much trouble. */
-#if 0
-w = y * log(x);
-if (aw > 1.0e-3 && fabs(w) < 1.0e-3)
- {
- z = ((((((
- w/7. + 1.)*w/6. + 1.)*w/5. + 1.)*w/4. + 1.)*w/3. + 1.)*w/2. + 1.)*w + 1.;
- goto done;
- }
-
-if(ya <= 1.0e-3 && aw <= 1.0e-4)
- {
- z = (((((
- wy*1./720.
- + (-w*1./48. + 1./120.) )*wy
- + ((w*17./144. - 1./12.)*w + 1./24.) )*wy
- + (((-w*5./16. + 7./24.)*w - 1./4.)*w + 1./6.) )*wy
- + ((((w*137./360. - 5./12.)*w + 11./24.)*w - 1./2.)*w + 1./2.) )*wy
- + (((((-w*1./6. + 1./5.)*w - 1./4)*w + 1./3.)*w -1./2.)*w ) )*wy
- + wy + 1.0;
- goto done;
- }
-#endif
-
-/* separate significand from exponent */
-x = frexp( x, &e );
-
-#if 0
-/* For debugging, check for gross overflow. */
-if( (e * y) > (MEXP + 1024) )
- goto overflow;
-#endif
-
-/* Find significand of x in antilog table A[]. */
-i = 1;
-if( x <= douba(9) )
- i = 9;
-if( x <= douba(i+4) )
- i += 4;
-if( x <= douba(i+2) )
- i += 2;
-if( x >= douba(1) )
- i = -1;
-i += 1;
-
-
-/* Find (x - A[i])/A[i]
- * in order to compute log(x/A[i]):
- *
- * log(x) = log( a x/a ) = log(a) + log(x/a)
- *
- * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
- */
-x -= douba(i);
-x -= doubb(i/2);
-x /= douba(i);
-
-
-/* rational approximation for log(1+v):
- *
- * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
- */
-z = x*x;
-w = x * ( z * polevl( x, P, 3 ) / p1evl( x, Q, 4 ) );
-w = w - ldexp( z, -1 ); /* w - 0.5 * z */
-
-/* Convert to base 2 logarithm:
- * multiply by log2(e)
- */
-w = w + LOG2EA * w;
-/* Note x was not yet added in
- * to above rational approximation,
- * so do it now, while multiplying
- * by log2(e).
- */
-z = w + LOG2EA * x;
-z = z + x;
-
-/* Compute exponent term of the base 2 logarithm. */
-w = -i;
-w = ldexp( w, -4 ); /* divide by 16 */
-w += e;
-/* Now base 2 log of x is w + z. */
-
-/* Multiply base 2 log by y, in extended precision. */
-
-/* separate y into large part ya
- * and small part yb less than 1/16
- */
-ya = reduc(y);
-yb = y - ya;
-
-
-F = z * y + w * yb;
-Fa = reduc(F);
-Fb = F - Fa;
-
-G = Fa + w * ya;
-Ga = reduc(G);
-Gb = G - Ga;
-
-H = Fb + Gb;
-Ha = reduc(H);
-w = ldexp( Ga+Ha, 4 );
-
-/* Test the power of 2 for overflow */
-if( w > MEXP )
- {
-#ifndef INFINITIES
- mtherr( fname, OVERFLOW );
-#endif
-#ifdef INFINITIES
- if( nflg && yoddint )
- return( -INFINITY );
- return( INFINITY );
-#else
- if( nflg && yoddint )
- return( -MAXNUM );
- return( MAXNUM );
-#endif
- }
-
-if( w < (MNEXP - 1) )
- {
-#ifndef DENORMAL
- mtherr( fname, UNDERFLOW );
-#endif
-#ifdef MINUSZERO
- if( nflg && yoddint )
- return( NEGZERO );
-#endif
- return( 0.0 );
- }
-
-e = w;
-Hb = H - Ha;
-
-if( Hb > 0.0 )
- {
- e += 1;
- Hb -= 0.0625;
- }
-
-/* Now the product y * log2(x) = Hb + e/16.0.
- *
- * Compute base 2 exponential of Hb,
- * where -0.0625 <= Hb <= 0.
- */
-z = Hb * polevl( Hb, R, 6 ); /* z = 2**Hb - 1 */
-
-/* Express e/16 as an integer plus a negative number of 16ths.
- * Find lookup table entry for the fractional power of 2.
- */
-if( e < 0 )
- i = 0;
-else
- i = 1;
-i = e/16 + i;
-e = 16*i - e;
-w = douba( e );
-z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
-z = ldexp( z, i ); /* multiply by integer power of 2 */
-
-done:
-
-/* Negate if odd integer power of negative number */
-if( nflg && yoddint )
- {
-#ifdef MINUSZERO
- if( z == 0.0 )
- z = NEGZERO;
- else
-#endif
- z = -z;
- }
-return( z );
-}
-
-
-/* Find a multiple of 1/16 that is within 1/16 of x. */
-static double reduc(x)
-double x;
-{
-double t;
-
-t = ldexp( x, 4 );
-t = floor( t );
-t = ldexp( t, -4 );
-return(t);
-}
+++ /dev/null
-/* powi.c
- *
- * Real raised to integer power
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, powi();
- * int n;
- *
- * y = powi( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns argument x raised to the nth power.
- * The routine efficiently decomposes n as a sum of powers of
- * two. The desired power is a product of two-to-the-kth
- * powers of x. Thus to compute the 32767 power of x requires
- * 28 multiplications instead of 32767 multiplications.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic x domain n domain # trials peak rms
- * DEC .04,26 -26,26 100000 2.7e-16 4.3e-17
- * IEEE .04,26 -26,26 50000 2.0e-15 3.8e-16
- * IEEE 1,2 -1022,1023 50000 8.6e-14 1.6e-14
- *
- * Returns MAXNUM on overflow, zero on underflow.
- *
- */
-\f
-/* powi.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double log ( double );
-extern double frexp ( double, int * );
-extern int signbit ( double );
-#else
-double log(), frexp();
-int signbit();
-#endif
-extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;
-
-double powi( x, nn )
-double x;
-int nn;
-{
-int n, e, sign, asign, lx;
-double w, y, s;
-
-/* See pow.c for these tests. */
-if( x == 0.0 )
- {
- if( nn == 0 )
- return( 1.0 );
- else if( nn < 0 )
- return( INFINITY );
- else
- {
- if( nn & 1 )
- return( x );
- else
- return( 0.0 );
- }
- }
-
-if( nn == 0 )
- return( 1.0 );
-
-if( nn == -1 )
- return( 1.0/x );
-
-if( x < 0.0 )
- {
- asign = -1;
- x = -x;
- }
-else
- asign = 0;
-
-
-if( nn < 0 )
- {
- sign = -1;
- n = -nn;
- }
-else
- {
- sign = 1;
- n = nn;
- }
-
-/* Even power will be positive. */
-if( (n & 1) == 0 )
- asign = 0;
-
-/* Overflow detection */
-
-/* Calculate approximate logarithm of answer */
-s = frexp( x, &lx );
-e = (lx - 1)*n;
-if( (e == 0) || (e > 64) || (e < -64) )
- {
- s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
- s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
- }
-else
- {
- s = LOGE2 * e;
- }
-
-if( s > MAXLOG )
- {
- mtherr( "powi", OVERFLOW );
- y = INFINITY;
- goto done;
- }
-
-#if DENORMAL
-if( s < MINLOG )
- {
- y = 0.0;
- goto done;
- }
-
-/* Handle tiny denormal answer, but with less accuracy
- * since roundoff error in 1.0/x will be amplified.
- * The precise demarcation should be the gradual underflow threshold.
- */
-if( (s < (-MAXLOG+2.0)) && (sign < 0) )
- {
- x = 1.0/x;
- sign = -sign;
- }
-#else
-/* do not produce denormal answer */
-if( s < -MAXLOG )
- return(0.0);
-#endif
-
-
-/* First bit of the power */
-if( n & 1 )
- y = x;
-
-else
- y = 1.0;
-
-w = x;
-n >>= 1;
-while( n )
- {
- w = w * w; /* arg to the 2-to-the-kth power */
- if( n & 1 ) /* if that bit is set, then include in product */
- y *= w;
- n >>= 1;
- }
-
-if( sign < 0 )
- y = 1.0/y;
-
-done:
-
-if( asign )
- {
- /* odd power of negative number */
- if( y == 0.0 )
- y = NEGZERO;
- else
- y = -y;
- }
-return(y);
-}
+++ /dev/null
-/* psi.c
- *
- * Psi (digamma) function
- *
- *
- * SYNOPSIS:
- *
- * double x, y, psi();
- *
- * y = psi( x );
- *
- *
- * DESCRIPTION:
- *
- * d -
- * psi(x) = -- ln | (x)
- * dx
- *
- * is the logarithmic derivative of the gamma function.
- * For integer x,
- * n-1
- * -
- * psi(n) = -EUL + > 1/k.
- * -
- * k=1
- *
- * This formula is used for 0 < n <= 10. If x is negative, it
- * is transformed to a positive argument by the reflection
- * formula psi(1-x) = psi(x) + pi cot(pi x).
- * For general positive x, the argument is made greater than 10
- * using the recurrence psi(x+1) = psi(x) + 1/x.
- * Then the following asymptotic expansion is applied:
- *
- * inf. B
- * - 2k
- * psi(x) = log(x) - 1/2x - > -------
- * - 2k
- * k=1 2k x
- *
- * where the B2k are Bernoulli numbers.
- *
- * ACCURACY:
- * Relative error (except absolute when |psi| < 1):
- * arithmetic domain # trials peak rms
- * DEC 0,30 2500 1.7e-16 2.0e-17
- * IEEE 0,30 30000 1.3e-15 1.4e-16
- * IEEE -30,0 40000 1.5e-15 2.2e-16
- *
- * ERROR MESSAGES:
- * message condition value returned
- * psi singularity x integer <=0 MAXNUM
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double A[] = {
- 8.33333333333333333333E-2,
--2.10927960927960927961E-2,
- 7.57575757575757575758E-3,
--4.16666666666666666667E-3,
- 3.96825396825396825397E-3,
--8.33333333333333333333E-3,
- 8.33333333333333333333E-2
-};
-#endif
-
-#ifdef DEC
-static unsigned short A[] = {
-0037252,0125252,0125252,0125253,
-0136654,0145314,0126312,0146255,
-0036370,0037017,0101740,0174076,
-0136210,0104210,0104210,0104211,
-0036202,0004040,0101010,0020202,
-0136410,0104210,0104210,0104211,
-0037252,0125252,0125252,0125253
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short A[] = {
-0x5555,0x5555,0x5555,0x3fb5,
-0x5996,0x9599,0x9959,0xbf95,
-0x1f08,0xf07c,0x07c1,0x3f7f,
-0x1111,0x1111,0x1111,0xbf71,
-0x0410,0x1041,0x4104,0x3f70,
-0x1111,0x1111,0x1111,0xbf81,
-0x5555,0x5555,0x5555,0x3fb5
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short A[] = {
-0x3fb5,0x5555,0x5555,0x5555,
-0xbf95,0x9959,0x9599,0x5996,
-0x3f7f,0x07c1,0xf07c,0x1f08,
-0xbf71,0x1111,0x1111,0x1111,
-0x3f70,0x4104,0x1041,0x0410,
-0xbf81,0x1111,0x1111,0x1111,
-0x3fb5,0x5555,0x5555,0x5555
-};
-#endif
-
-#define EUL 0.57721566490153286061
-
-#ifdef ANSIPROT
-extern double floor ( double );
-extern double log ( double );
-extern double tan ( double );
-extern double polevl ( double, void *, int );
-#else
-double floor(), log(), tan(), polevl();
-#endif
-extern double PI, MAXNUM;
-
-
-double psi(x)
-double x;
-{
-double p, q, nz, s, w, y, z;
-int i, n, negative;
-
-negative = 0;
-nz = 0.0;
-
-if( x <= 0.0 )
- {
- negative = 1;
- q = x;
- p = floor(q);
- if( p == q )
- {
- mtherr( "psi", SING );
- return( MAXNUM );
- }
-/* Remove the zeros of tan(PI x)
- * by subtracting the nearest integer from x
- */
- nz = q - p;
- if( nz != 0.5 )
- {
- if( nz > 0.5 )
- {
- p += 1.0;
- nz = q - p;
- }
- nz = PI/tan(PI*nz);
- }
- else
- {
- nz = 0.0;
- }
- x = 1.0 - x;
- }
-
-/* check for positive integer up to 10 */
-if( (x <= 10.0) && (x == floor(x)) )
- {
- y = 0.0;
- n = x;
- for( i=1; i<n; i++ )
- {
- w = i;
- y += 1.0/w;
- }
- y -= EUL;
- goto done;
- }
-
-s = x;
-w = 0.0;
-while( s < 10.0 )
- {
- w += 1.0/s;
- s += 1.0;
- }
-
-if( s < 1.0e17 )
- {
- z = 1.0/(s * s);
- y = z * polevl( z, A, 6 );
- }
-else
- y = 0.0;
-
-y = log(s) - (0.5/s) - y - w;
-
-done:
-
-if( negative )
- {
- y -= nz;
- }
-
-return(y);
-}
+++ /dev/null
-/* revers.c
- *
- * Reversion of power series
- *
- *
- *
- * SYNOPSIS:
- *
- * extern int MAXPOL;
- * int n;
- * double x[n+1], y[n+1];
- *
- * polini(n);
- * revers( y, x, n );
- *
- * Note, polini() initializes the polynomial arithmetic subroutines;
- * see polyn.c.
- *
- *
- * DESCRIPTION:
- *
- * If
- *
- * inf
- * - i
- * y(x) = > a x
- * - i
- * i=1
- *
- * then
- *
- * inf
- * - j
- * x(y) = > A y ,
- * - j
- * j=1
- *
- * where
- * 1
- * A = ---
- * 1 a
- * 1
- *
- * etc. The coefficients of x(y) are found by expanding
- *
- * inf inf
- * - - i
- * x(y) = > A > a x
- * - j - i
- * j=1 i=1
- *
- * and setting each coefficient of x , higher than the first,
- * to zero.
- *
- *
- *
- * RESTRICTIONS:
- *
- * y[0] must be zero, and y[1] must be nonzero.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern int MAXPOL; /* initialized by polini() */
-
-#ifdef ANSIPROT
-/* See polyn.c. */
-void polmov ( double *, int, double * );
-void polclr ( double *, int );
-void poladd ( double *, int, double *, int, double * );
-void polmul ( double *, int, double *, int, double * );
-void * malloc ( long );
-void free ( void * );
-#else
-void polmov(), polclr(), poladd(), polmul();
-void * malloc();
-void free ();
-#endif
-
-void revers( y, x, n)
-double y[], x[];
-int n;
-{
-double *yn, *yp, *ysum;
-int j;
-
-if( y[1] == 0.0 )
- mtherr( "revers", DOMAIN );
-/* printf( "revers: y[1] = 0\n" );*/
-j = (MAXPOL + 1) * sizeof(double);
-yn = (double *)malloc(j);
-yp = (double *)malloc(j);
-ysum = (double *)malloc(j);
-
-polmov( y, n, yn );
-polclr( ysum, n );
-x[0] = 0.0;
-x[1] = 1.0/y[1];
-for( j=2; j<=n; j++ )
- {
-/* A_(j-1) times the expansion of y^(j-1) */
- polmul( &x[j-1], 0, yn, n, yp );
-/* The expansion of the sum of A_k y^k up to k=j-1 */
- poladd( yp, n, ysum, n, ysum );
-/* The expansion of y^j */
- polmul( yn, n, y, n, yn );
-/* The coefficient A_j to make the sum up to k=j equal to zero */
- x[j] = -ysum[j]/yn[j];
- }
-free(yn);
-free(yp);
-free(ysum);
-}
-
-
-#if 0
-/* Demonstration program
- */
-#define N 10
-double y[N], x[N];
-double fac();
-
-main()
-{
-double a, odd;
-int i;
-
-polini( N-1 );
-a = 1.0;
-y[0] = 0.0;
-odd = 1.0;
-for( i=1; i<N; i++ )
- {
-/* sin(x) */
-/*
- if( i & 1 )
- {
- y[i] = odd/fac(i);
- odd = -odd;
- }
- else
- y[i] = 0.0;
-*/
- y[i] = 1.0/fac(i);
- }
-revers( y, x, N-1 );
-for( i=0; i<N; i++ )
- printf( "%2d %.10e %.10e\n", i, x[i], y[i] );
-}
-#endif
+++ /dev/null
-/* rgamma.c
- *
- * Reciprocal gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, rgamma();
- *
- * y = rgamma( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns one divided by the gamma function of the argument.
- *
- * The function is approximated by a Chebyshev expansion in
- * the interval [0,1]. Range reduction is by recurrence
- * for arguments between -34.034 and +34.84425627277176174.
- * 1/MAXNUM is returned for positive arguments outside this
- * range. For arguments less than -34.034 the cosecant
- * reflection formula is applied; lograrithms are employed
- * to avoid unnecessary overflow.
- *
- * The reciprocal gamma function has no singularities,
- * but overflow and underflow may occur for large arguments.
- * These conditions return either MAXNUM or 1/MAXNUM with
- * appropriate sign.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -30,+30 4000 1.2e-16 1.8e-17
- * IEEE -30,+30 30000 1.1e-15 2.0e-16
- * For arguments less than -34.034 the peak error is on the
- * order of 5e-15 (DEC), excepting overflow or underflow.
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1985, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for reciprocal gamma function
- * in interval 0 to 1. Function is 1/(x gamma(x)) - 1
- */
-
-#ifdef UNK
-static double R[] = {
- 3.13173458231230000000E-17,
--6.70718606477908000000E-16,
- 2.20039078172259550000E-15,
- 2.47691630348254132600E-13,
--6.60074100411295197440E-12,
- 5.13850186324226978840E-11,
- 1.08965386454418662084E-9,
--3.33964630686836942556E-8,
- 2.68975996440595483619E-7,
- 2.96001177518801696639E-6,
--8.04814124978471142852E-5,
- 4.16609138709688864714E-4,
- 5.06579864028608725080E-3,
--6.41925436109158228810E-2,
--4.98558728684003594785E-3,
- 1.27546015610523951063E-1
-};
-#endif
-
-#ifdef DEC
-static unsigned short R[] = {
-0022420,0066376,0176751,0071636,
-0123501,0051114,0042104,0131153,
-0024036,0107013,0126504,0033361,
-0025613,0070040,0035174,0162316,
-0126750,0037060,0077775,0122202,
-0027541,0177143,0037675,0105150,
-0030625,0141311,0075005,0115436,
-0132017,0067714,0125033,0014721,
-0032620,0063707,0105256,0152643,
-0033506,0122235,0072757,0170053,
-0134650,0144041,0015617,0016143,
-0035332,0066125,0000776,0006215,
-0036245,0177377,0137173,0131432,
-0137203,0073541,0055645,0141150,
-0136243,0057043,0026226,0017362,
-0037402,0115554,0033441,0012310
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short R[] = {
-0x2e74,0xdfbd,0x0d9f,0x3c82,
-0x964d,0x8888,0x2a49,0xbcc8,
-0x86de,0x75a8,0xd1c1,0x3ce3,
-0x9c9a,0x074f,0x6e04,0x3d51,
-0xb490,0x0fff,0x07c6,0xbd9d,
-0xb14d,0x67f7,0x3fcc,0x3dcc,
-0xb364,0x2f40,0xb859,0x3e12,
-0x633a,0x9543,0xedf9,0xbe61,
-0xdab4,0xf155,0x0cf8,0x3e92,
-0xfe05,0xaebd,0xd493,0x3ec8,
-0xe38c,0x2371,0x1904,0xbf15,
-0xc192,0xa03f,0x4d8a,0x3f3b,
-0x7663,0xf7cf,0xbfdf,0x3f74,
-0xb84d,0x2b74,0x6eec,0xbfb0,
-0xc3de,0x6592,0x6bc4,0xbf74,
-0x2299,0x86e4,0x536d,0x3fc0
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short R[] = {
-0x3c82,0x0d9f,0xdfbd,0x2e74,
-0xbcc8,0x2a49,0x8888,0x964d,
-0x3ce3,0xd1c1,0x75a8,0x86de,
-0x3d51,0x6e04,0x074f,0x9c9a,
-0xbd9d,0x07c6,0x0fff,0xb490,
-0x3dcc,0x3fcc,0x67f7,0xb14d,
-0x3e12,0xb859,0x2f40,0xb364,
-0xbe61,0xedf9,0x9543,0x633a,
-0x3e92,0x0cf8,0xf155,0xdab4,
-0x3ec8,0xd493,0xaebd,0xfe05,
-0xbf15,0x1904,0x2371,0xe38c,
-0x3f3b,0x4d8a,0xa03f,0xc192,
-0x3f74,0xbfdf,0xf7cf,0x7663,
-0xbfb0,0x6eec,0x2b74,0xb84d,
-0xbf74,0x6bc4,0x6592,0xc3de,
-0x3fc0,0x536d,0x86e4,0x2299
-};
-#endif
-
-static char name[] = "rgamma";
-
-#ifdef ANSIPROT
-extern double chbevl ( double, void *, int );
-extern double exp ( double );
-extern double log ( double );
-extern double sin ( double );
-extern double lgam ( double );
-#else
-double chbevl(), exp(), log(), sin(), lgam();
-#endif
-extern double PI, MAXLOG, MAXNUM;
-
-
-double rgamma(x)
-double x;
-{
-double w, y, z;
-int sign;
-
-if( x > 34.84425627277176174)
- {
- mtherr( name, UNDERFLOW );
- return(1.0/MAXNUM);
- }
-if( x < -34.034 )
- {
- w = -x;
- z = sin( PI*w );
- if( z == 0.0 )
- return(0.0);
- if( z < 0.0 )
- {
- sign = 1;
- z = -z;
- }
- else
- sign = -1;
-
- y = log( w * z ) - log(PI) + lgam(w);
- if( y < -MAXLOG )
- {
- mtherr( name, UNDERFLOW );
- return( sign * 1.0 / MAXNUM );
- }
- if( y > MAXLOG )
- {
- mtherr( name, OVERFLOW );
- return( sign * MAXNUM );
- }
- return( sign * exp(y));
- }
-z = 1.0;
-w = x;
-
-while( w > 1.0 ) /* Downward recurrence */
- {
- w -= 1.0;
- z *= w;
- }
-while( w < 0.0 ) /* Upward recurrence */
- {
- z /= w;
- w += 1.0;
- }
-if( w == 0.0 ) /* Nonpositive integer */
- return(0.0);
-if( w == 1.0 ) /* Other integer */
- return( 1.0/z );
-
-y = w * ( 1.0 + chbevl( 4.0*w-2.0, R, 16 ) ) / z;
-return(y);
-}
+++ /dev/null
-/*
- * June 19, 2001 Manuel Novoa III
- *
- * Replaced cephes round (which was actually round to nearest or even)
- * with a (really lame actually) version that always rounds away from 0
- * in conformance with ANSI/ISO.
- *
- * This doesn't check for inf or nan (hence the lame part) but the
- * cephes function it replaces didn't either. I plan to deal with
- * those issues when I rework things w.r.t. common code.
- *
- * Also, for now rename the original cephes round routine to rint since
- * it behaves the same for the default rounding mode (round to nearest).
- * This will have to be changed off course when floating point env
- * control functions are added.
- */
-
-#include <math.h>
-
-double round(x)
-double x;
-{
- double ax, fax;
-
- ax = fabs(x);
- fax = floor(ax);
- if (ax - fax >= 0.5) {
- fax += 1.0;
- }
- if (x < 0) {
- x = -fax;
- } else {
- x = fax;
- }
- return x;
-}
-
-/***********************************************************************/
-/*
- * Returns the nearest integer to x as a double precision
- * floating point result. If x ends in 0.5 exactly, the
- * nearest even integer is chosen.
- */
-/*
-Originally round from
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-double rint(x)
-double x;
-{
-double y, r;
-
-/* Largest integer <= x */
-y = floor(x);
-
-/* Fractional part */
-r = x - y;
-
-/* Round up to nearest. */
-if( r > 0.5 )
- goto rndup;
-
-/* Round to even */
-if( r == 0.5 )
- {
- r = y - 2.0 * floor( 0.5 * y );
- if( r == 1.0 )
- {
-rndup:
- y += 1.0;
- }
- }
-
-/* Else round down. */
-return(y);
-}
+++ /dev/null
-/* Null stubs for coprocessor precision settings */
-
-int
-sprec() {return 0; }
-
-int
-dprec() {return 0; }
-
-int
-ldprec() {return 0; }
+++ /dev/null
-/* shichi.c
- *
- * Hyperbolic sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, Chi, Shi, shichi();
- *
- * shichi( x, &Chi, &Shi );
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integrals
- *
- * x
- * -
- * | | cosh t - 1
- * Chi(x) = eul + ln x + | ----------- dt,
- * | | t
- * -
- * 0
- *
- * x
- * -
- * | | sinh t
- * Shi(x) = | ------ dt
- * | | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are evaluated by power series for x < 8
- * and by Chebyshev expansions for x between 8 and 88.
- * For large x, both functions approach exp(x)/2x.
- * Arguments greater than 88 in magnitude return MAXNUM.
- *
- *
- * ACCURACY:
- *
- * Test interval 0 to 88.
- * Relative error:
- * arithmetic function # trials peak rms
- * DEC Shi 3000 9.1e-17
- * IEEE Shi 30000 6.9e-16 1.6e-16
- * Absolute error, except relative when |Chi| > 1:
- * DEC Chi 2500 9.3e-17
- * IEEE Chi 30000 8.4e-16 1.4e-16
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-/* x exp(-x) shi(x), inverted interval 8 to 18 */
-static double S1[] = {
- 1.83889230173399459482E-17,
--9.55485532279655569575E-17,
- 2.04326105980879882648E-16,
- 1.09896949074905343022E-15,
--1.31313534344092599234E-14,
- 5.93976226264314278932E-14,
--3.47197010497749154755E-14,
--1.40059764613117131000E-12,
- 9.49044626224223543299E-12,
--1.61596181145435454033E-11,
--1.77899784436430310321E-10,
- 1.35455469767246947469E-9,
--1.03257121792819495123E-9,
--3.56699611114982536845E-8,
- 1.44818877384267342057E-7,
- 7.82018215184051295296E-7,
--5.39919118403805073710E-6,
--3.12458202168959833422E-5,
- 8.90136741950727517826E-5,
- 2.02558474743846862168E-3,
- 2.96064440855633256972E-2,
- 1.11847751047257036625E0
-};
-
-/* x exp(-x) shi(x), inverted interval 18 to 88 */
-static double S2[] = {
--1.05311574154850938805E-17,
- 2.62446095596355225821E-17,
- 8.82090135625368160657E-17,
--3.38459811878103047136E-16,
--8.30608026366935789136E-16,
- 3.93397875437050071776E-15,
- 1.01765565969729044505E-14,
--4.21128170307640802703E-14,
--1.60818204519802480035E-13,
- 3.34714954175994481761E-13,
- 2.72600352129153073807E-12,
- 1.66894954752839083608E-12,
--3.49278141024730899554E-11,
--1.58580661666482709598E-10,
--1.79289437183355633342E-10,
- 1.76281629144264523277E-9,
- 1.69050228879421288846E-8,
- 1.25391771228487041649E-7,
- 1.16229947068677338732E-6,
- 1.61038260117376323993E-5,
- 3.49810375601053973070E-4,
- 1.28478065259647610779E-2,
- 1.03665722588798326712E0
-};
-#endif
-
-#ifdef DEC
-static unsigned short S1[] = {
-0022251,0115635,0165120,0006574,
-0122734,0050751,0020305,0101356,
-0023153,0111154,0011103,0177462,
-0023636,0060321,0060253,0124246,
-0124554,0106655,0152525,0166400,
-0025205,0140145,0171006,0106556,
-0125034,0056427,0004205,0176022,
-0126305,0016731,0025011,0134453,
-0027046,0172453,0112604,0116235,
-0127216,0022071,0116600,0137667,
-0130103,0115126,0071104,0052535,
-0030672,0025450,0010071,0141414,
-0130615,0165136,0132137,0177737,
-0132031,0031611,0074436,0175407,
-0032433,0077602,0104345,0060076,
-0033121,0165741,0167177,0172433,
-0133665,0025262,0174621,0022612,
-0134403,0006761,0124566,0145405,
-0034672,0126332,0034737,0116744,
-0036004,0137654,0037332,0131766,
-0036762,0104466,0121445,0124326,
-0040217,0025105,0062145,0042640
-};
-
-static unsigned short S2[] = {
-0122102,0041774,0016051,0055137,
-0022362,0010125,0007651,0015773,
-0022713,0062551,0040227,0071645,
-0123303,0015732,0025731,0146570,
-0123557,0064016,0002067,0067711,
-0024215,0136214,0132374,0124234,
-0024467,0051425,0071066,0064210,
-0125075,0124305,0135123,0024170,
-0125465,0010261,0005560,0034232,
-0025674,0066602,0030724,0174557,
-0026477,0151520,0051510,0067250,
-0026352,0161076,0113154,0116271,
-0127431,0116470,0177465,0127274,
-0130056,0056174,0170315,0013321,
-0130105,0020575,0075327,0036710,
-0030762,0043625,0113046,0125035,
-0031621,0033211,0154354,0022077,
-0032406,0121555,0074270,0041141,
-0033234,0000116,0041611,0173743,
-0034207,0013263,0174715,0115563,
-0035267,0063300,0175753,0117266,
-0036522,0077633,0033255,0136200,
-0040204,0130457,0014454,0166254
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short S1[] = {
-0x01b0,0xbd4a,0x3373,0x3c75,
-0xb05e,0x2418,0x8a3d,0xbc9b,
-0x7fe6,0x8248,0x724d,0x3cad,
-0x7515,0x2c15,0xcc1a,0x3cd3,
-0xbda0,0xbaaa,0x91b5,0xbd0d,
-0xd1ae,0xbe40,0xb80c,0x3d30,
-0xbf82,0xe110,0x8ba2,0xbd23,
-0x3725,0x2541,0xa3bb,0xbd78,
-0x9394,0x72b0,0xdea5,0x3da4,
-0x17f7,0x33b0,0xc487,0xbdb1,
-0x8aac,0xce48,0x734a,0xbde8,
-0x3862,0x0207,0x4565,0x3e17,
-0xfffc,0xd68b,0xbd4b,0xbe11,
-0xdf61,0x2f23,0x2671,0xbe63,
-0xac08,0x511c,0x6ff0,0x3e83,
-0xfea3,0x3dcf,0x3d7c,0x3eaa,
-0x24b1,0x5f32,0xa556,0xbed6,
-0xd961,0x352e,0x61be,0xbf00,
-0xf3bd,0x473b,0x559b,0x3f17,
-0x567f,0x87db,0x97f5,0x3f60,
-0xb51b,0xd464,0x5126,0x3f9e,
-0xa8b4,0xac8c,0xe548,0x3ff1
-};
-
-static unsigned short S2[] = {
-0x2b4c,0x8385,0x487f,0xbc68,
-0x237f,0xa1f5,0x420a,0x3c7e,
-0xee75,0x2812,0x6cad,0x3c99,
-0x39af,0x457b,0x637b,0xbcb8,
-0xedf9,0xc086,0xed01,0xbccd,
-0x9513,0x969f,0xb791,0x3cf1,
-0xcd11,0xae46,0xea62,0x3d06,
-0x650f,0xb74a,0xb518,0xbd27,
-0x0713,0x216e,0xa216,0xbd46,
-0x9f2e,0x463a,0x8db0,0x3d57,
-0x0dd5,0x0a69,0xfa6a,0x3d87,
-0x9397,0xd2cd,0x5c47,0x3d7d,
-0xb5d8,0x1fe6,0x33a7,0xbdc3,
-0xa2da,0x9e19,0xcb8f,0xbde5,
-0xe7b9,0xaf5a,0xa42f,0xbde8,
-0xd544,0xb2c4,0x48f2,0x3e1e,
-0x8488,0x3b1d,0x26d1,0x3e52,
-0x084c,0xaf17,0xd46d,0x3e80,
-0x3efc,0xc871,0x8009,0x3eb3,
-0xb36e,0x7f39,0xe2d6,0x3ef0,
-0x73d7,0x1f7d,0xecd8,0x3f36,
-0xb790,0x66d5,0x4ff3,0x3f8a,
-0x9d96,0xe325,0x9625,0x3ff0
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short S1[] = {
-0x3c75,0x3373,0xbd4a,0x01b0,
-0xbc9b,0x8a3d,0x2418,0xb05e,
-0x3cad,0x724d,0x8248,0x7fe6,
-0x3cd3,0xcc1a,0x2c15,0x7515,
-0xbd0d,0x91b5,0xbaaa,0xbda0,
-0x3d30,0xb80c,0xbe40,0xd1ae,
-0xbd23,0x8ba2,0xe110,0xbf82,
-0xbd78,0xa3bb,0x2541,0x3725,
-0x3da4,0xdea5,0x72b0,0x9394,
-0xbdb1,0xc487,0x33b0,0x17f7,
-0xbde8,0x734a,0xce48,0x8aac,
-0x3e17,0x4565,0x0207,0x3862,
-0xbe11,0xbd4b,0xd68b,0xfffc,
-0xbe63,0x2671,0x2f23,0xdf61,
-0x3e83,0x6ff0,0x511c,0xac08,
-0x3eaa,0x3d7c,0x3dcf,0xfea3,
-0xbed6,0xa556,0x5f32,0x24b1,
-0xbf00,0x61be,0x352e,0xd961,
-0x3f17,0x559b,0x473b,0xf3bd,
-0x3f60,0x97f5,0x87db,0x567f,
-0x3f9e,0x5126,0xd464,0xb51b,
-0x3ff1,0xe548,0xac8c,0xa8b4
-};
-
-static unsigned short S2[] = {
-0xbc68,0x487f,0x8385,0x2b4c,
-0x3c7e,0x420a,0xa1f5,0x237f,
-0x3c99,0x6cad,0x2812,0xee75,
-0xbcb8,0x637b,0x457b,0x39af,
-0xbccd,0xed01,0xc086,0xedf9,
-0x3cf1,0xb791,0x969f,0x9513,
-0x3d06,0xea62,0xae46,0xcd11,
-0xbd27,0xb518,0xb74a,0x650f,
-0xbd46,0xa216,0x216e,0x0713,
-0x3d57,0x8db0,0x463a,0x9f2e,
-0x3d87,0xfa6a,0x0a69,0x0dd5,
-0x3d7d,0x5c47,0xd2cd,0x9397,
-0xbdc3,0x33a7,0x1fe6,0xb5d8,
-0xbde5,0xcb8f,0x9e19,0xa2da,
-0xbde8,0xa42f,0xaf5a,0xe7b9,
-0x3e1e,0x48f2,0xb2c4,0xd544,
-0x3e52,0x26d1,0x3b1d,0x8488,
-0x3e80,0xd46d,0xaf17,0x084c,
-0x3eb3,0x8009,0xc871,0x3efc,
-0x3ef0,0xe2d6,0x7f39,0xb36e,
-0x3f36,0xecd8,0x1f7d,0x73d7,
-0x3f8a,0x4ff3,0x66d5,0xb790,
-0x3ff0,0x9625,0xe325,0x9d96
-};
-#endif
-
-
-#ifdef UNK
-/* x exp(-x) chin(x), inverted interval 8 to 18 */
-static double C1[] = {
--8.12435385225864036372E-18,
- 2.17586413290339214377E-17,
- 5.22624394924072204667E-17,
--9.48812110591690559363E-16,
- 5.35546311647465209166E-15,
--1.21009970113732918701E-14,
--6.00865178553447437951E-14,
- 7.16339649156028587775E-13,
--2.93496072607599856104E-12,
--1.40359438136491256904E-12,
- 8.76302288609054966081E-11,
--4.40092476213282340617E-10,
--1.87992075640569295479E-10,
- 1.31458150989474594064E-8,
--4.75513930924765465590E-8,
--2.21775018801848880741E-7,
- 1.94635531373272490962E-6,
- 4.33505889257316408893E-6,
--6.13387001076494349496E-5,
--3.13085477492997465138E-4,
- 4.97164789823116062801E-4,
- 2.64347496031374526641E-2,
- 1.11446150876699213025E0
-};
-
-/* x exp(-x) chin(x), inverted interval 18 to 88 */
-static double C2[] = {
- 8.06913408255155572081E-18,
--2.08074168180148170312E-17,
--5.98111329658272336816E-17,
- 2.68533951085945765591E-16,
- 4.52313941698904694774E-16,
--3.10734917335299464535E-15,
--4.42823207332531972288E-15,
- 3.49639695410806959872E-14,
- 6.63406731718911586609E-14,
--3.71902448093119218395E-13,
--1.27135418132338309016E-12,
- 2.74851141935315395333E-12,
- 2.33781843985453438400E-11,
- 2.71436006377612442764E-11,
--2.56600180000355990529E-10,
--1.61021375163803438552E-9,
--4.72543064876271773512E-9,
--3.00095178028681682282E-9,
- 7.79387474390914922337E-8,
- 1.06942765566401507066E-6,
- 1.59503164802313196374E-5,
- 3.49592575153777996871E-4,
- 1.28475387530065247392E-2,
- 1.03665693917934275131E0
-};
-#endif
-
-#ifdef DEC
-static unsigned short C1[] = {
-0122025,0157055,0021702,0021427,
-0022310,0130043,0123265,0022340,
-0022561,0002231,0017746,0013043,
-0123610,0136375,0002352,0024467,
-0024300,0171555,0141300,0000446,
-0124531,0176777,0126210,0035616,
-0125207,0046604,0167760,0077132,
-0026111,0120666,0026606,0064143,
-0126516,0103615,0054127,0005436,
-0126305,0104721,0025415,0004134,
-0027700,0131556,0164725,0157553,
-0130361,0170602,0077274,0055406,
-0130116,0131420,0125472,0017231,
-0031541,0153747,0177312,0056304,
-0132114,0035517,0041545,0043151,
-0132556,0020415,0110044,0172442,
-0033402,0117041,0031152,0010364,
-0033621,0072737,0050647,0013720,
-0134600,0121366,0140010,0063265,
-0135244,0022637,0013756,0044742,
-0035402,0052052,0006523,0043564,
-0036730,0106660,0020277,0162146,
-0040216,0123254,0135147,0005724
-};
-
-static unsigned short C2[] = {
-0022024,0154550,0104311,0144257,
-0122277,0165037,0133443,0155601,
-0122611,0165102,0157053,0055252,
-0023232,0146235,0153511,0113222,
-0023402,0057340,0145304,0010471,
-0124137,0164171,0113071,0100002,
-0124237,0105473,0056130,0022022,
-0025035,0073266,0056746,0164433,
-0025225,0061313,0055600,0165407,
-0125721,0056312,0107613,0051215,
-0126262,0166534,0115336,0066653,
-0026501,0064307,0127442,0065573,
-0027315,0121375,0142020,0045356,
-0027356,0140764,0070641,0046570,
-0130215,0010503,0146335,0177737,
-0130735,0047134,0015215,0163665,
-0131242,0056523,0155276,0050053,
-0131116,0034515,0050707,0163512,
-0032247,0057507,0107545,0032007,
-0033217,0104501,0021706,0025047,
-0034205,0146413,0033746,0076562,
-0035267,0044605,0065355,0002772,
-0036522,0077173,0130716,0170304,
-0040204,0130454,0130571,0027270
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short C1[] = {
-0x4463,0xa478,0xbbc5,0xbc62,
-0xa49c,0x74d6,0x1604,0x3c79,
-0xc2c4,0x23fc,0x2093,0x3c8e,
-0x4527,0xa09d,0x179f,0xbcd1,
-0x0025,0xb858,0x1e6d,0x3cf8,
-0x0772,0xf591,0x3fbf,0xbd0b,
-0x0fcb,0x9dfe,0xe9b0,0xbd30,
-0xcd0c,0xc5b0,0x3436,0x3d69,
-0xe164,0xab0a,0xd0f1,0xbd89,
-0xa10c,0x2561,0xb13a,0xbd78,
-0xbbed,0xdd3a,0x166d,0x3dd8,
-0x8b61,0x4fd7,0x3e30,0xbdfe,
-0x43d3,0x1567,0xd662,0xbde9,
-0x4b98,0xffd9,0x3afc,0x3e4c,
-0xa8cd,0xe86c,0x8769,0xbe69,
-0x9ea4,0xb204,0xc421,0xbe8d,
-0x421f,0x264d,0x53c4,0x3ec0,
-0xe2fa,0xea34,0x2ebb,0x3ed2,
-0x0cd7,0xd801,0x145e,0xbf10,
-0xc93c,0xe2fd,0x84b3,0xbf34,
-0x68ef,0x41aa,0x4a85,0x3f40,
-0xfc8d,0x0417,0x11b6,0x3f9b,
-0xe17b,0x974c,0xd4d5,0x3ff1
-};
-
-static unsigned short C2[] = {
-0x3916,0x1119,0x9b2d,0x3c62,
-0x7b70,0xf6e4,0xfd43,0xbc77,
-0x6b55,0x5bc5,0x3d48,0xbc91,
-0x32d2,0xbae9,0x5993,0x3cb3,
-0x8227,0x1958,0x4bdc,0x3cc0,
-0x3000,0x32c7,0xfd0f,0xbceb,
-0x0482,0x6b8b,0xf167,0xbcf3,
-0xdd23,0xcbbc,0xaed6,0x3d23,
-0x1d61,0x6b70,0xac59,0x3d32,
-0x6a52,0x51f1,0x2b99,0xbd5a,
-0xcdb5,0x935b,0x5dab,0xbd76,
-0x4d6f,0xf5e4,0x2d18,0x3d88,
-0x095e,0xb882,0xb45f,0x3db9,
-0x29af,0x8e34,0xd83e,0x3dbd,
-0xbffc,0x799b,0xa228,0xbdf1,
-0xbcf7,0x8351,0xa9cb,0xbe1b,
-0xca05,0x7b57,0x4baa,0xbe34,
-0xfce9,0xaa38,0xc729,0xbe29,
-0xa681,0xf1ec,0xebe8,0x3e74,
-0xc545,0x2478,0xf128,0x3eb1,
-0xcfae,0x66fc,0xb9a1,0x3ef0,
-0xa0bf,0xad5d,0xe930,0x3f36,
-0xde19,0x7639,0x4fcf,0x3f8a,
-0x25d7,0x962f,0x9625,0x3ff0
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short C1[] = {
-0xbc62,0xbbc5,0xa478,0x4463,
-0x3c79,0x1604,0x74d6,0xa49c,
-0x3c8e,0x2093,0x23fc,0xc2c4,
-0xbcd1,0x179f,0xa09d,0x4527,
-0x3cf8,0x1e6d,0xb858,0x0025,
-0xbd0b,0x3fbf,0xf591,0x0772,
-0xbd30,0xe9b0,0x9dfe,0x0fcb,
-0x3d69,0x3436,0xc5b0,0xcd0c,
-0xbd89,0xd0f1,0xab0a,0xe164,
-0xbd78,0xb13a,0x2561,0xa10c,
-0x3dd8,0x166d,0xdd3a,0xbbed,
-0xbdfe,0x3e30,0x4fd7,0x8b61,
-0xbde9,0xd662,0x1567,0x43d3,
-0x3e4c,0x3afc,0xffd9,0x4b98,
-0xbe69,0x8769,0xe86c,0xa8cd,
-0xbe8d,0xc421,0xb204,0x9ea4,
-0x3ec0,0x53c4,0x264d,0x421f,
-0x3ed2,0x2ebb,0xea34,0xe2fa,
-0xbf10,0x145e,0xd801,0x0cd7,
-0xbf34,0x84b3,0xe2fd,0xc93c,
-0x3f40,0x4a85,0x41aa,0x68ef,
-0x3f9b,0x11b6,0x0417,0xfc8d,
-0x3ff1,0xd4d5,0x974c,0xe17b
-};
-
-static unsigned short C2[] = {
-0x3c62,0x9b2d,0x1119,0x3916,
-0xbc77,0xfd43,0xf6e4,0x7b70,
-0xbc91,0x3d48,0x5bc5,0x6b55,
-0x3cb3,0x5993,0xbae9,0x32d2,
-0x3cc0,0x4bdc,0x1958,0x8227,
-0xbceb,0xfd0f,0x32c7,0x3000,
-0xbcf3,0xf167,0x6b8b,0x0482,
-0x3d23,0xaed6,0xcbbc,0xdd23,
-0x3d32,0xac59,0x6b70,0x1d61,
-0xbd5a,0x2b99,0x51f1,0x6a52,
-0xbd76,0x5dab,0x935b,0xcdb5,
-0x3d88,0x2d18,0xf5e4,0x4d6f,
-0x3db9,0xb45f,0xb882,0x095e,
-0x3dbd,0xd83e,0x8e34,0x29af,
-0xbdf1,0xa228,0x799b,0xbffc,
-0xbe1b,0xa9cb,0x8351,0xbcf7,
-0xbe34,0x4baa,0x7b57,0xca05,
-0xbe29,0xc729,0xaa38,0xfce9,
-0x3e74,0xebe8,0xf1ec,0xa681,
-0x3eb1,0xf128,0x2478,0xc545,
-0x3ef0,0xb9a1,0x66fc,0xcfae,
-0x3f36,0xe930,0xad5d,0xa0bf,
-0x3f8a,0x4fcf,0x7639,0xde19,
-0x3ff0,0x9625,0x962f,0x25d7
-};
-#endif
-
-
-
-/* Sine and cosine integrals */
-
-#ifdef ANSIPROT
-extern double log ( double );
-extern double exp ( double );
-extern double fabs ( double );
-extern double chbevl ( double, void *, int );
-#else
-double log(), exp(), fabs(), chbevl();
-#endif
-#define EUL 0.57721566490153286061
-extern double MACHEP, MAXNUM, PIO2;
-
-int shichi( x, si, ci )
-double x;
-double *si, *ci;
-{
-double k, z, c, s, a;
-short sign;
-
-if( x < 0.0 )
- {
- sign = -1;
- x = -x;
- }
-else
- sign = 0;
-
-
-if( x == 0.0 )
- {
- *si = 0.0;
- *ci = -MAXNUM;
- return( 0 );
- }
-
-if( x >= 8.0 )
- goto chb;
-
-z = x * x;
-
-/* Direct power series expansion */
-
-a = 1.0;
-s = 1.0;
-c = 0.0;
-k = 2.0;
-
-do
- {
- a *= z/k;
- c += a/k;
- k += 1.0;
- a /= k;
- s += a/k;
- k += 1.0;
- }
-while( fabs(a/s) > MACHEP );
-
-s *= x;
-goto done;
-
-
-chb:
-
-if( x < 18.0 )
- {
- a = (576.0/x - 52.0)/10.0;
- k = exp(x) / x;
- s = k * chbevl( a, S1, 22 );
- c = k * chbevl( a, C1, 23 );
- goto done;
- }
-
-if( x <= 88.0 )
- {
- a = (6336.0/x - 212.0)/70.0;
- k = exp(x) / x;
- s = k * chbevl( a, S2, 23 );
- c = k * chbevl( a, C2, 24 );
- goto done;
- }
-else
- {
- if( sign )
- *si = -MAXNUM;
- else
- *si = MAXNUM;
- *ci = MAXNUM;
- return(0);
- }
-done:
-if( sign )
- s = -s;
-
-*si = s;
-
-*ci = EUL + log(x) + c;
-return(0);
-}
+++ /dev/null
-/* sici.c
- *
- * Sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, Ci, Si, sici();
- *
- * sici( x, &Si, &Ci );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the integrals
- *
- * x
- * -
- * | cos t - 1
- * Ci(x) = eul + ln x + | --------- dt,
- * | t
- * -
- * 0
- * x
- * -
- * | sin t
- * Si(x) = | ----- dt
- * | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are approximated by rational functions.
- * For x > 8 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * Ci(x) = f(x) sin(x) - g(x) cos(x)
- * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
- *
- *
- * ACCURACY:
- * Test interval = [0,50].
- * Absolute error, except relative when > 1:
- * arithmetic function # trials peak rms
- * IEEE Si 30000 4.4e-16 7.3e-17
- * IEEE Ci 30000 6.9e-16 5.1e-17
- * DEC Si 5000 4.4e-17 9.0e-18
- * DEC Ci 5300 7.9e-17 5.2e-18
- */
-\f
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double SN[] = {
--8.39167827910303881427E-11,
- 4.62591714427012837309E-8,
--9.75759303843632795789E-6,
- 9.76945438170435310816E-4,
--4.13470316229406538752E-2,
- 1.00000000000000000302E0,
-};
-static double SD[] = {
- 2.03269266195951942049E-12,
- 1.27997891179943299903E-9,
- 4.41827842801218905784E-7,
- 9.96412122043875552487E-5,
- 1.42085239326149893930E-2,
- 9.99999999999999996984E-1,
-};
-#endif
-#ifdef DEC
-static unsigned short SN[] = {
-0127670,0104362,0167505,0035161,
-0032106,0127177,0032131,0056461,
-0134043,0132213,0000476,0172351,
-0035600,0006331,0064761,0032665,
-0137051,0055601,0044667,0017645,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short SD[] = {
-0026417,0004674,0052064,0001573,
-0030657,0165501,0014666,0131526,
-0032755,0032133,0034147,0024124,
-0034720,0173167,0166624,0154477,
-0036550,0145336,0063534,0063220,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short SN[] = {
-0xa74e,0x5de8,0x111e,0xbdd7,
-0x2ba6,0xe68b,0xd5cf,0x3e68,
-0xde9d,0x6027,0x7691,0xbee4,
-0x26b7,0x2d3e,0x019b,0x3f50,
-0xe3f5,0x2936,0x2b70,0xbfa5,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short SD[] = {
-0x806f,0x8a86,0xe137,0x3d81,
-0xd66b,0x2336,0xfd68,0x3e15,
-0xe50a,0x670c,0xa68b,0x3e9d,
-0x9b28,0xfdb2,0x1ece,0x3f1a,
-0x8cd2,0xcceb,0x195b,0x3f8d,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short SN[] = {
-0xbdd7,0x111e,0x5de8,0xa74e,
-0x3e68,0xd5cf,0xe68b,0x2ba6,
-0xbee4,0x7691,0x6027,0xde9d,
-0x3f50,0x019b,0x2d3e,0x26b7,
-0xbfa5,0x2b70,0x2936,0xe3f5,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short SD[] = {
-0x3d81,0xe137,0x8a86,0x806f,
-0x3e15,0xfd68,0x2336,0xd66b,
-0x3e9d,0xa68b,0x670c,0xe50a,
-0x3f1a,0x1ece,0xfdb2,0x9b28,
-0x3f8d,0x195b,0xcceb,0x8cd2,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-#ifdef UNK
-static double CN[] = {
- 2.02524002389102268789E-11,
--1.35249504915790756375E-8,
- 3.59325051419993077021E-6,
--4.74007206873407909465E-4,
- 2.89159652607555242092E-2,
--1.00000000000000000080E0,
-};
-static double CD[] = {
- 4.07746040061880559506E-12,
- 3.06780997581887812692E-9,
- 1.23210355685883423679E-6,
- 3.17442024775032769882E-4,
- 5.10028056236446052392E-2,
- 4.00000000000000000080E0,
-};
-#endif
-#ifdef DEC
-static unsigned short CN[] = {
-0027262,0022131,0160257,0020166,
-0131550,0055534,0077637,0000557,
-0033561,0021622,0161463,0026575,
-0135370,0102053,0116333,0000466,
-0036754,0160454,0122022,0024622,
-0140200,0000000,0000000,0000000,
-};
-static unsigned short CD[] = {
-0026617,0073177,0107543,0104425,
-0031122,0150573,0156453,0041517,
-0033245,0057301,0077706,0110510,
-0035246,0067130,0165424,0044543,
-0037120,0164121,0061206,0053657,
-0040600,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short CN[] = {
-0xe40f,0x3c15,0x448b,0x3db6,
-0xe02e,0x8ff3,0x0b6b,0xbe4d,
-0x65b0,0x5c66,0x2472,0x3ece,
-0x6027,0x739b,0x1085,0xbf3f,
-0x4532,0x9482,0x9c25,0x3f9d,
-0x0000,0x0000,0x0000,0xbff0,
-};
-static unsigned short CD[] = {
-0x7123,0xf1ec,0xeecf,0x3d91,
-0x686a,0x7ba5,0x5a2f,0x3e2a,
-0xd229,0x2ff8,0xabd8,0x3eb4,
-0x892c,0x1d62,0xcdcb,0x3f34,
-0xcaf6,0x2c50,0x1d0a,0x3faa,
-0x0000,0x0000,0x0000,0x4010,
-};
-#endif
-#ifdef MIEEE
-static unsigned short CN[] = {
-0x3db6,0x448b,0x3c15,0xe40f,
-0xbe4d,0x0b6b,0x8ff3,0xe02e,
-0x3ece,0x2472,0x5c66,0x65b0,
-0xbf3f,0x1085,0x739b,0x6027,
-0x3f9d,0x9c25,0x9482,0x4532,
-0xbff0,0x0000,0x0000,0x0000,
-};
-static unsigned short CD[] = {
-0x3d91,0xeecf,0xf1ec,0x7123,
-0x3e2a,0x5a2f,0x7ba5,0x686a,
-0x3eb4,0xabd8,0x2ff8,0xd229,
-0x3f34,0xcdcb,0x1d62,0x892c,
-0x3faa,0x1d0a,0x2c50,0xcaf6,
-0x4010,0x0000,0x0000,0x0000,
-};
-#endif
-
-
-#ifdef UNK
-static double FN4[] = {
- 4.23612862892216586994E0,
- 5.45937717161812843388E0,
- 1.62083287701538329132E0,
- 1.67006611831323023771E-1,
- 6.81020132472518137426E-3,
- 1.08936580650328664411E-4,
- 5.48900223421373614008E-7,
-};
-static double FD4[] = {
-/* 1.00000000000000000000E0,*/
- 8.16496634205391016773E0,
- 7.30828822505564552187E0,
- 1.86792257950184183883E0,
- 1.78792052963149907262E-1,
- 7.01710668322789753610E-3,
- 1.10034357153915731354E-4,
- 5.48900252756255700982E-7,
-};
-#endif
-#ifdef DEC
-static unsigned short FN4[] = {
-0040607,0107135,0120133,0153471,
-0040656,0131467,0140424,0017567,
-0040317,0073563,0121610,0002511,
-0037453,0001710,0000040,0006334,
-0036337,0024033,0176003,0171425,
-0034744,0072341,0121657,0126035,
-0033023,0054042,0154652,0000451,
-};
-static unsigned short FD4[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041002,0121663,0137500,0177450,
-0040751,0156577,0042213,0061552,
-0040357,0014026,0045465,0147265,
-0037467,0012503,0110413,0131772,
-0036345,0167701,0155706,0160551,
-0034746,0141076,0162250,0123547,
-0033023,0054043,0056706,0151050,
-};
-#endif
-#ifdef IBMPC
-static unsigned short FN4[] = {
-0x7ae7,0xb40b,0xf1cb,0x4010,
-0x83ef,0xf822,0xd666,0x4015,
-0x00a9,0x7471,0xeeee,0x3ff9,
-0x019c,0x0004,0x6079,0x3fc5,
-0x7e63,0x7f80,0xe503,0x3f7b,
-0xf584,0x3475,0x8e9c,0x3f1c,
-0x4025,0x5b35,0x6b04,0x3ea2,
-};
-static unsigned short FD4[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x1fe5,0x77e8,0x5476,0x4020,
-0x6c6d,0xe891,0x3baf,0x401d,
-0xb9d7,0xc966,0xe302,0x3ffd,
-0x767f,0x7221,0xe2a8,0x3fc6,
-0xdc2d,0x3b78,0xbdf8,0x3f7c,
-0x14ed,0xdc95,0xd847,0x3f1c,
-0xda45,0x6bb8,0x6b04,0x3ea2,
-};
-#endif
-#ifdef MIEEE
-static unsigned short FN4[] = {
-0x4010,0xf1cb,0xb40b,0x7ae7,
-0x4015,0xd666,0xf822,0x83ef,
-0x3ff9,0xeeee,0x7471,0x00a9,
-0x3fc5,0x6079,0x0004,0x019c,
-0x3f7b,0xe503,0x7f80,0x7e63,
-0x3f1c,0x8e9c,0x3475,0xf584,
-0x3ea2,0x6b04,0x5b35,0x4025,
-};
-static unsigned short FD4[] = {
-/* 0x3ff0,0x0000,0x0000,0x0000,*/
-0x4020,0x5476,0x77e8,0x1fe5,
-0x401d,0x3baf,0xe891,0x6c6d,
-0x3ffd,0xe302,0xc966,0xb9d7,
-0x3fc6,0xe2a8,0x7221,0x767f,
-0x3f7c,0xbdf8,0x3b78,0xdc2d,
-0x3f1c,0xd847,0xdc95,0x14ed,
-0x3ea2,0x6b04,0x6bb8,0xda45,
-};
-#endif
-
-#ifdef UNK
-static double FN8[] = {
- 4.55880873470465315206E-1,
- 7.13715274100146711374E-1,
- 1.60300158222319456320E-1,
- 1.16064229408124407915E-2,
- 3.49556442447859055605E-4,
- 4.86215430826454749482E-6,
- 3.20092790091004902806E-8,
- 9.41779576128512936592E-11,
- 9.70507110881952024631E-14,
-};
-static double FD8[] = {
-/* 1.00000000000000000000E0,*/
- 9.17463611873684053703E-1,
- 1.78685545332074536321E-1,
- 1.22253594771971293032E-2,
- 3.58696481881851580297E-4,
- 4.92435064317881464393E-6,
- 3.21956939101046018377E-8,
- 9.43720590350276732376E-11,
- 9.70507110881952025725E-14,
-};
-#endif
-#ifdef DEC
-static unsigned short FN8[] = {
-0037751,0064467,0142332,0164573,
-0040066,0133013,0050352,0071102,
-0037444,0022671,0102157,0013535,
-0036476,0024335,0136423,0146444,
-0035267,0042253,0164110,0110460,
-0033643,0022626,0062535,0060320,
-0032011,0075223,0010110,0153413,
-0027717,0014572,0011360,0014034,
-0025332,0104755,0004563,0152354,
-};
-static unsigned short FD8[] = {
-/*0040200,0000000,0000000,0000000,*/
-0040152,0157345,0030104,0075616,
-0037466,0174527,0172740,0071060,
-0036510,0046337,0144272,0156552,
-0035274,0007555,0042537,0015572,
-0033645,0035731,0112465,0026474,
-0032012,0043612,0030613,0030123,
-0027717,0103277,0004564,0151000,
-0025332,0104755,0004563,0152354,
-};
-#endif
-#ifdef IBMPC
-static unsigned short FN8[] = {
-0x5d2f,0xf89b,0x2d26,0x3fdd,
-0x4e48,0x6a1d,0xd6c1,0x3fe6,
-0xe2ec,0x308d,0x84b7,0x3fc4,
-0x79a4,0xb7a2,0xc51b,0x3f87,
-0x1226,0x7d09,0xe895,0x3f36,
-0xac1a,0xccab,0x64b2,0x3ed4,
-0x1ae1,0x6209,0x2f52,0x3e61,
-0x0304,0x425e,0xe32f,0x3dd9,
-0x7a9d,0xa12e,0x513d,0x3d3b,
-};
-static unsigned short FD8[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x8f72,0xa608,0x5bdc,0x3fed,
-0x0e46,0xfebc,0xdf2a,0x3fc6,
-0x5bad,0xf917,0x099b,0x3f89,
-0xe36f,0xa8ab,0x81ed,0x3f37,
-0xa5a8,0x32a6,0xa77b,0x3ed4,
-0x660a,0x4631,0x48f1,0x3e61,
-0x9a40,0xe12e,0xf0d7,0x3dd9,
-0x7a9d,0xa12e,0x513d,0x3d3b,
-};
-#endif
-#ifdef MIEEE
-static unsigned short FN8[] = {
-0x3fdd,0x2d26,0xf89b,0x5d2f,
-0x3fe6,0xd6c1,0x6a1d,0x4e48,
-0x3fc4,0x84b7,0x308d,0xe2ec,
-0x3f87,0xc51b,0xb7a2,0x79a4,
-0x3f36,0xe895,0x7d09,0x1226,
-0x3ed4,0x64b2,0xccab,0xac1a,
-0x3e61,0x2f52,0x6209,0x1ae1,
-0x3dd9,0xe32f,0x425e,0x0304,
-0x3d3b,0x513d,0xa12e,0x7a9d,
-};
-static unsigned short FD8[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3fed,0x5bdc,0xa608,0x8f72,
-0x3fc6,0xdf2a,0xfebc,0x0e46,
-0x3f89,0x099b,0xf917,0x5bad,
-0x3f37,0x81ed,0xa8ab,0xe36f,
-0x3ed4,0xa77b,0x32a6,0xa5a8,
-0x3e61,0x48f1,0x4631,0x660a,
-0x3dd9,0xf0d7,0xe12e,0x9a40,
-0x3d3b,0x513d,0xa12e,0x7a9d,
-};
-#endif
-
-#ifdef UNK
-static double GN4[] = {
- 8.71001698973114191777E-2,
- 6.11379109952219284151E-1,
- 3.97180296392337498885E-1,
- 7.48527737628469092119E-2,
- 5.38868681462177273157E-3,
- 1.61999794598934024525E-4,
- 1.97963874140963632189E-6,
- 7.82579040744090311069E-9,
-};
-static double GD4[] = {
-/* 1.00000000000000000000E0,*/
- 1.64402202413355338886E0,
- 6.66296701268987968381E-1,
- 9.88771761277688796203E-2,
- 6.22396345441768420760E-3,
- 1.73221081474177119497E-4,
- 2.02659182086343991969E-6,
- 7.82579218933534490868E-9,
-};
-#endif
-#ifdef DEC
-static unsigned short GN4[] = {
-0037262,0060622,0164572,0157515,
-0040034,0101527,0061263,0147204,
-0037713,0055467,0037475,0144512,
-0037231,0046151,0035234,0045261,
-0036260,0111624,0150617,0053536,
-0035051,0157175,0016675,0155456,
-0033404,0154757,0041211,0000055,
-0031406,0071060,0130322,0033322,
-};
-static unsigned short GD4[] = {
-/* 0040200,0000000,0000000,0000000,*/
-0040322,0067520,0046707,0053275,
-0040052,0111153,0126542,0005516,
-0037312,0100035,0167121,0014552,
-0036313,0171143,0137176,0014213,
-0035065,0121256,0012033,0150603,
-0033410,0000225,0013121,0071643,
-0031406,0071062,0131152,0150454,
-};
-#endif
-#ifdef IBMPC
-static unsigned short GN4[] = {
-0x5bea,0x5d2f,0x4c32,0x3fb6,
-0x79d1,0xec56,0x906a,0x3fe3,
-0xb929,0xe7e7,0x6b66,0x3fd9,
-0x8956,0x2753,0x298d,0x3fb3,
-0xeaec,0x9a31,0x1272,0x3f76,
-0xbb66,0xa3b7,0x3bcf,0x3f25,
-0x2006,0xe851,0x9b3d,0x3ec0,
-0x46da,0x161a,0xce46,0x3e40,
-};
-static unsigned short GD4[] = {
-/* 0x0000,0x0000,0x0000,0x3ff0,*/
-0xead8,0x09b8,0x4dea,0x3ffa,
-0x416a,0x75ac,0x524d,0x3fe5,
-0x232d,0xbdca,0x5003,0x3fb9,
-0xc311,0x77cf,0x7e4c,0x3f79,
-0x7a30,0xc283,0xb455,0x3f26,
-0x2e74,0xa2ca,0x0012,0x3ec1,
-0x5a26,0x564d,0xce46,0x3e40,
-};
-#endif
-#ifdef MIEEE
-static unsigned short GN4[] = {
-0x3fb6,0x4c32,0x5d2f,0x5bea,
-0x3fe3,0x906a,0xec56,0x79d1,
-0x3fd9,0x6b66,0xe7e7,0xb929,
-0x3fb3,0x298d,0x2753,0x8956,
-0x3f76,0x1272,0x9a31,0xeaec,
-0x3f25,0x3bcf,0xa3b7,0xbb66,
-0x3ec0,0x9b3d,0xe851,0x2006,
-0x3e40,0xce46,0x161a,0x46da,
-};
-static unsigned short GD4[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3ffa,0x4dea,0x09b8,0xead8,
-0x3fe5,0x524d,0x75ac,0x416a,
-0x3fb9,0x5003,0xbdca,0x232d,
-0x3f79,0x7e4c,0x77cf,0xc311,
-0x3f26,0xb455,0xc283,0x7a30,
-0x3ec1,0x0012,0xa2ca,0x2e74,
-0x3e40,0xce46,0x564d,0x5a26,
-};
-#endif
-
-#ifdef UNK
-static double GN8[] = {
- 6.97359953443276214934E-1,
- 3.30410979305632063225E-1,
- 3.84878767649974295920E-2,
- 1.71718239052347903558E-3,
- 3.48941165502279436777E-5,
- 3.47131167084116673800E-7,
- 1.70404452782044526189E-9,
- 3.85945925430276600453E-12,
- 3.14040098946363334640E-15,
-};
-static double GD8[] = {
-/* 1.00000000000000000000E0,*/
- 1.68548898811011640017E0,
- 4.87852258695304967486E-1,
- 4.67913194259625806320E-2,
- 1.90284426674399523638E-3,
- 3.68475504442561108162E-5,
- 3.57043223443740838771E-7,
- 1.72693748966316146736E-9,
- 3.87830166023954706752E-12,
- 3.14040098946363335242E-15,
-};
-#endif
-#ifdef DEC
-static unsigned short GN8[] = {
-0040062,0103056,0110624,0033123,
-0037651,0025640,0136266,0145647,
-0037035,0122566,0137770,0061777,
-0035741,0011424,0065311,0013370,
-0034422,0055505,0134324,0016755,
-0032672,0056530,0022565,0014747,
-0030752,0031674,0114735,0013162,
-0026607,0145353,0022020,0123625,
-0024142,0045054,0060033,0016505,
-};
-static unsigned short GD8[] = {
-/*0040200,0000000,0000000,0000000,*/
-0040327,0137032,0064331,0136425,
-0037771,0143705,0070300,0105711,
-0037077,0124101,0025275,0035356,
-0035771,0064333,0145103,0105357,
-0034432,0106301,0105311,0010713,
-0032677,0127645,0120034,0157551,
-0030755,0054466,0010743,0105566,
-0026610,0072242,0142530,0135744,
-0024142,0045054,0060033,0016505,
-};
-#endif
-#ifdef IBMPC
-static unsigned short GN8[] = {
-0x86ca,0xd232,0x50c5,0x3fe6,
-0xd975,0x1796,0x2574,0x3fd5,
-0x0c80,0xd7ff,0xb4ae,0x3fa3,
-0x22df,0x8d59,0x2262,0x3f5c,
-0x83be,0xb71a,0x4b68,0x3f02,
-0xa33d,0x04ae,0x4bab,0x3e97,
-0xa2ce,0x933b,0x4677,0x3e1d,
-0x14f3,0x6482,0xf95d,0x3d90,
-0x63a9,0x8c03,0x4945,0x3cec,
-};
-static unsigned short GD8[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x37a3,0x4d1b,0xf7c3,0x3ffa,
-0x1179,0xae18,0x38f8,0x3fdf,
-0xa75e,0x2557,0xf508,0x3fa7,
-0x715e,0x7948,0x2d1b,0x3f5f,
-0x2239,0x3159,0x5198,0x3f03,
-0x9bed,0xb403,0xf5f4,0x3e97,
-0x716f,0xc23c,0xab26,0x3e1d,
-0x177c,0x58ab,0x0e94,0x3d91,
-0x63a9,0x8c03,0x4945,0x3cec,
-};
-#endif
-#ifdef MIEEE
-static unsigned short GN8[] = {
-0x3fe6,0x50c5,0xd232,0x86ca,
-0x3fd5,0x2574,0x1796,0xd975,
-0x3fa3,0xb4ae,0xd7ff,0x0c80,
-0x3f5c,0x2262,0x8d59,0x22df,
-0x3f02,0x4b68,0xb71a,0x83be,
-0x3e97,0x4bab,0x04ae,0xa33d,
-0x3e1d,0x4677,0x933b,0xa2ce,
-0x3d90,0xf95d,0x6482,0x14f3,
-0x3cec,0x4945,0x8c03,0x63a9,
-};
-static unsigned short GD8[] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x3ffa,0xf7c3,0x4d1b,0x37a3,
-0x3fdf,0x38f8,0xae18,0x1179,
-0x3fa7,0xf508,0x2557,0xa75e,
-0x3f5f,0x2d1b,0x7948,0x715e,
-0x3f03,0x5198,0x3159,0x2239,
-0x3e97,0xf5f4,0xb403,0x9bed,
-0x3e1d,0xab26,0xc23c,0x716f,
-0x3d91,0x0e94,0x58ab,0x177c,
-0x3cec,0x4945,0x8c03,0x63a9,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double log ( double );
-extern double sin ( double );
-extern double cos ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double log(), sin(), cos(), polevl(), p1evl();
-#endif
-#define EUL 0.57721566490153286061
-extern double MAXNUM, PIO2, MACHEP;
-
-
-int sici( x, si, ci )
-double x;
-double *si, *ci;
-{
-double z, c, s, f, g;
-short sign;
-
-if( x < 0.0 )
- {
- sign = -1;
- x = -x;
- }
-else
- sign = 0;
-
-
-if( x == 0.0 )
- {
- *si = 0.0;
- *ci = -MAXNUM;
- return( 0 );
- }
-
-
-if( x > 1.0e9 )
- {
- *si = PIO2 - cos(x)/x;
- *ci = sin(x)/x;
- return( 0 );
- }
-
-
-
-if( x > 4.0 )
- goto asympt;
-
-z = x * x;
-s = x * polevl( z, SN, 5 ) / polevl( z, SD, 5 );
-c = z * polevl( z, CN, 5 ) / polevl( z, CD, 5 );
-
-if( sign )
- s = -s;
-*si = s;
-*ci = EUL + log(x) + c; /* real part if x < 0 */
-return(0);
-
-
-
-/* The auxiliary functions are:
- *
- *
- * *si = *si - PIO2;
- * c = cos(x);
- * s = sin(x);
- *
- * t = *ci * s - *si * c;
- * a = *ci * c + *si * s;
- *
- * *si = t;
- * *ci = -a;
- */
-
-
-asympt:
-
-s = sin(x);
-c = cos(x);
-z = 1.0/(x*x);
-if( x < 8.0 )
- {
- f = polevl( z, FN4, 6 ) / (x * p1evl( z, FD4, 7 ));
- g = z * polevl( z, GN4, 7 ) / p1evl( z, GD4, 7 );
- }
-else
- {
- f = polevl( z, FN8, 8 ) / (x * p1evl( z, FD8, 8 ));
- g = z * polevl( z, GN8, 8 ) / p1evl( z, GD8, 9 );
- }
-*si = PIO2 - f * c - g * s;
-if( sign )
- *si = -( *si );
-*ci = f * s - g * c;
-
-return(0);
-}
+++ /dev/null
-/* simpsn.c */
-/* simpsn.c
- * Numerical integration of function tabulated
- * at equally spaced arguments
- */
-
-/* Coefficients for Cote integration formulas */
-
-/* Note: these numbers were computed using 40-decimal precision. */
-
-#define NCOTE 8
-
-/* 6th order formula */
-/*
-static double simcon[] =
-{
- 4.88095238095238095E-2,
- 2.57142857142857142857E-1,
- 3.2142857142857142857E-2,
- 3.2380952380952380952E-1,
-};
-*/
-
-/* 8th order formula */
-static double simcon[] =
-{
- 3.488536155202821869E-2,
- 2.076895943562610229E-1,
- -3.27336860670194003527E-2,
- 3.7022927689594356261E-1,
- -1.6014109347442680776E-1,
-};
-
-/* 10th order formula */
-/*
-static double simcon[] =
-{
- 2.68341483619261397039E-2,
- 1.77535941424830313719E-1,
- -8.1043570626903960237E-2,
- 4.5494628827962161295E-1,
- -4.3515512265512265512E-1,
- 7.1376463043129709796E-1,
-};
-*/
-\f
-/* simpsn.c 2 */
-/* 20th order formula */
-/*
-static double simcon[] =
-{
- 1.182527324903160319E-2,
- 1.14137717644606974987E-1,
- -2.36478370511426964E-1,
- 1.20618689348187566E+0,
- -3.7710317267153304677E+0,
- 1.03367982199398011435E+1,
- -2.270881584397951229796E+1,
- 4.1828057422193554603E+1,
- -6.4075279490154004651555E+1,
- 8.279728347247285172085E+1,
- -9.0005367135242894657916E+1,
-};
-*/
-\f
-/* simpsn.c 3 */
-double simpsn( f, delta )
-double f[]; /* tabulated function */
-double delta; /* spacing of arguments */
-{
-extern double simcon[];
-double ans;
-int i;
-
-
-ans = simcon[NCOTE/2] * f[NCOTE/2];
-for( i=0; i < NCOTE/2; i++ )
- ans += simcon[i] * ( f[i] + f[NCOTE-i] );
-
-return( ans * delta * NCOTE );
-}
+++ /dev/null
-/* simq.c
- *
- * Solution of simultaneous linear equations AX = B
- * by Gaussian elimination with partial pivoting
- *
- *
- *
- * SYNOPSIS:
- *
- * double A[n*n], B[n], X[n];
- * int n, flag;
- * int IPS[];
- * int simq();
- *
- * ercode = simq( A, B, X, n, flag, IPS );
- *
- *
- *
- * DESCRIPTION:
- *
- * B, X, IPS are vectors of length n.
- * A is an n x n matrix (i.e., a vector of length n*n),
- * stored row-wise: that is, A(i,j) = A[ij],
- * where ij = i*n + j, which is the transpose of the normal
- * column-wise storage.
- *
- * The contents of matrix A are destroyed.
- *
- * Set flag=0 to solve.
- * Set flag=-1 to do a new back substitution for different B vector
- * using the same A matrix previously reduced when flag=0.
- *
- * The routine returns nonzero on error; messages are printed.
- *
- *
- * ACCURACY:
- *
- * Depends on the conditioning (range of eigenvalues) of matrix A.
- *
- *
- * REFERENCE:
- *
- * Computer Solution of Linear Algebraic Systems,
- * by George E. Forsythe and Cleve B. Moler; Prentice-Hall, 1967.
- *
- */
-\f
-/* simq 2 */
-
-#include <stdio.h>
-#define fabs(x) ((x) < 0 ? -(x) : (x))
-
-int simq( A, B, X, n, flag, IPS )
-double A[], B[], X[];
-int n, flag;
-int IPS[];
-{
-int i, j, ij, ip, ipj, ipk, ipn;
-int idxpiv, iback;
-int k, kp, kp1, kpk, kpn;
-int nip, nkp, nm1;
-double em, q, rownrm, big, size, pivot, sum;
-
-nm1 = n-1;
-if( flag < 0 )
- goto solve;
-
-/* Initialize IPS and X */
-
-ij=0;
-for( i=0; i<n; i++ )
- {
- IPS[i] = i;
- rownrm = 0.0;
- for( j=0; j<n; j++ )
- {
- q = fabs( A[ij] );
- if( rownrm < q )
- rownrm = q;
- ++ij;
- }
- if( rownrm == 0.0 )
- {
- printf("SIMQ ROWNRM=0");
- return(1);
- }
- X[i] = 1.0/rownrm;
- }
-\f
-/* simq 3 */
-/* Gaussian elimination with partial pivoting */
-
-for( k=0; k<nm1; k++ )
- {
- big= 0.0;
- idxpiv = 0;
- for( i=k; i<n; i++ )
- {
- ip = IPS[i];
- ipk = n*ip + k;
- size = fabs( A[ipk] ) * X[ip];
- if( size > big )
- {
- big = size;
- idxpiv = i;
- }
- }
-
- if( big == 0.0 )
- {
- printf( "SIMQ BIG=0" );
- return(2);
- }
- if( idxpiv != k )
- {
- j = IPS[k];
- IPS[k] = IPS[idxpiv];
- IPS[idxpiv] = j;
- }
- kp = IPS[k];
- kpk = n*kp + k;
- pivot = A[kpk];
- kp1 = k+1;
- for( i=kp1; i<n; i++ )
- {
- ip = IPS[i];
- ipk = n*ip + k;
- em = -A[ipk]/pivot;
- A[ipk] = -em;
- nip = n*ip;
- nkp = n*kp;
- for( j=kp1; j<n; j++ )
- {
- ipj = nip + j;
- A[ipj] = A[ipj] + em * A[nkp + j];
- }
- }
- }
-kpn = n * IPS[n-1] + n - 1; /* last element of IPS[n] th row */
-if( A[kpn] == 0.0 )
- {
- printf( "SIMQ A[kpn]=0");
- return(3);
- }
-\f
-/* simq 4 */
-/* back substitution */
-
-solve:
-ip = IPS[0];
-X[0] = B[ip];
-for( i=1; i<n; i++ )
- {
- ip = IPS[i];
- ipj = n * ip;
- sum = 0.0;
- for( j=0; j<i; j++ )
- {
- sum += A[ipj] * X[j];
- ++ipj;
- }
- X[i] = B[ip] - sum;
- }
-
-ipn = n * IPS[n-1] + n - 1;
-X[n-1] = X[n-1]/A[ipn];
-
-for( iback=1; iback<n; iback++ )
- {
-/* i goes (n-1),...,1 */
- i = nm1 - iback;
- ip = IPS[i];
- nip = n*ip;
- sum = 0.0;
- for( j=i+1; j<n; j++ )
- sum += A[nip+j] * X[j];
- X[i] = (X[i] - sum)/A[nip+i];
- }
-return(0);
-}
+++ /dev/null
-/* sin.c
- *
- * Circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sin();
- *
- * y = sin( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 Q(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 10 150000 3.0e-17 7.8e-18
- * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 1.073741824e9 0.0
- *
- * Partial loss of accuracy begins to occur at x = 2**30
- * = 1.074e9. The loss is not gradual, but jumps suddenly to
- * about 1 part in 10e7. Results may be meaningless for
- * x > 2**49 = 5.6e14. The routine as implemented flags a
- * TLOSS error for x > 2**30 and returns 0.0.
- */
-\f/* cos.c
- *
- * Circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cos();
- *
- * y = cos( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 Q(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
- * DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
- */
-\f
-/* sin.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1985, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double sincof[] = {
- 1.58962301576546568060E-10,
--2.50507477628578072866E-8,
- 2.75573136213857245213E-6,
--1.98412698295895385996E-4,
- 8.33333333332211858878E-3,
--1.66666666666666307295E-1,
-};
-static double coscof[6] = {
--1.13585365213876817300E-11,
- 2.08757008419747316778E-9,
--2.75573141792967388112E-7,
- 2.48015872888517045348E-5,
--1.38888888888730564116E-3,
- 4.16666666666665929218E-2,
-};
-static double DP1 = 7.85398125648498535156E-1;
-static double DP2 = 3.77489470793079817668E-8;
-static double DP3 = 2.69515142907905952645E-15;
-/* static double lossth = 1.073741824e9; */
-#endif
-
-#ifdef DEC
-static unsigned short sincof[] = {
-0030056,0143750,0177214,0163153,
-0131727,0027455,0044510,0175352,
-0033470,0167432,0131752,0042414,
-0135120,0006400,0146776,0174027,
-0036410,0104210,0104207,0137202,
-0137452,0125252,0125252,0125103,
-};
-static unsigned short coscof[24] = {
-0127107,0151115,0002060,0152325,
-0031017,0072353,0155161,0174053,
-0132623,0171173,0172542,0057056,
-0034320,0006400,0147102,0023652,
-0135666,0005540,0133012,0076213,
-0037052,0125252,0125252,0125126,
-};
-/* 7.853981629014015197753906250000E-1 */
-static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
-/* 4.960467869796758577649598009884E-10 */
-static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
-/* 2.860594363054915898381331279295E-18 */
-static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef IBMPC
-static unsigned short sincof[] = {
-0x9ccd,0x1fd1,0xd8fd,0x3de5,
-0x1f5d,0xa929,0xe5e5,0xbe5a,
-0x48a1,0x567d,0x1de3,0x3ec7,
-0xdf03,0x19bf,0x01a0,0xbf2a,
-0xf7d0,0x1110,0x1111,0x3f81,
-0x5548,0x5555,0x5555,0xbfc5,
-};
-static unsigned short coscof[24] = {
-0x1a9b,0xa086,0xfa49,0xbda8,
-0x3f05,0x7b4e,0xee9d,0x3e21,
-0x4bc6,0x7eac,0x7e4f,0xbe92,
-0x44f5,0x19c8,0x01a0,0x3efa,
-0x4f91,0x16c1,0xc16c,0xbf56,
-0x554b,0x5555,0x5555,0x3fa5,
-};
-/*
- 7.85398125648498535156E-1,
- 3.77489470793079817668E-8,
- 2.69515142907905952645E-15,
-*/
-static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
-static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
-static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef MIEEE
-static unsigned short sincof[] = {
-0x3de5,0xd8fd,0x1fd1,0x9ccd,
-0xbe5a,0xe5e5,0xa929,0x1f5d,
-0x3ec7,0x1de3,0x567d,0x48a1,
-0xbf2a,0x01a0,0x19bf,0xdf03,
-0x3f81,0x1111,0x1110,0xf7d0,
-0xbfc5,0x5555,0x5555,0x5548,
-};
-static unsigned short coscof[24] = {
-0xbda8,0xfa49,0xa086,0x1a9b,
-0x3e21,0xee9d,0x7b4e,0x3f05,
-0xbe92,0x7e4f,0x7eac,0x4bc6,
-0x3efa,0x01a0,0x19c8,0x44f5,
-0xbf56,0xc16c,0x16c1,0x4f91,
-0x3fa5,0x5555,0x5555,0x554b,
-};
-static unsigned short P1[] = {0x3fe9,0x21fb,0x4000,0x0000};
-static unsigned short P2[] = {0x3e64,0x442d,0x0000,0x0000};
-static unsigned short P3[] = {0x3ce8,0x4698,0x98cc,0x5170};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double ldexp ( double, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double polevl(), floor(), ldexp();
-int isnan(), isfinite();
-#endif
-extern double PIO4;
-static double lossth = 1.073741824e9;
-#ifdef NANS
-extern double NAN;
-#endif
-#ifdef INFINITIES
-extern double INFINITY;
-#endif
-
-
-double sin(x)
-double x;
-{
-double y, z, zz;
-int j, sign;
-
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-#ifdef NANS
-if( isnan(x) )
- return(x);
-if( !isfinite(x) )
- {
- mtherr( "sin", DOMAIN );
- return(NAN);
- }
-#endif
-/* make argument positive but save the sign */
-sign = 1;
-if( x < 0 )
- {
- x = -x;
- sign = -1;
- }
-
-if( x > lossth )
- {
- mtherr( "sin", TLOSS );
- return(0.0);
- }
-
-y = floor( x/PIO4 ); /* integer part of x/PIO4 */
-
-/* strip high bits of integer part to prevent integer overflow */
-z = ldexp( y, -4 );
-z = floor(z); /* integer part of y/8 */
-z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
-
-j = z; /* convert to integer for tests on the phase angle */
-/* map zeros to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-j = j & 07; /* octant modulo 360 degrees */
-/* reflect in x axis */
-if( j > 3)
- {
- sign = -sign;
- j -= 4;
- }
-
-/* Extended precision modular arithmetic */
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-
-if( (j==1) || (j==2) )
- {
- y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
- }
-else
- {
-/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
- y = z + z * z * z * polevl( zz, sincof, 5 );
- }
-
-if(sign < 0)
- y = -y;
-
-return(y);
-}
-
-
-
-
-
-double cos(x)
-double x;
-{
-double y, z, zz;
-long i;
-int j, sign;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-if( !isfinite(x) )
- {
- mtherr( "cos", DOMAIN );
- return(NAN);
- }
-#endif
-
-/* make argument positive */
-sign = 1;
-if( x < 0 )
- x = -x;
-
-if( x > lossth )
- {
- mtherr( "cos", TLOSS );
- return(0.0);
- }
-
-y = floor( x/PIO4 );
-z = ldexp( y, -4 );
-z = floor(z); /* integer part of y/8 */
-z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
-
-/* integer and fractional part modulo one octant */
-i = z;
-if( i & 1 ) /* map zeros to origin */
- {
- i += 1;
- y += 1.0;
- }
-j = i & 07;
-if( j > 3)
- {
- j -=4;
- sign = -sign;
- }
-
-if( j > 1 )
- sign = -sign;
-
-/* Extended precision modular arithmetic */
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-
-if( (j==1) || (j==2) )
- {
-/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
- y = z + z * z * z * polevl( zz, sincof, 5 );
- }
-else
- {
- y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
- }
-
-if(sign < 0)
- y = -y;
-
-return(y);
-}
-
-
-
-
-
-/* Degrees, minutes, seconds to radians: */
-
-/* 1 arc second, in radians = 4.8481368110953599358991410e-5 */
-#ifdef DEC
-static unsigned short P648[] = {034513,054170,0176773,0116043,};
-#define P64800 *(double *)P648
-#else
-static double P64800 = 4.8481368110953599358991410e-5;
-#endif
-
-double radian(d,m,s)
-double d,m,s;
-{
-
-return( ((d*60.0 + m)*60.0 + s)*P64800 );
-}
+++ /dev/null
-/* sincos.c
- *
- * Circular sine and cosine of argument in degrees
- * Table lookup and interpolation algorithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, sine, cosine, flg, sincos();
- *
- * sincos( x, &sine, &cosine, flg );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns both the sine and the cosine of the argument x.
- * Several different compile time options and minimax
- * approximations are supplied to permit tailoring the
- * tradeoff between computation speed and accuracy.
- *
- * Since range reduction is time consuming, the reduction
- * of x modulo 360 degrees is also made optional.
- *
- * sin(i) is internally tabulated for 0 <= i <= 90 degrees.
- * Approximation polynomials, ranging from linear interpolation
- * to cubics in (x-i)**2, compute the sine and cosine
- * of the residual x-i which is between -0.5 and +0.5 degree.
- * In the case of the high accuracy options, the residual
- * and the tabulated values are combined using the trigonometry
- * formulas for sin(A+B) and cos(A+B).
- *
- * Compile time options are supplied for 5, 11, or 17 decimal
- * relative accuracy (ACC5, ACC11, ACC17 respectively).
- * A subroutine flag argument "flg" chooses betwen this
- * accuracy and table lookup only (peak absolute error
- * = 0.0087).
- *
- * If the argument flg = 1, then the tabulated value is
- * returned for the nearest whole number of degrees. The
- * approximation polynomials are not computed. At
- * x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087.
- *
- * An intermediate speed and precision can be obtained using
- * the compile time option LINTERP and flg = 1. This yields
- * a linear interpolation using a slope estimated from the sine
- * or cosine at the nearest integer argument. The peak absolute
- * error with this option is 3.8e-5. Relative error at small
- * angles is about 1e-5.
- *
- * If flg = 0, then the approximation polynomials are computed
- * and applied.
- *
- *
- *
- * SPEED:
- *
- * Relative speed comparisons follow for 6MHz IBM AT clone
- * and Microsoft C version 4.0. These figures include
- * software overhead of do loop and function calls.
- * Since system hardware and software vary widely, the
- * numbers should be taken as representative only.
- *
- * flg=0 flg=0 flg=1 flg=1
- * ACC11 ACC5 LINTERP Lookup only
- * In-line 8087 (/FPi)
- * sin(), cos() 1.0 1.0 1.0 1.0
- *
- * In-line 8087 (/FPi)
- * sincos() 1.1 1.4 1.9 3.0
- *
- * Software (/FPa)
- * sin(), cos() 0.19 0.19 0.19 0.19
- *
- * Software (/FPa)
- * sincos() 0.39 0.50 0.73 1.7
- *
- *
- *
- * ACCURACY:
- *
- * The accurate approximations are designed with a relative error
- * criterion. The absolute error is greatest at x = 0.5 degree.
- * It decreases from a local maximum at i+0.5 degrees to full
- * machine precision at each integer i degrees. With the
- * ACC5 option, the relative error of 6.3e-6 is equivalent to
- * an absolute angular error of 0.01 arc second in the argument
- * at x = i+0.5 degrees. For small angles < 0.5 deg, the ACC5
- * accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute
- * error decreases in proportion to the argument. This is true
- * for both the sine and cosine approximations, since the latter
- * is for the function 1 - cos(x).
- *
- * If absolute error is of most concern, use the compile time
- * option ABSERR to obtain an absolute error of 2.7e-8 for ACC5
- * precision. This is about half the absolute error of the
- * relative precision option. In this case the relative error
- * for small angles will increase to 9.5e-6 -- a reasonable
- * tradeoff.
- */
-
-
-#include <math.h>
-
-/* Define one of the following to be 1:
- */
-#define ACC5 1
-#define ACC11 0
-#define ACC17 0
-
-/* Option for linear interpolation when flg = 1
- */
-#define LINTERP 1
-
-/* Option for absolute error criterion
- */
-#define ABSERR 1
-
-/* Option to include modulo 360 function:
- */
-#define MOD360 0
-
-/*
-Cephes Math Library Release 2.1
-Copyright 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/* Table of sin(i degrees)
- * for 0 <= i <= 90
- */
-static double sintbl[92] = {
- 0.00000000000000000000E0,
- 1.74524064372835128194E-2,
- 3.48994967025009716460E-2,
- 5.23359562429438327221E-2,
- 6.97564737441253007760E-2,
- 8.71557427476581735581E-2,
- 1.04528463267653471400E-1,
- 1.21869343405147481113E-1,
- 1.39173100960065444112E-1,
- 1.56434465040230869010E-1,
- 1.73648177666930348852E-1,
- 1.90808995376544812405E-1,
- 2.07911690817759337102E-1,
- 2.24951054343864998051E-1,
- 2.41921895599667722560E-1,
- 2.58819045102520762349E-1,
- 2.75637355816999185650E-1,
- 2.92371704722736728097E-1,
- 3.09016994374947424102E-1,
- 3.25568154457156668714E-1,
- 3.42020143325668733044E-1,
- 3.58367949545300273484E-1,
- 3.74606593415912035415E-1,
- 3.90731128489273755062E-1,
- 4.06736643075800207754E-1,
- 4.22618261740699436187E-1,
- 4.38371146789077417453E-1,
- 4.53990499739546791560E-1,
- 4.69471562785890775959E-1,
- 4.84809620246337029075E-1,
- 5.00000000000000000000E-1,
- 5.15038074910054210082E-1,
- 5.29919264233204954047E-1,
- 5.44639035015027082224E-1,
- 5.59192903470746830160E-1,
- 5.73576436351046096108E-1,
- 5.87785252292473129169E-1,
- 6.01815023152048279918E-1,
- 6.15661475325658279669E-1,
- 6.29320391049837452706E-1,
- 6.42787609686539326323E-1,
- 6.56059028990507284782E-1,
- 6.69130606358858213826E-1,
- 6.81998360062498500442E-1,
- 6.94658370458997286656E-1,
- 7.07106781186547524401E-1,
- 7.19339800338651139356E-1,
- 7.31353701619170483288E-1,
- 7.43144825477394235015E-1,
- 7.54709580222771997943E-1,
- 7.66044443118978035202E-1,
- 7.77145961456970879980E-1,
- 7.88010753606721956694E-1,
- 7.98635510047292846284E-1,
- 8.09016994374947424102E-1,
- 8.19152044288991789684E-1,
- 8.29037572555041692006E-1,
- 8.38670567945424029638E-1,
- 8.48048096156425970386E-1,
- 8.57167300702112287465E-1,
- 8.66025403784438646764E-1,
- 8.74619707139395800285E-1,
- 8.82947592858926942032E-1,
- 8.91006524188367862360E-1,
- 8.98794046299166992782E-1,
- 9.06307787036649963243E-1,
- 9.13545457642600895502E-1,
- 9.20504853452440327397E-1,
- 9.27183854566787400806E-1,
- 9.33580426497201748990E-1,
- 9.39692620785908384054E-1,
- 9.45518575599316810348E-1,
- 9.51056516295153572116E-1,
- 9.56304755963035481339E-1,
- 9.61261695938318861916E-1,
- 9.65925826289068286750E-1,
- 9.70295726275996472306E-1,
- 9.74370064785235228540E-1,
- 9.78147600733805637929E-1,
- 9.81627183447663953497E-1,
- 9.84807753012208059367E-1,
- 9.87688340595137726190E-1,
- 9.90268068741570315084E-1,
- 9.92546151641322034980E-1,
- 9.94521895368273336923E-1,
- 9.96194698091745532295E-1,
- 9.97564050259824247613E-1,
- 9.98629534754573873784E-1,
- 9.99390827019095730006E-1,
- 9.99847695156391239157E-1,
- 1.00000000000000000000E0,
- 9.99847695156391239157E-1,
-};
-
-#ifdef ANSIPROT
-double floor ( double );
-#else
-double floor();
-#endif
-
-int sincos(x, s, c, flg)
-double x;
-double *s, *c;
-int flg;
-{
-int ix, ssign, csign, xsign;
-double y, z, sx, sz, cx, cz;
-
-/* Make argument nonnegative.
- */
-xsign = 1;
-if( x < 0.0 )
- {
- xsign = -1;
- x = -x;
- }
-
-
-#if MOD360
-x = x - 360.0 * floor( x/360.0 );
-#endif
-
-/* Find nearest integer to x.
- * Note there should be a domain error test here,
- * but this is omitted to gain speed.
- */
-ix = x + 0.5;
-z = x - ix; /* the residual */
-
-/* Look up the sine and cosine of the integer.
- */
-if( ix <= 180 )
- {
- ssign = 1;
- csign = 1;
- }
-else
- {
- ssign = -1;
- csign = -1;
- ix -= 180;
- }
-
-if( ix > 90 )
- {
- csign = -csign;
- ix = 180 - ix;
- }
-
-sx = sintbl[ix];
-if( ssign < 0 )
- sx = -sx;
-cx = sintbl[ 90-ix ];
-if( csign < 0 )
- cx = -cx;
-
-/* If the flag argument is set, then just return
- * the tabulated values for arg to the nearest whole degree.
- */
-if( flg )
- {
-#if LINTERP
- y = sx + 1.74531263774940077459e-2 * z * cx;
- cx -= 1.74531263774940077459e-2 * z * sx;
- sx = y;
-#endif
- if( xsign < 0 )
- sx = -sx;
- *s = sx; /* sine */
- *c = cx; /* cosine */
- return 0;
- }
-
-
-if( ssign < 0 )
- sx = -sx;
-if( csign < 0 )
- cx = -cx;
-
-/* Find sine and cosine
- * of the residual angle between -0.5 and +0.5 degree.
- */
-#if ACC5
-#if ABSERR
-/* absolute error = 2.769e-8: */
-sz = 1.74531263774940077459e-2 * z;
-/* absolute error = 4.146e-11: */
-cz = 1.0 - 1.52307909153324666207e-4 * z * z;
-#else
-/* relative error = 6.346e-6: */
-sz = 1.74531817576426662296e-2 * z;
-/* relative error = 3.173e-6: */
-cz = 1.0 - 1.52308226602566149927e-4 * z * z;
-#endif
-#else
-y = z * z;
-#endif
-
-
-#if ACC11
-sz = ( -8.86092781698004819918e-7 * y
- + 1.74532925198378577601e-2 ) * z;
-
-cz = 1.0 - ( -3.86631403698859047896e-9 * y
- + 1.52308709893047593702e-4 ) * y;
-#endif
-
-
-#if ACC17
-sz = (( 1.34959795251974073996e-11 * y
- - 8.86096155697856783296e-7 ) * y
- + 1.74532925199432957214e-2 ) * z;
-
-cz = 1.0 - (( 3.92582397764340914444e-14 * y
- - 3.86632385155548605680e-9 ) * y
- + 1.52308709893354299569e-4 ) * y;
-#endif
-
-
-/* Combine the tabulated part and the calculated part
- * by trigonometry.
- */
-y = sx * cz + cx * sz;
-if( xsign < 0 )
- y = - y;
-*s = y; /* sine */
-
-*c = cx * cz - sx * sz; /* cosine */
-return 0;
-}
+++ /dev/null
-/* sindg.c
- *
- * Circular sine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sindg();
- *
- * y = sindg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 P(x**2).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +-1000 3100 3.3e-17 9.0e-18
- * IEEE +-1000 30000 2.3e-16 5.6e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sindg total loss x > 8.0e14 (DEC) 0.0
- * x > 1.0e14 (IEEE)
- *
- */
-\f/* cosdg.c
- *
- * Circular cosine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cosdg();
- *
- * y = cosdg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 P(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +-1000 3400 3.5e-17 9.1e-18
- * IEEE +-1000 30000 2.1e-16 5.7e-17
- * See also sin().
- *
- */
-\f
-/* Cephes Math Library Release 2.0: April, 1987
- * Copyright 1985, 1987 by Stephen L. Moshier
- * Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */
-
-#include <math.h>
-
-#ifdef UNK
-static double sincof[] = {
- 1.58962301572218447952E-10,
--2.50507477628503540135E-8,
- 2.75573136213856773549E-6,
--1.98412698295895384658E-4,
- 8.33333333332211858862E-3,
--1.66666666666666307295E-1
-};
-static double coscof[] = {
- 1.13678171382044553091E-11,
--2.08758833757683644217E-9,
- 2.75573155429816611547E-7,
--2.48015872936186303776E-5,
- 1.38888888888806666760E-3,
--4.16666666666666348141E-2,
- 4.99999999999999999798E-1
-};
-static double PI180 = 1.74532925199432957692E-2; /* pi/180 */
-static double lossth = 1.0e14;
-#endif
-
-#ifdef DEC
-static unsigned short sincof[] = {
-0030056,0143750,0177170,0073013,
-0131727,0027455,0044510,0132205,
-0033470,0167432,0131752,0042263,
-0135120,0006400,0146776,0174027,
-0036410,0104210,0104207,0137202,
-0137452,0125252,0125252,0125103
-};
-static unsigned short coscof[] = {
-0027107,0176030,0153315,0110312,
-0131017,0072476,0007450,0123243,
-0032623,0171174,0070066,0146445,
-0134320,0006400,0147355,0163313,
-0035666,0005540,0133012,0165067,
-0137052,0125252,0125252,0125206,
-0040000,0000000,0000000,0000000
-};
-static unsigned short P1[] = {0036616,0175065,0011224,0164711};
-#define PI180 *(double *)P1
-static double lossth = 8.0e14;
-#endif
-
-#ifdef IBMPC
-static unsigned short sincof[] = {
-0x0ec1,0x1fcf,0xd8fd,0x3de5,
-0x1691,0xa929,0xe5e5,0xbe5a,
-0x4896,0x567d,0x1de3,0x3ec7,
-0xdf03,0x19bf,0x01a0,0xbf2a,
-0xf7d0,0x1110,0x1111,0x3f81,
-0x5548,0x5555,0x5555,0xbfc5
-};
-static unsigned short coscof[] = {
-0xb219,0x1ad9,0xff83,0x3da8,
-0x14d4,0xc1e5,0xeea7,0xbe21,
-0xd9a5,0x8e06,0x7e4f,0x3e92,
-0xbcd9,0x19dd,0x01a0,0xbefa,
-0x5d47,0x16c1,0xc16c,0x3f56,
-0x5551,0x5555,0x5555,0xbfa5,
-0x0000,0x0000,0x0000,0x3fe0
-};
-
-static unsigned short P1[] = {0x9d39,0xa252,0xdf46,0x3f91};
-#define PI180 *(double *)P1
-static double lossth = 1.0e14;
-#endif
-
-#ifdef MIEEE
-static unsigned short sincof[] = {
-0x3de5,0xd8fd,0x1fcf,0x0ec1,
-0xbe5a,0xe5e5,0xa929,0x1691,
-0x3ec7,0x1de3,0x567d,0x4896,
-0xbf2a,0x01a0,0x19bf,0xdf03,
-0x3f81,0x1111,0x1110,0xf7d0,
-0xbfc5,0x5555,0x5555,0x5548
-};
-static unsigned short coscof[] = {
-0x3da8,0xff83,0x1ad9,0xb219,
-0xbe21,0xeea7,0xc1e5,0x14d4,
-0x3e92,0x7e4f,0x8e06,0xd9a5,
-0xbefa,0x01a0,0x19dd,0xbcd9,
-0x3f56,0xc16c,0x16c1,0x5d47,
-0xbfa5,0x5555,0x5555,0x5551,
-0x3fe0,0x0000,0x0000,0x0000
-};
-
-static unsigned short P1[] = {
-0x3f91,0xdf46,0xa252,0x9d39
-};
-#define PI180 *(double *)P1
-static double lossth = 1.0e14;
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double floor ( double );
-extern double ldexp ( double, int );
-#else
-double polevl(), floor(), ldexp();
-#endif
-extern double PIO4;
-
-double sindg(x)
-double x;
-{
-double y, z, zz;
-int j, sign;
-
-/* make argument positive but save the sign */
-sign = 1;
-if( x < 0 )
- {
- x = -x;
- sign = -1;
- }
-
-if( x > lossth )
- {
- mtherr( "sindg", TLOSS );
- return(0.0);
- }
-
-y = floor( x/45.0 ); /* integer part of x/PIO4 */
-
-/* strip high bits of integer part to prevent integer overflow */
-z = ldexp( y, -4 );
-z = floor(z); /* integer part of y/8 */
-z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
-
-j = z; /* convert to integer for tests on the phase angle */
-/* map zeros to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-j = j & 07; /* octant modulo 360 degrees */
-/* reflect in x axis */
-if( j > 3)
- {
- sign = -sign;
- j -= 4;
- }
-
-z = x - y * 45.0; /* x mod 45 degrees */
-z *= PI180; /* multiply by pi/180 to convert to radians */
-zz = z * z;
-
-if( (j==1) || (j==2) )
- {
- y = 1.0 - zz * polevl( zz, coscof, 6 );
- }
-else
- {
- y = z + z * (zz * polevl( zz, sincof, 5 ));
- }
-
-if(sign < 0)
- y = -y;
-
-return(y);
-}
-
-
-
-
-
-double cosdg(x)
-double x;
-{
-double y, z, zz;
-int j, sign;
-
-/* make argument positive */
-sign = 1;
-if( x < 0 )
- x = -x;
-
-if( x > lossth )
- {
- mtherr( "cosdg", TLOSS );
- return(0.0);
- }
-
-y = floor( x/45.0 );
-z = ldexp( y, -4 );
-z = floor(z); /* integer part of y/8 */
-z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
-
-/* integer and fractional part modulo one octant */
-j = z;
-if( j & 1 ) /* map zeros to origin */
- {
- j += 1;
- y += 1.0;
- }
-j = j & 07;
-if( j > 3)
- {
- j -=4;
- sign = -sign;
- }
-
-if( j > 1 )
- sign = -sign;
-
-z = x - y * 45.0; /* x mod 45 degrees */
-z *= PI180; /* multiply by pi/180 to convert to radians */
-
-zz = z * z;
-
-if( (j==1) || (j==2) )
- {
- y = z + z * (zz * polevl( zz, sincof, 5 ));
- }
-else
- {
- y = 1.0 - zz * polevl( zz, coscof, 6 );
- }
-
-if(sign < 0)
- y = -y;
-
-return(y);
-}
+++ /dev/null
-/* sinh.c
- *
- * Hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sinh();
- *
- * y = sinh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic sine of argument in the range MINLOG to
- * MAXLOG.
- *
- * The range is partitioned into two segments. If |x| <= 1, a
- * rational function of the form x + x**3 P(x)/Q(x) is employed.
- * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +- 88 50000 4.0e-17 7.7e-18
- * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
--7.89474443963537015605E-1,
--1.63725857525983828727E2,
--1.15614435765005216044E4,
--3.51754964808151394800E5
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
--2.77711081420602794433E2,
- 3.61578279834431989373E4,
--2.11052978884890840399E6
-};
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0140112,0015377,0042731,0163255,
-0142043,0134721,0146177,0123761,
-0143464,0122706,0034353,0006017,
-0144653,0140536,0157665,0054045
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0142212,0155404,0133513,0022040,
-0044015,0036723,0173271,0011053,
-0145400,0150407,0023710,0001034
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x3cd6,0xe8bb,0x435f,0xbfe9,
-0xf4fe,0x398f,0x773a,0xc064,
-0x6182,0xc71d,0x94b8,0xc0c6,
-0xab05,0xdbf6,0x782b,0xc115
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x6484,0x96e9,0x5b60,0xc071,
-0x2245,0x7ed7,0xa7ba,0x40e1,
-0x0044,0xe4f9,0x1a20,0xc140
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0xbfe9,0x435f,0xe8bb,0x3cd6,
-0xc064,0x773a,0x398f,0xf4fe,
-0xc0c6,0x94b8,0xc71d,0x6182,
-0xc115,0x782b,0xdbf6,0xab05
-};
-static unsigned short Q[] = {
-0xc071,0x5b60,0x96e9,0x6484,
-0x40e1,0xa7ba,0x7ed7,0x2245,
-0xc140,0x1a20,0xe4f9,0x0044
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double exp ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double fabs(), exp(), polevl(), p1evl();
-#endif
-extern double INFINITY, MINLOG, MAXLOG, LOGE2;
-
-double sinh(x)
-double x;
-{
-double a;
-
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-a = fabs(x);
-if( (x > (MAXLOG + LOGE2)) || (x > -(MINLOG-LOGE2) ) )
- {
- mtherr( "sinh", DOMAIN );
- if( x > 0 )
- return( INFINITY );
- else
- return( -INFINITY );
- }
-if( a > 1.0 )
- {
- if( a >= (MAXLOG - LOGE2) )
- {
- a = exp(0.5*a);
- a = (0.5 * a) * a;
- if( x < 0 )
- a = -a;
- return(a);
- }
- a = exp(a);
- a = 0.5*a - (0.5/a);
- if( x < 0 )
- a = -a;
- return(a);
- }
-
-a *= a;
-return( x + x * a * (polevl(a,P,3)/p1evl(a,Q,3)) );
-}
+++ /dev/null
-/* spence.c
- *
- * Dilogarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, spence();
- *
- * y = spence( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral
- *
- * x
- * -
- * | | log t
- * spence(x) = - | ----- dt
- * | | t - 1
- * -
- * 1
- *
- * for x >= 0. A rational approximation gives the integral in
- * the interval (0.5, 1.5). Transformation formulas for 1/x
- * and 1-x are employed outside the basic expansion range.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,4 30000 3.9e-15 5.4e-16
- * DEC 0,4 3000 2.5e-16 4.5e-17
- *
- *
- */
-\f
-/* spence.c */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1985, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double A[8] = {
- 4.65128586073990045278E-5,
- 7.31589045238094711071E-3,
- 1.33847639578309018650E-1,
- 8.79691311754530315341E-1,
- 2.71149851196553469920E0,
- 4.25697156008121755724E0,
- 3.29771340985225106936E0,
- 1.00000000000000000126E0,
-};
-static double B[8] = {
- 6.90990488912553276999E-4,
- 2.54043763932544379113E-2,
- 2.82974860602568089943E-1,
- 1.41172597751831069617E0,
- 3.63800533345137075418E0,
- 5.03278880143316990390E0,
- 3.54771340985225096217E0,
- 9.99999999999999998740E-1,
-};
-#endif
-#ifdef DEC
-static unsigned short A[32] = {
-0034503,0013315,0034120,0157771,
-0036357,0135043,0016766,0150637,
-0037411,0007533,0005212,0161475,
-0040141,0031563,0023217,0120331,
-0040455,0104461,0007002,0155522,
-0040610,0034434,0065721,0120465,
-0040523,0006674,0105671,0054427,
-0040200,0000000,0000000,0000000,
-};
-static unsigned short B[32] = {
-0035465,0021626,0032367,0144157,
-0036720,0016326,0134431,0000406,
-0037620,0161024,0133701,0120766,
-0040264,0131557,0152055,0064512,
-0040550,0152424,0051166,0034272,
-0040641,0006233,0014672,0111572,
-0040543,0006674,0105671,0054425,
-0040200,0000000,0000000,0000000,
-};
-#endif
-#ifdef IBMPC
-static unsigned short A[32] = {
-0x1bff,0xa70a,0x62d9,0x3f08,
-0xda34,0x63be,0xf744,0x3f7d,
-0x5c68,0x6151,0x21eb,0x3fc1,
-0xf41b,0x64d1,0x266e,0x3fec,
-0x5b6a,0x21c0,0xb126,0x4005,
-0x3427,0x8d7a,0x0723,0x4011,
-0x2b23,0x9177,0x61b7,0x400a,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-static unsigned short B[32] = {
-0xf90e,0xc69e,0xa472,0x3f46,
-0x2021,0xd723,0x039a,0x3f9a,
-0x343f,0x96f8,0x1c42,0x3fd2,
-0xad29,0xfa85,0x966d,0x3ff6,
-0xc717,0x8a4e,0x1aa2,0x400d,
-0x526f,0x6337,0x2193,0x4014,
-0x2b23,0x9177,0x61b7,0x400c,
-0x0000,0x0000,0x0000,0x3ff0,
-};
-#endif
-#ifdef MIEEE
-static unsigned short A[32] = {
-0x3f08,0x62d9,0xa70a,0x1bff,
-0x3f7d,0xf744,0x63be,0xda34,
-0x3fc1,0x21eb,0x6151,0x5c68,
-0x3fec,0x266e,0x64d1,0xf41b,
-0x4005,0xb126,0x21c0,0x5b6a,
-0x4011,0x0723,0x8d7a,0x3427,
-0x400a,0x61b7,0x9177,0x2b23,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-static unsigned short B[32] = {
-0x3f46,0xa472,0xc69e,0xf90e,
-0x3f9a,0x039a,0xd723,0x2021,
-0x3fd2,0x1c42,0x96f8,0x343f,
-0x3ff6,0x966d,0xfa85,0xad29,
-0x400d,0x1aa2,0x8a4e,0xc717,
-0x4014,0x2193,0x6337,0x526f,
-0x400c,0x61b7,0x9177,0x2b23,
-0x3ff0,0x0000,0x0000,0x0000,
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double log ( double );
-extern double polevl ( double, void *, int );
-#else
-double fabs(), log(), polevl();
-#endif
-extern double PI, MACHEP;
-
-double spence(x)
-double x;
-{
-double w, y, z;
-int flag;
-
-if( x < 0.0 )
- {
- mtherr( "spence", DOMAIN );
- return(0.0);
- }
-
-if( x == 1.0 )
- return( 0.0 );
-
-if( x == 0.0 )
- return( PI*PI/6.0 );
-
-flag = 0;
-
-if( x > 2.0 )
- {
- x = 1.0/x;
- flag |= 2;
- }
-
-if( x > 1.5 )
- {
- w = (1.0/x) - 1.0;
- flag |= 2;
- }
-
-else if( x < 0.5 )
- {
- w = -x;
- flag |= 1;
- }
-
-else
- w = x - 1.0;
-
-
-y = -w * polevl( w, A, 7) / polevl( w, B, 7 );
-
-if( flag & 1 )
- y = (PI * PI)/6.0 - log(x) * log(1.0-x) - y;
-
-if( flag & 2 )
- {
- z = log(x);
- y = -0.5 * z * z - y;
- }
-
-return( y );
-}
+++ /dev/null
-/* sqrt.c
- *
- * Square root
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, sqrt();
- *
- * y = sqrt( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the square root of x.
- *
- * Range reduction involves isolating the power of two of the
- * argument and using a polynomial approximation to obtain
- * a rough value for the square root. Then Heron's iteration
- * is used three times to converge to an accurate value.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0, 10 60000 2.1e-17 7.9e-18
- * IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sqrt domain x < 0 0.0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-#else
-double frexp(), ldexp();
-#endif
-extern double SQRT2; /* SQRT2 = 1.41421356237309504880 */
-
-double sqrt(x)
-double x;
-{
-int e;
-#ifndef UNK
-short *q;
-#endif
-double z, w;
-
-if( x <= 0.0 )
- {
- if( x < 0.0 )
- mtherr( "sqrt", DOMAIN );
- return( 0.0 );
- }
-w = x;
-/* separate exponent and significand */
-#ifdef UNK
-z = frexp( x, &e );
-#endif
-#ifdef DEC
-q = (short *)&x;
-e = ((*q >> 7) & 0377) - 0200;
-*q &= 0177;
-*q |= 040000;
-z = x;
-#endif
-
-/* Note, frexp and ldexp are used in order to
- * handle denormal numbers properly.
- */
-#ifdef IBMPC
-z = frexp( x, &e );
-q = (short *)&x;
-q += 3;
-/*
-e = ((*q >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x000f;
-*q |= 0x3fe0;
-z = x;
-*/
-#endif
-#ifdef MIEEE
-z = frexp( x, &e );
-q = (short *)&x;
-/*
-e = ((*q >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x000f;
-*q |= 0x3fe0;
-z = x;
-*/
-#endif
-
-/* approximate square root of number between 0.5 and 1
- * relative error of approximation = 7.47e-3
- */
-x = 4.173075996388649989089E-1 + 5.9016206709064458299663E-1 * z;
-
-/* adjust for odd powers of 2 */
-if( (e & 1) != 0 )
- x *= SQRT2;
-
-/* re-insert exponent */
-#ifdef UNK
-x = ldexp( x, (e >> 1) );
-#endif
-#ifdef DEC
-*q += ((e >> 1) & 0377) << 7;
-*q &= 077777;
-#endif
-#ifdef IBMPC
-x = ldexp( x, (e >> 1) );
-/*
-*q += ((e >>1) & 0x7ff) << 4;
-*q &= 077777;
-*/
-#endif
-#ifdef MIEEE
-x = ldexp( x, (e >> 1) );
-/*
-*q += ((e >>1) & 0x7ff) << 4;
-*q &= 077777;
-*/
-#endif
-
-/* Newton iterations: */
-#ifdef UNK
-x = 0.5*(x + w/x);
-x = 0.5*(x + w/x);
-x = 0.5*(x + w/x);
-#endif
-
-/* Note, assume the square root cannot be denormal,
- * so it is safe to use integer exponent operations here.
- */
-#ifdef DEC
-x += w/x;
-*q -= 0200;
-x += w/x;
-*q -= 0200;
-x += w/x;
-*q -= 0200;
-#endif
-#ifdef IBMPC
-x += w/x;
-*q -= 0x10;
-x += w/x;
-*q -= 0x10;
-x += w/x;
-*q -= 0x10;
-#endif
-#ifdef MIEEE
-x += w/x;
-*q -= 0x10;
-x += w/x;
-*q -= 0x10;
-x += w/x;
-*q -= 0x10;
-#endif
-
-return(x);
-}
+++ /dev/null
-/* stdtr.c
- *
- * Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double t, stdtr();
- * short k;
- *
- * y = stdtr( k, t );
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral from minus infinity to t of the Student
- * t distribution with integer k > 0 degrees of freedom:
- *
- * t
- * -
- * | |
- * - | 2 -(k+1)/2
- * | ( (k+1)/2 ) | ( x )
- * ---------------------- | ( 1 + --- ) dx
- * - | ( k )
- * sqrt( k pi ) | ( k/2 ) |
- * | |
- * -
- * -inf.
- *
- * Relation to incomplete beta integral:
- *
- * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
- * where
- * z = k/(k + t**2).
- *
- * For t < -2, this is the method of computation. For higher t,
- * a direct method is derived from integration by parts.
- * Since the function is symmetric about t=0, the area under the
- * right tail of the density is found by calling the function
- * with -t instead of t.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 25. The "domain" refers to t.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -100,-2 50000 5.9e-15 1.4e-15
- * IEEE -2,100 500000 2.7e-15 4.9e-17
- */
-\f
-/* stdtri.c
- *
- * Functional inverse of Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * double p, t, stdtri();
- * int k;
- *
- * t = stdtri( k, p );
- *
- *
- * DESCRIPTION:
- *
- * Given probability p, finds the argument t such that stdtr(k,t)
- * is equal to p.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 100. The "domain" refers to p:
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE .001,.999 25000 5.7e-15 8.0e-16
- * IEEE 10^-6,.001 25000 2.0e-12 2.9e-14
- */
-\f
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern double PI, MACHEP, MAXNUM;
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double atan ( double );
-extern double incbet ( double, double, double );
-extern double incbi ( double, double, double );
-extern double fabs ( double );
-#else
-double sqrt(), atan(), incbet(), incbi(), fabs();
-#endif
-
-double stdtr( k, t )
-int k;
-double t;
-{
-double x, rk, z, f, tz, p, xsqk;
-int j;
-
-if( k <= 0 )
- {
- mtherr( "stdtr", DOMAIN );
- return(0.0);
- }
-
-if( t == 0 )
- return( 0.5 );
-
-if( t < -2.0 )
- {
- rk = k;
- z = rk / (rk + t * t);
- p = 0.5 * incbet( 0.5*rk, 0.5, z );
- return( p );
- }
-
-/* compute integral from -t to + t */
-
-if( t < 0 )
- x = -t;
-else
- x = t;
-
-rk = k; /* degrees of freedom */
-z = 1.0 + ( x * x )/rk;
-
-/* test if k is odd or even */
-if( (k & 1) != 0)
- {
-
- /* computation for odd k */
-
- xsqk = x/sqrt(rk);
- p = atan( xsqk );
- if( k > 1 )
- {
- f = 1.0;
- tz = 1.0;
- j = 3;
- while( (j<=(k-2)) && ( (tz/f) > MACHEP ) )
- {
- tz *= (j-1)/( z * j );
- f += tz;
- j += 2;
- }
- p += f * xsqk/z;
- }
- p *= 2.0/PI;
- }
-
-
-else
- {
-
- /* computation for even k */
-
- f = 1.0;
- tz = 1.0;
- j = 2;
-
- while( ( j <= (k-2) ) && ( (tz/f) > MACHEP ) )
- {
- tz *= (j - 1)/( z * j );
- f += tz;
- j += 2;
- }
- p = f * x/sqrt(z*rk);
- }
-
-/* common exit */
-
-
-if( t < 0 )
- p = -p; /* note destruction of relative accuracy */
-
- p = 0.5 + 0.5 * p;
-return(p);
-}
-
-double stdtri( k, p )
-int k;
-double p;
-{
-double t, rk, z;
-int rflg;
-
-if( k <= 0 || p <= 0.0 || p >= 1.0 )
- {
- mtherr( "stdtri", DOMAIN );
- return(0.0);
- }
-
-rk = k;
-
-if( p > 0.25 && p < 0.75 )
- {
- if( p == 0.5 )
- return( 0.0 );
- z = 1.0 - 2.0 * p;
- z = incbi( 0.5, 0.5*rk, fabs(z) );
- t = sqrt( rk*z/(1.0-z) );
- if( p < 0.5 )
- t = -t;
- return( t );
- }
-rflg = -1;
-if( p >= 0.5)
- {
- p = 1.0 - p;
- rflg = 1;
- }
-z = incbi( 0.5*rk, 0.5, 2.0*p );
-
-if( MAXNUM * z < rk )
- return(rflg* MAXNUM);
-t = sqrt( rk/z - rk );
-return( rflg * t );
-}
+++ /dev/null
-/* struve.c
- *
- * Struve function
- *
- *
- *
- * SYNOPSIS:
- *
- * double v, x, y, struve();
- *
- * y = struve( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the Struve function Hv(x) of order v, argument x.
- * Negative x is rejected unless v is an integer.
- *
- * This module also contains the hypergeometric functions 1F2
- * and 3F0 and a routine for the Bessel function Yv(x) with
- * noninteger v.
- *
- *
- *
- * ACCURACY:
- *
- * Not accurately characterized, but spot checked against tables.
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.81: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-#include <math.h>
-#define DEBUG 0
-#ifdef ANSIPROT
-extern double gamma ( double );
-extern double pow ( double, double );
-extern double sqrt ( double );
-extern double yn ( int, double );
-extern double jv ( double, double );
-extern double fabs ( double );
-extern double floor ( double );
-extern double sin ( double );
-extern double cos ( double );
-double yv ( double, double );
-double onef2 (double, double, double, double, double * );
-double threef0 (double, double, double, double, double * );
-#else
-double gamma(), pow(), sqrt(), yn(), yv(), jv(), fabs(), floor();
-double sin(), cos();
-double onef2(), threef0();
-#endif
-static double stop = 1.37e-17;
-extern double MACHEP;
-
-double onef2( a, b, c, x, err )
-double a, b, c, x;
-double *err;
-{
-double n, a0, sum, t;
-double an, bn, cn, max, z;
-
-an = a;
-bn = b;
-cn = c;
-a0 = 1.0;
-sum = 1.0;
-n = 1.0;
-t = 1.0;
-max = 0.0;
-
-do
- {
- if( an == 0 )
- goto done;
- if( bn == 0 )
- goto error;
- if( cn == 0 )
- goto error;
- if( (a0 > 1.0e34) || (n > 200) )
- goto error;
- a0 *= (an * x) / (bn * cn * n);
- sum += a0;
- an += 1.0;
- bn += 1.0;
- cn += 1.0;
- n += 1.0;
- z = fabs( a0 );
- if( z > max )
- max = z;
- if( sum != 0 )
- t = fabs( a0 / sum );
- else
- t = z;
- }
-while( t > stop );
-
-done:
-
-*err = fabs( MACHEP*max /sum );
-
-#if DEBUG
- printf(" onef2 cancellation error %.5E\n", *err );
-#endif
-
-goto xit;
-
-error:
-#if DEBUG
-printf("onef2 does not converge\n");
-#endif
-*err = 1.0e38;
-
-xit:
-
-#if DEBUG
-printf("onef2( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
-#endif
-return(sum);
-}
-
-
-
-
-double threef0( a, b, c, x, err )
-double a, b, c, x;
-double *err;
-{
-double n, a0, sum, t, conv, conv1;
-double an, bn, cn, max, z;
-
-an = a;
-bn = b;
-cn = c;
-a0 = 1.0;
-sum = 1.0;
-n = 1.0;
-t = 1.0;
-max = 0.0;
-conv = 1.0e38;
-conv1 = conv;
-
-do
- {
- if( an == 0.0 )
- goto done;
- if( bn == 0.0 )
- goto done;
- if( cn == 0.0 )
- goto done;
- if( (a0 > 1.0e34) || (n > 200) )
- goto error;
- a0 *= (an * bn * cn * x) / n;
- an += 1.0;
- bn += 1.0;
- cn += 1.0;
- n += 1.0;
- z = fabs( a0 );
- if( z > max )
- max = z;
- if( z >= conv )
- {
- if( (z < max) && (z > conv1) )
- goto done;
- }
- conv1 = conv;
- conv = z;
- sum += a0;
- if( sum != 0 )
- t = fabs( a0 / sum );
- else
- t = z;
- }
-while( t > stop );
-
-done:
-
-t = fabs( MACHEP*max/sum );
-#if DEBUG
- printf(" threef0 cancellation error %.5E\n", t );
-#endif
-
-max = fabs( conv/sum );
-if( max > t )
- t = max;
-#if DEBUG
- printf(" threef0 convergence %.5E\n", max );
-#endif
-
-goto xit;
-
-error:
-#if DEBUG
-printf("threef0 does not converge\n");
-#endif
-t = 1.0e38;
-
-xit:
-
-#if DEBUG
-printf("threef0( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
-#endif
-
-*err = t;
-return(sum);
-}
-
-
-
-
-extern double PI;
-
-double struve( v, x )
-double v, x;
-{
-double y, ya, f, g, h, t;
-double onef2err, threef0err;
-
-f = floor(v);
-if( (v < 0) && ( v-f == 0.5 ) )
- {
- y = jv( -v, x );
- f = 1.0 - f;
- g = 2.0 * floor(f/2.0);
- if( g != f )
- y = -y;
- return(y);
- }
-t = 0.25*x*x;
-f = fabs(x);
-g = 1.5 * fabs(v);
-if( (f > 30.0) && (f > g) )
- {
- onef2err = 1.0e38;
- y = 0.0;
- }
-else
- {
- y = onef2( 1.0, 1.5, 1.5+v, -t, &onef2err );
- }
-
-if( (f < 18.0) || (x < 0.0) )
- {
- threef0err = 1.0e38;
- ya = 0.0;
- }
-else
- {
- ya = threef0( 1.0, 0.5, 0.5-v, -1.0/t, &threef0err );
- }
-
-f = sqrt( PI );
-h = pow( 0.5*x, v-1.0 );
-
-if( onef2err <= threef0err )
- {
- g = gamma( v + 1.5 );
- y = y * h * t / ( 0.5 * f * g );
- return(y);
- }
-else
- {
- g = gamma( v + 0.5 );
- ya = ya * h / ( f * g );
- ya = ya + yv( v, x );
- return(ya);
- }
-}
-
-
-
-
-/* Bessel function of noninteger order
- */
-
-double yv( v, x )
-double v, x;
-{
-double y, t;
-int n;
-
-y = floor( v );
-if( y == v )
- {
- n = v;
- y = yn( n, x );
- return( y );
- }
-t = PI * v;
-y = (cos(t) * jv( v, x ) - jv( -v, x ))/sin(t);
-return( y );
-}
-
-/* Crossover points between ascending series and asymptotic series
- * for Struve function
- *
- * v x
- *
- * 0 19.2
- * 1 18.95
- * 2 19.15
- * 3 19.3
- * 5 19.7
- * 10 21.35
- * 20 26.35
- * 30 32.31
- * 40 40.0
- */
+++ /dev/null
-/* tan.c
- *
- * Circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, tan();
- *
- * y = tan( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC +-1.07e9 44000 4.1e-17 1.0e-17
- * IEEE +-1.07e9 30000 2.9e-16 8.1e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tan total loss x > 1.073741824e9 0.0
- *
- */
-\f/* cot.c
- *
- * Circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cot();
- *
- * y = cot( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-1.07e9 30000 2.9e-16 8.2e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 1.073741824e9 0.0
- * cot singularity x = 0 INFINITY
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-yright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
--1.30936939181383777646E4,
- 1.15351664838587416140E6,
--1.79565251976484877988E7
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 1.36812963470692954678E4,
--1.32089234440210967447E6,
- 2.50083801823357915839E7,
--5.38695755929454629881E7
-};
-static double DP1 = 7.853981554508209228515625E-1;
-static double DP2 = 7.94662735614792836714E-9;
-static double DP3 = 3.06161699786838294307E-17;
-static double lossth = 1.073741824e9;
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0143514,0113306,0111171,0174674,
-0045214,0147545,0027744,0167346,
-0146210,0177526,0114514,0105660
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0043525,0142457,0072633,0025617,
-0145241,0036742,0140525,0162256,
-0046276,0146176,0013526,0143573,
-0146515,0077401,0162762,0150607
-};
-/* 7.853981629014015197753906250000E-1 */
-static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
-/* 4.960467869796758577649598009884E-10 */
-static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
-/* 2.860594363054915898381331279295E-18 */
-static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-static double lossth = 1.073741824e9;
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x3f38,0xd24f,0x92d8,0xc0c9,
-0x9ddd,0xa5fc,0x99ec,0x4131,
-0x9176,0xd329,0x1fea,0xc171
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x6572,0xeeb3,0xb8a5,0x40ca,
-0xbc96,0x582a,0x27bc,0xc134,
-0xd8ef,0xc2ea,0xd98f,0x4177,
-0x5a31,0x3cbe,0xafe0,0xc189
-};
-/*
- 7.85398125648498535156E-1,
- 3.77489470793079817668E-8,
- 2.69515142907905952645E-15,
-*/
-static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
-static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
-static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-static double lossth = 1.073741824e9;
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0xc0c9,0x92d8,0xd24f,0x3f38,
-0x4131,0x99ec,0xa5fc,0x9ddd,
-0xc171,0x1fea,0xd329,0x9176
-};
-static unsigned short Q[] = {
-0x40ca,0xb8a5,0xeeb3,0x6572,
-0xc134,0x27bc,0x582a,0xbc96,
-0x4177,0xd98f,0xc2ea,0xd8ef,
-0xc189,0xafe0,0x3cbe,0x5a31
-};
-static unsigned short P1[] = {
-0x3fe9,0x21fb,0x4000,0x0000
-};
-static unsigned short P2[] = {
-0x3e64,0x442d,0x0000,0x0000
-};
-static unsigned short P3[] = {
-0x3ce8,0x4698,0x98cc,0x5170,
-};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-static double lossth = 1.073741824e9;
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double ldexp ( double, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-static double tancot(double, int);
-#else
-double polevl(), p1evl(), floor(), ldexp();
-static double tancot();
-int isnan(), isfinite();
-#endif
-extern double PIO4;
-extern double INFINITY;
-extern double NAN;
-
-double tan(x)
-double x;
-{
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-#ifdef NANS
-if( isnan(x) )
- return(x);
-if( !isfinite(x) )
- {
- mtherr( "tan", DOMAIN );
- return(NAN);
- }
-#endif
-return( tancot(x,0) );
-}
-
-
-double cot(x)
-double x;
-{
-
-if( x == 0.0 )
- {
- mtherr( "cot", SING );
- return( INFINITY );
- }
-return( tancot(x,1) );
-}
-
-
-static double tancot( xx, cotflg )
-double xx;
-int cotflg;
-{
-double x, y, z, zz;
-int j, sign;
-
-/* make argument positive but save the sign */
-if( xx < 0 )
- {
- x = -xx;
- sign = -1;
- }
-else
- {
- x = xx;
- sign = 1;
- }
-
-if( x > lossth )
- {
- if( cotflg )
- mtherr( "cot", TLOSS );
- else
- mtherr( "tan", TLOSS );
- return(0.0);
- }
-
-/* compute x mod PIO4 */
-y = floor( x/PIO4 );
-
-/* strip high bits of integer part */
-z = ldexp( y, -3 );
-z = floor(z); /* integer part of y/8 */
-z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
-
-/* integer and fractional part modulo one octant */
-j = z;
-
-/* map zeros and singularities to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-
-if( zz > 1.0e-14 )
- y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
-else
- y = z;
-
-if( j & 2 )
- {
- if( cotflg )
- y = -y;
- else
- y = -1.0/y;
- }
-else
- {
- if( cotflg )
- y = 1.0/y;
- }
-
-if( sign < 0 )
- y = -y;
-
-return( y );
-}
+++ /dev/null
-/* tandg.c
- *
- * Circular tangent of argument in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, tandg();
- *
- * y = tandg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the argument x in degrees.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,10 8000 3.4e-17 1.2e-17
- * IEEE 0,10 30000 3.2e-16 8.4e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tandg total loss x > 8.0e14 (DEC) 0.0
- * x > 1.0e14 (IEEE)
- * tandg singularity x = 180 k + 90 MAXNUM
- */
-\f/* cotdg.c
- *
- * Circular cotangent of argument in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cotdg();
- *
- * y = cotdg( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the argument x in degrees.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cotdg total loss x > 8.0e14 (DEC) 0.0
- * x > 1.0e14 (IEEE)
- * cotdg singularity x = 180 k MAXNUM
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
--1.30936939181383777646E4,
- 1.15351664838587416140E6,
--1.79565251976484877988E7
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 1.36812963470692954678E4,
--1.32089234440210967447E6,
- 2.50083801823357915839E7,
--5.38695755929454629881E7
-};
-static double PI180 = 1.74532925199432957692E-2;
-static double lossth = 1.0e14;
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0143514,0113306,0111171,0174674,
-0045214,0147545,0027744,0167346,
-0146210,0177526,0114514,0105660
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0043525,0142457,0072633,0025617,
-0145241,0036742,0140525,0162256,
-0046276,0146176,0013526,0143573,
-0146515,0077401,0162762,0150607
-};
-static unsigned short P1[] = {0036616,0175065,0011224,0164711};
-#define PI180 *(double *)P1
-static double lossth = 8.0e14;
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x3f38,0xd24f,0x92d8,0xc0c9,
-0x9ddd,0xa5fc,0x99ec,0x4131,
-0x9176,0xd329,0x1fea,0xc171
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x6572,0xeeb3,0xb8a5,0x40ca,
-0xbc96,0x582a,0x27bc,0xc134,
-0xd8ef,0xc2ea,0xd98f,0x4177,
-0x5a31,0x3cbe,0xafe0,0xc189
-};
-static unsigned short P1[] = {0x9d39,0xa252,0xdf46,0x3f91};
-#define PI180 *(double *)P1
-static double lossth = 1.0e14;
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0xc0c9,0x92d8,0xd24f,0x3f38,
-0x4131,0x99ec,0xa5fc,0x9ddd,
-0xc171,0x1fea,0xd329,0x9176
-};
-static unsigned short Q[] = {
-0x40ca,0xb8a5,0xeeb3,0x6572,
-0xc134,0x27bc,0x582a,0xbc96,
-0x4177,0xd98f,0xc2ea,0xd8ef,
-0xc189,0xafe0,0x3cbe,0x5a31
-};
-static unsigned short P1[] = {
-0x3f91,0xdf46,0xa252,0x9d39
-};
-#define PI180 *(double *)P1
-static double lossth = 1.0e14;
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double floor ( double );
-extern double ldexp ( double, int );
-static double tancot( double, int );
-#else
-double polevl(), p1evl(), floor(), ldexp();
-static double tancot();
-#endif
-extern double MAXNUM;
-extern double PIO4;
-
-
-double tandg(x)
-double x;
-{
-
-return( tancot(x,0) );
-}
-
-
-double cotdg(x)
-double x;
-{
-
-return( tancot(x,1) );
-}
-
-
-static double tancot( xx, cotflg )
-double xx;
-int cotflg;
-{
-double x, y, z, zz;
-int j, sign;
-
-/* make argument positive but save the sign */
-if( xx < 0 )
- {
- x = -xx;
- sign = -1;
- }
-else
- {
- x = xx;
- sign = 1;
- }
-
-if( x > lossth )
- {
- mtherr( "tandg", TLOSS );
- return(0.0);
- }
-
-/* compute x mod PIO4 */
-y = floor( x/45.0 );
-
-/* strip high bits of integer part */
-z = ldexp( y, -3 );
-z = floor(z); /* integer part of y/8 */
-z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
-
-/* integer and fractional part modulo one octant */
-j = z;
-
-/* map zeros and singularities to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-
-z = x - y * 45.0;
-z *= PI180;
-
-zz = z * z;
-
-if( zz > 1.0e-14 )
- y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
-else
- y = z;
-
-if( j & 2 )
- {
- if( cotflg )
- y = -y;
- else
- {
- if( y != 0.0 )
- {
- y = -1.0/y;
- }
- else
- {
- mtherr( "tandg", SING );
- y = MAXNUM;
- }
- }
- }
-else
- {
- if( cotflg )
- {
- if( y != 0.0 )
- y = 1.0/y;
- else
- {
- mtherr( "cotdg", SING );
- y = MAXNUM;
- }
- }
- }
-
-if( sign < 0 )
- y = -y;
-
-return( y );
-}
+++ /dev/null
-/* tanh.c
- *
- * Hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, tanh();
- *
- * y = tanh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic tangent of argument in the range MINLOG to
- * MAXLOG.
- *
- * A rational function is used for |x| < 0.625. The form
- * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
- * Otherwise,
- * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -2,2 50000 3.3e-17 6.4e-18
- * IEEE -2,2 30000 2.5e-16 5.8e-17
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static double P[] = {
--9.64399179425052238628E-1,
--9.92877231001918586564E1,
--1.61468768441708447952E3
-};
-static double Q[] = {
-/* 1.00000000000000000000E0,*/
- 1.12811678491632931402E2,
- 2.23548839060100448583E3,
- 4.84406305325125486048E3
-};
-#endif
-#ifdef DEC
-static unsigned short P[] = {
-0140166,0161335,0053753,0075126,
-0141706,0111520,0070463,0040552,
-0142711,0153001,0101300,0025430
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041741,0117624,0051300,0156060,
-0043013,0133720,0071251,0127717,
-0043227,0060201,0021020,0020136
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x6f4b,0xaafd,0xdc5b,0xbfee,
-0x682d,0x0e26,0xd26a,0xc058,
-0x0563,0x3058,0x3ac0,0xc099
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x1b86,0x8a58,0x33f2,0x405c,
-0x35fa,0x0e55,0x76fa,0x40a1,
-0x040c,0x2442,0xec10,0x40b2
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0xbfee,0xdc5b,0xaafd,0x6f4b,
-0xc058,0xd26a,0x0e26,0x682d,
-0xc099,0x3ac0,0x3058,0x0563
-};
-static unsigned short Q[] = {
-0x405c,0x33f2,0x8a58,0x1b86,
-0x40a1,0x76fa,0x0e55,0x35fa,
-0x40b2,0xec10,0x2442,0x040c
-};
-#endif
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double exp ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-#else
-double fabs(), exp(), polevl(), p1evl();
-#endif
-extern double MAXLOG;
-
-double tanh(x)
-double x;
-{
-double s, z;
-
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-z = fabs(x);
-if( z > 0.5 * MAXLOG )
- {
- if( x > 0 )
- return( 1.0 );
- else
- return( -1.0 );
- }
-if( z >= 0.625 )
- {
- s = exp(2.0*z);
- z = 1.0 - 2.0/(s + 1.0);
- if( x < 0 )
- z = -z;
- }
-else
- {
- if( x == 0.0 )
- return(x);
- s = x * x;
- z = polevl( s, P, 2 )/p1evl(s, Q, 3);
- z = x * s * z;
- z = x + z;
- }
-return( z );
-}
+++ /dev/null
-/* Reports run time, in seconds, for a command.
- The command argument can have multiple words, but then
- it has to be quoted, as for example
-
- time-it "command < file1 > file2"
-
- The time interval resolution is one whole second. */
-
-
-#include <time.h>
-int system ();
-int printf ();
-
-int
-main (argv, argc)
- int argv;
- char **argc;
-{
- time_t t0, t1;
-
- if (argv < 2)
- {
- printf ("Usage: time-it name_of_program_to_be_timed\n");
- exit (1);
- }
- time (&t0);
- /* Wait til the clock changes before starting. */
- do
- {
- time (&t1);
- }
- while (t1 == t0);
- system (argc[1]);
- t0 = t1;
- time (&t1);
- printf ("%ld seconds.\n", t1 - t0);
- exit (0);
-}
+++ /dev/null
-/* unity.c
- *
- * Relative error approximations for function arguments near
- * unity.
- *
- * log1p(x) = log(1+x)
- * expm1(x) = exp(x) - 1
- * cosm1(x) = cos(x) - 1
- *
- */
-
-#include <math.h>
-
-#ifdef ANSIPROT
-extern int isnan (double);
-extern int isfinite (double);
-extern double log ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double exp ( double );
-extern double cos ( double );
-#else
-double log(), polevl(), p1evl(), exp(), cos();
-int isnan(), isfinite();
-#endif
-extern double INFINITY;
-
-/* log1p(x) = log(1 + x) */
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 2.32e-20
- */
-static double LP[] = {
- 4.5270000862445199635215E-5,
- 4.9854102823193375972212E-1,
- 6.5787325942061044846969E0,
- 2.9911919328553073277375E1,
- 6.0949667980987787057556E1,
- 5.7112963590585538103336E1,
- 2.0039553499201281259648E1,
-};
-static double LQ[] = {
-/* 1.0000000000000000000000E0,*/
- 1.5062909083469192043167E1,
- 8.3047565967967209469434E1,
- 2.2176239823732856465394E2,
- 3.0909872225312059774938E2,
- 2.1642788614495947685003E2,
- 6.0118660497603843919306E1,
-};
-
-#define SQRTH 0.70710678118654752440
-#define SQRT2 1.41421356237309504880
-
-double log1p(x)
-double x;
-{
-double z;
-
-z = 1.0 + x;
-if( (z < SQRTH) || (z > SQRT2) )
- return( log(z) );
-z = x*x;
-z = -0.5 * z + x * ( z * polevl( x, LP, 6 ) / p1evl( x, LQ, 6 ) );
-return (x + z);
-}
-
-
-
-/* expm1(x) = exp(x) - 1 */
-
-/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
- * -0.5 <= x <= 0.5
- */
-
-static double EP[3] = {
- 1.2617719307481059087798E-4,
- 3.0299440770744196129956E-2,
- 9.9999999999999999991025E-1,
-};
-static double EQ[4] = {
- 3.0019850513866445504159E-6,
- 2.5244834034968410419224E-3,
- 2.2726554820815502876593E-1,
- 2.0000000000000000000897E0,
-};
-
-double expm1(x)
-double x;
-{
-double r, xx;
-
-#ifdef NANS
-if( isnan(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITY )
- return(INFINITY);
-if( x == -INFINITY )
- return(-1.0);
-#endif
-if( (x < -0.5) || (x > 0.5) )
- return( exp(x) - 1.0 );
-xx = x * x;
-r = x * polevl( xx, EP, 2 );
-r = r/( polevl( xx, EQ, 3 ) - r );
-return (r + r);
-}
-
-
-
-/* cosm1(x) = cos(x) - 1 */
-
-static double coscof[7] = {
- 4.7377507964246204691685E-14,
--1.1470284843425359765671E-11,
- 2.0876754287081521758361E-9,
--2.7557319214999787979814E-7,
- 2.4801587301570552304991E-5,
--1.3888888888888872993737E-3,
- 4.1666666666666666609054E-2,
-};
-
-extern double PIO4;
-
-double cosm1(x)
-double x;
-{
-double xx;
-
-if( (x < -PIO4) || (x > PIO4) )
- return( cos(x) - 1.0 );
-xx = x * x;
-xx = -0.5*xx + xx * xx * polevl( xx, coscof, 6 );
-return xx;
-}
+++ /dev/null
-/* yn.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, yn();
- * int n;
- *
- * y = yn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0() and y1().
- *
- * If n = 0 or 1 the routine for y0 or y1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative
- * when y > 1:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 2200 2.9e-16 5.3e-17
- * IEEE 0, 30 30000 3.4e-15 4.3e-16
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * yn singularity x = 0 MAXNUM
- * yn overflow MAXNUM
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double y0 ( double );
-extern double y1 ( double );
-extern double log ( double );
-#else
-double y0(), y1(), log();
-#endif
-extern double MAXNUM, MAXLOG;
-
-double yn( n, x )
-int n;
-double x;
-{
-double an, anm1, anm2, r;
-int k, sign;
-
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) == 0 ) /* -1**n */
- sign = 1;
- else
- sign = -1;
- }
-else
- sign = 1;
-
-
-if( n == 0 )
- return( sign * y0(x) );
-if( n == 1 )
- return( sign * y1(x) );
-
-/* test for overflow */
-if( x <= 0.0 )
- {
- mtherr( "yn", SING );
- return( -MAXNUM );
- }
-
-/* forward recurrence on n */
-
-anm2 = y0(x);
-anm1 = y1(x);
-k = 1;
-r = 2 * k;
-do
- {
- an = r * anm1 / x - anm2;
- anm2 = anm1;
- anm1 = an;
- r += 2.0;
- ++k;
- }
-while( k < n );
-
-
-return( sign * an );
-}
+++ /dev/null
-/* zeta.c
- *
- * Riemann zeta function of two arguments
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, q, y, zeta();
- *
- * y = zeta( x, q );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=0
- *
- * where x > 1 and q is not a negative integer or zero.
- * The Euler-Maclaurin summation formula is used to obtain
- * the expansion
- *
- * n
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=1
- *
- * 1-x inf. B x(x+1)...(x+2j)
- * (n+q) 1 - 2j
- * + --------- - ------- + > --------------------
- * x-1 x - x+2j+1
- * 2(n+q) j=1 (2j)! (n+q)
- *
- * where the B2j are Bernoulli numbers. Note that (see zetac.c)
- * zeta(x,1) = zetac(x) + 1.
- *
- *
- *
- * ACCURACY:
- *
- *
- *
- * REFERENCE:
- *
- * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
- * Series, and Products, p. 1073; Academic Press, 1980.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double pow ( double, double );
-extern double floor ( double );
-#else
-double fabs(), pow(), floor();
-#endif
-extern double MAXNUM, MACHEP;
-
-/* Expansion coefficients
- * for Euler-Maclaurin summation formula
- * (2k)! / B2k
- * where B2k are Bernoulli numbers
- */
-static double A[] = {
-12.0,
--720.0,
-30240.0,
--1209600.0,
-47900160.0,
--1.8924375803183791606e9, /*1.307674368e12/691*/
-7.47242496e10,
--2.950130727918164224e12, /*1.067062284288e16/3617*/
-1.1646782814350067249e14, /*5.109094217170944e18/43867*/
--4.5979787224074726105e15, /*8.028576626982912e20/174611*/
-1.8152105401943546773e17, /*1.5511210043330985984e23/854513*/
--7.1661652561756670113e18 /*1.6938241367317436694528e27/236364091*/
-};
-/* 30 Nov 86 -- error in third coefficient fixed */
-
-
-double zeta(x,q)
-double x,q;
-{
-int i;
-double a, b, k, s, t, w;
-
-if( x == 1.0 )
- goto retinf;
-
-if( x < 1.0 )
- {
-domerr:
- mtherr( "zeta", DOMAIN );
- return(0.0);
- }
-
-if( q <= 0.0 )
- {
- if(q == floor(q))
- {
- mtherr( "zeta", SING );
-retinf:
- return( MAXNUM );
- }
- if( x != floor(x) )
- goto domerr; /* because q^-x not defined */
- }
-
-/* Euler-Maclaurin summation formula */
-/*
-if( x < 25.0 )
-*/
-{
-/* Permit negative q but continue sum until n+q > +9 .
- * This case should be handled by a reflection formula.
- * If q<0 and x is an integer, there is a relation to
- * the polygamma function.
- */
-s = pow( q, -x );
-a = q;
-i = 0;
-b = 0.0;
-while( (i < 9) || (a <= 9.0) )
- {
- i += 1;
- a += 1.0;
- b = pow( a, -x );
- s += b;
- if( fabs(b/s) < MACHEP )
- goto done;
- }
-
-w = a;
-s += b*w/(x-1.0);
-s -= 0.5 * b;
-a = 1.0;
-k = 0.0;
-for( i=0; i<12; i++ )
- {
- a *= x + k;
- b /= w;
- t = a*b/A[i];
- s = s + t;
- t = fabs(t/s);
- if( t < MACHEP )
- goto done;
- k += 1.0;
- a *= x + k;
- b /= w;
- k += 1.0;
- }
-done:
-return(s);
-}
-
-
-
-/* Basic sum of inverse powers */
-/*
-pseres:
-
-s = pow( q, -x );
-a = q;
-do
- {
- a += 2.0;
- b = pow( a, -x );
- s += b;
- }
-while( b/s > MACHEP );
-
-b = pow( 2.0, -x );
-s = (s + b)/(1.0-b);
-return(s);
-*/
-}
+++ /dev/null
- /* zetac.c
- *
- * Riemann zeta function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, zetac();
- *
- * y = zetac( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zetac(x) = > k , x > 1,
- * -
- * k=2
- *
- * is related to the Riemann zeta function by
- *
- * Riemann zeta(x) = zetac(x) + 1.
- *
- * Extension of the function definition for x < 1 is implemented.
- * Zero is returned for x > log2(MAXNUM).
- *
- * An overflow error may occur for large negative x, due to the
- * gamma function in the reflection formula.
- *
- * ACCURACY:
- *
- * Tabulated values have full machine accuracy.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,50 10000 9.8e-16 1.3e-16
- * DEC 1,50 2000 1.1e-16 1.9e-17
- *
- *
- */
-\f
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern double MAXNUM, PI;
-
-/* Riemann zeta(x) - 1
- * for integer arguments between 0 and 30.
- */
-#ifdef UNK
-static double azetac[] = {
--1.50000000000000000000E0,
- 1.70141183460469231730E38, /* infinity. */
- 6.44934066848226436472E-1,
- 2.02056903159594285400E-1,
- 8.23232337111381915160E-2,
- 3.69277551433699263314E-2,
- 1.73430619844491397145E-2,
- 8.34927738192282683980E-3,
- 4.07735619794433937869E-3,
- 2.00839282608221441785E-3,
- 9.94575127818085337146E-4,
- 4.94188604119464558702E-4,
- 2.46086553308048298638E-4,
- 1.22713347578489146752E-4,
- 6.12481350587048292585E-5,
- 3.05882363070204935517E-5,
- 1.52822594086518717326E-5,
- 7.63719763789976227360E-6,
- 3.81729326499983985646E-6,
- 1.90821271655393892566E-6,
- 9.53962033872796113152E-7,
- 4.76932986787806463117E-7,
- 2.38450502727732990004E-7,
- 1.19219925965311073068E-7,
- 5.96081890512594796124E-8,
- 2.98035035146522801861E-8,
- 1.49015548283650412347E-8,
- 7.45071178983542949198E-9,
- 3.72533402478845705482E-9,
- 1.86265972351304900640E-9,
- 9.31327432419668182872E-10
-};
-#endif
-
-#ifdef DEC
-static unsigned short azetac[] = {
-0140300,0000000,0000000,0000000,
-0077777,0177777,0177777,0177777,
-0040045,0015146,0022460,0076462,
-0037516,0164001,0036001,0104116,
-0037250,0114425,0061754,0022033,
-0037027,0040616,0145174,0146670,
-0036616,0011411,0100444,0104437,
-0036410,0145550,0051474,0161067,
-0036205,0115527,0141434,0133506,
-0036003,0117475,0100553,0053403,
-0035602,0056147,0045567,0027703,
-0035401,0106157,0111054,0145242,
-0035201,0002455,0113151,0101015,
-0035000,0126235,0004273,0157260,
-0034600,0071127,0112647,0005261,
-0034400,0045736,0057610,0157550,
-0034200,0031146,0172621,0074172,
-0034000,0020603,0115503,0032007,
-0033600,0013114,0124672,0023135,
-0033400,0007330,0043715,0151117,
-0033200,0004742,0145043,0033514,
-0033000,0003225,0152624,0004411,
-0032600,0002143,0033166,0035746,
-0032400,0001354,0074234,0026143,
-0032200,0000762,0147776,0170220,
-0032000,0000514,0072452,0130631,
-0031600,0000335,0114266,0063315,
-0031400,0000223,0132710,0041045,
-0031200,0000142,0073202,0153426,
-0031000,0000101,0121400,0152065,
-0030600,0000053,0140525,0072761
-};
-#endif
-
-#ifdef IBMPC
-static unsigned short azetac[] = {
-0x0000,0x0000,0x0000,0xbff8,
-0xffff,0xffff,0xffff,0x7fef,
-0x0fa6,0xc4a6,0xa34c,0x3fe4,
-0x310a,0x2780,0xdd00,0x3fc9,
-0x8483,0xac7d,0x1322,0x3fb5,
-0x99b7,0xd94f,0xe831,0x3fa2,
-0x9124,0x3024,0xc261,0x3f91,
-0x9c47,0x0a67,0x196d,0x3f81,
-0x96e9,0xf863,0xb36a,0x3f70,
-0x6ae0,0xb02d,0x73e7,0x3f60,
-0xe5f8,0xe96e,0x4b8c,0x3f50,
-0x9954,0xf245,0x318d,0x3f40,
-0x3042,0xb2cd,0x20a5,0x3f30,
-0x7bd6,0xa117,0x1593,0x3f20,
-0xe156,0xf2b4,0x0e4a,0x3f10,
-0x1bed,0xcbf1,0x097b,0x3f00,
-0x2f0f,0xdeb2,0x064c,0x3ef0,
-0x6681,0x7368,0x0430,0x3ee0,
-0x44cc,0x9537,0x02c9,0x3ed0,
-0xba4a,0x08f9,0x01db,0x3ec0,
-0x66ea,0x5944,0x013c,0x3eb0,
-0x8121,0xbab2,0x00d2,0x3ea0,
-0xc77d,0x66ce,0x008c,0x3e90,
-0x858c,0x8f13,0x005d,0x3e80,
-0xde12,0x59ff,0x003e,0x3e70,
-0x5633,0x8ea5,0x0029,0x3e60,
-0xccda,0xb316,0x001b,0x3e50,
-0x0845,0x76b9,0x0012,0x3e40,
-0x5ae3,0x4ed0,0x000c,0x3e30,
-0x1a87,0x3460,0x0008,0x3e20,
-0xaebe,0x782a,0x0005,0x3e10
-};
-#endif
-
-#ifdef MIEEE
-static unsigned short azetac[] = {
-0xbff8,0x0000,0x0000,0x0000,
-0x7fef,0xffff,0xffff,0xffff,
-0x3fe4,0xa34c,0xc4a6,0x0fa6,
-0x3fc9,0xdd00,0x2780,0x310a,
-0x3fb5,0x1322,0xac7d,0x8483,
-0x3fa2,0xe831,0xd94f,0x99b7,
-0x3f91,0xc261,0x3024,0x9124,
-0x3f81,0x196d,0x0a67,0x9c47,
-0x3f70,0xb36a,0xf863,0x96e9,
-0x3f60,0x73e7,0xb02d,0x6ae0,
-0x3f50,0x4b8c,0xe96e,0xe5f8,
-0x3f40,0x318d,0xf245,0x9954,
-0x3f30,0x20a5,0xb2cd,0x3042,
-0x3f20,0x1593,0xa117,0x7bd6,
-0x3f10,0x0e4a,0xf2b4,0xe156,
-0x3f00,0x097b,0xcbf1,0x1bed,
-0x3ef0,0x064c,0xdeb2,0x2f0f,
-0x3ee0,0x0430,0x7368,0x6681,
-0x3ed0,0x02c9,0x9537,0x44cc,
-0x3ec0,0x01db,0x08f9,0xba4a,
-0x3eb0,0x013c,0x5944,0x66ea,
-0x3ea0,0x00d2,0xbab2,0x8121,
-0x3e90,0x008c,0x66ce,0xc77d,
-0x3e80,0x005d,0x8f13,0x858c,
-0x3e70,0x003e,0x59ff,0xde12,
-0x3e60,0x0029,0x8ea5,0x5633,
-0x3e50,0x001b,0xb316,0xccda,
-0x3e40,0x0012,0x76b9,0x0845,
-0x3e30,0x000c,0x4ed0,0x5ae3,
-0x3e20,0x0008,0x3460,0x1a87,
-0x3e10,0x0005,0x782a,0xaebe
-};
-#endif
-
-
-/* 2**x (1 - 1/x) (zeta(x) - 1) = P(1/x)/Q(1/x), 1 <= x <= 10 */
-#ifdef UNK
-static double P[9] = {
- 5.85746514569725319540E11,
- 2.57534127756102572888E11,
- 4.87781159567948256438E10,
- 5.15399538023885770696E9,
- 3.41646073514754094281E8,
- 1.60837006880656492731E7,
- 5.92785467342109522998E5,
- 1.51129169964938823117E4,
- 2.01822444485997955865E2,
-};
-static double Q[8] = {
-/* 1.00000000000000000000E0,*/
- 3.90497676373371157516E11,
- 5.22858235368272161797E10,
- 5.64451517271280543351E9,
- 3.39006746015350418834E8,
- 1.79410371500126453702E7,
- 5.66666825131384797029E5,
- 1.60382976810944131506E4,
- 1.96436237223387314144E2,
-};
-#endif
-#ifdef DEC
-static unsigned short P[36] = {
-0052010,0060466,0101211,0134657,
-0051557,0154353,0135060,0064411,
-0051065,0133157,0133514,0133633,
-0050231,0114735,0035036,0111344,
-0047242,0164327,0146036,0033545,
-0046165,0065364,0130045,0011005,
-0045020,0134427,0075073,0134107,
-0043554,0021653,0000440,0177426,
-0042111,0151213,0134312,0021402,
-};
-static unsigned short Q[32] = {
-/*0040200,0000000,0000000,0000000,*/
-0051665,0153363,0054252,0137010,
-0051102,0143645,0121415,0036107,
-0050250,0034073,0131133,0036465,
-0047241,0123250,0150037,0070012,
-0046210,0160426,0111463,0116507,
-0045012,0054255,0031674,0173612,
-0043572,0114460,0151520,0012221,
-0042104,0067655,0037037,0137421,
-};
-#endif
-#ifdef IBMPC
-static unsigned short P[36] = {
-0x3736,0xd051,0x0c26,0x4261,
-0x0d21,0x7746,0xfb1d,0x424d,
-0x96f3,0xf6e9,0xb6cd,0x4226,
-0xd25c,0xa743,0x333b,0x41f3,
-0xc6ed,0xf983,0x5d1a,0x41b4,
-0xa241,0x9604,0xad5e,0x416e,
-0x7709,0xef47,0x1722,0x4122,
-0x1fe3,0x6024,0x8475,0x40cd,
-0x4460,0x7719,0x3a51,0x4069,
-};
-static unsigned short Q[32] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x57c1,0x6b15,0xbade,0x4256,
-0xa789,0xb461,0x58f4,0x4228,
-0x67a7,0x764b,0x0707,0x41f5,
-0xee01,0x1a03,0x34d5,0x41b4,
-0x73a9,0xd266,0x1c22,0x4171,
-0x9ef1,0xa677,0x4b15,0x4121,
-0x0292,0x1a6a,0x5326,0x40cf,
-0xf7e2,0xa7c3,0x8df5,0x4068,
-};
-#endif
-#ifdef MIEEE
-static unsigned short P[36] = {
-0x4261,0x0c26,0xd051,0x3736,
-0x424d,0xfb1d,0x7746,0x0d21,
-0x4226,0xb6cd,0xf6e9,0x96f3,
-0x41f3,0x333b,0xa743,0xd25c,
-0x41b4,0x5d1a,0xf983,0xc6ed,
-0x416e,0xad5e,0x9604,0xa241,
-0x4122,0x1722,0xef47,0x7709,
-0x40cd,0x8475,0x6024,0x1fe3,
-0x4069,0x3a51,0x7719,0x4460,
-};
-static unsigned short Q[32] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4256,0xbade,0x6b15,0x57c1,
-0x4228,0x58f4,0xb461,0xa789,
-0x41f5,0x0707,0x764b,0x67a7,
-0x41b4,0x34d5,0x1a03,0xee01,
-0x4171,0x1c22,0xd266,0x73a9,
-0x4121,0x4b15,0xa677,0x9ef1,
-0x40cf,0x5326,0x1a6a,0x0292,
-0x4068,0x8df5,0xa7c3,0xf7e2,
-};
-#endif
-
-/* log(zeta(x) - 1 - 2**-x), 10 <= x <= 50 */
-#ifdef UNK
-static double A[11] = {
- 8.70728567484590192539E6,
- 1.76506865670346462757E8,
- 2.60889506707483264896E10,
- 5.29806374009894791647E11,
- 2.26888156119238241487E13,
- 3.31884402932705083599E14,
- 5.13778997975868230192E15,
--1.98123688133907171455E15,
--9.92763810039983572356E16,
- 7.82905376180870586444E16,
- 9.26786275768927717187E16,
-};
-static double B[10] = {
-/* 1.00000000000000000000E0,*/
--7.92625410563741062861E6,
--1.60529969932920229676E8,
--2.37669260975543221788E10,
--4.80319584350455169857E11,
--2.07820961754173320170E13,
--2.96075404507272223680E14,
--4.86299103694609136686E15,
- 5.34589509675789930199E15,
- 5.71464111092297631292E16,
--1.79915597658676556828E16,
-};
-#endif
-#ifdef DEC
-static unsigned short A[44] = {
-0046004,0156325,0126302,0131567,
-0047050,0052177,0015271,0136466,
-0050702,0060271,0070727,0171112,
-0051766,0132727,0064363,0145042,
-0053245,0012466,0056000,0117230,
-0054226,0166155,0174275,0170213,
-0055222,0003127,0112544,0101322,
-0154741,0036625,0010346,0053767,
-0156260,0054653,0154052,0031113,
-0056213,0011152,0021000,0007111,
-0056244,0120534,0040576,0163262,
-};
-static unsigned short B[40] = {
-/*0040200,0000000,0000000,0000000,*/
-0145761,0161734,0033026,0015520,
-0147031,0013743,0017355,0036703,
-0150661,0011720,0061061,0136402,
-0151737,0125216,0070274,0164414,
-0153227,0032653,0127211,0145250,
-0154206,0121666,0123774,0042035,
-0155212,0033352,0125154,0132533,
-0055227,0170201,0110775,0072132,
-0056113,0003133,0127132,0122303,
-0155577,0126351,0141462,0171037,
-};
-#endif
-#ifdef IBMPC
-static unsigned short A[44] = {
-0x566f,0xb598,0x9b9a,0x4160,
-0x37a7,0xe357,0x0a8f,0x41a5,
-0xfe49,0x2e3a,0x4c17,0x4218,
-0x7944,0xed1e,0xd6ba,0x425e,
-0x13d3,0xcb80,0xa2a6,0x42b4,
-0xbe11,0xbf17,0xdd8d,0x42f2,
-0x905a,0xf2ac,0x40ca,0x4332,
-0xcaff,0xa21c,0x27b2,0xc31c,
-0x4649,0x7b05,0x0b35,0xc376,
-0x01c9,0x4440,0x624d,0x4371,
-0xdcd6,0x882f,0x942b,0x4374,
-};
-static unsigned short B[40] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0xc36a,0x86c2,0x3c7b,0xc15e,
-0xa7b8,0x63dd,0x22fc,0xc1a3,
-0x37a0,0x0c46,0x227a,0xc216,
-0x9d22,0xce17,0xf551,0xc25b,
-0x3955,0x75d1,0xe6b5,0xc2b2,
-0x8884,0xd4ff,0xd476,0xc2f0,
-0x96ab,0x554d,0x46dd,0xc331,
-0xae8b,0x323f,0xfe10,0x4332,
-0x5498,0x75cb,0x60cb,0x4369,
-0x5e44,0x3866,0xf59d,0xc34f,
-};
-#endif
-#ifdef MIEEE
-static unsigned short A[44] = {
-0x4160,0x9b9a,0xb598,0x566f,
-0x41a5,0x0a8f,0xe357,0x37a7,
-0x4218,0x4c17,0x2e3a,0xfe49,
-0x425e,0xd6ba,0xed1e,0x7944,
-0x42b4,0xa2a6,0xcb80,0x13d3,
-0x42f2,0xdd8d,0xbf17,0xbe11,
-0x4332,0x40ca,0xf2ac,0x905a,
-0xc31c,0x27b2,0xa21c,0xcaff,
-0xc376,0x0b35,0x7b05,0x4649,
-0x4371,0x624d,0x4440,0x01c9,
-0x4374,0x942b,0x882f,0xdcd6,
-};
-static unsigned short B[40] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0xc15e,0x3c7b,0x86c2,0xc36a,
-0xc1a3,0x22fc,0x63dd,0xa7b8,
-0xc216,0x227a,0x0c46,0x37a0,
-0xc25b,0xf551,0xce17,0x9d22,
-0xc2b2,0xe6b5,0x75d1,0x3955,
-0xc2f0,0xd476,0xd4ff,0x8884,
-0xc331,0x46dd,0x554d,0x96ab,
-0x4332,0xfe10,0x323f,0xae8b,
-0x4369,0x60cb,0x75cb,0x5498,
-0xc34f,0xf59d,0x3866,0x5e44,
-};
-#endif
-
-/* (1-x) (zeta(x) - 1), 0 <= x <= 1 */
-
-#ifdef UNK
-static double R[6] = {
--3.28717474506562731748E-1,
- 1.55162528742623950834E1,
--2.48762831680821954401E2,
- 1.01050368053237678329E3,
- 1.26726061410235149405E4,
--1.11578094770515181334E5,
-};
-static double S[5] = {
-/* 1.00000000000000000000E0,*/
- 1.95107674914060531512E1,
- 3.17710311750646984099E2,
- 3.03835500874445748734E3,
- 2.03665876435770579345E4,
- 7.43853965136767874343E4,
-};
-#endif
-#ifdef DEC
-static unsigned short R[24] = {
-0137650,0046650,0022502,0040316,
-0041170,0041222,0057666,0142216,
-0142170,0141510,0167741,0075646,
-0042574,0120074,0046505,0106053,
-0043506,0001154,0130073,0101413,
-0144331,0166414,0020560,0131652,
-};
-static unsigned short S[20] = {
-/*0040200,0000000,0000000,0000000,*/
-0041234,0013015,0042073,0113570,
-0042236,0155353,0077325,0077445,
-0043075,0162656,0016646,0031723,
-0043637,0016454,0157636,0071126,
-0044221,0044262,0140365,0146434,
-};
-#endif
-#ifdef IBMPC
-static unsigned short R[24] = {
-0x481a,0x04a8,0x09b5,0xbfd5,
-0xd892,0x4bf6,0x0852,0x402f,
-0x2f75,0x1dfc,0x1869,0xc06f,
-0xb185,0x89a8,0x9407,0x408f,
-0x7061,0x9607,0xc04d,0x40c8,
-0x1675,0x842e,0x3da1,0xc0fb,
-};
-static unsigned short S[20] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x72ef,0xa887,0x82c1,0x4033,
-0xafe5,0x6fda,0xdb5d,0x4073,
-0xc67a,0xc3b4,0xbcb5,0x40a7,
-0xce4b,0x9bf3,0xe3a5,0x40d3,
-0xb9a3,0x581e,0x2916,0x40f2,
-};
-#endif
-#ifdef MIEEE
-static unsigned short R[24] = {
-0xbfd5,0x09b5,0x04a8,0x481a,
-0x402f,0x0852,0x4bf6,0xd892,
-0xc06f,0x1869,0x1dfc,0x2f75,
-0x408f,0x9407,0x89a8,0xb185,
-0x40c8,0xc04d,0x9607,0x7061,
-0xc0fb,0x3da1,0x842e,0x1675,
-};
-static unsigned short S[20] = {
-/*0x3ff0,0x0000,0x0000,0x0000,*/
-0x4033,0x82c1,0xa887,0x72ef,
-0x4073,0xdb5d,0x6fda,0xafe5,
-0x40a7,0xbcb5,0xc3b4,0xc67a,
-0x40d3,0xe3a5,0x9bf3,0xce4b,
-0x40f2,0x2916,0x581e,0xb9a3,
-};
-#endif
-
-#define MAXL2 127
-
-/*
- * Riemann zeta function, minus one
- */
-#ifdef ANSIPROT
-extern double sin ( double );
-extern double floor ( double );
-extern double gamma ( double );
-extern double pow ( double, double );
-extern double exp ( double );
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-double zetac ( double );
-#else
-double sin(), floor(), gamma(), pow(), exp();
-double polevl(), p1evl(), zetac();
-#endif
-extern double MACHEP;
-
-double zetac(x)
-double x;
-{
-int i;
-double a, b, s, w;
-
-if( x < 0.0 )
- {
-#ifdef DEC
- if( x < -30.8148 )
-#else
- if( x < -170.6243 )
-#endif
- {
- mtherr( "zetac", OVERFLOW );
- return(0.0);
- }
- s = 1.0 - x;
- w = zetac( s );
- b = sin(0.5*PI*x) * pow(2.0*PI, x) * gamma(s) * (1.0 + w) / PI;
- return(b - 1.0);
- }
-
-if( x >= MAXL2 )
- return(0.0); /* because first term is 2**-x */
-
-/* Tabulated values for integer argument */
-w = floor(x);
-if( w == x )
- {
- i = x;
- if( i < 31 )
- {
-#ifdef UNK
- return( azetac[i] );
-#else
- return( *(double *)&azetac[4*i] );
-#endif
- }
- }
-
-
-if( x < 1.0 )
- {
- w = 1.0 - x;
- a = polevl( x, R, 5 ) / ( w * p1evl( x, S, 5 ));
- return( a );
- }
-
-if( x == 1.0 )
- {
- mtherr( "zetac", SING );
- return( MAXNUM );
- }
-
-if( x <= 10.0 )
- {
- b = pow( 2.0, x ) * (x - 1.0);
- w = 1.0/x;
- s = (x * polevl( w, P, 8 )) / (b * p1evl( w, Q, 8 ));
- return( s );
- }
-
-if( x <= 50.0 )
- {
- b = pow( 2.0, -x );
- w = polevl( x, A, 10 ) / p1evl( x, B, 10 );
- w = exp(w) + b;
- return(w);
- }
-
-
-/* Basic sum of inverse powers */
-
-
-s = 0.0;
-a = 1.0;
-do
- {
- a += 2.0;
- b = pow( a, -x );
- s += b;
- }
-while( b/s > MACHEP );
-
-b = pow( 2.0, -x );
-s = (s + b)/(1.0-b);
-return(s);
-}
--- /dev/null
+/* @(#)e_acos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
+#endif
+
+/* __ieee754_acos(x)
+ * Method :
+ * acos(x) = pi/2 - asin(x)
+ * acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
+ * For x>0.5
+ * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ * = 2asin(sqrt((1-x)/2))
+ * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
+ * = 2f + (2c + 2s*z*R(z))
+ * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ * for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: __ieee754_sqrt
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#ifdef __STDC__
+ double __ieee754_acos(double x)
+#else
+ double __ieee754_acos(x)
+ double x;
+#endif
+{
+ double z,p,q,r,w,s,c,df;
+ int32_t hx,ix;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x3ff00000) { /* |x| >= 1 */
+ u_int32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
+ if(hx>0) return 0.0; /* acos(1) = 0 */
+ else return pi+2.0*pio2_lo; /* acos(-1)= pi */
+ }
+ return (x-x)/(x-x); /* acos(|x|>1) is NaN */
+ }
+ if(ix<0x3fe00000) { /* |x| < 0.5 */
+ if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+ z = x*x;
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ r = p/q;
+ return pio2_hi - (x - (pio2_lo-x*r));
+ } else if (hx<0) { /* x < -0.5 */
+ z = (one+x)*0.5;
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ s = __ieee754_sqrt(z);
+ r = p/q;
+ w = r*s-pio2_lo;
+ return pi - 2.0*(s+w);
+ } else { /* x > 0.5 */
+ z = (one-x)*0.5;
+ s = __ieee754_sqrt(z);
+ df = s;
+ SET_LOW_WORD(df,0);
+ c = (z-df*df)/(s+df);
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ r = p/q;
+ w = r*s+c;
+ return 2.0*(df+w);
+ }
+}
--- /dev/null
+/* @(#)e_acosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";
+#endif
+
+/* __ieee754_acosh(x)
+ * Method :
+ * Based on
+ * acosh(x) = log [ x + sqrt(x*x-1) ]
+ * we have
+ * acosh(x) := log(x)+ln2, if x is large; else
+ * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+ * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+ *
+ * Special cases:
+ * acosh(x) is NaN with signal if x<1.
+ * acosh(NaN) is NaN without signal.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.0,
+ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
+
+#ifdef __STDC__
+ double __ieee754_acosh(double x)
+#else
+ double __ieee754_acosh(x)
+ double x;
+#endif
+{
+ double t;
+ int32_t hx;
+ u_int32_t lx;
+ EXTRACT_WORDS(hx,lx,x);
+ if(hx<0x3ff00000) { /* x < 1 */
+ return (x-x)/(x-x);
+ } else if(hx >=0x41b00000) { /* x > 2**28 */
+ if(hx >=0x7ff00000) { /* x is inf of NaN */
+ return x+x;
+ } else
+ return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
+ } else if(((hx-0x3ff00000)|lx)==0) {
+ return 0.0; /* acosh(1) = 0 */
+ } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
+ t=x*x;
+ return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
+ } else { /* 1<x<2 */
+ t = x-one;
+ return log1p(t+sqrt(2.0*t+t*t));
+ }
+}
--- /dev/null
+/* @(#)e_asin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc Exp $";
+#endif
+
+/* __ieee754_asin(x)
+ * Method :
+ * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ * we approximate asin(x) on [0,0.5] by
+ * asin(x) = x + x*x^2*R(x^2)
+ * where
+ * R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ * and its remez error is bounded by
+ * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ * For x in [0.5,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ * then for x>0.98
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ * For x<=0.98, let pio4_hi = pio2_hi/2, then
+ * f = hi part of s;
+ * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
+ * and
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+huge = 1.000e+300,
+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+ /* coefficient for R(x^2) */
+pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#ifdef __STDC__
+ double __ieee754_asin(double x)
+#else
+ double __ieee754_asin(x)
+ double x;
+#endif
+{
+ double t,w,p,q,c,r,s;
+ int32_t hx,ix;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>= 0x3ff00000) { /* |x|>= 1 */
+ u_int32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((ix-0x3ff00000)|lx)==0)
+ /* asin(1)=+-pi/2 with inexact */
+ return x*pio2_hi+x*pio2_lo;
+ return (x-x)/(x-x); /* asin(|x|>1) is NaN */
+ } else if (ix<0x3fe00000) { /* |x|<0.5 */
+ if(ix<0x3e400000) { /* if |x| < 2**-27 */
+ if(huge+x>one) return x;/* return x with inexact if x!=0*/
+ } else
+ t = x*x;
+ p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+ q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+ w = p/q;
+ return x+x*w;
+ }
+ /* 1> |x|>= 0.5 */
+ w = one-fabs(x);
+ t = w*0.5;
+ p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+ q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+ s = __ieee754_sqrt(t);
+ if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
+ w = p/q;
+ t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
+ } else {
+ w = s;
+ SET_LOW_WORD(w,0);
+ c = (t-w*w)/(s+w);
+ r = p/q;
+ p = 2.0*s*r-(pio2_lo-2.0*c);
+ q = pio4_hi-2.0*w;
+ t = pio4_hi-(p-q);
+ }
+ if(hx>0) return t; else return -t;
+}
--- /dev/null
+/* @(#)e_atan2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $";
+#endif
+
+/* __ieee754_atan2(y,x)
+ * Method :
+ * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
+ * 2. Reduce x to positive by (if x and y are unexceptional):
+ * ARG (x+iy) = arctan(y/x) ... if x > 0,
+ * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
+ *
+ * Special cases:
+ *
+ * ATAN2((anything), NaN ) is NaN;
+ * ATAN2(NAN , (anything) ) is NaN;
+ * ATAN2(+-0, +(anything but NaN)) is +-0 ;
+ * ATAN2(+-0, -(anything but NaN)) is +-pi ;
+ * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
+ * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
+ * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
+ * ATAN2(+-INF,+INF ) is +-pi/4 ;
+ * ATAN2(+-INF,-INF ) is +-3pi/4;
+ * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+tiny = 1.0e-300,
+zero = 0.0,
+pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
+pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
+pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
+pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+#ifdef __STDC__
+ double __ieee754_atan2(double y, double x)
+#else
+ double __ieee754_atan2(y,x)
+ double y,x;
+#endif
+{
+ double z;
+ int32_t k,m,hx,hy,ix,iy;
+ u_int32_t lx,ly;
+
+ EXTRACT_WORDS(hx,lx,x);
+ ix = hx&0x7fffffff;
+ EXTRACT_WORDS(hy,ly,y);
+ iy = hy&0x7fffffff;
+ if(((ix|((lx|-lx)>>31))>0x7ff00000)||
+ ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
+ return x+y;
+ if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */
+ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
+
+ /* when y = 0 */
+ if((iy|ly)==0) {
+ switch(m) {
+ case 0:
+ case 1: return y; /* atan(+-0,+anything)=+-0 */
+ case 2: return pi+tiny;/* atan(+0,-anything) = pi */
+ case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+ }
+ }
+ /* when x = 0 */
+ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+ /* when x is INF */
+ if(ix==0x7ff00000) {
+ if(iy==0x7ff00000) {
+ switch(m) {
+ case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
+ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+ case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+ case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+ }
+ } else {
+ switch(m) {
+ case 0: return zero ; /* atan(+...,+INF) */
+ case 1: return -zero ; /* atan(-...,+INF) */
+ case 2: return pi+tiny ; /* atan(+...,-INF) */
+ case 3: return -pi-tiny ; /* atan(-...,-INF) */
+ }
+ }
+ }
+ /* when y is INF */
+ if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+ /* compute y/x */
+ k = (iy-ix)>>20;
+ if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
+ else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
+ else z=atan(fabs(y/x)); /* safe to do y/x */
+ switch (m) {
+ case 0: return z ; /* atan(+,+) */
+ case 1: {
+ u_int32_t zh;
+ GET_HIGH_WORD(zh,z);
+ SET_HIGH_WORD(z,zh ^ 0x80000000);
+ }
+ return z ; /* atan(-,+) */
+ case 2: return pi-(z-pi_lo);/* atan(+,-) */
+ default: /* case 3 */
+ return (z-pi_lo)-pi;/* atan(-,-) */
+ }
+}
--- /dev/null
+/* @(#)e_atanh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $";
+#endif
+
+/* __ieee754_atanh(x)
+ * Method :
+ * 1.Reduced x to positive by atanh(-x) = -atanh(x)
+ * 2.For x>=0.5
+ * 1 2x x
+ * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
+ * 2 1 - x 1 - x
+ *
+ * For x<0.5
+ * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
+ *
+ * Special cases:
+ * atanh(x) is NaN if |x| > 1 with signal;
+ * atanh(NaN) is that NaN with no signal;
+ * atanh(+-1) is +-INF with signal.
+ *
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, huge = 1e300;
+#else
+static double one = 1.0, huge = 1e300;
+#endif
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_atanh(double x)
+#else
+ double __ieee754_atanh(x)
+ double x;
+#endif
+{
+ double t;
+ int32_t hx,ix;
+ u_int32_t lx;
+ EXTRACT_WORDS(hx,lx,x);
+ ix = hx&0x7fffffff;
+ if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
+ return (x-x)/(x-x);
+ if(ix==0x3ff00000)
+ return x/zero;
+ if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
+ SET_HIGH_WORD(x,ix);
+ if(ix<0x3fe00000) { /* x < 0.5 */
+ t = x+x;
+ t = 0.5*log1p(t+t*x/(one-x));
+ } else
+ t = 0.5*log1p((x+x)/(one-x));
+ if(hx>=0) return t; else return -t;
+}
--- /dev/null
+/* @(#)e_cosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
+#endif
+
+/* __ieee754_cosh(x)
+ * Method :
+ * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
+ * 1. Replace x by |x| (cosh(x) = cosh(-x)).
+ * 2.
+ * [ exp(x) - 1 ]^2
+ * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
+ * 2*exp(x)
+ *
+ * exp(x) + 1/exp(x)
+ * ln2/2 <= x <= 22 : cosh(x) := -------------------
+ * 2
+ * 22 <= x <= lnovft : cosh(x) := exp(x)/2
+ * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
+ * ln2ovft < x : cosh(x) := huge*huge (overflow)
+ *
+ * Special cases:
+ * cosh(x) is |x| if x is +INF, -INF, or NaN.
+ * only cosh(0)=1 is exact for finite x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, half=0.5, huge = 1.0e300;
+#else
+static double one = 1.0, half=0.5, huge = 1.0e300;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_cosh(double x)
+#else
+ double __ieee754_cosh(x)
+ double x;
+#endif
+{
+ double t,w;
+ int32_t ix;
+ u_int32_t lx;
+
+ /* High word of |x|. */
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) return x*x;
+
+ /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+ if(ix<0x3fd62e43) {
+ t = expm1(fabs(x));
+ w = one+t;
+ if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
+ return one+(t*t)/(w+w);
+ }
+
+ /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+ if (ix < 0x40360000) {
+ t = __ieee754_exp(fabs(x));
+ return half*t+half/t;
+ }
+
+ /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+ if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ GET_LOW_WORD(lx,x);
+ if (ix<0x408633CE ||
+ (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
+ w = __ieee754_exp(half*fabs(x));
+ t = half*w;
+ return t*w;
+ }
+
+ /* |x| > overflowthresold, cosh(x) overflow */
+ return huge*huge;
+}
--- /dev/null
+/* @(#)e_exp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_exp.c,v 1.8 1995/05/10 20:45:03 jtc Exp $";
+#endif
+
+/* __ieee754_exp(x)
+ * Returns the exponential of x.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2.
+ *
+ * Here r will be represented as r = hi-lo for better
+ * accuracy.
+ *
+ * 2. Approximation of exp(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Write
+ * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+ * We use a special Reme algorithm on [0,0.34658] to generate
+ * a polynomial of degree 5 to approximate R. The maximum error
+ * of this polynomial approximation is bounded by 2**-59. In
+ * other words,
+ * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+ * (where z=r*r, and the values of P1 to P5 are listed below)
+ * and
+ * | 5 | -59
+ * | 2.0+P1*z+...+P5*z - R(z) | <= 2
+ * | |
+ * The computation of exp(r) thus becomes
+ * 2*r
+ * exp(r) = 1 + -------
+ * R - r
+ * r*R1(r)
+ * = 1 + r + ----------- (for better accuracy)
+ * 2 - R1(r)
+ * where
+ * 2 4 10
+ * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
+ *
+ * 3. Scale back to obtain exp(x):
+ * From step 1, we have
+ * exp(x) = 2^k * exp(r)
+ *
+ * Special cases:
+ * exp(INF) is INF, exp(NaN) is NaN;
+ * exp(-INF) is 0, and
+ * for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 7.09782712893383973096e+02 then exp(x) overflow
+ * if x < -7.45133219101941108420e+02 then exp(x) underflow
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.0,
+halF[2] = {0.5,-0.5,},
+huge = 1.0e+300,
+twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
+o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
+ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
+ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
+invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+
+#ifdef __STDC__
+ double __ieee754_exp(double x) /* default IEEE double exp */
+#else
+ double __ieee754_exp(x) /* default IEEE double exp */
+ double x;
+#endif
+{
+ double y,hi,lo,c,t;
+ int32_t k,xsb;
+ u_int32_t hx;
+
+ GET_HIGH_WORD(hx,x);
+ xsb = (hx>>31)&1; /* sign bit of x */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out non-finite argument */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ u_int32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((hx&0xfffff)|lx)!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ if(x < u_threshold) return twom1000*twom1000; /* underflow */
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+ } else {
+ k = invln2*x+halF[xsb];
+ t = k;
+ hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
+ lo = t*ln2LO[0];
+ }
+ x = hi - lo;
+ }
+ else if(hx < 0x3e300000) { /* when |x|<2**-28 */
+ if(huge+x>one) return one+x;/* trigger inexact */
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ t = x*x;
+ c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+ if(k==0) return one-((x*c)/(c-2.0)-x);
+ else y = one-((lo-(x*c)/(2.0-c))-hi);
+ if(k >= -1021) {
+ u_int32_t hy;
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
+ return y;
+ } else {
+ u_int32_t hy;
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
+ return y*twom1000;
+ }
+}
--- /dev/null
+/* @(#)e_fmod.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_fmod.c,v 1.8 1995/05/10 20:45:07 jtc Exp $";
+#endif
+
+/*
+ * __ieee754_fmod(x,y)
+ * Return x mod y in exact arithmetic
+ * Method: shift and subtract
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, Zero[] = {0.0, -0.0,};
+#else
+static double one = 1.0, Zero[] = {0.0, -0.0,};
+#endif
+
+#ifdef __STDC__
+ double __ieee754_fmod(double x, double y)
+#else
+ double __ieee754_fmod(x,y)
+ double x,y ;
+#endif
+{
+ int32_t n,hx,hy,hz,ix,iy,sx,i;
+ u_int32_t lx,ly,lz;
+
+ EXTRACT_WORDS(hx,lx,x);
+ EXTRACT_WORDS(hy,ly,y);
+ sx = hx&0x80000000; /* sign of x */
+ hx ^=sx; /* |x| */
+ hy &= 0x7fffffff; /* |y| */
+
+ /* purge off exception values */
+ if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
+ ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
+ return (x*y)/(x*y);
+ if(hx<=hy) {
+ if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
+ if(lx==ly)
+ return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
+ }
+
+ /* determine ix = ilogb(x) */
+ if(hx<0x00100000) { /* subnormal x */
+ if(hx==0) {
+ for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
+ } else {
+ for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
+ }
+ } else ix = (hx>>20)-1023;
+
+ /* determine iy = ilogb(y) */
+ if(hy<0x00100000) { /* subnormal y */
+ if(hy==0) {
+ for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
+ } else {
+ for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
+ }
+ } else iy = (hy>>20)-1023;
+
+ /* set up {hx,lx}, {hy,ly} and align y to x */
+ if(ix >= -1022)
+ hx = 0x00100000|(0x000fffff&hx);
+ else { /* subnormal x, shift x to normal */
+ n = -1022-ix;
+ if(n<=31) {
+ hx = (hx<<n)|(lx>>(32-n));
+ lx <<= n;
+ } else {
+ hx = lx<<(n-32);
+ lx = 0;
+ }
+ }
+ if(iy >= -1022)
+ hy = 0x00100000|(0x000fffff&hy);
+ else { /* subnormal y, shift y to normal */
+ n = -1022-iy;
+ if(n<=31) {
+ hy = (hy<<n)|(ly>>(32-n));
+ ly <<= n;
+ } else {
+ hy = ly<<(n-32);
+ ly = 0;
+ }
+ }
+
+ /* fix point fmod */
+ n = ix - iy;
+ while(n--) {
+ hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
+ if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
+ else {
+ if((hz|lz)==0) /* return sign(x)*0 */
+ return Zero[(u_int32_t)sx>>31];
+ hx = hz+hz+(lz>>31); lx = lz+lz;
+ }
+ }
+ hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
+ if(hz>=0) {hx=hz;lx=lz;}
+
+ /* convert back to floating value and restore the sign */
+ if((hx|lx)==0) /* return sign(x)*0 */
+ return Zero[(u_int32_t)sx>>31];
+ while(hx<0x00100000) { /* normalize x */
+ hx = hx+hx+(lx>>31); lx = lx+lx;
+ iy -= 1;
+ }
+ if(iy>= -1022) { /* normalize output */
+ hx = ((hx-0x00100000)|((iy+1023)<<20));
+ INSERT_WORDS(x,hx|sx,lx);
+ } else { /* subnormal output */
+ n = -1022 - iy;
+ if(n<=20) {
+ lx = (lx>>n)|((u_int32_t)hx<<(32-n));
+ hx >>= n;
+ } else if (n<=31) {
+ lx = (hx<<(32-n))|(lx>>n); hx = sx;
+ } else {
+ lx = hx>>(n-32); hx = sx;
+ }
+ INSERT_WORDS(x,hx|sx,lx);
+ x *= one; /* create necessary signal */
+ }
+ return x; /* exact output */
+}
--- /dev/null
+
+/* @(#)e_gamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+/* __ieee754_gamma(x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_gamma_r
+ */
+
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+ //__private_extern__
+ double __ieee754_gamma(double x)
+#else
+ double __ieee754_gamma(x)
+ double x;
+#endif
+{
+ return __ieee754_gamma_r(x,&signgam);
+}
--- /dev/null
+
+/* @(#)e_gamma_r.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+/* __ieee754_gamma_r(x, signgamp)
+ * Reentrant version of the logarithm of the Gamma function
+ * with user provide pointer for the sign of Gamma(x).
+ *
+ * Method: See __ieee754_lgamma_r
+ */
+
+#include "math_private.h"
+
+#ifdef __STDC__
+ //__private_extern__
+ double __ieee754_gamma_r(double x, int *signgamp)
+#else
+ double __ieee754_gamma_r(x,signgamp)
+ double x; int *signgamp;
+#endif
+{
+ return __ieee754_lgamma_r(x,signgamp);
+}
--- /dev/null
+/* @(#)e_hypot.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
+#endif
+
+/* __ieee754_hypot(x,y)
+ *
+ * Method :
+ * If (assume round-to-nearest) z=x*x+y*y
+ * has error less than sqrt(2)/2 ulp, than
+ * sqrt(z) has error less than 1 ulp (exercise).
+ *
+ * So, compute sqrt(x*x+y*y) with some care as
+ * follows to get the error below 1 ulp:
+ *
+ * Assume x>y>0;
+ * (if possible, set rounding to round-to-nearest)
+ * 1. if x > 2y use
+ * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
+ * 2. if x <= 2y use
+ * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
+ * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
+ * y1= y with lower 32 bits chopped, y2 = y-y1.
+ *
+ * NOTE: scaling may be necessary if some argument is too
+ * large or too tiny
+ *
+ * Special cases:
+ * hypot(x,y) is INF if x or y is +INF or -INF; else
+ * hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * hypot(x,y) returns sqrt(x^2+y^2) with error less
+ * than 1 ulps (units in the last place)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double __ieee754_hypot(double x, double y)
+#else
+ double __ieee754_hypot(x,y)
+ double x, y;
+#endif
+{
+ double a=x,b=y,t1,t2,y1,y2,w;
+ int32_t j,k,ha,hb;
+
+ GET_HIGH_WORD(ha,x);
+ ha &= 0x7fffffff;
+ GET_HIGH_WORD(hb,y);
+ hb &= 0x7fffffff;
+ if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+ SET_HIGH_WORD(a,ha); /* a <- |a| */
+ SET_HIGH_WORD(b,hb); /* b <- |b| */
+ if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
+ k=0;
+ if(ha > 0x5f300000) { /* a>2**500 */
+ if(ha >= 0x7ff00000) { /* Inf or NaN */
+ u_int32_t low;
+ w = a+b; /* for sNaN */
+ GET_LOW_WORD(low,a);
+ if(((ha&0xfffff)|low)==0) w = a;
+ GET_LOW_WORD(low,b);
+ if(((hb^0x7ff00000)|low)==0) w = b;
+ return w;
+ }
+ /* scale a and b by 2**-600 */
+ ha -= 0x25800000; hb -= 0x25800000; k += 600;
+ SET_HIGH_WORD(a,ha);
+ SET_HIGH_WORD(b,hb);
+ }
+ if(hb < 0x20b00000) { /* b < 2**-500 */
+ if(hb <= 0x000fffff) { /* subnormal b or 0 */
+ u_int32_t low;
+ GET_LOW_WORD(low,b);
+ if((hb|low)==0) return a;
+ t1=0;
+ SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
+ b *= t1;
+ a *= t1;
+ k -= 1022;
+ } else { /* scale a and b by 2^600 */
+ ha += 0x25800000; /* a *= 2^600 */
+ hb += 0x25800000; /* b *= 2^600 */
+ k -= 600;
+ SET_HIGH_WORD(a,ha);
+ SET_HIGH_WORD(b,hb);
+ }
+ }
+ /* medium size a and b */
+ w = a-b;
+ if (w>b) {
+ t1 = 0;
+ SET_HIGH_WORD(t1,ha);
+ t2 = a-t1;
+ w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+ } else {
+ a = a+a;
+ y1 = 0;
+ SET_HIGH_WORD(y1,hb);
+ y2 = b - y1;
+ t1 = 0;
+ SET_HIGH_WORD(t1,ha+0x00100000);
+ t2 = a - t1;
+ w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+ }
+ if(k!=0) {
+ u_int32_t high;
+ t1 = 1.0;
+ GET_HIGH_WORD(high,t1);
+ SET_HIGH_WORD(t1,high+(k<<20));
+ return t1*w;
+ } else return w;
+}
--- /dev/null
+/* @(#)e_j0.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $";
+#endif
+
+/* __ieee754_j0(x), __ieee754_y0(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j0(x):
+ * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
+ * 2. Reduce x to |x| since j0(x)=j0(-x), and
+ * for x in (0,2)
+ * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
+ * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
+ * for x in (2,inf)
+ * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
+ * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ * as follow:
+ * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+ * = 1/sqrt(2) * (cos(x) + sin(x))
+ * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
+ * = 1/sqrt(2) * (sin(x) - cos(x))
+ * (To avoid cancellation, use
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * to compute the worse one.)
+ *
+ * 3 Special cases
+ * j0(nan)= nan
+ * j0(0) = 1
+ * j0(inf) = 0
+ *
+ * Method -- y0(x):
+ * 1. For x<2.
+ * Since
+ * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
+ * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
+ * We use the following function to approximate y0,
+ * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
+ * where
+ * U(z) = u00 + u01*z + ... + u06*z^6
+ * V(z) = 1 + v01*z + ... + v04*z^4
+ * with absolute approximation error bounded by 2**-72.
+ * Note: For tiny x, U/V = u0 and j0(x)~1, hence
+ * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
+ * 2. For x>=2.
+ * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
+ * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ * by the method mentioned above.
+ * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static double pzero(double), qzero(double);
+#else
+static double pzero(), qzero();
+#endif
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+huge = 1e300,
+one = 1.0,
+invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+ /* R0/S0 on [0, 2.00] */
+R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
+R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
+R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
+R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
+S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
+S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
+S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
+S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_j0(double x)
+#else
+ double __ieee754_j0(x)
+ double x;
+#endif
+{
+ double z, s,c,ss,cc,r,u,v;
+ int32_t hx,ix;
+
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7ff00000) return one/(x*x);
+ x = fabs(x);
+ if(ix >= 0x40000000) { /* |x| >= 2.0 */
+ s = sin(x);
+ c = cos(x);
+ ss = s-c;
+ cc = s+c;
+ if(ix<0x7fe00000) { /* make sure x+x not overflow */
+ z = -cos(x+x);
+ if ((s*c)<zero) cc = z/ss;
+ else ss = z/cc;
+ }
+ /*
+ * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+ * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+ */
+ if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);
+ else {
+ u = pzero(x); v = qzero(x);
+ z = invsqrtpi*(u*cc-v*ss)/sqrt(x);
+ }
+ return z;
+ }
+ if(ix<0x3f200000) { /* |x| < 2**-13 */
+ if(huge+x>one) { /* raise inexact if x != 0 */
+ if(ix<0x3e400000) return one; /* |x|<2**-27 */
+ else return one - 0.25*x*x;
+ }
+ }
+ z = x*x;
+ r = z*(R02+z*(R03+z*(R04+z*R05)));
+ s = one+z*(S01+z*(S02+z*(S03+z*S04)));
+ if(ix < 0x3FF00000) { /* |x| < 1.00 */
+ return one + z*(-0.25+(r/s));
+ } else {
+ u = 0.5*x;
+ return((one+u)*(one-u)+z*(r/s));
+ }
+}
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
+u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
+u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
+u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
+u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
+u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
+u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
+v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
+v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
+v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
+v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
+
+#ifdef __STDC__
+ double __ieee754_y0(double x)
+#else
+ double __ieee754_y0(x)
+ double x;
+#endif
+{
+ double z, s,c,ss,cc,u,v;
+ int32_t hx,ix,lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+ ix = 0x7fffffff&hx;
+ /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
+ if(ix>=0x7ff00000) return one/(x+x*x);
+ if((ix|lx)==0) return -one/zero;
+ if(hx<0) return zero/zero;
+ if(ix >= 0x40000000) { /* |x| >= 2.0 */
+ /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
+ * where x0 = x-pi/4
+ * Better formula:
+ * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+ * = 1/sqrt(2) * (sin(x) + cos(x))
+ * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+ * = 1/sqrt(2) * (sin(x) - cos(x))
+ * To avoid cancellation, use
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * to compute the worse one.
+ */
+ s = sin(x);
+ c = cos(x);
+ ss = s-c;
+ cc = s+c;
+ /*
+ * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+ * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+ */
+ if(ix<0x7fe00000) { /* make sure x+x not overflow */
+ z = -cos(x+x);
+ if ((s*c)<zero) cc = z/ss;
+ else ss = z/cc;
+ }
+ if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
+ else {
+ u = pzero(x); v = qzero(x);
+ z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
+ }
+ return z;
+ }
+ if(ix<=0x3e400000) { /* x < 2**-27 */
+ return(u00 + tpi*__ieee754_log(x));
+ }
+ z = x*x;
+ u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
+ v = one+z*(v01+z*(v02+z*(v03+z*v04)));
+ return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
+}
+
+/* The asymptotic expansions of pzero is
+ * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ * pzero(x) = 1 + (R/S)
+ * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ * S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
+ */
+#ifdef __STDC__
+static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
+ -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
+ -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
+ -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
+ -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
+};
+#ifdef __STDC__
+static const double pS8[5] = {
+#else
+static double pS8[5] = {
+#endif
+ 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
+ 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
+ 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
+ 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
+ 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
+};
+
+#ifdef __STDC__
+static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
+ -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
+ -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
+ -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
+ -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
+ -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
+};
+#ifdef __STDC__
+static const double pS5[5] = {
+#else
+static double pS5[5] = {
+#endif
+ 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
+ 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
+ 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
+ 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
+ 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
+};
+
+#ifdef __STDC__
+static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#else
+static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
+ -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
+ -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
+ -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
+ -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
+ -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
+};
+#ifdef __STDC__
+static const double pS3[5] = {
+#else
+static double pS3[5] = {
+#endif
+ 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
+ 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
+ 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
+ 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
+ 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
+};
+
+#ifdef __STDC__
+static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
+ -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
+ -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
+ -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
+ -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
+ -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
+};
+#ifdef __STDC__
+static const double pS2[5] = {
+#else
+static double pS2[5] = {
+#endif
+ 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
+ 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
+ 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
+ 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
+ 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
+};
+
+#ifdef __STDC__
+ static double pzero(double x)
+#else
+ static double pzero(x)
+ double x;
+#endif
+{
+#ifdef __STDC__
+ const double *p,*q;
+#else
+ double *p,*q;
+#endif
+ double z,r,s;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+ if(ix>=0x40200000) {p = pR8; q= pS8;}
+ else if(ix>=0x40122E8B){p = pR5; q= pS5;}
+ else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
+ else if(ix>=0x40000000){p = pR2; q= pS2;}
+ z = one/(x*x);
+ r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+ s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+ return one+ r/s;
+}
+
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ * qzero(x) = s*(-1.25 + (R/S))
+ * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ * S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
+ */
+#ifdef __STDC__
+static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
+ 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
+ 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
+ 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
+ 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
+};
+#ifdef __STDC__
+static const double qS8[6] = {
+#else
+static double qS8[6] = {
+#endif
+ 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
+ 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
+ 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
+ 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
+ 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
+ -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
+};
+
+#ifdef __STDC__
+static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
+ 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
+ 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
+ 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
+ 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
+ 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
+};
+#ifdef __STDC__
+static const double qS5[6] = {
+#else
+static double qS5[6] = {
+#endif
+ 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
+ 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
+ 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
+ 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
+ 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
+ -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
+};
+
+#ifdef __STDC__
+static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#else
+static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
+ 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
+ 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
+ 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
+ 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
+ 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
+};
+#ifdef __STDC__
+static const double qS3[6] = {
+#else
+static double qS3[6] = {
+#endif
+ 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
+ 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
+ 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
+ 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
+ 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
+ -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
+};
+
+#ifdef __STDC__
+static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
+ 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
+ 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
+ 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
+ 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
+ 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
+};
+#ifdef __STDC__
+static const double qS2[6] = {
+#else
+static double qS2[6] = {
+#endif
+ 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
+ 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
+ 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
+ 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
+ 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
+ -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
+};
+
+#ifdef __STDC__
+ static double qzero(double x)
+#else
+ static double qzero(x)
+ double x;
+#endif
+{
+#ifdef __STDC__
+ const double *p,*q;
+#else
+ double *p,*q;
+#endif
+ double s,r,z;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+ if(ix>=0x40200000) {p = qR8; q= qS8;}
+ else if(ix>=0x40122E8B){p = qR5; q= qS5;}
+ else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
+ else if(ix>=0x40000000){p = qR2; q= qS2;}
+ z = one/(x*x);
+ r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+ s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+ return (-.125 + r/s)/x;
+}
--- /dev/null
+/* @(#)e_j1.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $";
+#endif
+
+/* __ieee754_j1(x), __ieee754_y1(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j1(x):
+ * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
+ * 2. Reduce x to |x| since j1(x)=-j1(-x), and
+ * for x in (0,2)
+ * j1(x) = x/2 + x*z*R0/S0, where z = x*x;
+ * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
+ * for x in (2,inf)
+ * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
+ * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ * as follow:
+ * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+ * = 1/sqrt(2) * (sin(x) - cos(x))
+ * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+ * = -1/sqrt(2) * (sin(x) + cos(x))
+ * (To avoid cancellation, use
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * to compute the worse one.)
+ *
+ * 3 Special cases
+ * j1(nan)= nan
+ * j1(0) = 0
+ * j1(inf) = 0
+ *
+ * Method -- y1(x):
+ * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
+ * 2. For x<2.
+ * Since
+ * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
+ * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
+ * We use the following function to approximate y1,
+ * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
+ * where for x in [0,2] (abs err less than 2**-65.89)
+ * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
+ * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
+ * Note: For tiny x, 1/x dominate y1 and hence
+ * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
+ * 3. For x>=2.
+ * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ * by method mentioned above.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static double pone(double), qone(double);
+#else
+static double pone(), qone();
+#endif
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+huge = 1e300,
+one = 1.0,
+invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+ /* R0/S0 on [0,2] */
+r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
+r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
+r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
+r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
+s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
+s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
+s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
+s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
+s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_j1(double x)
+#else
+ double __ieee754_j1(x)
+ double x;
+#endif
+{
+ double z, s,c,ss,cc,r,u,v,y;
+ int32_t hx,ix;
+
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7ff00000) return one/x;
+ y = fabs(x);
+ if(ix >= 0x40000000) { /* |x| >= 2.0 */
+ s = sin(y);
+ c = cos(y);
+ ss = -s-c;
+ cc = s-c;
+ if(ix<0x7fe00000) { /* make sure y+y not overflow */
+ z = cos(y+y);
+ if ((s*c)>zero) cc = z/ss;
+ else ss = z/cc;
+ }
+ /*
+ * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
+ * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
+ */
+ if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
+ else {
+ u = pone(y); v = qone(y);
+ z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
+ }
+ if(hx<0) return -z;
+ else return z;
+ }
+ if(ix<0x3e400000) { /* |x|<2**-27 */
+ if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
+ }
+ z = x*x;
+ r = z*(r00+z*(r01+z*(r02+z*r03)));
+ s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
+ r *= x;
+ return(x*0.5+r/s);
+}
+
+#ifdef __STDC__
+static const double U0[5] = {
+#else
+static double U0[5] = {
+#endif
+ -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
+ 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
+ -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
+ 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
+ -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
+};
+#ifdef __STDC__
+static const double V0[5] = {
+#else
+static double V0[5] = {
+#endif
+ 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
+ 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
+ 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
+ 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
+ 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
+};
+
+#ifdef __STDC__
+ double __ieee754_y1(double x)
+#else
+ double __ieee754_y1(x)
+ double x;
+#endif
+{
+ double z, s,c,ss,cc,u,v;
+ int32_t hx,ix,lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+ ix = 0x7fffffff&hx;
+ /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
+ if(ix>=0x7ff00000) return one/(x+x*x);
+ if((ix|lx)==0) return -one/zero;
+ if(hx<0) return zero/zero;
+ if(ix >= 0x40000000) { /* |x| >= 2.0 */
+ s = sin(x);
+ c = cos(x);
+ ss = -s-c;
+ cc = s-c;
+ if(ix<0x7fe00000) { /* make sure x+x not overflow */
+ z = cos(x+x);
+ if ((s*c)>zero) cc = z/ss;
+ else ss = z/cc;
+ }
+ /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
+ * where x0 = x-3pi/4
+ * Better formula:
+ * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+ * = 1/sqrt(2) * (sin(x) - cos(x))
+ * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+ * = -1/sqrt(2) * (cos(x) + sin(x))
+ * To avoid cancellation, use
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * to compute the worse one.
+ */
+ if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
+ else {
+ u = pone(x); v = qone(x);
+ z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
+ }
+ return z;
+ }
+ if(ix<=0x3c900000) { /* x < 2**-54 */
+ return(-tpi/x);
+ }
+ z = x*x;
+ u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
+ v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
+ return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
+}
+
+/* For x >= 8, the asymptotic expansions of pone is
+ * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
+ * We approximate pone by
+ * pone(x) = 1 + (R/S)
+ * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ * S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ * | pone(x)-1-R/S | <= 2 ** ( -60.06)
+ */
+
+#ifdef __STDC__
+static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
+ 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
+ 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
+ 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
+ 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
+};
+#ifdef __STDC__
+static const double ps8[5] = {
+#else
+static double ps8[5] = {
+#endif
+ 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
+ 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
+ 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
+ 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
+ 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
+};
+
+#ifdef __STDC__
+static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
+ 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
+ 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
+ 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
+ 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
+ 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
+};
+#ifdef __STDC__
+static const double ps5[5] = {
+#else
+static double ps5[5] = {
+#endif
+ 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
+ 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
+ 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
+ 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
+ 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
+};
+
+#ifdef __STDC__
+static const double pr3[6] = {
+#else
+static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
+ 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
+ 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
+ 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
+ 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
+ 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
+};
+#ifdef __STDC__
+static const double ps3[5] = {
+#else
+static double ps3[5] = {
+#endif
+ 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
+ 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
+ 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
+ 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
+ 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
+};
+
+#ifdef __STDC__
+static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
+ 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
+ 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
+ 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
+ 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
+ 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
+};
+#ifdef __STDC__
+static const double ps2[5] = {
+#else
+static double ps2[5] = {
+#endif
+ 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
+ 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
+ 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
+ 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
+ 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
+};
+
+#ifdef __STDC__
+ static double pone(double x)
+#else
+ static double pone(x)
+ double x;
+#endif
+{
+#ifdef __STDC__
+ const double *p,*q;
+#else
+ double *p,*q;
+#endif
+ double z,r,s;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+ if(ix>=0x40200000) {p = pr8; q= ps8;}
+ else if(ix>=0x40122E8B){p = pr5; q= ps5;}
+ else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
+ else if(ix>=0x40000000){p = pr2; q= ps2;}
+ z = one/(x*x);
+ r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+ s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+ return one+ r/s;
+}
+
+
+/* For x >= 8, the asymptotic expansions of qone is
+ * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ * qone(x) = s*(0.375 + (R/S))
+ * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ * S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
+ */
+
+#ifdef __STDC__
+static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
+ -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
+ -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
+ -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
+ -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
+};
+#ifdef __STDC__
+static const double qs8[6] = {
+#else
+static double qs8[6] = {
+#endif
+ 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
+ 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
+ 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
+ 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
+ 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
+ -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
+};
+
+#ifdef __STDC__
+static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
+ -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
+ -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
+ -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
+ -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
+ -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
+};
+#ifdef __STDC__
+static const double qs5[6] = {
+#else
+static double qs5[6] = {
+#endif
+ 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
+ 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
+ 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
+ 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
+ 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
+ -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
+};
+
+#ifdef __STDC__
+static const double qr3[6] = {
+#else
+static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
+ -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
+ -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
+ -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
+ -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
+ -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
+};
+#ifdef __STDC__
+static const double qs3[6] = {
+#else
+static double qs3[6] = {
+#endif
+ 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
+ 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
+ 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
+ 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
+ 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
+ -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
+};
+
+#ifdef __STDC__
+static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
+ -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
+ -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
+ -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
+ -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
+ -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
+};
+#ifdef __STDC__
+static const double qs2[6] = {
+#else
+static double qs2[6] = {
+#endif
+ 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
+ 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
+ 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
+ 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
+ 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
+ -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
+};
+
+#ifdef __STDC__
+ static double qone(double x)
+#else
+ static double qone(x)
+ double x;
+#endif
+{
+#ifdef __STDC__
+ const double *p,*q;
+#else
+ double *p,*q;
+#endif
+ double s,r,z;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+ if(ix>=0x40200000) {p = qr8; q= qs8;}
+ else if(ix>=0x40122E8B){p = qr5; q= qs5;}
+ else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
+ else if(ix>=0x40000000){p = qr2; q= qs2;}
+ z = one/(x*x);
+ r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+ s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+ return (.375 + r/s)/x;
+}
--- /dev/null
+/* @(#)e_jn.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
+#endif
+
+/*
+ * __ieee754_jn(n, x), __ieee754_yn(n, x)
+ * floating point Bessel's function of the 1st and 2nd kind
+ * of order n
+ *
+ * Special cases:
+ * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
+ * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
+ * Note 2. About jn(n,x), yn(n,x)
+ * For n=0, j0(x) is called,
+ * for n=1, j1(x) is called,
+ * for n<x, forward recursion us used starting
+ * from values of j0(x) and j1(x).
+ * for n>x, a continued fraction approximation to
+ * j(n,x)/j(n-1,x) is evaluated and then backward
+ * recursion is used starting from a supposed value
+ * for j(n,x). The resulting value of j(0,x) is
+ * compared with the actual value to correct the
+ * supposed value of j(n,x).
+ *
+ * yn(n,x) is similar in all respects, except
+ * that forward recursion is used for all
+ * values of n>1.
+ *
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
+one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
+
+#ifdef __STDC__
+static const double zero = 0.00000000000000000000e+00;
+#else
+static double zero = 0.00000000000000000000e+00;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_jn(int n, double x)
+#else
+ double __ieee754_jn(n,x)
+ int n; double x;
+#endif
+{
+ int32_t i,hx,ix,lx, sgn;
+ double a, b, temp, di;
+ double z, w;
+
+ /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+ * Thus, J(-n,x) = J(n,-x)
+ */
+ EXTRACT_WORDS(hx,lx,x);
+ ix = 0x7fffffff&hx;
+ /* if J(n,NaN) is NaN */
+ if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
+ if(n<0){
+ n = -n;
+ x = -x;
+ hx ^= 0x80000000;
+ }
+ if(n==0) return(__ieee754_j0(x));
+ if(n==1) return(__ieee754_j1(x));
+ sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
+ x = fabs(x);
+ if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
+ b = zero;
+ else if((double)n<=x) {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if(ix>=0x52D00000) { /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ switch(n&3) {
+ case 0: temp = cos(x)+sin(x); break;
+ case 1: temp = -cos(x)+sin(x); break;
+ case 2: temp = -cos(x)-sin(x); break;
+ case 3: temp = cos(x)-sin(x); break;
+ }
+ b = invsqrtpi*temp/sqrt(x);
+ } else {
+ a = __ieee754_j0(x);
+ b = __ieee754_j1(x);
+ for(i=1;i<n;i++){
+ temp = b;
+ b = b*((double)(i+i)/x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ } else {
+ if(ix<0x3e100000) { /* x < 2**-29 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if(n>33) /* underflow */
+ b = zero;
+ else {
+ temp = x*0.5; b = temp;
+ for (a=one,i=2;i<=n;i++) {
+ a *= (double)i; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ }
+ b = b/a;
+ }
+ } else {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ double t,v;
+ double q0,q1,h,tmp; int32_t k,m;
+ w = (n+n)/(double)x; h = 2.0/(double)x;
+ q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
+ while(q1<1.0e9) {
+ k += 1; z += h;
+ tmp = z*q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ m = n+n;
+ for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
+ a = t;
+ b = one;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = n;
+ v = two/x;
+ tmp = tmp*__ieee754_log(fabs(v*tmp));
+ if(tmp<7.09782712893383973096e+02) {
+ for(i=n-1,di=(double)(i+i);i>0;i--){
+ temp = b;
+ b *= di;
+ b = b/x - a;
+ a = temp;
+ di -= two;
+ }
+ } else {
+ for(i=n-1,di=(double)(i+i);i>0;i--){
+ temp = b;
+ b *= di;
+ b = b/x - a;
+ a = temp;
+ di -= two;
+ /* scale b to avoid spurious overflow */
+ if(b>1e100) {
+ a /= b;
+ t /= b;
+ b = one;
+ }
+ }
+ }
+ b = (t*__ieee754_j0(x)/b);
+ }
+ }
+ if(sgn==1) return -b; else return b;
+}
+
+#ifdef __STDC__
+ double __ieee754_yn(int n, double x)
+#else
+ double __ieee754_yn(n,x)
+ int n; double x;
+#endif
+{
+ int32_t i,hx,ix,lx;
+ int32_t sign;
+ double a, b, temp;
+
+ EXTRACT_WORDS(hx,lx,x);
+ ix = 0x7fffffff&hx;
+ /* if Y(n,NaN) is NaN */
+ if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
+ if((ix|lx)==0) return -one/zero;
+ if(hx<0) return zero/zero;
+ sign = 1;
+ if(n<0){
+ n = -n;
+ sign = 1 - ((n&1)<<1);
+ }
+ if(n==0) return(__ieee754_y0(x));
+ if(n==1) return(sign*__ieee754_y1(x));
+ if(ix==0x7ff00000) return zero;
+ if(ix>=0x52D00000) { /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ switch(n&3) {
+ case 0: temp = sin(x)-cos(x); break;
+ case 1: temp = -sin(x)-cos(x); break;
+ case 2: temp = -sin(x)+cos(x); break;
+ case 3: temp = sin(x)+cos(x); break;
+ }
+ b = invsqrtpi*temp/sqrt(x);
+ } else {
+ u_int32_t high;
+ a = __ieee754_y0(x);
+ b = __ieee754_y1(x);
+ /* quit if b is -inf */
+ GET_HIGH_WORD(high,b);
+ for(i=1;i<n&&high!=0xfff00000;i++){
+ temp = b;
+ b = ((double)(i+i)/x)*b - a;
+ GET_HIGH_WORD(high,b);
+ a = temp;
+ }
+ }
+ if(sign>0) return b; else return -b;
+}
--- /dev/null
+
+/* @(#)e_lgamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+/* __ieee754_lgamma(x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_lgamma_r
+ */
+
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+ //__private_extern__
+ double __ieee754_lgamma(double x)
+#else
+ double __ieee754_lgamma(x)
+ double x;
+#endif
+{
+ return __ieee754_lgamma_r(x,&signgam);
+}
--- /dev/null
+/* @(#)er_lgamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_lgamma_r.c,v 1.7 1995/05/10 20:45:42 jtc Exp $";
+#endif
+
+/* __ieee754_lgamma_r(x, signgamp)
+ * Reentrant version of the logarithm of the Gamma function
+ * with user provide pointer for the sign of Gamma(x).
+ *
+ * Method:
+ * 1. Argument Reduction for 0 < x <= 8
+ * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
+ * reduce x to a number in [1.5,2.5] by
+ * lgamma(1+s) = log(s) + lgamma(s)
+ * for example,
+ * lgamma(7.3) = log(6.3) + lgamma(6.3)
+ * = log(6.3*5.3) + lgamma(5.3)
+ * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
+ * 2. Polynomial approximation of lgamma around its
+ * minimun ymin=1.461632144968362245 to maintain monotonicity.
+ * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
+ * Let z = x-ymin;
+ * lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
+ * where
+ * poly(z) is a 14 degree polynomial.
+ * 2. Rational approximation in the primary interval [2,3]
+ * We use the following approximation:
+ * s = x-2.0;
+ * lgamma(x) = 0.5*s + s*P(s)/Q(s)
+ * with accuracy
+ * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
+ * Our algorithms are based on the following observation
+ *
+ * zeta(2)-1 2 zeta(3)-1 3
+ * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
+ * 2 3
+ *
+ * where Euler = 0.5771... is the Euler constant, which is very
+ * close to 0.5.
+ *
+ * 3. For x>=8, we have
+ * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
+ * (better formula:
+ * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
+ * Let z = 1/x, then we approximation
+ * f(z) = lgamma(x) - (x-0.5)(log(x)-1)
+ * by
+ * 3 5 11
+ * w = w0 + w1*z + w2*z + w3*z + ... + w6*z
+ * where
+ * |w - f(z)| < 2**-58.74
+ *
+ * 4. For negative x, since (G is gamma function)
+ * -x*G(-x)*G(x) = pi/sin(pi*x),
+ * we have
+ * G(x) = pi/(sin(pi*x)*(-x)*G(-x))
+ * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
+ * Hence, for x<0, signgam = sign(sin(pi*x)) and
+ * lgamma(x) = log(|Gamma(x)|)
+ * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
+ * Note: one should avoid compute pi*(-x) directly in the
+ * computation of sin(pi*(-x)).
+ *
+ * 5. Special Cases
+ * lgamma(2+s) ~ s*(1-Euler) for tiny s
+ * lgamma(1)=lgamma(2)=0
+ * lgamma(x) ~ -log(x) for tiny x
+ * lgamma(0) = lgamma(inf) = inf
+ * lgamma(-integer) = +-inf
+ *
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
+half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
+a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
+a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
+a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
+a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
+a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
+a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
+a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
+a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
+a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
+a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
+a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
+tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
+tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
+/* tt = -(tail of tf) */
+tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
+t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
+t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
+t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
+t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
+t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
+t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
+t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
+t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
+t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
+t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
+t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
+t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
+t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
+t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
+t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
+u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
+u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
+u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
+u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
+u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
+u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
+v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
+v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
+v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
+v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
+v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
+s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
+s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
+s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
+s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
+s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
+s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
+s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
+r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
+r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
+r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
+r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
+r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
+r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
+w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
+w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
+w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
+w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
+w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
+w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
+w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
+
+#ifdef __STDC__
+static const double zero= 0.00000000000000000000e+00;
+#else
+static double zero= 0.00000000000000000000e+00;
+#endif
+
+static
+#ifdef __GNUC__
+__inline__
+#endif
+#ifdef __STDC__
+ double sin_pi(double x)
+#else
+ double sin_pi(x)
+ double x;
+#endif
+{
+ double y,z;
+ int n,ix;
+
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+
+ if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
+ y = -x; /* x is assume negative */
+
+ /*
+ * argument reduction, make sure inexact flag not raised if input
+ * is an integer
+ */
+ z = floor(y);
+ if(z!=y) { /* inexact anyway */
+ y *= 0.5;
+ y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */
+ n = (int) (y*4.0);
+ } else {
+ if(ix>=0x43400000) {
+ y = zero; n = 0; /* y must be even */
+ } else {
+ if(ix<0x43300000) z = y+two52; /* exact */
+ GET_LOW_WORD(n,z);
+ n &= 1;
+ y = n;
+ n<<= 2;
+ }
+ }
+ switch (n) {
+ case 0: y = __kernel_sin(pi*y,zero,0); break;
+ case 1:
+ case 2: y = __kernel_cos(pi*(0.5-y),zero); break;
+ case 3:
+ case 4: y = __kernel_sin(pi*(one-y),zero,0); break;
+ case 5:
+ case 6: y = -__kernel_cos(pi*(y-1.5),zero); break;
+ default: y = __kernel_sin(pi*(y-2.0),zero,0); break;
+ }
+ return -y;
+}
+
+
+#ifdef __STDC__
+ double __ieee754_lgamma_r(double x, int *signgamp)
+#else
+ double __ieee754_lgamma_r(x,signgamp)
+ double x; int *signgamp;
+#endif
+{
+ double t,y,z,nadj,p,p1,p2,p3,q,r,w;
+ int i,hx,lx,ix;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ /* purge off +-inf, NaN, +-0, and negative arguments */
+ *signgamp = 1;
+ ix = hx&0x7fffffff;
+ if(ix>=0x7ff00000) return x*x;
+ if((ix|lx)==0) return one/zero;
+ if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
+ if(hx<0) {
+ *signgamp = -1;
+ return -__ieee754_log(-x);
+ } else return -__ieee754_log(x);
+ }
+ if(hx<0) {
+ if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
+ return one/zero;
+ t = sin_pi(x);
+ if(t==zero) return one/zero; /* -integer */
+ nadj = __ieee754_log(pi/fabs(t*x));
+ if(t<zero) *signgamp = -1;
+ x = -x;
+ }
+
+ /* purge off 1 and 2 */
+ if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
+ /* for x < 2.0 */
+ else if(ix<0x40000000) {
+ if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
+ r = -__ieee754_log(x);
+ if(ix>=0x3FE76944) {y = one-x; i= 0;}
+ else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
+ else {y = x; i=2;}
+ } else {
+ r = zero;
+ if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
+ else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
+ else {y=x-one;i=2;}
+ }
+ switch(i) {
+ case 0:
+ z = y*y;
+ p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
+ p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
+ p = y*p1+p2;
+ r += (p-0.5*y); break;
+ case 1:
+ z = y*y;
+ w = z*y;
+ p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
+ p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
+ p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
+ p = z*p1-(tt-w*(p2+y*p3));
+ r += (tf + p); break;
+ case 2:
+ p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
+ p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
+ r += (-0.5*y + p1/p2);
+ }
+ }
+ else if(ix<0x40200000) { /* x < 8.0 */
+ i = (int)x;
+ t = zero;
+ y = x-(double)i;
+ p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
+ q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
+ r = half*y+p/q;
+ z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
+ switch(i) {
+ case 7: z *= (y+6.0); /* FALLTHRU */
+ case 6: z *= (y+5.0); /* FALLTHRU */
+ case 5: z *= (y+4.0); /* FALLTHRU */
+ case 4: z *= (y+3.0); /* FALLTHRU */
+ case 3: z *= (y+2.0); /* FALLTHRU */
+ r += __ieee754_log(z); break;
+ }
+ /* 8.0 <= x < 2**58 */
+ } else if (ix < 0x43900000) {
+ t = __ieee754_log(x);
+ z = one/x;
+ y = z*z;
+ w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
+ r = (x-half)*(t-one)+w;
+ } else
+ /* 2**58 <= x <= inf */
+ r = x*(__ieee754_log(x)-one);
+ if(hx<0) r = nadj - r;
+ return r;
+}
--- /dev/null
+/* @(#)e_log.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
+#endif
+
+/* __ieee754_log(x)
+ * Return the logrithm of x
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * 2. Approximation of log(1+f).
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ * = 2s + s*R
+ * We use a special Reme algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * of this polynomial approximation is bounded by 2**-58.45. In
+ * other words,
+ * 2 4 6 8 10 12 14
+ * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
+ * (the values of Lg1 to Lg7 are listed in the program)
+ * and
+ * | 2 14 | -58.45
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2
+ * | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ * In order to guarantee error in log below 1ulp, we compute log
+ * by
+ * log(1+f) = f - s*(f - R) (if f is not too large)
+ * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
+ *
+ * 3. Finally, log(x) = k*ln2 + log(1+f).
+ * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ * Here ln2 is split into two floating point number:
+ * ln2_hi + ln2_lo,
+ * where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ * log(x) is NaN with signal if x < 0 (including -INF) ;
+ * log(+INF) is +INF; log(0) is -INF with signal;
+ * log(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
+ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
+two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_log(double x)
+#else
+ double __ieee754_log(x)
+ double x;
+#endif
+{
+ double hfsq,f,s,z,R,w,t1,t2,dk;
+ int32_t k,hx,i,j;
+ u_int32_t lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ k=0;
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx&0x7fffffff)|lx)==0)
+ return -two54/zero; /* log(+-0)=-inf */
+ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ hx &= 0x000fffff;
+ i = (hx+0x95f64)&0x100000;
+ SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
+ k += (i>>20);
+ f = x-1.0;
+ if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
+ if(f==zero) if(k==0) return zero; else {dk=(double)k;
+ return dk*ln2_hi+dk*ln2_lo;}
+ R = f*f*(0.5-0.33333333333333333*f);
+ if(k==0) return f-R; else {dk=(double)k;
+ return dk*ln2_hi-((R-dk*ln2_lo)-f);}
+ }
+ s = f/(2.0+f);
+ dk = (double)k;
+ z = s*s;
+ i = hx-0x6147a;
+ w = z*z;
+ j = 0x6b851-hx;
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ i |= j;
+ R = t2+t1;
+ if(i>0) {
+ hfsq=0.5*f*f;
+ if(k==0) return f-(hfsq-s*(hfsq+R)); else
+ return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
+ } else {
+ if(k==0) return f-s*(f-R); else
+ return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
+ }
+}
--- /dev/null
+/* @(#)e_log10.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $";
+#endif
+
+/* __ieee754_log10(x)
+ * Return the base 10 logarithm of x
+ *
+ * Method :
+ * Let log10_2hi = leading 40 bits of log10(2) and
+ * log10_2lo = log10(2) - log10_2hi,
+ * ivln10 = 1/log(10) rounded.
+ * Then
+ * n = ilogb(x),
+ * if(n<0) n = n+1;
+ * x = scalbn(x,-n);
+ * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
+ *
+ * Note 1:
+ * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
+ * mode must set to Round-to-Nearest.
+ * Note 2:
+ * [1/log(10)] rounded to 53 bits has error .198 ulps;
+ * log10 is monotonic at all binary break points.
+ *
+ * Special cases:
+ * log10(x) is NaN with signal if x < 0;
+ * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
+ * log10(NaN) is that NaN with no signal;
+ * log10(10**N) = N for N=0,1,...,22.
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
+log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
+log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_log10(double x)
+#else
+ double __ieee754_log10(x)
+ double x;
+#endif
+{
+ double y,z;
+ int32_t i,k,hx;
+ u_int32_t lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ k=0;
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx&0x7fffffff)|lx)==0)
+ return -two54/zero; /* log(+-0)=-inf */
+ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ i = ((u_int32_t)k&0x80000000)>>31;
+ hx = (hx&0x000fffff)|((0x3ff-i)<<20);
+ y = (double)(k+i);
+ SET_HIGH_WORD(x,hx);
+ z = y*log10_2lo + ivln10*__ieee754_log(x);
+ return z+y*log10_2hi;
+}
--- /dev/null
+/* @(#)e_pow.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
+#endif
+
+/* __ieee754_pow(x,y) return x**y
+ *
+ * n
+ * Method: Let x = 2 * (1+f)
+ * 1. Compute and return log2(x) in two pieces:
+ * log2(x) = w1 + w2,
+ * where w1 has 53-24 = 29 bit trailing zeros.
+ * 2. Perform y*log2(x) = n+y' by simulating muti-precision
+ * arithmetic, where |y'|<=0.5.
+ * 3. Return x**y = 2**n*exp(y'*log2)
+ *
+ * Special cases:
+ * 1. (anything) ** 0 is 1
+ * 2. (anything) ** 1 is itself
+ * 3. (anything) ** NAN is NAN
+ * 4. NAN ** (anything except 0) is NAN
+ * 5. +-(|x| > 1) ** +INF is +INF
+ * 6. +-(|x| > 1) ** -INF is +0
+ * 7. +-(|x| < 1) ** +INF is +0
+ * 8. +-(|x| < 1) ** -INF is +INF
+ * 9. +-1 ** +-INF is NAN
+ * 10. +0 ** (+anything except 0, NAN) is +0
+ * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
+ * 12. +0 ** (-anything except 0, NAN) is +INF
+ * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
+ * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
+ * 15. +INF ** (+anything except 0,NAN) is +INF
+ * 16. +INF ** (-anything except 0,NAN) is +0
+ * 17. -INF ** (anything) = -0 ** (-anything)
+ * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ * 19. (-anything except 0 and inf) ** (non-integer) is NAN
+ *
+ * Accuracy:
+ * pow(x,y) returns x**y nearly rounded. In particular
+ * pow(integer,integer)
+ * always returns the correct integer provided it is
+ * representable.
+ *
+ * Constants :
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+bp[] = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
+dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
+zero = 0.0,
+one = 1.0,
+two = 2.0,
+two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
+huge = 1.0e300,
+tiny = 1.0e-300,
+ /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
+L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
+L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
+L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
+L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
+L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
+P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
+lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
+lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
+ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
+cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
+cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
+cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
+ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
+ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
+ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
+
+#ifdef __STDC__
+ double __ieee754_pow(double x, double y)
+#else
+ double __ieee754_pow(x,y)
+ double x, y;
+#endif
+{
+ double z,ax,z_h,z_l,p_h,p_l;
+ double y1,t1,t2,r,s,t,u,v,w;
+ int32_t i,j,k,yisint,n;
+ int32_t hx,hy,ix,iy;
+ u_int32_t lx,ly;
+
+ EXTRACT_WORDS(hx,lx,x);
+ EXTRACT_WORDS(hy,ly,y);
+ ix = hx&0x7fffffff; iy = hy&0x7fffffff;
+
+ /* y==zero: x**0 = 1 */
+ if((iy|ly)==0) return one;
+
+ /* +-NaN return x+y */
+ if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
+ iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
+ return x+y;
+
+ /* determine if y is an odd int when x < 0
+ * yisint = 0 ... y is not an integer
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ yisint = 0;
+ if(hx<0) {
+ if(iy>=0x43400000) yisint = 2; /* even integer y */
+ else if(iy>=0x3ff00000) {
+ k = (iy>>20)-0x3ff; /* exponent */
+ if(k>20) {
+ j = ly>>(52-k);
+ if((j<<(52-k))==ly) yisint = 2-(j&1);
+ } else if(ly==0) {
+ j = iy>>(20-k);
+ if((j<<(20-k))==iy) yisint = 2-(j&1);
+ }
+ }
+ }
+
+ /* special value of y */
+ if(ly==0) {
+ if (iy==0x7ff00000) { /* y is +-inf */
+ if(((ix-0x3ff00000)|lx)==0)
+ return y - y; /* inf**+-1 is NaN */
+ else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
+ return (hy>=0)? y: zero;
+ else /* (|x|<1)**-,+inf = inf,0 */
+ return (hy<0)?-y: zero;
+ }
+ if(iy==0x3ff00000) { /* y is +-1 */
+ if(hy<0) return one/x; else return x;
+ }
+ if(hy==0x40000000) return x*x; /* y is 2 */
+ if(hy==0x3fe00000) { /* y is 0.5 */
+ if(hx>=0) /* x >= +0 */
+ return __ieee754_sqrt(x);
+ }
+ }
+
+ ax = fabs(x);
+ /* special value of x */
+ if(lx==0) {
+ if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
+ z = ax; /*x is +-0,+-inf,+-1*/
+ if(hy<0) z = one/z; /* z = (1/|x|) */
+ if(hx<0) {
+ if(((ix-0x3ff00000)|yisint)==0) {
+ z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+ } else if(yisint==1)
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ return z;
+ }
+ }
+
+ /* (x<0)**(non-int) is NaN */
+ if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
+
+ /* |y| is huge */
+ if(iy>0x41e00000) { /* if |y| > 2**31 */
+ if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
+ if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+ if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+ }
+ /* over/underflow if x is not close to one */
+ if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+ if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ t = x-1; /* t has 20 trailing zeros */
+ w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
+ u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
+ v = t*ivln2_l-w*ivln2;
+ t1 = u+v;
+ SET_LOW_WORD(t1,0);
+ t2 = v-(t1-u);
+ } else {
+ double s2,s_h,s_l,t_h,t_l;
+ n = 0;
+ /* take care subnormal number */
+ if(ix<0x00100000)
+ {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
+ n += ((ix)>>20)-0x3ff;
+ j = ix&0x000fffff;
+ /* determine interval */
+ ix = j|0x3ff00000; /* normalize ix */
+ if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
+ else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
+ else {k=0;n+=1;ix -= 0x00100000;}
+ SET_HIGH_WORD(ax,ix);
+
+ /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+ u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
+ v = one/(ax+bp[k]);
+ s = u*v;
+ s_h = s;
+ SET_LOW_WORD(s_h,0);
+ /* t_h=ax+bp[k] High */
+ t_h = zero;
+ SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
+ t_l = ax - (t_h-bp[k]);
+ s_l = v*((u-s_h*t_h)-s_h*t_l);
+ /* compute log(ax) */
+ s2 = s*s;
+ r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+ r += s_l*(s_h+s);
+ s2 = s_h*s_h;
+ t_h = 3.0+s2+r;
+ SET_LOW_WORD(t_h,0);
+ t_l = r-((t_h-3.0)-s2);
+ /* u+v = s*(1+...) */
+ u = s_h*t_h;
+ v = s_l*t_h+t_l*s;
+ /* 2/(3log2)*(s+...) */
+ p_h = u+v;
+ SET_LOW_WORD(p_h,0);
+ p_l = v-(p_h-u);
+ z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
+ z_l = cp_l*p_h+p_l*cp+dp_l[k];
+ /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+ t = (double)n;
+ t1 = (((z_h+z_l)+dp_h[k])+t);
+ SET_LOW_WORD(t1,0);
+ t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+ }
+
+ s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+ if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
+ s = -one;/* (-ve)**(odd int) */
+
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ y1 = y;
+ SET_LOW_WORD(y1,0);
+ p_l = (y-y1)*t1+y*t2;
+ p_h = y1*t1;
+ z = p_l+p_h;
+ EXTRACT_WORDS(j,i,z);
+ if (j>=0x40900000) { /* z >= 1024 */
+ if(((j-0x40900000)|i)!=0) /* if z > 1024 */
+ return s*huge*huge; /* overflow */
+ else {
+ if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
+ }
+ } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
+ if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
+ return s*tiny*tiny; /* underflow */
+ else {
+ if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
+ }
+ }
+ /*
+ * compute 2**(p_h+p_l)
+ */
+ i = j&0x7fffffff;
+ k = (i>>20)-0x3ff;
+ n = 0;
+ if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
+ n = j+(0x00100000>>(k+1));
+ k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
+ t = zero;
+ SET_HIGH_WORD(t,n&~(0x000fffff>>k));
+ n = ((n&0x000fffff)|0x00100000)>>(20-k);
+ if(j<0) n = -n;
+ p_h -= t;
+ }
+ t = p_l+p_h;
+ SET_LOW_WORD(t,0);
+ u = t*lg2_h;
+ v = (p_l-(t-p_h))*lg2+t*lg2_l;
+ z = u+v;
+ w = v-(z-u);
+ t = z*z;
+ t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+ r = (z*t1)/(t1-two)-(w+z*w);
+ z = one-(r-z);
+ GET_HIGH_WORD(j,z);
+ j += (n<<20);
+ if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
+ else SET_HIGH_WORD(z,j);
+ return s*z;
+}
--- /dev/null
+/* @(#)e_rem_pio2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
+#endif
+
+/* __ieee754_rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __kernel_rem_pio2()
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/*
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+ */
+#ifdef __STDC__
+static const int32_t two_over_pi[] = {
+#else
+static int32_t two_over_pi[] = {
+#endif
+0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
+0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
+0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
+0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
+0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
+0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
+0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
+0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
+0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
+0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
+0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
+};
+
+#ifdef __STDC__
+static const int32_t npio2_hw[] = {
+#else
+static int32_t npio2_hw[] = {
+#endif
+0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
+0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
+0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
+0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
+0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
+0x404858EB, 0x404921FB,
+};
+
+/*
+ * invpio2: 53 bits of 2/pi
+ * pio2_1: first 33 bit of pi/2
+ * pio2_1t: pi/2 - pio2_1
+ * pio2_2: second 33 bit of pi/2
+ * pio2_2t: pi/2 - (pio2_1+pio2_2)
+ * pio2_3: third 33 bit of pi/2
+ * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+#ifdef __STDC__
+ int32_t __ieee754_rem_pio2(double x, double *y)
+#else
+ int32_t __ieee754_rem_pio2(x,y)
+ double x,y[];
+#endif
+{
+ double z,w,t,r,fn;
+ double tx[3];
+ int32_t e0,i,j,nx,n,ix,hx;
+ u_int32_t low;
+
+ GET_HIGH_WORD(hx,x); /* high word of x */
+ ix = hx&0x7fffffff;
+ if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
+ {y[0] = x; y[1] = 0; return 0;}
+ if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
+ if(hx>0) {
+ z = x - pio2_1;
+ if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
+ y[0] = z - pio2_1t;
+ y[1] = (z-y[0])-pio2_1t;
+ } else { /* near pi/2, use 33+33+53 bit pi */
+ z -= pio2_2;
+ y[0] = z - pio2_2t;
+ y[1] = (z-y[0])-pio2_2t;
+ }
+ return 1;
+ } else { /* negative x */
+ z = x + pio2_1;
+ if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
+ y[0] = z + pio2_1t;
+ y[1] = (z-y[0])+pio2_1t;
+ } else { /* near pi/2, use 33+33+53 bit pi */
+ z += pio2_2;
+ y[0] = z + pio2_2t;
+ y[1] = (z-y[0])+pio2_2t;
+ }
+ return -1;
+ }
+ }
+ if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
+ t = fabs(x);
+ n = (int32_t) (t*invpio2+half);
+ fn = (double)n;
+ r = t-fn*pio2_1;
+ w = fn*pio2_1t; /* 1st round good to 85 bit */
+ if(n<32&&ix!=npio2_hw[n-1]) {
+ y[0] = r-w; /* quick check no cancellation */
+ } else {
+ u_int32_t high;
+ j = ix>>20;
+ y[0] = r-w;
+ GET_HIGH_WORD(high,y[0]);
+ i = j-((high>>20)&0x7ff);
+ if(i>16) { /* 2nd iteration needed, good to 118 */
+ t = r;
+ w = fn*pio2_2;
+ r = t-w;
+ w = fn*pio2_2t-((t-r)-w);
+ y[0] = r-w;
+ GET_HIGH_WORD(high,y[0]);
+ i = j-((high>>20)&0x7ff);
+ if(i>49) { /* 3rd iteration need, 151 bits acc */
+ t = r; /* will cover all possible cases */
+ w = fn*pio2_3;
+ r = t-w;
+ w = fn*pio2_3t-((t-r)-w);
+ y[0] = r-w;
+ }
+ }
+ }
+ y[1] = (r-y[0])-w;
+ if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+ else return n;
+ }
+ /*
+ * all other (large) arguments
+ */
+ if(ix>=0x7ff00000) { /* x is inf or NaN */
+ y[0]=y[1]=x-x; return 0;
+ }
+ /* set z = scalbn(|x|,ilogb(x)-23) */
+ GET_LOW_WORD(low,x);
+ SET_LOW_WORD(z,low);
+ e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
+ SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
+ for(i=0;i<2;i++) {
+ tx[i] = (double)((int32_t)(z));
+ z = (z-tx[i])*two24;
+ }
+ tx[2] = z;
+ nx = 3;
+ while(tx[nx-1]==zero) nx--; /* skip zero term */
+ n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
+ if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+ return n;
+}
--- /dev/null
+/* @(#)e_remainder.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_remainder.c,v 1.8 1995/05/10 20:46:05 jtc Exp $";
+#endif
+
+/* __ieee754_remainder(x,p)
+ * Return :
+ * returns x REM p = x - [x/p]*p as if in infinite
+ * precise arithmetic, where [x/p] is the (infinite bit)
+ * integer nearest x/p (in half way case choose the even one).
+ * Method :
+ * Based on fmod() return x-[x/p]chopped*p exactlp.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+
+#ifdef __STDC__
+ double __ieee754_remainder(double x, double p)
+#else
+ double __ieee754_remainder(x,p)
+ double x,p;
+#endif
+{
+ int32_t hx,hp;
+ u_int32_t sx,lx,lp;
+ double p_half;
+
+ EXTRACT_WORDS(hx,lx,x);
+ EXTRACT_WORDS(hp,lp,p);
+ sx = hx&0x80000000;
+ hp &= 0x7fffffff;
+ hx &= 0x7fffffff;
+
+ /* purge off exception values */
+ if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
+ if((hx>=0x7ff00000)|| /* x not finite */
+ ((hp>=0x7ff00000)&& /* p is NaN */
+ (((hp-0x7ff00000)|lp)!=0)))
+ return (x*p)/(x*p);
+
+
+ if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
+ if (((hx-hp)|(lx-lp))==0) return zero*x;
+ x = fabs(x);
+ p = fabs(p);
+ if (hp<0x00200000) {
+ if(x+x>p) {
+ x-=p;
+ if(x+x>=p) x -= p;
+ }
+ } else {
+ p_half = 0.5*p;
+ if(x>p_half) {
+ x-=p;
+ if(x>=p_half) x -= p;
+ }
+ }
+ GET_HIGH_WORD(hx,x);
+ SET_HIGH_WORD(x,hx^sx);
+ return x;
+}
--- /dev/null
+/* @(#)e_scalb.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_scalb.c,v 1.6 1995/05/10 20:46:09 jtc Exp $";
+#endif
+
+/*
+ * __ieee754_scalb(x, fn) is provide for
+ * passing various standard test suite. One
+ * should use scalbn() instead.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef _SCALB_INT
+#ifdef __STDC__
+ double __ieee754_scalb(double x, int fn)
+#else
+ double __ieee754_scalb(x,fn)
+ double x; int fn;
+#endif
+#else
+#ifdef __STDC__
+ double __ieee754_scalb(double x, double fn)
+#else
+ double __ieee754_scalb(x,fn)
+ double x, fn;
+#endif
+#endif
+{
+#ifdef _SCALB_INT
+ return scalbn(x,fn);
+#else
+ if (isnan(x)||isnan(fn)) return x*fn;
+ if (!finite(fn)) {
+ if(fn>0.0) return x*fn;
+ else return x/(-fn);
+ }
+ if (rint(fn)!=fn) return (fn-fn)/(fn-fn);
+ if ( fn > 65000.0) return scalbn(x, 65000);
+ if (-fn > 65000.0) return scalbn(x,-65000);
+ return scalbn(x,(int)fn);
+#endif
+}
--- /dev/null
+/* @(#)e_sinh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
+#endif
+
+/* __ieee754_sinh(x)
+ * Method :
+ * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
+ * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
+ * 2.
+ * E + E/(E+1)
+ * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
+ * 2
+ *
+ * 22 <= x <= lnovft : sinh(x) := exp(x)/2
+ * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
+ * ln2ovft < x : sinh(x) := x*shuge (overflow)
+ *
+ * Special cases:
+ * sinh(x) is |x| if x is +INF, -INF, or NaN.
+ * only sinh(0)=0 is exact for finite x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, shuge = 1.0e307;
+#else
+static double one = 1.0, shuge = 1.0e307;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_sinh(double x)
+#else
+ double __ieee754_sinh(x)
+ double x;
+#endif
+{
+ double t,w,h;
+ int32_t ix,jx;
+ u_int32_t lx;
+
+ /* High word of |x|. */
+ GET_HIGH_WORD(jx,x);
+ ix = jx&0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) return x+x;
+
+ h = 0.5;
+ if (jx<0) h = -h;
+ /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+ if (ix < 0x40360000) { /* |x|<22 */
+ if (ix<0x3e300000) /* |x|<2**-28 */
+ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+ t = expm1(fabs(x));
+ if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
+ return h*(t+t/(t+one));
+ }
+
+ /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+ if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ GET_LOW_WORD(lx,x);
+ if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
+ w = __ieee754_exp(0.5*fabs(x));
+ t = h*w;
+ return t*w;
+ }
+
+ /* |x| > overflowthresold, sinh(x) overflow */
+ return x*shuge;
+}
--- /dev/null
+/* @(#)e_sqrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $";
+#endif
+
+/* __ieee754_sqrt(x)
+ * Return correctly rounded sqrt.
+ * ------------------------------------------
+ * | Use the hardware sqrt if you have one |
+ * ------------------------------------------
+ * Method:
+ * Bit by bit method using integer arithmetic. (Slow, but portable)
+ * 1. Normalization
+ * Scale x to y in [1,4) with even powers of 2:
+ * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
+ * sqrt(x) = 2^k * sqrt(y)
+ * 2. Bit by bit computation
+ * Let q = sqrt(y) truncated to i bit after binary point (q = 1),
+ * i 0
+ * i+1 2
+ * s = 2*q , and y = 2 * ( y - q ). (1)
+ * i i i i
+ *
+ * To compute q from q , one checks whether
+ * i+1 i
+ *
+ * -(i+1) 2
+ * (q + 2 ) <= y. (2)
+ * i
+ * -(i+1)
+ * If (2) is false, then q = q ; otherwise q = q + 2 .
+ * i+1 i i+1 i
+ *
+ * With some algebric manipulation, it is not difficult to see
+ * that (2) is equivalent to
+ * -(i+1)
+ * s + 2 <= y (3)
+ * i i
+ *
+ * The advantage of (3) is that s and y can be computed by
+ * i i
+ * the following recurrence formula:
+ * if (3) is false
+ *
+ * s = s , y = y ; (4)
+ * i+1 i i+1 i
+ *
+ * otherwise,
+ * -i -(i+1)
+ * s = s + 2 , y = y - s - 2 (5)
+ * i+1 i i+1 i i
+ *
+ * One may easily use induction to prove (4) and (5).
+ * Note. Since the left hand side of (3) contain only i+2 bits,
+ * it does not necessary to do a full (53-bit) comparison
+ * in (3).
+ * 3. Final rounding
+ * After generating the 53 bits result, we compute one more bit.
+ * Together with the remainder, we can decide whether the
+ * result is exact, bigger than 1/2ulp, or less than 1/2ulp
+ * (it will never equal to 1/2ulp).
+ * The rounding mode can be detected by checking whether
+ * huge + tiny is equal to huge, and whether huge - tiny is
+ * equal to huge for some floating point number "huge" and "tiny".
+ *
+ * Special cases:
+ * sqrt(+-0) = +-0 ... exact
+ * sqrt(inf) = inf
+ * sqrt(-ve) = NaN ... with invalid signal
+ * sqrt(NaN) = NaN ... with invalid signal for signaling NaN
+ *
+ * Other methods : see the appended file at the end of the program below.
+ *---------------
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, tiny=1.0e-300;
+#else
+static double one = 1.0, tiny=1.0e-300;
+#endif
+
+#ifdef __STDC__
+ double __ieee754_sqrt(double x)
+#else
+ double __ieee754_sqrt(x)
+ double x;
+#endif
+{
+ double z;
+ int32_t sign = (int)0x80000000;
+ int32_t ix0,s0,q,m,t,i;
+ u_int32_t r,t1,s1,ix1,q1;
+
+ EXTRACT_WORDS(ix0,ix1,x);
+
+ /* take care of Inf and NaN */
+ if((ix0&0x7ff00000)==0x7ff00000) {
+ return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+ sqrt(-inf)=sNaN */
+ }
+ /* take care of zero */
+ if(ix0<=0) {
+ if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
+ else if(ix0<0)
+ return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
+ }
+ /* normalize x */
+ m = (ix0>>20);
+ if(m==0) { /* subnormal x */
+ while(ix0==0) {
+ m -= 21;
+ ix0 |= (ix1>>11); ix1 <<= 21;
+ }
+ for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
+ m -= i-1;
+ ix0 |= (ix1>>(32-i));
+ ix1 <<= i;
+ }
+ m -= 1023; /* unbias exponent */
+ ix0 = (ix0&0x000fffff)|0x00100000;
+ if(m&1){ /* odd m, double x to make it even */
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ }
+ m >>= 1; /* m = [m/2] */
+
+ /* generate sqrt(x) bit by bit */
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
+ r = 0x00200000; /* r = moving bit from right to left */
+
+ while(r!=0) {
+ t = s0+r;
+ if(t<=ix0) {
+ s0 = t+r;
+ ix0 -= t;
+ q += r;
+ }
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ r>>=1;
+ }
+
+ r = sign;
+ while(r!=0) {
+ t1 = s1+r;
+ t = s0;
+ if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
+ s1 = t1+r;
+ if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
+ ix0 -= t;
+ if (ix1 < t1) ix0 -= 1;
+ ix1 -= t1;
+ q1 += r;
+ }
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ r>>=1;
+ }
+
+ /* use floating add to find out rounding direction */
+ if((ix0|ix1)!=0) {
+ z = one-tiny; /* trigger inexact flag */
+ if (z>=one) {
+ z = one+tiny;
+ if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
+ else if (z>one) {
+ if (q1==(u_int32_t)0xfffffffe) q+=1;
+ q1+=2;
+ } else
+ q1 += (q1&1);
+ }
+ }
+ ix0 = (q>>1)+0x3fe00000;
+ ix1 = q1>>1;
+ if ((q&1)==1) ix1 |= sign;
+ ix0 += (m <<20);
+ INSERT_WORDS(z,ix0,ix1);
+ return z;
+}
+
+/*
+Other methods (use floating-point arithmetic)
+-------------
+(This is a copy of a drafted paper by Prof W. Kahan
+and K.C. Ng, written in May, 1986)
+
+ Two algorithms are given here to implement sqrt(x)
+ (IEEE double precision arithmetic) in software.
+ Both supply sqrt(x) correctly rounded. The first algorithm (in
+ Section A) uses newton iterations and involves four divisions.
+ The second one uses reciproot iterations to avoid division, but
+ requires more multiplications. Both algorithms need the ability
+ to chop results of arithmetic operations instead of round them,
+ and the INEXACT flag to indicate when an arithmetic operation
+ is executed exactly with no roundoff error, all part of the
+ standard (IEEE 754-1985). The ability to perform shift, add,
+ subtract and logical AND operations upon 32-bit words is needed
+ too, though not part of the standard.
+
+A. sqrt(x) by Newton Iteration
+
+ (1) Initial approximation
+
+ Let x0 and x1 be the leading and the trailing 32-bit words of
+ a floating point number x (in IEEE double format) respectively
+
+ 1 11 52 ...widths
+ ------------------------------------------------------
+ x: |s| e | f |
+ ------------------------------------------------------
+ msb lsb msb lsb ...order
+
+
+ ------------------------ ------------------------
+ x0: |s| e | f1 | x1: | f2 |
+ ------------------------ ------------------------
+
+ By performing shifts and subtracts on x0 and x1 (both regarded
+ as integers), we obtain an 8-bit approximation of sqrt(x) as
+ follows.
+
+ k := (x0>>1) + 0x1ff80000;
+ y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
+ Here k is a 32-bit integer and T1[] is an integer array containing
+ correction terms. Now magically the floating value of y (y's
+ leading 32-bit word is y0, the value of its trailing word is 0)
+ approximates sqrt(x) to almost 8-bit.
+
+ Value of T1:
+ static int T1[32]= {
+ 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
+ 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
+ 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
+ 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
+
+ (2) Iterative refinement
+
+ Apply Heron's rule three times to y, we have y approximates
+ sqrt(x) to within 1 ulp (Unit in the Last Place):
+
+ y := (y+x/y)/2 ... almost 17 sig. bits
+ y := (y+x/y)/2 ... almost 35 sig. bits
+ y := y-(y-x/y)/2 ... within 1 ulp
+
+
+ Remark 1.
+ Another way to improve y to within 1 ulp is:
+
+ y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
+ y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
+
+ 2
+ (x-y )*y
+ y := y + 2* ---------- ...within 1 ulp
+ 2
+ 3y + x
+
+
+ This formula has one division fewer than the one above; however,
+ it requires more multiplications and additions. Also x must be
+ scaled in advance to avoid spurious overflow in evaluating the
+ expression 3y*y+x. Hence it is not recommended uless division
+ is slow. If division is very slow, then one should use the
+ reciproot algorithm given in section B.
+
+ (3) Final adjustment
+
+ By twiddling y's last bit it is possible to force y to be
+ correctly rounded according to the prevailing rounding mode
+ as follows. Let r and i be copies of the rounding mode and
+ inexact flag before entering the square root program. Also we
+ use the expression y+-ulp for the next representable floating
+ numbers (up and down) of y. Note that y+-ulp = either fixed
+ point y+-1, or multiply y by nextafter(1,+-inf) in chopped
+ mode.
+
+ I := FALSE; ... reset INEXACT flag I
+ R := RZ; ... set rounding mode to round-toward-zero
+ z := x/y; ... chopped quotient, possibly inexact
+ If(not I) then { ... if the quotient is exact
+ if(z=y) {
+ I := i; ... restore inexact flag
+ R := r; ... restore rounded mode
+ return sqrt(x):=y.
+ } else {
+ z := z - ulp; ... special rounding
+ }
+ }
+ i := TRUE; ... sqrt(x) is inexact
+ If (r=RN) then z=z+ulp ... rounded-to-nearest
+ If (r=RP) then { ... round-toward-+inf
+ y = y+ulp; z=z+ulp;
+ }
+ y := y+z; ... chopped sum
+ y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
+ I := i; ... restore inexact flag
+ R := r; ... restore rounded mode
+ return sqrt(x):=y.
+
+ (4) Special cases
+
+ Square root of +inf, +-0, or NaN is itself;
+ Square root of a negative number is NaN with invalid signal.
+
+
+B. sqrt(x) by Reciproot Iteration
+
+ (1) Initial approximation
+
+ Let x0 and x1 be the leading and the trailing 32-bit words of
+ a floating point number x (in IEEE double format) respectively
+ (see section A). By performing shifs and subtracts on x0 and y0,
+ we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
+
+ k := 0x5fe80000 - (x0>>1);
+ y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
+
+ Here k is a 32-bit integer and T2[] is an integer array
+ containing correction terms. Now magically the floating
+ value of y (y's leading 32-bit word is y0, the value of
+ its trailing word y1 is set to zero) approximates 1/sqrt(x)
+ to almost 7.8-bit.
+
+ Value of T2:
+ static int T2[64]= {
+ 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
+ 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
+ 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
+ 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
+ 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
+ 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
+ 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
+ 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
+
+ (2) Iterative refinement
+
+ Apply Reciproot iteration three times to y and multiply the
+ result by x to get an approximation z that matches sqrt(x)
+ to about 1 ulp. To be exact, we will have
+ -1ulp < sqrt(x)-z<1.0625ulp.
+
+ ... set rounding mode to Round-to-nearest
+ y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
+ y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
+ ... special arrangement for better accuracy
+ z := x*y ... 29 bits to sqrt(x), with z*y<1
+ z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
+
+ Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
+ (a) the term z*y in the final iteration is always less than 1;
+ (b) the error in the final result is biased upward so that
+ -1 ulp < sqrt(x) - z < 1.0625 ulp
+ instead of |sqrt(x)-z|<1.03125ulp.
+
+ (3) Final adjustment
+
+ By twiddling y's last bit it is possible to force y to be
+ correctly rounded according to the prevailing rounding mode
+ as follows. Let r and i be copies of the rounding mode and
+ inexact flag before entering the square root program. Also we
+ use the expression y+-ulp for the next representable floating
+ numbers (up and down) of y. Note that y+-ulp = either fixed
+ point y+-1, or multiply y by nextafter(1,+-inf) in chopped
+ mode.
+
+ R := RZ; ... set rounding mode to round-toward-zero
+ switch(r) {
+ case RN: ... round-to-nearest
+ if(x<= z*(z-ulp)...chopped) z = z - ulp; else
+ if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
+ break;
+ case RZ:case RM: ... round-to-zero or round-to--inf
+ R:=RP; ... reset rounding mod to round-to-+inf
+ if(x<z*z ... rounded up) z = z - ulp; else
+ if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
+ break;
+ case RP: ... round-to-+inf
+ if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
+ if(x>z*z ...chopped) z = z+ulp;
+ break;
+ }
+
+ Remark 3. The above comparisons can be done in fixed point. For
+ example, to compare x and w=z*z chopped, it suffices to compare
+ x1 and w1 (the trailing parts of x and w), regarding them as
+ two's complement integers.
+
+ ...Is z an exact square root?
+ To determine whether z is an exact square root of x, let z1 be the
+ trailing part of z, and also let x0 and x1 be the leading and
+ trailing parts of x.
+
+ If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
+ I := 1; ... Raise Inexact flag: z is not exact
+ else {
+ j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
+ k := z1 >> 26; ... get z's 25-th and 26-th
+ fraction bits
+ I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
+ }
+ R:= r ... restore rounded mode
+ return sqrt(x):=z.
+
+ If multiplication is cheaper then the foregoing red tape, the
+ Inexact flag can be evaluated by
+
+ I := i;
+ I := (z*z!=x) or I.
+
+ Note that z*z can overwrite I; this value must be sensed if it is
+ True.
+
+ Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
+ zero.
+
+ --------------------
+ z1: | f2 |
+ --------------------
+ bit 31 bit 0
+
+ Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
+ or even of logb(x) have the following relations:
+
+ -------------------------------------------------
+ bit 27,26 of z1 bit 1,0 of x1 logb(x)
+ -------------------------------------------------
+ 00 00 odd and even
+ 01 01 even
+ 10 10 odd
+ 10 00 even
+ 11 01 even
+ -------------------------------------------------
+
+ (4) Special cases (see (4) of Section A).
+
+ */
+
+++ /dev/null
-# Makefile for uClibc's math library
-# Copyright (C) 2001 by Lineo, inc.
-#
-# This math library is derived primarily from the Cephes Math Library,
-# copyright by Stephen L. Moshier <moshier@world.std.com>
-#
-# This program is free software; you can redistribute it and/or modify it under
-# the terms of the GNU Library General Public License as published by the Free
-# Software Foundation; either version 2 of the License, or (at your option) any
-# later version.
-#
-# This program is distributed in the hope that it will be useful, but WITHOUT
-# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
-# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
-# details.
-#
-# You should have received a copy of the GNU Library General Public License
-# along with this program; if not, write to the Free Software Foundation, Inc.,
-# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-#
-
-TOPDIR=../../
-include $(TOPDIR)Rules.mak
-
-LIBM=../libm.a
-TARGET_CC= $(TOPDIR)/extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
-
-CSRC= acoshf.c airyf.c asinf.c asinhf.c atanf.c \
- atanhf.c bdtrf.c betaf.c cbrtf.c chbevlf.c chdtrf.c \
- clogf.c cmplxf.c constf.c coshf.c dawsnf.c ellief.c \
- ellikf.c ellpef.c ellpkf.c ellpjf.c expf.c exp2f.c \
- exp10f.c expnf.c facf.c fdtrf.c floorf.c fresnlf.c \
- gammaf.c gdtrf.c hypergf.c hyp2f1f.c igamf.c igamif.c \
- incbetf.c incbif.c i0f.c i1f.c ivf.c j0f.c j1f.c \
- jnf.c jvf.c k0f.c k1f.c knf.c logf.c log2f.c \
- log10f.c nbdtrf.c ndtrf.c ndtrif.c pdtrf.c polynf.c \
- powif.c powf.c psif.c rgammaf.c shichif.c sicif.c \
- sindgf.c sinf.c sinhf.c spencef.c sqrtf.c stdtrf.c \
- struvef.c tandgf.c tanf.c tanhf.c ynf.c zetaf.c \
- zetacf.c polevlf.c setprec.c mtherr.c
-COBJS=$(patsubst %.c,%.o, $(CSRC))
-OBJS=$(COBJS)
-
-all: $(OBJS) $(LIBM)
-
-$(LIBM): ar-target
-
-ar-target: $(OBJS)
- $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
-
-$(COBJS): %.o : %.c
- $(TARGET_CC) $(TARGET_CFLAGS) -c $< -o $@
- $(STRIPTOOL) -x -R .note -R .comment $*.o
-
-$(OBJ): Makefile
-
-clean:
- rm -f *.[oa] *~ core
-
+++ /dev/null
-/* acoshf.c
- *
- * Inverse hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, acoshf();
- *
- * y = acoshf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a polynomial approximation
- *
- * sqrt(z) * P(z)
- *
- * where z = x-1, is used. Otherwise,
- *
- * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,3 100000 1.8e-7 3.9e-8
- * IEEE 1,2000 100000 3.0e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acoshf domain |x| < 1 0.0
- *
- */
-\f
-/* airy.c
- *
- * Airy function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, ai, aip, bi, bip;
- * int airyf();
- *
- * airyf( x, _&ai, _&aip, _&bi, _&bip );
- *
- *
- *
- * DESCRIPTION:
- *
- * Solution of the differential equation
- *
- * y"(x) = xy.
- *
- * The function returns the two independent solutions Ai, Bi
- * and their first derivatives Ai'(x), Bi'(x).
- *
- * Evaluation is by power series summation for small x,
- * by rational minimax approximations for large x.
- *
- *
- *
- * ACCURACY:
- * Error criterion is absolute when function <= 1, relative
- * when function > 1, except * denotes relative error criterion.
- * For large negative x, the absolute error increases as x^1.5.
- * For large positive x, the relative error increases as x^1.5.
- *
- * Arithmetic domain function # trials peak rms
- * IEEE -10, 0 Ai 50000 7.0e-7 1.2e-7
- * IEEE 0, 10 Ai 50000 9.9e-6* 6.8e-7*
- * IEEE -10, 0 Ai' 50000 2.4e-6 3.5e-7
- * IEEE 0, 10 Ai' 50000 8.7e-6* 6.2e-7*
- * IEEE -10, 10 Bi 100000 2.2e-6 2.6e-7
- * IEEE -10, 10 Bi' 50000 2.2e-6 3.5e-7
- *
- */
-\f
-/* asinf.c
- *
- * Inverse circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, asinf();
- *
- * y = asinf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
- *
- * A polynomial of the form x + x**3 P(x**2)
- * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
- * transformed by the identity
- *
- * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 100000 2.5e-7 5.0e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asinf domain |x| > 1 0.0
- *
- */
-\f/* acosf()
- *
- * Inverse circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, acosf();
- *
- * y = acosf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 100000 1.4e-7 4.2e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acosf domain |x| > 1 0.0
- */
-\f
-/* asinhf.c
- *
- * Inverse hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, asinhf();
- *
- * y = asinhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic sine of argument.
- *
- * If |x| < 0.5, the function is approximated by a rational
- * form x + x**3 P(x)/Q(x). Otherwise,
- *
- * asinh(x) = log( x + sqrt(1 + x*x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -3,3 100000 2.4e-7 4.1e-8
- *
- */
-\f
-/* atanf.c
- *
- * Inverse circular tangent
- * (arctangent)
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, atanf();
- *
- * y = atanf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose tangent
- * is x.
- *
- * Range reduction is from four intervals into the interval
- * from zero to tan( pi/8 ). A polynomial approximates
- * the function in this basic interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 100000 1.9e-7 4.1e-8
- *
- */
-\f/* atan2f()
- *
- * Quadrant correct inverse circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, z, atan2f();
- *
- * z = atan2f( y, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle whose tangent is y/x.
- * Define compile time symbol ANSIC = 1 for ANSI standard,
- * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
- * 0 to 2PI, args (x,y).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 100000 1.9e-7 4.1e-8
- * See atan.c.
- *
- */
-\f
-/* atanhf.c
- *
- * Inverse hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, atanhf();
- *
- * y = atanhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic tangent of argument in the range
- * MINLOGF to MAXLOGF.
- *
- * If |x| < 0.5, a polynomial approximation is used.
- * Otherwise,
- * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1,1 100000 1.4e-7 3.1e-8
- *
- */
-\f
-/* bdtrf.c
- *
- * Binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, bdtrf();
- *
- * y = bdtrf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the Binomial
- * probability density:
- *
- * k
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error (p varies from 0 to 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,100 2000 6.9e-5 1.1e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrf domain k < 0 0.0
- * n < k
- * x < 0, x > 1
- *
- */
-\f/* bdtrcf()
- *
- * Complemented binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, bdtrcf();
- *
- * y = bdtrcf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 through n of the Binomial
- * probability density:
- *
- * n
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error (p varies from 0 to 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,100 2000 6.0e-5 1.2e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrcf domain x<0, x>1, n<k 0.0
- */
-\f/* bdtrif()
- *
- * Inverse binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, bdtrif();
- *
- * p = bdtrf( k, n, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the event probability p such that the sum of the
- * terms 0 through k of the Binomial probability density
- * is equal to the given cumulative probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relation
- *
- * 1 - p = incbi( n-k, k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error (p varies from 0 to 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,100 2000 3.5e-5 3.3e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrif domain k < 0, n <= k 0.0
- * x < 0, x > 1
- *
- */
-\f
-/* betaf.c
- *
- * Beta function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, y, betaf();
- *
- * y = betaf( a, b );
- *
- *
- *
- * DESCRIPTION:
- *
- * - -
- * | (a) | (b)
- * beta( a, b ) = -----------.
- * -
- * | (a+b)
- *
- * For large arguments the logarithm of the function is
- * evaluated using lgam(), then exponentiated.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 10000 4.0e-5 6.0e-6
- * IEEE -20,0 10000 4.9e-3 5.4e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * betaf overflow log(beta) > MAXLOG 0.0
- * a or b <0 integer 0.0
- *
- */
-\f
-/* cbrtf.c
- *
- * Cube root
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cbrtf();
- *
- * y = cbrtf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the cube root of the argument, which may be negative.
- *
- * Range reduction involves determining the power of 2 of
- * the argument. A polynomial of degree 2 applied to the
- * mantissa, and multiplication by the cube root of 1, 2, or 4
- * approximates the root to within about 0.1%. Then Newton's
- * iteration is used to converge to an accurate result.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1e38 100000 7.6e-8 2.7e-8
- *
- */
-\f
-/* chbevlf.c
- *
- * Evaluate Chebyshev series
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * float x, y, coef[N], chebevlf();
- *
- * y = chbevlf( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the series
- *
- * N-1
- * - '
- * y = > coef[i] T (x/2)
- * - i
- * i=0
- *
- * of Chebyshev polynomials Ti at argument x/2.
- *
- * Coefficients are stored in reverse order, i.e. the zero
- * order term is last in the array. Note N is the number of
- * coefficients, not the order.
- *
- * If coefficients are for the interval a to b, x must
- * have been transformed to x -> 2(2x - b - a)/(b-a) before
- * entering the routine. This maps x from (a, b) to (-1, 1),
- * over which the Chebyshev polynomials are defined.
- *
- * If the coefficients are for the inverted interval, in
- * which (a, b) is mapped to (1/b, 1/a), the transformation
- * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
- * this becomes x -> 4a/x - 1.
- *
- *
- *
- * SPEED:
- *
- * Taking advantage of the recurrence properties of the
- * Chebyshev polynomials, the routine requires one more
- * addition per loop than evaluating a nested polynomial of
- * the same degree.
- *
- */
-\f
-/* chdtrf.c
- *
- * Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float df, x, y, chdtrf();
- *
- * y = chdtrf( df, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the left hand tail (from 0 to x)
- * of the Chi square probability density function with
- * v degrees of freedom.
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 3.2e-5 5.0e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrf domain x < 0 or v < 1 0.0
- */
-\f/* chdtrcf()
- *
- * Complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, chdtrcf();
- *
- * y = chdtrcf( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the right hand tail (from x to
- * infinity) of the Chi square probability density function
- * with v degrees of freedom:
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 2.7e-5 3.2e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrc domain x < 0 or v < 1 0.0
- */
-\f/* chdtrif()
- *
- * Inverse of complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float df, x, y, chdtrif();
- *
- * x = chdtrif( df, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Chi-square argument x such that the integral
- * from x to infinity of the Chi-square density is equal
- * to the given cumulative probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * x/2 = igami( df/2, y );
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 10000 2.2e-5 8.5e-7
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtri domain y < 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* clogf.c
- *
- * Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clogf();
- * cmplxf z, w;
- *
- * clogf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns complex logarithm to the base e (2.718...) of
- * the complex argument x.
- *
- * If z = x + iy, r = sqrt( x**2 + y**2 ),
- * then
- * w = log(r) + i arctan(y/x).
- *
- * The arctangent ranges from -PI to +PI.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.9e-6 6.2e-8
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 3.1e-7.
- *
- */
-\f/* cexpf()
- *
- * Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexpf();
- * cmplxf z, w;
- *
- * cexpf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the exponential of the complex argument z
- * into the complex result w.
- *
- * If
- * z = x + iy,
- * r = exp(x),
- *
- * then
- *
- * w = r cos y + i r sin y.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.4e-7 4.5e-8
- *
- */
-\f/* csinf()
- *
- * Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csinf();
- * cmplxf z, w;
- *
- * csinf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = sin x cosh y + i cos x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.9e-7 5.5e-8
- *
- */
-\f/* ccosf()
- *
- * Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccosf();
- * cmplxf z, w;
- *
- * ccosf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = cos x cosh y - i sin x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.8e-7 5.5e-8
- */
-\f/* ctanf()
- *
- * Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctanf();
- * cmplxf z, w;
- *
- * ctanf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x + i sinh 2y
- * w = --------------------.
- * cos 2x + cosh 2y
- *
- * On the real axis the denominator is zero at odd multiples
- * of PI/2. The denominator is evaluated by its Taylor
- * series near these points.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 3.3e-7 5.1e-8
- */
-\f/* ccotf()
- *
- * Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccotf();
- * cmplxf z, w;
- *
- * ccotf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x - i sinh 2y
- * w = --------------------.
- * cosh 2y - cos 2x
- *
- * On the real axis, the denominator has zeros at even
- * multiples of PI/2. Near these points it is evaluated
- * by a Taylor series.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 3.6e-7 5.7e-8
- * Also tested by ctan * ccot = 1 + i0.
- */
-\f/* casinf()
- *
- * Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casinf();
- * cmplxf z, w;
- *
- * casinf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- * 2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.1e-5 1.5e-6
- * Larger relative error can be observed for z near zero.
- *
- */
-\f/* cacosf()
- *
- * Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacosf();
- * cmplxf z, w;
- *
- * cacosf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z = PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 9.2e-6 1.2e-6
- *
- */
-\f/* catan()
- *
- * Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catan();
- * cmplxf z, w;
- *
- * catan( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- * 1 ( 2x )
- * Re w = - arctan(-----------) + k PI
- * 2 ( 2 2)
- * (1 - x - y )
- *
- * ( 2 2)
- * 1 (x + (y+1) )
- * Im w = - log(------------)
- * 4 ( 2 2)
- * (x + (y-1) )
- *
- * Where k is an arbitrary integer.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 2.3e-6 5.2e-8
- *
- */
-\f
-/* cmplxf.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * float r; real part
- * float i; imaginary part
- * }cmplxf;
- *
- * cmplxf *a, *b, *c;
- *
- * caddf( a, b, c ); c = b + a
- * csubf( a, b, c ); c = b - a
- * cmulf( a, b, c ); c = b * a
- * cdivf( a, b, c ); c = b / a
- * cnegf( c ); c = -c
- * cmovf( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
- * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * IEEE cadd 30000 5.9e-8 2.6e-8
- * IEEE csub 30000 6.0e-8 2.6e-8
- * IEEE cmul 30000 1.1e-7 3.7e-8
- * IEEE cdiv 30000 2.1e-7 5.7e-8
- */
-\f
-/* cabsf()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * float cabsf();
- * cmplxf z;
- * float a;
- *
- * a = cabsf( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.2e-7 3.4e-8
- */
-\f/* csqrtf()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrtf();
- * cmplxf z, w;
- *
- * csqrtf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The solution
- * reported is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 100000 1.8e-7 4.2e-8
- *
- */
-\f
-/* coshf.c
- *
- * Hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, coshf();
- *
- * y = coshf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic cosine of argument in the range MINLOGF to
- * MAXLOGF.
- *
- * cosh(x) = ( exp(x) + exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-MAXLOGF 100000 1.2e-7 2.8e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * coshf overflow |x| > MAXLOGF MAXNUMF
- *
- *
- */
-\f
-/* dawsnf.c
- *
- * Dawson's Integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, dawsnf();
- *
- * y = dawsnf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- * x
- * -
- * 2 | | 2
- * dawsn(x) = exp( -x ) | exp( t ) dt
- * | |
- * -
- * 0
- *
- * Three different rational approximations are employed, for
- * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10 50000 4.4e-7 6.3e-8
- *
- *
- */
-\f
-/* ellief.c
- *
- * Incomplete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float phi, m, y, ellief();
- *
- * y = ellief( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * phi
- * -
- * | |
- * | 2
- * E(phi\m) = | sqrt( 1 - m sin t ) dt
- * |
- * | |
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random arguments with phi in [0, 2] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,2 10000 4.5e-7 7.4e-8
- *
- *
- */
-\f
-/* ellikf.c
- *
- * Incomplete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float phi, m, y, ellikf();
- *
- * y = ellikf( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * phi
- * -
- * | |
- * | dt
- * F(phi\m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points with phi in [0, 2] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,2 10000 2.9e-7 5.8e-8
- *
- *
- */
-\f
-/* ellpef.c
- *
- * Complete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float m1, y, ellpef();
- *
- * y = ellpef( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * pi/2
- * -
- * | | 2
- * E(m) = | sqrt( 1 - m sin t ) dt
- * | |
- * -
- * 0
- *
- * Where m = 1 - m1, using the approximation
- *
- * P(x) - x log x Q(x).
- *
- * Though there are no singularities, the argument m1 is used
- * rather than m for compatibility with ellpk().
- *
- * E(1) = 1; E(0) = pi/2.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 1 30000 1.1e-7 3.9e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpef domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpjf.c
- *
- * Jacobian Elliptic Functions
- *
- *
- *
- * SYNOPSIS:
- *
- * float u, m, sn, cn, dn, phi;
- * int ellpj();
- *
- * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
- * and dn(u|m) of parameter m between 0 and 1, and real
- * argument u.
- *
- * These functions are periodic, with quarter-period on the
- * real axis equal to the complete elliptic integral
- * ellpk(1.0-m).
- *
- * Relation to incomplete elliptic integral:
- * If u = ellik(phi,m), then sn(u|m) = sin(phi),
- * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
- *
- * Computation is by means of the arithmetic-geometric mean
- * algorithm, except when m is within 1e-9 of 0 or 1. In the
- * latter case with m close to 1, the approximation applies
- * only for phi < pi/2.
- *
- * ACCURACY:
- *
- * Tested at random points with u between 0 and 10, m between
- * 0 and 1.
- *
- * Absolute error (* = relative error):
- * arithmetic function # trials peak rms
- * IEEE sn 10000 1.7e-6 2.2e-7
- * IEEE cn 10000 1.6e-6 2.2e-7
- * IEEE dn 10000 1.4e-3 1.9e-5
- * IEEE phi 10000 3.9e-7* 6.7e-8*
- *
- * Peak error observed in consistency check using addition
- * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
- * the above relation to the incomplete elliptic integral.
- * Accuracy deteriorates when u is large.
- *
- */
-\f
-/* ellpkf.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float m1, y, ellpkf();
- *
- * y = ellpkf( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * pi/2
- * -
- * | |
- * | dt
- * K(m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * where m = 1 - m1, using the approximation
- *
- * P(x) - log x Q(x).
- *
- * The argument m1 is used rather than m so that the logarithmic
- * singularity at m = 1 will be shifted to the origin; this
- * preserves maximum accuracy.
- *
- * K(0) = pi/2.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 30000 1.3e-7 3.4e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpkf domain x<0, x>1 0.0
- *
- */
-\f
-/* exp10f.c
- *
- * Base 10 exponential function
- * (Common antilogarithm)
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, exp10f();
- *
- * y = exp10f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 10 raised to the x power.
- *
- * Range reduction is accomplished by expressing the argument
- * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
- * A polynomial approximates 10**f.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -38,+38 100000 9.8e-8 2.8e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp10 underflow x < -MAXL10 0.0
- * exp10 overflow x > MAXL10 MAXNUM
- *
- * IEEE single arithmetic: MAXL10 = 38.230809449325611792.
- *
- */
-\f
-/* exp2f.c
- *
- * Base 2 exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, exp2f();
- *
- * y = exp2f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 2 raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- * x k f
- * 2 = 2 2.
- *
- * A polynomial approximates 2**x in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -127,+127 100000 1.7e-7 2.8e-8
- *
- *
- * See exp.c for comments on error amplification.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < -MAXL2 0.0
- * exp overflow x > MAXL2 MAXNUMF
- *
- * For IEEE arithmetic, MAXL2 = 127.
- */
-\f
-/* expf.c
- *
- * Exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, expf();
- *
- * y = expf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns e (2.71828...) raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- *
- * x k f
- * e = 2 e.
- *
- * A polynomial is used to approximate exp(f)
- * in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +- MAXLOG 100000 1.7e-7 2.8e-8
- *
- *
- * Error amplification in the exponential function can be
- * a serious matter. The error propagation involves
- * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
- * which shows that a 1 lsb error in representing X produces
- * a relative error of X times 1 lsb in the function.
- * While the routine gives an accurate result for arguments
- * that are exactly represented by a double precision
- * computer number, the result contains amplified roundoff
- * error for large arguments not exactly represented.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * expf underflow x < MINLOGF 0.0
- * expf overflow x > MAXLOGF MAXNUMF
- *
- */
-\f
-/* expnf.c
- *
- * Exponential integral En
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * float x, y, expnf();
- *
- * y = expnf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the exponential integral
- *
- * inf.
- * -
- * | | -xt
- * | e
- * E (x) = | ---- dt.
- * n | n
- * | | t
- * -
- * 1
- *
- *
- * Both n and x must be nonnegative.
- *
- * The routine employs either a power series, a continued
- * fraction, or an asymptotic formula depending on the
- * relative values of n and x.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 10000 5.6e-7 1.2e-7
- *
- */
-\f
-/* facf.c
- *
- * Factorial function
- *
- *
- *
- * SYNOPSIS:
- *
- * float y, facf();
- * int i;
- *
- * y = facf( i );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns factorial of i = 1 * 2 * 3 * ... * i.
- * fac(0) = 1.0.
- *
- * Due to machine arithmetic bounds the largest value of
- * i accepted is 33 in single precision arithmetic.
- * Greater values, or negative ones,
- * produce an error message and return MAXNUM.
- *
- *
- *
- * ACCURACY:
- *
- * For i < 34 the values are simply tabulated, and have
- * full machine accuracy.
- *
- */
-\f
-/* fdtrf.c
- *
- * F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * float x, y, fdtrf();
- *
- * y = fdtrf( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density). This is the density
- * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
- * variables having Chi square distributions with df1
- * and df2 degrees of freedom, respectively.
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
- *
- *
- * The arguments a and b are greater than zero, and x
- * x is nonnegative.
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 2.2e-5 1.1e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrf domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrcf()
- *
- * Complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * float x, y, fdtrcf();
- *
- * y = fdtrcf( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from x to infinity under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density).
- *
- *
- * inf.
- * -
- * 1 | | a-1 b-1
- * 1-P(x) = ------ | t (1-t) dt
- * B(a,b) | |
- * -
- * x
- *
- * (See fdtr.c.)
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 7.3e-5 1.2e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrcf domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrif()
- *
- * Inverse of complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float df1, df2, x, y, fdtrif();
- *
- * x = fdtrif( df1, df2, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the F density argument x such that the integral
- * from x to infinity of the F density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relations
- *
- * z = incbi( df2/2, df1/2, y )
- * x = df2 (1-z) / (df1 z).
- *
- * Note: the following relations hold for the inverse of
- * the uncomplemented F distribution:
- *
- * z = incbi( df1/2, df2/2, y )
- * x = df2 z / (df1 (1-z)).
- *
- *
- *
- * ACCURACY:
- *
- * arithmetic domain # trials peak rms
- * Absolute error:
- * IEEE 0,100 5000 4.0e-5 3.2e-6
- * Relative error:
- * IEEE 0,100 5000 1.2e-3 1.8e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrif domain y <= 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* ceilf()
- * floorf()
- * frexpf()
- * ldexpf()
- *
- * Single precision floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y;
- * float ceilf(), floorf(), frexpf(), ldexpf();
- * int expnt, n;
- *
- * y = floorf(x);
- * y = ceilf(x);
- * y = frexpf( x, &expnt );
- * y = ldexpf( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * All four routines return a single precision floating point
- * result.
- *
- * sfloor() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * sceil() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * sfrexp() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * sldexp() multiplies x by 2**n.
- *
- * These functions are part of the standard C run time library
- * for many but not all C compilers. The ones supplied are
- * written in C for either DEC or IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-/* fresnlf.c
- *
- * Fresnel integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, S, C;
- * void fresnlf();
- *
- * fresnlf( x, _&S, _&C );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the Fresnel integrals
- *
- * x
- * -
- * | |
- * C(x) = | cos(pi/2 t**2) dt,
- * | |
- * -
- * 0
- *
- * x
- * -
- * | |
- * S(x) = | sin(pi/2 t**2) dt.
- * | |
- * -
- * 0
- *
- *
- * The integrals are evaluated by power series for small x.
- * For x >= 1 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
- * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
- *
- *
- *
- * ACCURACY:
- *
- * Relative error.
- *
- * Arithmetic function domain # trials peak rms
- * IEEE S(x) 0, 10 30000 1.1e-6 1.9e-7
- * IEEE C(x) 0, 10 30000 1.1e-6 2.0e-7
- */
-\f
-/* gammaf.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, gammaf();
- * extern int sgngamf;
- *
- * y = gammaf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngamf.
- * This same variable is also filled in by the logarithmic
- * gamma function lgam().
- *
- * Arguments between 0 and 10 are reduced by recurrence and the
- * function is approximated by a polynomial function covering
- * the interval (2,3). Large arguments are handled by Stirling's
- * formula. Negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,-33 100,000 5.7e-7 1.0e-7
- * IEEE -33,0 100,000 6.1e-7 1.2e-7
- *
- *
- */\f
-/* lgamf()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, lgamf();
- * extern int sgngamf;
- *
- * y = lgamf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngamf.
- *
- * For arguments greater than 6.5, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula. Arguments between 0 and +6.5 are reduced by
- * by recurrence to the interval [.75,1.25] or [1.5,2.5] of a rational
- * approximation. The cosecant reflection formula is employed for
- * arguments less than zero.
- *
- * Arguments greater than MAXLGM = 2.035093e36 return MAXNUM and an
- * error message.
- *
- *
- *
- * ACCURACY:
- *
- *
- *
- * arithmetic domain # trials peak rms
- * IEEE -100,+100 500,000 7.4e-7 6.8e-8
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- * The routine has low relative error for positive arguments.
- *
- * The following test used the relative error criterion.
- * IEEE -2, +3 100000 4.0e-7 5.6e-8
- *
- */
-\f
-/* gdtrf.c
- *
- * Gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, gdtrf();
- *
- * y = gdtrf( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from zero to x of the gamma probability
- * density function:
- *
- *
- * x
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * 0
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igam( b, ax ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 5.8e-5 3.0e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrf domain x < 0 0.0
- *
- */
-\f/* gdtrcf.c
- *
- * Complemented gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, gdtrcf();
- *
- * y = gdtrcf( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from x to infinity of the gamma
- * probability density function:
- *
- *
- * inf.
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * x
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igamc( b, ax ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 9.1e-5 1.5e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrcf domain x < 0 0.0
- *
- */
-\f
-/* hyp2f1f.c
- *
- * Gauss hypergeometric function F
- * 2 1
- *
- *
- * SYNOPSIS:
- *
- * float a, b, c, x, y, hyp2f1f();
- *
- * y = hyp2f1f( a, b, c, x );
- *
- *
- * DESCRIPTION:
- *
- *
- * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
- * 2 1
- *
- * inf.
- * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
- * = 1 + > ----------------------------- x .
- * - c(c+1)...(c+k) (k+1)!
- * k = 0
- *
- * Cases addressed are
- * Tests and escapes for negative integer a, b, or c
- * Linear transformation if c - a or c - b negative integer
- * Special case c = a or c = b
- * Linear transformation for x near +1
- * Transformation for x < -0.5
- * Psi function expansion if x > 0.5 and c - a - b integer
- * Conditionally, a recurrence on c to make c-a-b > 0
- *
- * |x| > 1 is rejected.
- *
- * The parameters a, b, c are considered to be integer
- * valued if they are within 1.0e-6 of the nearest integer.
- *
- * ACCURACY:
- *
- * Relative error (-1 < x < 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,3 30000 5.8e-4 4.3e-6
- */
-\f
-/* hypergf.c
- *
- * Confluent hypergeometric function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, hypergf();
- *
- * y = hypergf( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the confluent hypergeometric function
- *
- * 1 2
- * a x a(a+1) x
- * F ( a,b;x ) = 1 + ---- + --------- + ...
- * 1 1 b 1! b(b+1) 2!
- *
- * Many higher transcendental functions are special cases of
- * this power series.
- *
- * As is evident from the formula, b must not be a negative
- * integer or zero unless a is an integer with 0 >= a > b.
- *
- * The routine attempts both a direct summation of the series
- * and an asymptotic expansion. In each case error due to
- * roundoff, cancellation, and nonconvergence is estimated.
- * The result with smaller estimated error is returned.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (a, b, x), all three variables
- * ranging from 0 to 30.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,5 10000 6.6e-7 1.3e-7
- * IEEE 0,30 30000 1.1e-5 6.5e-7
- *
- * Larger errors can be observed when b is near a negative
- * integer or zero. Certain combinations of arguments yield
- * serious cancellation error in the power series summation
- * and also are not in the region of near convergence of the
- * asymptotic series. An error message is printed if the
- * self-estimated relative error is greater than 1.0e-3.
- *
- */
-\f
-/* i0f.c
- *
- * Modified Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i0();
- *
- * y = i0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order zero of the
- * argument.
- *
- * The function is defined as i0(x) = j0( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 100000 4.0e-7 7.9e-8
- *
- */
-\f/* i0ef.c
- *
- * Modified Bessel function of order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i0ef();
- *
- * y = i0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order zero of the argument.
- *
- * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 100000 3.7e-7 7.0e-8
- * See i0f().
- *
- */
-\f
-/* i1f.c
- *
- * Modified Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i1f();
- *
- * y = i1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order one of the
- * argument.
- *
- * The function is defined as i1(x) = -i j1( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 100000 1.5e-6 1.6e-7
- *
- *
- */
-\f/* i1ef.c
- *
- * Modified Bessel function of order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i1ef();
- *
- * y = i1ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order one of the argument.
- *
- * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.5e-6 1.5e-7
- * See i1().
- *
- */
-\f
-/* igamf.c
- *
- * Incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, x, y, igamf();
- *
- * y = igamf( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 20000 7.8e-6 5.9e-7
- *
- */
-\f/* igamcf()
- *
- * Complemented incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, x, y, igamcf();
- *
- * y = igamcf( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 7.8e-6 5.9e-7
- *
- */
-\f
-/* igamif()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, x, y, igamif();
- *
- * x = igamif( a, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * igamc( a, x ) = y.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(y) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Tested for a ranging from 0 to 100 and x from 0 to 1.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 1.0e-5 1.5e-6
- *
- */
-\f
-/* incbetf.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, incbetf();
- *
- * y = incbetf( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion.
- * If a < 1, the function calls itself recursively after a
- * transformation to increase a to a+1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) with a and b in the indicated
- * interval and x between 0 and 1.
- *
- * arithmetic domain # trials peak rms
- * Relative error:
- * IEEE 0,30 10000 3.7e-5 5.1e-6
- * IEEE 0,100 10000 1.7e-4 2.5e-5
- * The useful domain for relative error is limited by underflow
- * of the single precision exponential function.
- * Absolute error:
- * IEEE 0,30 100000 2.2e-5 9.6e-7
- * IEEE 0,100 10000 6.5e-5 3.7e-6
- *
- * Larger errors may occur for extreme ratios of a and b.
- *
- * ERROR MESSAGES:
- * message condition value returned
- * incbetf domain x<0, x>1 0.0
- */
-\f
-/* incbif()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, incbif();
- *
- * x = incbif( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y.
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 0,100 5000 2.8e-4 8.3e-6
- *
- * Overflow and larger errors may occur for one of a or b near zero
- * and the other large.
- */
-\f
-/* ivf.c
- *
- * Modified Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, ivf();
- *
- * y = ivf( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order v of the
- * argument. If x is negative, v must be integer valued.
- *
- * The function is defined as Iv(x) = Jv( ix ). It is
- * here computed in terms of the confluent hypergeometric
- * function, according to the formula
- *
- * v -x
- * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
- *
- * If v is a negative integer, then v is replaced by -v.
- *
- *
- * ACCURACY:
- *
- * Tested at random points (v, x), with v between 0 and
- * 30, x between 0 and 28.
- * arithmetic domain # trials peak rms
- * Relative error:
- * IEEE 0,15 3000 4.7e-6 5.4e-7
- * Absolute error (relative when function > 1)
- * IEEE 0,30 5000 8.5e-6 1.3e-6
- *
- * Accuracy is diminished if v is near a negative integer.
- * The useful domain for relative error is limited by overflow
- * of the single precision exponential function.
- *
- * See also hyperg.c.
- *
- */
-\f
-/* j0f.c
- *
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j0f();
- *
- * y = j0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval the following polynomial
- * approximation is used:
- *
- *
- * 2 2 2
- * (w - r ) (w - r ) (w - r ) P(w)
- * 1 2 3
- *
- * 2
- * where w = x and the three r's are zeros of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.3e-7 3.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.4e-8
- *
- */
-\f/* y0f.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, y0f();
- *
- * y = y0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2 2 2
- * y0(x) = (w - r ) (w - r ) (w - r ) R(x) + 2/pi ln(x) j0(x).
- * 1 2 3
- *
- * Thus a call to j0() is required. The three zeros are removed
- * from R(x) to improve its numerical stability.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.4e-7 3.4e-8
- * IEEE 2, 32 100000 1.8e-7 5.3e-8
- *
- */
-\f
-/* j1f.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j1f();
- *
- * y = j1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a polynomial approximation
- * 2
- * (w - r ) x P(w)
- * 1
- * 2
- * is used, where w = x and r is the first zero of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.2e-7 2.5e-8
- * IEEE 2, 32 100000 2.0e-7 5.3e-8
- *
- *
- */
-\f/* y1.c
- *
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2
- * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
- * 1
- *
- * Thus a call to j1() is required.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.2e-7 4.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.3e-8
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-\f
-/* jnf.c
- *
- * Bessel function of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * float x, y, jnf();
- *
- * y = jnf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The ratio of jn(x) to j0(x) is computed by backward
- * recurrence. First the ratio jn/jn-1 is found by a
- * continued fraction expansion. Then the recurrence
- * relating successive orders is applied until j0 or j1 is
- * reached.
- *
- * If n = 0 or 1 the routine for j0 or j1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic range # trials peak rms
- * IEEE 0, 15 30000 3.6e-7 3.6e-8
- *
- *
- * Not suitable for large n or x. Use jvf() instead.
- *
- */
-\f
-/* jvf.c
- *
- * Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, jvf();
- *
- * y = jvf( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order v of the argument,
- * where v is real. Negative x is allowed if v is an integer.
- *
- * Several expansions are included: the ascending power
- * series, the Hankel expansion, and two transitional
- * expansions for large v. If v is not too large, it
- * is reduced by recurrence to a region of best accuracy.
- *
- * The single precision routine accepts negative v, but with
- * reduced accuracy.
- *
- *
- *
- * ACCURACY:
- * Results for integer v are indicated by *.
- * Error criterion is absolute, except relative when |jv()| > 1.
- *
- * arithmetic domain # trials peak rms
- * v x
- * IEEE 0,125 0,125 30000 2.0e-6 2.0e-7
- * IEEE -17,0 0,125 30000 1.1e-5 4.0e-7
- * IEEE -100,0 0,125 3000 1.5e-4 7.8e-6
- */
-\f
-/* k0f.c
- *
- * Modified Bessel function, third kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0f();
- *
- * y = k0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order zero of the argument.
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at 2000 random points between 0 and 8. Peak absolute
- * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-7 8.5e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * K0 domain x <= 0 MAXNUM
- *
- */
-\f/* k0ef()
- *
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0ef();
- *
- * y = k0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 8.1e-7 7.8e-8
- * See k0().
- *
- */
-\f
-/* k1f.c
- *
- * Modified Bessel function, third kind, order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1f();
- *
- * y = k1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the modified Bessel function of the third kind
- * of order one of the argument.
- *
- * The range is partitioned into the two intervals [0,2] and
- * (2, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.6e-7 7.6e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * k1 domain x <= 0 MAXNUM
- *
- */
-\f/* k1ef.c
- *
- * Modified Bessel function, third kind, order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1ef();
- *
- * y = k1ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order one of the argument:
- *
- * k1e(x) = exp(x) * k1(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.9e-7 6.7e-8
- * See k1().
- *
- */
-\f
-/* knf.c
- *
- * Modified Bessel function, third kind, integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, knf();
- * int n;
- *
- * y = knf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order n of the argument.
- *
- * The range is partitioned into the two intervals [0,9.55] and
- * (9.55, infinity). An ascending power series is used in the
- * low range, and an asymptotic expansion in the high range.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, relative when function > 1:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 10000 2.0e-4 3.8e-6
- *
- * Error is high only near the crossover point x = 9.55
- * between the two expansions used.
- */
-\f
-/* log10f.c
- *
- * Common logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, log10f();
- *
- * y = log10f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns logarithm to the base 10 of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. The logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 100000 1.3e-7 3.4e-8
- * IEEE 0, MAXNUMF 100000 1.3e-7 2.6e-8
- *
- * In the tests over the interval [0, MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [-MAXL10, MAXL10].
- *
- * ERROR MESSAGES:
- *
- * log10f singularity: x = 0; returns -MAXL10
- * log10f domain: x < 0; returns -MAXL10
- * MAXL10 = 38.230809449325611792
- */
-\f
-/* log2f.c
- *
- * Base 2 logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, log2f();
- *
- * y = log2f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 2 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the base e
- * logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE exp(+-88) 100000 1.1e-7 2.4e-8
- * IEEE 0.5, 2.0 100000 1.1e-7 3.0e-8
- *
- * In the tests over the interval [exp(+-88)], the logarithms
- * of the random arguments were uniformly distributed.
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns MINLOGF/log(2)
- * log domain: x < 0; returns MINLOGF/log(2)
- */
-\f
-/* logf.c
- *
- * Natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, logf();
- *
- * y = logf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 100000 7.6e-8 2.7e-8
- * IEEE 1, MAXNUMF 100000 2.6e-8
- *
- * In the tests over the interval [1, MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [0, MAXLOGF].
- *
- * ERROR MESSAGES:
- *
- * logf singularity: x = 0; returns MINLOG
- * logf domain: x < 0; returns MINLOG
- */
-\f
-/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * void mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file math.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * math.h
- *
- */
-\f
-/* nbdtrf.c
- *
- * Negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, nbdtrf();
- *
- * y = nbdtrf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the negative
- * binomial distribution:
- *
- * k
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * In a sequence of Bernoulli trials, this is the probability
- * that k or fewer failures precede the nth success.
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 1.5e-4 1.9e-5
- *
- */
-\f/* nbdtrcf.c
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, nbdtrcf();
- *
- * y = nbdtrcf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 1.4e-4 2.0e-5
- *
- */
-\f
-/* ndtrf.c
- *
- * Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, ndtrf();
- *
- * y = ndtrf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the Gaussian probability density
- * function, integrated from minus infinity to x:
- *
- * x
- * -
- * 1 | | 2
- * ndtr(x) = --------- | exp( - t /2 ) dt
- * sqrt(2pi) | |
- * -
- * -inf.
- *
- * = ( 1 + erf(z) ) / 2
- * = erfc(z) / 2
- *
- * where z = x/sqrt(2). Computation is via the functions
- * erf and erfc.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -13,0 50000 1.5e-5 2.6e-6
- *
- *
- * ERROR MESSAGES:
- *
- * See erfcf().
- *
- */
-\f/* erff.c
- *
- * Error function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, erff();
- *
- * y = erff( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The integral is
- *
- * x
- * -
- * 2 | | 2
- * erf(x) = -------- | exp( - t ) dt.
- * sqrt(pi) | |
- * -
- * 0
- *
- * The magnitude of x is limited to 9.231948545 for DEC
- * arithmetic; 1 or -1 is returned outside this range.
- *
- * For 0 <= |x| < 1, erf(x) = x * P(x**2); otherwise
- * erf(x) = 1 - erfc(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -9.3,9.3 50000 1.7e-7 2.8e-8
- *
- */
-\f/* erfcf.c
- *
- * Complementary error function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, erfcf();
- *
- * y = erfcf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * 1 - erf(x) =
- *
- * inf.
- * -
- * 2 | | 2
- * erfc(x) = -------- | exp( - t ) dt
- * sqrt(pi) | |
- * -
- * x
- *
- *
- * For small x, erfc(x) = 1 - erf(x); otherwise polynomial
- * approximations 1/x P(1/x**2) are computed.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -9.3,9.3 50000 3.9e-6 7.2e-7
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfcf underflow x**2 > MAXLOGF 0.0
- *
- *
- */
-\f
-/* ndtrif.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, ndtrif();
- *
- * x = ndtrif( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2.0 * log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
- * There are two rational functions P/Q, one for 0 < y < exp(-32)
- * and the other for y up to exp(-2). For larger arguments,
- * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1e-38, 1 30000 3.6e-7 5.0e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtrif domain x <= 0 -MAXNUM
- * ndtrif domain x >= 1 MAXNUM
- *
- */
-\f
-/* pdtrf.c
- *
- * Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * float m, y, pdtrf();
- *
- * y = pdtrf( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the first k terms of the Poisson
- * distribution:
- *
- * k j
- * -- -m m
- * > e --
- * -- j!
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the relation
- *
- * y = pdtr( k, m ) = igamc( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 6.9e-5 8.0e-6
- *
- */
-\f/* pdtrcf()
- *
- * Complemented poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * float m, y, pdtrcf();
- *
- * y = pdtrcf( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the Poisson
- * distribution:
- *
- * inf. j
- * -- -m m
- * > e --
- * -- j!
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the formula
- *
- * y = pdtrc( k, m ) = igam( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 8.4e-5 1.2e-5
- *
- */
-\f/* pdtrif()
- *
- * Inverse Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * float m, y, pdtrf();
- *
- * m = pdtrif( k, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Poisson variable x such that the integral
- * from 0 to x of the Poisson density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * m = igami( k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 8.7e-6 1.4e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pdtri domain y < 0 or y >= 1 0.0
- * k < 0
- *
- */
-\f
-/* polevlf.c
- * p1evlf.c
- *
- * Evaluate polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * float x, y, coef[N+1], polevlf[];
- *
- * y = polevlf( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates polynomial of degree N:
- *
- * 2 N
- * y = C + C x + C x +...+ C x
- * 0 1 2 N
- *
- * Coefficients are stored in reverse order:
- *
- * coef[0] = C , ..., coef[N] = C .
- * N 0
- *
- * The function p1evl() assumes that coef[N] = 1.0 and is
- * omitted from the array. Its calling arguments are
- * otherwise the same as polevl().
- *
- *
- * SPEED:
- *
- * In the interest of speed, there are no checks for out
- * of bounds arithmetic. This routine is used by most of
- * the functions in the library. Depending on available
- * equipment features, the user may wish to rewrite the
- * program in microcode or assembly language.
- *
- */
-\f
-/* polynf.c
- * polyrf.c
- * Arithmetic operations on polynomials
- *
- * In the following descriptions a, b, c are polynomials of degree
- * na, nb, nc respectively. The degree of a polynomial cannot
- * exceed a run-time value MAXPOLF. An operation that attempts
- * to use or generate a polynomial of higher degree may produce a
- * result that suffers truncation at degree MAXPOL. The value of
- * MAXPOL is set by calling the function
- *
- * polinif( maxpol );
- *
- * where maxpol is the desired maximum degree. This must be
- * done prior to calling any of the other functions in this module.
- * Memory for internal temporary polynomial storage is allocated
- * by polinif().
- *
- * Each polynomial is represented by an array containing its
- * coefficients, together with a separately declared integer equal
- * to the degree of the polynomial. The coefficients appear in
- * ascending order; that is,
- *
- * 2 na
- * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
- *
- *
- *
- * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
- * polprtf( a, na, D ); Print the coefficients of a to D digits.
- * polclrf( a, na ); Set a identically equal to zero, up to a[na].
- * polmovf( a, na, b ); Set b = a.
- * poladdf( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
- * polsubf( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
- * polmulf( a, na, b, nb, c ); c = b * a, nc = na+nb
- *
- *
- * Division:
- *
- * i = poldivf( a, na, b, nb, c ); c = b / a, nc = MAXPOL
- *
- * returns i = the degree of the first nonzero coefficient of a.
- * The computed quotient c must be divided by x^i. An error message
- * is printed if a is identically zero.
- *
- *
- * Change of variables:
- * If a and b are polynomials, and t = a(x), then
- * c(t) = b(a(x))
- * is a polynomial found by substituting a(x) for t. The
- * subroutine call for this is
- *
- * polsbtf( a, na, b, nb, c );
- *
- *
- * Notes:
- * poldivf() is an integer routine; polevaf() is float.
- * Any of the arguments a, b, c may refer to the same array.
- *
- */
-\f
-/* powf.c
- *
- * Power function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, z, powf();
- *
- * z = powf( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/16 and pseudo extended precision arithmetic to
- * obtain an extra three bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 100,000 1.4e-7 3.6e-8
- * 1/10 < x < 10, x uniformly distributed.
- * -10 < y < 10, y uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * powf overflow x**y > MAXNUMF MAXNUMF
- * powf underflow x**y < 1/MAXNUMF 0.0
- * powf domain x<0 and y noninteger 0.0
- *
- */
-\f
-/* powif.c
- *
- * Real raised to integer power
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, powif();
- * int n;
- *
- * y = powif( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns argument x raised to the nth power.
- * The routine efficiently decomposes n as a sum of powers of
- * two. The desired power is a product of two-to-the-kth
- * powers of x. Thus to compute the 32767 power of x requires
- * 28 multiplications instead of 32767 multiplications.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic x domain n domain # trials peak rms
- * IEEE .04,26 -26,26 100000 1.1e-6 2.0e-7
- * IEEE 1,2 -128,128 100000 1.1e-5 1.0e-6
- *
- * Returns MAXNUMF on overflow, zero on underflow.
- *
- */
-\f
-/* psif.c
- *
- * Psi (digamma) function
- *
- *
- * SYNOPSIS:
- *
- * float x, y, psif();
- *
- * y = psif( x );
- *
- *
- * DESCRIPTION:
- *
- * d -
- * psi(x) = -- ln | (x)
- * dx
- *
- * is the logarithmic derivative of the gamma function.
- * For integer x,
- * n-1
- * -
- * psi(n) = -EUL + > 1/k.
- * -
- * k=1
- *
- * This formula is used for 0 < n <= 10. If x is negative, it
- * is transformed to a positive argument by the reflection
- * formula psi(1-x) = psi(x) + pi cot(pi x).
- * For general positive x, the argument is made greater than 10
- * using the recurrence psi(x+1) = psi(x) + 1/x.
- * Then the following asymptotic expansion is applied:
- *
- * inf. B
- * - 2k
- * psi(x) = log(x) - 1/2x - > -------
- * - 2k
- * k=1 2k x
- *
- * where the B2k are Bernoulli numbers.
- *
- * ACCURACY:
- * Absolute error, relative when |psi| > 1 :
- * arithmetic domain # trials peak rms
- * IEEE -33,0 30000 8.2e-7 1.2e-7
- * IEEE 0,33 100000 7.3e-7 7.7e-8
- *
- * ERROR MESSAGES:
- * message condition value returned
- * psi singularity x integer <=0 MAXNUMF
- */
-\f
-/* rgammaf.c
- *
- * Reciprocal gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, rgammaf();
- *
- * y = rgammaf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns one divided by the gamma function of the argument.
- *
- * The function is approximated by a Chebyshev expansion in
- * the interval [0,1]. Range reduction is by recurrence
- * for arguments between -34.034 and +34.84425627277176174.
- * 1/MAXNUMF is returned for positive arguments outside this
- * range.
- *
- * The reciprocal gamma function has no singularities,
- * but overflow and underflow may occur for large arguments.
- * These conditions return either MAXNUMF or 1/MAXNUMF with
- * appropriate sign.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -34,+34 100000 8.9e-7 1.1e-7
- */
-\f
-/* shichif.c
- *
- * Hyperbolic sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, Chi, Shi;
- *
- * shichi( x, &Chi, &Shi );
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integrals
- *
- * x
- * -
- * | | cosh t - 1
- * Chi(x) = eul + ln x + | ----------- dt,
- * | | t
- * -
- * 0
- *
- * x
- * -
- * | | sinh t
- * Shi(x) = | ------ dt
- * | | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are evaluated by power series for x < 8
- * and by Chebyshev expansions for x between 8 and 88.
- * For large x, both functions approach exp(x)/2x.
- * Arguments greater than 88 in magnitude return MAXNUM.
- *
- *
- * ACCURACY:
- *
- * Test interval 0 to 88.
- * Relative error:
- * arithmetic function # trials peak rms
- * IEEE Shi 20000 3.5e-7 7.0e-8
- * Absolute error, except relative when |Chi| > 1:
- * IEEE Chi 20000 3.8e-7 7.6e-8
- */
-\f
-/* sicif.c
- *
- * Sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, Ci, Si;
- *
- * sicif( x, &Si, &Ci );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the integrals
- *
- * x
- * -
- * | cos t - 1
- * Ci(x) = eul + ln x + | --------- dt,
- * | t
- * -
- * 0
- * x
- * -
- * | sin t
- * Si(x) = | ----- dt
- * | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are approximated by rational functions.
- * For x > 8 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * Ci(x) = f(x) sin(x) - g(x) cos(x)
- * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
- *
- *
- * ACCURACY:
- * Test interval = [0,50].
- * Absolute error, except relative when > 1:
- * arithmetic function # trials peak rms
- * IEEE Si 30000 2.1e-7 4.3e-8
- * IEEE Ci 30000 3.9e-7 2.2e-8
- */
-\f
-/* sindgf.c
- *
- * Circular sine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sindgf();
- *
- * y = sindgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 Q(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-3600 100,000 1.2e-7 3.0e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 2^24 0.0
- *
- */
-\f
-/* cosdgf.c
- *
- * Circular cosine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cosdgf();
- *
- * y = cosdgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 Q(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
- */
-\f
-/* sinf.c
- *
- * Circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sinf();
- *
- * y = sinf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 Q(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -4096,+4096 100,000 1.2e-7 3.0e-8
- * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 2^24 0.0
- *
- * Partial loss of accuracy begins to occur at x = 2^13
- * = 8192. Results may be meaningless for x >= 2^24
- * The routine as implemented flags a TLOSS error
- * for x >= 2^24 and returns 0.0.
- */
-\f
-/* cosf.c
- *
- * Circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cosf();
- *
- * y = cosf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 Q(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
- */
-\f
-/* sinhf.c
- *
- * Hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sinhf();
- *
- * y = sinhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic sine of argument in the range MINLOGF to
- * MAXLOGF.
- *
- * The range is partitioned into two segments. If |x| <= 1, a
- * polynomial approximation is used.
- * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-MAXLOG 100000 1.1e-7 2.9e-8
- *
- */
-\f
-/* spencef.c
- *
- * Dilogarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, spencef();
- *
- * y = spencef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral
- *
- * x
- * -
- * | | log t
- * spence(x) = - | ----- dt
- * | | t - 1
- * -
- * 1
- *
- * for x >= 0. A rational approximation gives the integral in
- * the interval (0.5, 1.5). Transformation formulas for 1/x
- * and 1-x are employed outside the basic expansion range.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,4 30000 4.4e-7 6.3e-8
- *
- *
- */
-\f
-/* sqrtf.c
- *
- * Square root
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sqrtf();
- *
- * y = sqrtf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the square root of x.
- *
- * Range reduction involves isolating the power of two of the
- * argument and using a polynomial approximation to obtain
- * a rough value for the square root. Then Heron's iteration
- * is used three times to converge to an accurate value.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1.e38 100000 8.7e-8 2.9e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sqrtf domain x < 0 0.0
- *
- */
-\f
-/* stdtrf.c
- *
- * Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float t, stdtrf();
- * short k;
- *
- * y = stdtrf( k, t );
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral from minus infinity to t of the Student
- * t distribution with integer k > 0 degrees of freedom:
- *
- * t
- * -
- * | |
- * - | 2 -(k+1)/2
- * | ( (k+1)/2 ) | ( x )
- * ---------------------- | ( 1 + --- ) dx
- * - | ( k )
- * sqrt( k pi ) | ( k/2 ) |
- * | |
- * -
- * -inf.
- *
- * Relation to incomplete beta integral:
- *
- * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
- * where
- * z = k/(k + t**2).
- *
- * For t < -1, this is the method of computation. For higher t,
- * a direct method is derived from integration by parts.
- * Since the function is symmetric about t=0, the area under the
- * right tail of the density is found by calling the function
- * with -t instead of t.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +/- 100 5000 2.3e-5 2.9e-6
- */
-\f
-/* struvef.c
- *
- * Struve function
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, struvef();
- *
- * y = struvef( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the Struve function Hv(x) of order v, argument x.
- * Negative x is rejected unless v is an integer.
- *
- * This module also contains the hypergeometric functions 1F2
- * and 3F0 and a routine for the Bessel function Yv(x) with
- * noninteger v.
- *
- *
- *
- * ACCURACY:
- *
- * v varies from 0 to 10.
- * Absolute error (relative error when |Hv(x)| > 1):
- * arithmetic domain # trials peak rms
- * IEEE -10,10 100000 9.0e-5 4.0e-6
- *
- */
-\f
-/* tandgf.c
- *
- * Circular tangent of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, tandgf();
- *
- * y = tandgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is into intervals of 45 degrees.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-2^24 50000 2.4e-7 4.8e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tanf total loss x > 2^24 0.0
- *
- */
-\f/* cotdgf.c
- *
- * Circular cotangent of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cotdgf();
- *
- * y = cotdgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- * A common routine computes either the tangent or cotangent.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-2^24 50000 2.4e-7 4.8e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 2^24 0.0
- * cot singularity x = 0 MAXNUMF
- *
- */
-\f
-/* tanf.c
- *
- * Circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, tanf();
- *
- * y = tanf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A polynomial approximation
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-4096 100000 3.3e-7 4.5e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tanf total loss x > 2^24 0.0
- *
- */
-\f/* cotf.c
- *
- * Circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cotf();
- *
- * y = cotf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the radian argument x.
- * A common routine computes either the tangent or cotangent.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-4096 100000 3.0e-7 4.5e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 2^24 0.0
- * cot singularity x = 0 MAXNUMF
- *
- */
-\f
-/* tanhf.c
- *
- * Hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, tanhf();
- *
- * y = tanhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic tangent of argument in the range MINLOG to
- * MAXLOG.
- *
- * A polynomial approximation is used for |x| < 0.625.
- * Otherwise,
- *
- * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -2,2 100000 1.3e-7 2.6e-8
- *
- */
-\f
-/* ynf.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, ynf();
- * int n;
- *
- * y = ynf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0() and y1().
- *
- * If n = 0 or 1 the routine for y0 or y1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative when y > 1:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 10000 2.3e-6 3.4e-7
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * yn singularity x = 0 MAXNUMF
- * yn overflow MAXNUMF
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
-\f
- /* zetacf.c
- *
- * Riemann zeta function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, zetacf();
- *
- * y = zetacf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zetac(x) = > k , x > 1,
- * -
- * k=2
- *
- * is related to the Riemann zeta function by
- *
- * Riemann zeta(x) = zetac(x) + 1.
- *
- * Extension of the function definition for x < 1 is implemented.
- * Zero is returned for x > log2(MAXNUM).
- *
- * An overflow error may occur for large negative x, due to the
- * gamma function in the reflection formula.
- *
- * ACCURACY:
- *
- * Tabulated values have full machine accuracy.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,50 30000 5.5e-7 7.5e-8
- *
- *
- */
-\f
-/* zetaf.c
- *
- * Riemann zeta function of two arguments
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, q, y, zetaf();
- *
- * y = zetaf( x, q );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=0
- *
- * where x > 1 and q is not a negative integer or zero.
- * The Euler-Maclaurin summation formula is used to obtain
- * the expansion
- *
- * n
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=1
- *
- * 1-x inf. B x(x+1)...(x+2j)
- * (n+q) 1 - 2j
- * + --------- - ------- + > --------------------
- * x-1 x - x+2j+1
- * 2(n+q) j=1 (2j)! (n+q)
- *
- * where the B2j are Bernoulli numbers. Note that (see zetac.c)
- * zeta(x,1) = zetac(x) + 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,25 10000 6.9e-7 1.0e-7
- *
- * Large arguments may produce underflow in powf(), in which
- * case the results are inaccurate.
- *
- * REFERENCE:
- *
- * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
- * Series, and Products, p. 1073; Academic Press, 1980.
- *
- */
+++ /dev/null
-/* acoshf.c
- *
- * Inverse hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, acoshf();
- *
- * y = acoshf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a polynomial approximation
- *
- * sqrt(z) * P(z)
- *
- * where z = x-1, is used. Otherwise,
- *
- * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,3 100000 1.8e-7 3.9e-8
- * IEEE 1,2000 100000 3.0e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acoshf domain |x| < 1 0.0
- *
- */
-\f
-/* acosh.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision inverse hyperbolic cosine
- * test interval: [1.0, 1.5]
- * trials: 10000
- * peak relative error: 1.7e-7
- * rms relative error: 5.0e-8
- *
- * Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
- */
-#include <math.h>
-extern float LOGE2F;
-
-float sqrtf( float );
-float logf( float );
-
-float acoshf( float xx )
-{
-float x, z;
-
-x = xx;
-if( x < 1.0 )
- {
- mtherr( "acoshf", DOMAIN );
- return(0.0);
- }
-
-if( x > 1500.0 )
- return( logf(x) + LOGE2F );
-
-z = x - 1.0;
-
-if( z < 0.5 )
- {
- z =
- (((( 1.7596881071E-3 * z
- - 7.5272886713E-3) * z
- + 2.6454905019E-2) * z
- - 1.1784741703E-1) * z
- + 1.4142135263E0) * sqrtf( z );
- }
-else
- {
- z = sqrtf( z*(x+1.0) );
- z = logf(x + z);
- }
-return( z );
-}
+++ /dev/null
-/* airy.c
- *
- * Airy function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, ai, aip, bi, bip;
- * int airyf();
- *
- * airyf( x, _&ai, _&aip, _&bi, _&bip );
- *
- *
- *
- * DESCRIPTION:
- *
- * Solution of the differential equation
- *
- * y"(x) = xy.
- *
- * The function returns the two independent solutions Ai, Bi
- * and their first derivatives Ai'(x), Bi'(x).
- *
- * Evaluation is by power series summation for small x,
- * by rational minimax approximations for large x.
- *
- *
- *
- * ACCURACY:
- * Error criterion is absolute when function <= 1, relative
- * when function > 1, except * denotes relative error criterion.
- * For large negative x, the absolute error increases as x^1.5.
- * For large positive x, the relative error increases as x^1.5.
- *
- * Arithmetic domain function # trials peak rms
- * IEEE -10, 0 Ai 50000 7.0e-7 1.2e-7
- * IEEE 0, 10 Ai 50000 9.9e-6* 6.8e-7*
- * IEEE -10, 0 Ai' 50000 2.4e-6 3.5e-7
- * IEEE 0, 10 Ai' 50000 8.7e-6* 6.2e-7*
- * IEEE -10, 10 Bi 100000 2.2e-6 2.6e-7
- * IEEE -10, 10 Bi' 50000 2.2e-6 3.5e-7
- *
- */
-\f/* airy.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-static float c1 = 0.35502805388781723926;
-static float c2 = 0.258819403792806798405;
-static float sqrt3 = 1.732050807568877293527;
-static float sqpii = 5.64189583547756286948E-1;
-extern float PIF;
-
-extern float MAXNUMF, MACHEPF;
-#define MAXAIRY 25.77
-
-/* Note, these expansions are for double precision accuracy;
- * they have not yet been redesigned for single precision.
- */
-static float AN[8] = {
- 3.46538101525629032477e-1,
- 1.20075952739645805542e1,
- 7.62796053615234516538e1,
- 1.68089224934630576269e2,
- 1.59756391350164413639e2,
- 7.05360906840444183113e1,
- 1.40264691163389668864e1,
- 9.99999999999999995305e-1,
-};
-static float AD[8] = {
- 5.67594532638770212846e-1,
- 1.47562562584847203173e1,
- 8.45138970141474626562e1,
- 1.77318088145400459522e2,
- 1.64234692871529701831e2,
- 7.14778400825575695274e1,
- 1.40959135607834029598e1,
- 1.00000000000000000470e0,
-};
-
-
-static float APN[8] = {
- 6.13759184814035759225e-1,
- 1.47454670787755323881e1,
- 8.20584123476060982430e1,
- 1.71184781360976385540e2,
- 1.59317847137141783523e2,
- 6.99778599330103016170e1,
- 1.39470856980481566958e1,
- 1.00000000000000000550e0,
-};
-static float APD[8] = {
- 3.34203677749736953049e-1,
- 1.11810297306158156705e1,
- 7.11727352147859965283e1,
- 1.58778084372838313640e2,
- 1.53206427475809220834e2,
- 6.86752304592780337944e1,
- 1.38498634758259442477e1,
- 9.99999999999999994502e-1,
-};
-
-static float BN16[5] = {
--2.53240795869364152689e-1,
- 5.75285167332467384228e-1,
--3.29907036873225371650e-1,
- 6.44404068948199951727e-2,
--3.82519546641336734394e-3,
-};
-static float BD16[5] = {
-/* 1.00000000000000000000e0,*/
--7.15685095054035237902e0,
- 1.06039580715664694291e1,
--5.23246636471251500874e0,
- 9.57395864378383833152e-1,
--5.50828147163549611107e-2,
-};
-
-static float BPPN[5] = {
- 4.65461162774651610328e-1,
--1.08992173800493920734e0,
- 6.38800117371827987759e-1,
--1.26844349553102907034e-1,
- 7.62487844342109852105e-3,
-};
-static float BPPD[5] = {
-/* 1.00000000000000000000e0,*/
--8.70622787633159124240e0,
- 1.38993162704553213172e1,
--7.14116144616431159572e0,
- 1.34008595960680518666e0,
--7.84273211323341930448e-2,
-};
-
-static float AFN[9] = {
--1.31696323418331795333e-1,
--6.26456544431912369773e-1,
--6.93158036036933542233e-1,
--2.79779981545119124951e-1,
--4.91900132609500318020e-2,
--4.06265923594885404393e-3,
--1.59276496239262096340e-4,
--2.77649108155232920844e-6,
--1.67787698489114633780e-8,
-};
-static float AFD[9] = {
-/* 1.00000000000000000000e0,*/
- 1.33560420706553243746e1,
- 3.26825032795224613948e1,
- 2.67367040941499554804e1,
- 9.18707402907259625840e0,
- 1.47529146771666414581e0,
- 1.15687173795188044134e-1,
- 4.40291641615211203805e-3,
- 7.54720348287414296618e-5,
- 4.51850092970580378464e-7,
-};
-
-static float AGN[11] = {
- 1.97339932091685679179e-2,
- 3.91103029615688277255e-1,
- 1.06579897599595591108e0,
- 9.39169229816650230044e-1,
- 3.51465656105547619242e-1,
- 6.33888919628925490927e-2,
- 5.85804113048388458567e-3,
- 2.82851600836737019778e-4,
- 6.98793669997260967291e-6,
- 8.11789239554389293311e-8,
- 3.41551784765923618484e-10,
-};
-static float AGD[10] = {
-/* 1.00000000000000000000e0,*/
- 9.30892908077441974853e0,
- 1.98352928718312140417e1,
- 1.55646628932864612953e1,
- 5.47686069422975497931e0,
- 9.54293611618961883998e-1,
- 8.64580826352392193095e-2,
- 4.12656523824222607191e-3,
- 1.01259085116509135510e-4,
- 1.17166733214413521882e-6,
- 4.91834570062930015649e-9,
-};
-
-static float APFN[9] = {
- 1.85365624022535566142e-1,
- 8.86712188052584095637e-1,
- 9.87391981747398547272e-1,
- 4.01241082318003734092e-1,
- 7.10304926289631174579e-2,
- 5.90618657995661810071e-3,
- 2.33051409401776799569e-4,
- 4.08718778289035454598e-6,
- 2.48379932900442457853e-8,
-};
-static float APFD[9] = {
-/* 1.00000000000000000000e0,*/
- 1.47345854687502542552e1,
- 3.75423933435489594466e1,
- 3.14657751203046424330e1,
- 1.09969125207298778536e1,
- 1.78885054766999417817e0,
- 1.41733275753662636873e-1,
- 5.44066067017226003627e-3,
- 9.39421290654511171663e-5,
- 5.65978713036027009243e-7,
-};
-
-static float APGN[11] = {
--3.55615429033082288335e-2,
--6.37311518129435504426e-1,
--1.70856738884312371053e0,
--1.50221872117316635393e0,
--5.63606665822102676611e-1,
--1.02101031120216891789e-1,
--9.48396695961445269093e-3,
--4.60325307486780994357e-4,
--1.14300836484517375919e-5,
--1.33415518685547420648e-7,
--5.63803833958893494476e-10,
-};
-static float APGD[11] = {
-/* 1.00000000000000000000e0,*/
- 9.85865801696130355144e0,
- 2.16401867356585941885e1,
- 1.73130776389749389525e1,
- 6.17872175280828766327e0,
- 1.08848694396321495475e0,
- 9.95005543440888479402e-2,
- 4.78468199683886610842e-3,
- 1.18159633322838625562e-4,
- 1.37480673554219441465e-6,
- 5.79912514929147598821e-9,
-};
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-float polevlf(float, float *, int);
-float p1evlf(float, float *, int);
-float sinf(float), cosf(float), expf(float), sqrtf(float);
-
-int airyf( float xx, float *ai, float *aip, float *bi, float *bip )
-{
-float x, z, zz, t, f, g, uf, ug, k, zeta, theta;
-int domflg;
-
-x = xx;
-domflg = 0;
-if( x > MAXAIRY )
- {
- *ai = 0;
- *aip = 0;
- *bi = MAXNUMF;
- *bip = MAXNUMF;
- return(-1);
- }
-
-if( x < -2.09 )
- {
- domflg = 15;
- t = sqrtf(-x);
- zeta = -2.0 * x * t / 3.0;
- t = sqrtf(t);
- k = sqpii / t;
- z = 1.0/zeta;
- zz = z * z;
- uf = 1.0 + zz * polevlf( zz, AFN, 8 ) / p1evlf( zz, AFD, 9 );
- ug = z * polevlf( zz, AGN, 10 ) / p1evlf( zz, AGD, 10 );
- theta = zeta + 0.25 * PIF;
- f = sinf( theta );
- g = cosf( theta );
- *ai = k * (f * uf - g * ug);
- *bi = k * (g * uf + f * ug);
- uf = 1.0 + zz * polevlf( zz, APFN, 8 ) / p1evlf( zz, APFD, 9 );
- ug = z * polevlf( zz, APGN, 10 ) / p1evlf( zz, APGD, 10 );
- k = sqpii * t;
- *aip = -k * (g * uf + f * ug);
- *bip = k * (f * uf - g * ug);
- return(0);
- }
-
-if( x >= 2.09 ) /* cbrt(9) */
- {
- domflg = 5;
- t = sqrtf(x);
- zeta = 2.0 * x * t / 3.0;
- g = expf( zeta );
- t = sqrtf(t);
- k = 2.0 * t * g;
- z = 1.0/zeta;
- f = polevlf( z, AN, 7 ) / polevlf( z, AD, 7 );
- *ai = sqpii * f / k;
- k = -0.5 * sqpii * t / g;
- f = polevlf( z, APN, 7 ) / polevlf( z, APD, 7 );
- *aip = f * k;
-
- if( x > 8.3203353 ) /* zeta > 16 */
- {
- f = z * polevlf( z, BN16, 4 ) / p1evlf( z, BD16, 5 );
- k = sqpii * g;
- *bi = k * (1.0 + f) / t;
- f = z * polevlf( z, BPPN, 4 ) / p1evlf( z, BPPD, 5 );
- *bip = k * t * (1.0 + f);
- return(0);
- }
- }
-
-f = 1.0;
-g = x;
-t = 1.0;
-uf = 1.0;
-ug = x;
-k = 1.0;
-z = x * x * x;
-while( t > MACHEPF )
- {
- uf *= z;
- k += 1.0;
- uf /=k;
- ug *= z;
- k += 1.0;
- ug /=k;
- uf /=k;
- f += uf;
- k += 1.0;
- ug /=k;
- g += ug;
- t = fabsf(uf/f);
- }
-uf = c1 * f;
-ug = c2 * g;
-if( (domflg & 1) == 0 )
- *ai = uf - ug;
-if( (domflg & 2) == 0 )
- *bi = sqrt3 * (uf + ug);
-
-/* the deriviative of ai */
-k = 4.0;
-uf = x * x/2.0;
-ug = z/3.0;
-f = uf;
-g = 1.0 + ug;
-uf /= 3.0;
-t = 1.0;
-
-while( t > MACHEPF )
- {
- uf *= z;
- ug /=k;
- k += 1.0;
- ug *= z;
- uf /=k;
- f += uf;
- k += 1.0;
- ug /=k;
- uf /=k;
- g += ug;
- k += 1.0;
- t = fabsf(ug/g);
- }
-
-uf = c1 * f;
-ug = c2 * g;
-if( (domflg & 4) == 0 )
- *aip = uf - ug;
-if( (domflg & 8) == 0 )
- *bip = sqrt3 * (uf + ug);
-return(0);
-}
+++ /dev/null
-/* asinf.c
- *
- * Inverse circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, asinf();
- *
- * y = asinf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
- *
- * A polynomial of the form x + x**3 P(x**2)
- * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
- * transformed by the identity
- *
- * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 100000 2.5e-7 5.0e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asinf domain |x| > 1 0.0
- *
- */
-\f/* acosf()
- *
- * Inverse circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, acosf();
- *
- * y = acosf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 100000 1.4e-7 4.2e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acosf domain |x| > 1 0.0
- */
-\f
-/* asin.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision circular arcsine
- * test interval: [-0.5, +0.5]
- * trials: 10000
- * peak relative error: 6.7e-8
- * rms relative error: 2.5e-8
- */
-#include <math.h>
-extern float PIF, PIO2F;
-
-float sqrtf( float );
-
-float asinf( float xx )
-{
-float a, x, z;
-int sign, flag;
-
-x = xx;
-
-if( x > 0 )
- {
- sign = 1;
- a = x;
- }
-else
- {
- sign = -1;
- a = -x;
- }
-
-if( a > 1.0 )
- {
- mtherr( "asinf", DOMAIN );
- return( 0.0 );
- }
-
-if( a < 1.0e-4 )
- {
- z = a;
- goto done;
- }
-
-if( a > 0.5 )
- {
- z = 0.5 * (1.0 - a);
- x = sqrtf( z );
- flag = 1;
- }
-else
- {
- x = a;
- z = x * x;
- flag = 0;
- }
-
-z =
-(((( 4.2163199048E-2 * z
- + 2.4181311049E-2) * z
- + 4.5470025998E-2) * z
- + 7.4953002686E-2) * z
- + 1.6666752422E-1) * z * x
- + x;
-
-if( flag != 0 )
- {
- z = z + z;
- z = PIO2F - z;
- }
-done:
-if( sign < 0 )
- z = -z;
-return( z );
-}
-
-
-
-
-float acosf( float x )
-{
-
-if( x < -1.0 )
- goto domerr;
-
-if( x < -0.5)
- return( PIF - 2.0 * asinf( sqrtf(0.5*(1.0+x)) ) );
-
-if( x > 1.0 )
- {
-domerr: mtherr( "acosf", DOMAIN );
- return( 0.0 );
- }
-
-if( x > 0.5 )
- return( 2.0 * asinf( sqrtf(0.5*(1.0-x) ) ) );
-
-return( PIO2F - asinf(x) );
-}
-
+++ /dev/null
-/* asinhf.c
- *
- * Inverse hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, asinhf();
- *
- * y = asinhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic sine of argument.
- *
- * If |x| < 0.5, the function is approximated by a rational
- * form x + x**3 P(x)/Q(x). Otherwise,
- *
- * asinh(x) = log( x + sqrt(1 + x*x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -3,3 100000 2.4e-7 4.1e-8
- *
- */
-\f
-/* asinh.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision inverse hyperbolic sine
- * test interval: [-0.5, +0.5]
- * trials: 10000
- * peak relative error: 8.8e-8
- * rms relative error: 3.2e-8
- */
-#include <math.h>
-extern float LOGE2F;
-
-float logf( float );
-float sqrtf( float );
-
-float asinhf( float xx )
-{
-float x, z;
-
-if( xx < 0 )
- x = -xx;
-else
- x = xx;
-
-if( x > 1500.0 )
- {
- z = logf(x) + LOGE2F;
- goto done;
- }
-z = x * x;
-if( x < 0.5 )
- {
- z =
- ((( 2.0122003309E-2 * z
- - 4.2699340972E-2) * z
- + 7.4847586088E-2) * z
- - 1.6666288134E-1) * z * x
- + x;
- }
-else
- {
- z = sqrtf( z + 1.0 );
- z = logf( x + z );
- }
-done:
-if( xx < 0 )
- z = -z;
-return( z );
-}
-
+++ /dev/null
-/* atanf.c
- *
- * Inverse circular tangent
- * (arctangent)
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, atanf();
- *
- * y = atanf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose tangent
- * is x.
- *
- * Range reduction is from four intervals into the interval
- * from zero to tan( pi/8 ). A polynomial approximates
- * the function in this basic interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 100000 1.9e-7 4.1e-8
- *
- */
-\f/* atan2f()
- *
- * Quadrant correct inverse circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, z, atan2f();
- *
- * z = atan2f( y, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle whose tangent is y/x.
- * Define compile time symbol ANSIC = 1 for ANSI standard,
- * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
- * 0 to 2PI, args (x,y).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 100000 1.9e-7 4.1e-8
- * See atan.c.
- *
- */
-\f
-/* atan.c */
-
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision circular arcsine
- * test interval: [-tan(pi/8), +tan(pi/8)]
- * trials: 10000
- * peak relative error: 7.7e-8
- * rms relative error: 2.9e-8
- */
-#include <math.h>
-extern float PIF, PIO2F, PIO4F;
-
-float atanf( float xx )
-{
-float x, y, z;
-int sign;
-
-x = xx;
-
-/* make argument positive and save the sign */
-if( xx < 0.0 )
- {
- sign = -1;
- x = -xx;
- }
-else
- {
- sign = 1;
- x = xx;
- }
-/* range reduction */
-if( x > 2.414213562373095 ) /* tan 3pi/8 */
- {
- y = PIO2F;
- x = -( 1.0/x );
- }
-
-else if( x > 0.4142135623730950 ) /* tan pi/8 */
- {
- y = PIO4F;
- x = (x-1.0)/(x+1.0);
- }
-else
- y = 0.0;
-
-z = x * x;
-y +=
-((( 8.05374449538e-2 * z
- - 1.38776856032E-1) * z
- + 1.99777106478E-1) * z
- - 3.33329491539E-1) * z * x
- + x;
-
-if( sign < 0 )
- y = -y;
-
-return( y );
-}
-
-
-
-
-float atan2f( float y, float x )
-{
-float z, w;
-int code;
-
-
-code = 0;
-
-if( x < 0.0 )
- code = 2;
-if( y < 0.0 )
- code |= 1;
-
-if( x == 0.0 )
- {
- if( code & 1 )
- {
-#if ANSIC
- return( -PIO2F );
-#else
- return( 3.0*PIO2F );
-#endif
- }
- if( y == 0.0 )
- return( 0.0 );
- return( PIO2F );
- }
-
-if( y == 0.0 )
- {
- if( code & 2 )
- return( PIF );
- return( 0.0 );
- }
-
-
-switch( code )
- {
- default:
-#if ANSIC
- case 0:
- case 1: w = 0.0; break;
- case 2: w = PIF; break;
- case 3: w = -PIF; break;
-#else
- case 0: w = 0.0; break;
- case 1: w = 2.0 * PIF; break;
- case 2:
- case 3: w = PIF; break;
-#endif
- }
-
-z = atanf( y/x );
-
-return( w + z );
-}
-
+++ /dev/null
-/* atanhf.c
- *
- * Inverse hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, atanhf();
- *
- * y = atanhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic tangent of argument in the range
- * MINLOGF to MAXLOGF.
- *
- * If |x| < 0.5, a polynomial approximation is used.
- * Otherwise,
- * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1,1 100000 1.4e-7 3.1e-8
- *
- */
-\f
-/* atanh.c */
-
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright (C) 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision inverse hyperbolic tangent
- * test interval: [-0.5, +0.5]
- * trials: 10000
- * peak relative error: 8.2e-8
- * rms relative error: 3.0e-8
- */
-#include <math.h>
-extern float MAXNUMF;
-
-float logf( float );
-
-float atanhf( float xx )
-{
-float x, z;
-
-x = xx;
-if( x < 0 )
- z = -x;
-else
- z = x;
-if( z >= 1.0 )
- {
- if( x == 1.0 )
- return( MAXNUMF );
- if( x == -1.0 )
- return( -MAXNUMF );
- mtherr( "atanhl", DOMAIN );
- return( MAXNUMF );
- }
-
-if( z < 1.0e-4 )
- return(x);
-
-if( z < 0.5 )
- {
- z = x * x;
- z =
- (((( 1.81740078349E-1 * z
- + 8.24370301058E-2) * z
- + 1.46691431730E-1) * z
- + 1.99782164500E-1) * z
- + 3.33337300303E-1) * z * x
- + x;
- }
-else
- {
- z = 0.5 * logf( (1.0+x)/(1.0-x) );
- }
-return( z );
-}
+++ /dev/null
-/* bdtrf.c
- *
- * Binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, bdtrf();
- *
- * y = bdtrf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the Binomial
- * probability density:
- *
- * k
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error (p varies from 0 to 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,100 2000 6.9e-5 1.1e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrf domain k < 0 0.0
- * n < k
- * x < 0, x > 1
- *
- */
-\f/* bdtrcf()
- *
- * Complemented binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, bdtrcf();
- *
- * y = bdtrcf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 through n of the Binomial
- * probability density:
- *
- * n
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error (p varies from 0 to 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,100 2000 6.0e-5 1.2e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrcf domain x<0, x>1, n<k 0.0
- */
-\f/* bdtrif()
- *
- * Inverse binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, bdtrif();
- *
- * p = bdtrf( k, n, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the event probability p such that the sum of the
- * terms 0 through k of the Binomial probability density
- * is equal to the given cumulative probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relation
- *
- * 1 - p = incbi( n-k, k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error (p varies from 0 to 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,100 2000 3.5e-5 3.3e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrif domain k < 0, n <= k 0.0
- * x < 0, x > 1
- *
- */
-\f
-/* bdtr() */
-
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef ANSIC
-float incbetf(float, float, float), powf(float, float);
-float incbif( float, float, float );
-#else
-float incbetf(), powf(), incbif();
-#endif
-
-float bdtrcf( int k, int n, float pp )
-{
-float p, dk, dn;
-
-p = pp;
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- return( 1.0 );
-
-if( n < k )
- {
-domerr:
- mtherr( "bdtrcf", DOMAIN );
- return( 0.0 );
- }
-
-if( k == n )
- return( 0.0 );
-dn = n - k;
-if( k == 0 )
- {
- dk = 1.0 - powf( 1.0-p, dn );
- }
-else
- {
- dk = k + 1;
- dk = incbetf( dk, dn, p );
- }
-return( dk );
-}
-
-
-
-float bdtrf( int k, int n, float pp )
-{
-float p, dk, dn;
-
-p = pp;
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( (k < 0) || (n < k) )
- {
-domerr:
- mtherr( "bdtrf", DOMAIN );
- return( 0.0 );
- }
-
-if( k == n )
- return( 1.0 );
-
-dn = n - k;
-if( k == 0 )
- {
- dk = powf( 1.0-p, dn );
- }
-else
- {
- dk = k + 1;
- dk = incbetf( dn, dk, 1.0 - p );
- }
-return( dk );
-}
-
-
-float bdtrif( int k, int n, float yy )
-{
-float y, dk, dn, p;
-
-y = yy;
-if( (y < 0.0) || (y > 1.0) )
- goto domerr;
-if( (k < 0) || (n <= k) )
- {
-domerr:
- mtherr( "bdtrif", DOMAIN );
- return( 0.0 );
- }
-
-dn = n - k;
-if( k == 0 )
- {
- p = 1.0 - powf( y, 1.0/dn );
- }
-else
- {
- dk = k + 1;
- p = 1.0 - incbif( dn, dk, y );
- }
-return( p );
-}
+++ /dev/null
-/* betaf.c
- *
- * Beta function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, y, betaf();
- *
- * y = betaf( a, b );
- *
- *
- *
- * DESCRIPTION:
- *
- * - -
- * | (a) | (b)
- * beta( a, b ) = -----------.
- * -
- * | (a+b)
- *
- * For large arguments the logarithm of the function is
- * evaluated using lgam(), then exponentiated.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 10000 4.0e-5 6.0e-6
- * IEEE -20,0 10000 4.9e-3 5.4e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * betaf overflow log(beta) > MAXLOG 0.0
- * a or b <0 integer 0.0
- *
- */
-\f
-/* beta.c */
-
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#define MAXGAM 34.84425627277176174
-
-
-extern float MAXLOGF, MAXNUMF;
-extern int sgngamf;
-
-#ifdef ANSIC
-float gammaf(float), lgamf(float), expf(float), floorf(float);
-#else
-float gammaf(), lgamf(), expf(), floorf();
-#endif
-
-float betaf( float aa, float bb )
-{
-float a, b, y;
-int sign;
-
-sign = 1;
-a = aa;
-b = bb;
-if( a <= 0.0 )
- {
- if( a == floorf(a) )
- goto over;
- }
-if( b <= 0.0 )
- {
- if( b == floorf(b) )
- goto over;
- }
-
-
-y = a + b;
-if( fabsf(y) > MAXGAM )
- {
- y = lgamf(y);
- sign *= sgngamf; /* keep track of the sign */
- y = lgamf(b) - y;
- sign *= sgngamf;
- y = lgamf(a) + y;
- sign *= sgngamf;
- if( y > MAXLOGF )
- {
-over:
- mtherr( "betaf", OVERFLOW );
- return( sign * MAXNUMF );
- }
- return( sign * expf(y) );
- }
-
-y = gammaf(y);
-if( y == 0.0 )
- goto over;
-
-if( a > b )
- {
- y = gammaf(a)/y;
- y *= gammaf(b);
- }
-else
- {
- y = gammaf(b)/y;
- y *= gammaf(a);
- }
-
-return(y);
-}
+++ /dev/null
-/* cbrtf.c
- *
- * Cube root
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cbrtf();
- *
- * y = cbrtf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the cube root of the argument, which may be negative.
- *
- * Range reduction involves determining the power of 2 of
- * the argument. A polynomial of degree 2 applied to the
- * mantissa, and multiplication by the cube root of 1, 2, or 4
- * approximates the root to within about 0.1%. Then Newton's
- * iteration is used to converge to an accurate result.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1e38 100000 7.6e-8 2.7e-8
- *
- */
-\f/* cbrt.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-static float CBRT2 = 1.25992104989487316477;
-static float CBRT4 = 1.58740105196819947475;
-
-
-float frexpf(float, int *), ldexpf(float, int);
-
-float cbrtf( float xx )
-{
-int e, rem, sign;
-float x, z;
-
-x = xx;
-if( x == 0 )
- return( 0.0 );
-if( x > 0 )
- sign = 1;
-else
- {
- sign = -1;
- x = -x;
- }
-
-z = x;
-/* extract power of 2, leaving
- * mantissa between 0.5 and 1
- */
-x = frexpf( x, &e );
-
-/* Approximate cube root of number between .5 and 1,
- * peak relative error = 9.2e-6
- */
-x = (((-0.13466110473359520655053 * x
- + 0.54664601366395524503440 ) * x
- - 0.95438224771509446525043 ) * x
- + 1.1399983354717293273738 ) * x
- + 0.40238979564544752126924;
-
-/* exponent divided by 3 */
-if( e >= 0 )
- {
- rem = e;
- e /= 3;
- rem -= 3*e;
- if( rem == 1 )
- x *= CBRT2;
- else if( rem == 2 )
- x *= CBRT4;
- }
-
-
-/* argument less than 1 */
-
-else
- {
- e = -e;
- rem = e;
- e /= 3;
- rem -= 3*e;
- if( rem == 1 )
- x /= CBRT2;
- else if( rem == 2 )
- x /= CBRT4;
- e = -e;
- }
-
-/* multiply by power of 2 */
-x = ldexpf( x, e );
-
-/* Newton iteration */
-x -= ( x - (z/(x*x)) ) * 0.333333333333;
-
-if( sign < 0 )
- x = -x;
-return(x);
-}
+++ /dev/null
-/* chbevlf.c
- *
- * Evaluate Chebyshev series
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * float x, y, coef[N], chebevlf();
- *
- * y = chbevlf( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the series
- *
- * N-1
- * - '
- * y = > coef[i] T (x/2)
- * - i
- * i=0
- *
- * of Chebyshev polynomials Ti at argument x/2.
- *
- * Coefficients are stored in reverse order, i.e. the zero
- * order term is last in the array. Note N is the number of
- * coefficients, not the order.
- *
- * If coefficients are for the interval a to b, x must
- * have been transformed to x -> 2(2x - b - a)/(b-a) before
- * entering the routine. This maps x from (a, b) to (-1, 1),
- * over which the Chebyshev polynomials are defined.
- *
- * If the coefficients are for the inverted interval, in
- * which (a, b) is mapped to (1/b, 1/a), the transformation
- * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
- * this becomes x -> 4a/x - 1.
- *
- *
- *
- * SPEED:
- *
- * Taking advantage of the recurrence properties of the
- * Chebyshev polynomials, the routine requires one more
- * addition per loop than evaluating a nested polynomial of
- * the same degree.
- *
- */
-\f/* chbevl.c */
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1985, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#ifdef ANSIC
-float chbevlf( float x, float *array, int n )
-#else
-float chbevlf( x, array, n )
-float x;
-float *array;
-int n;
-#endif
-{
-float b0, b1, b2, *p;
-int i;
-
-p = array;
-b0 = *p++;
-b1 = 0.0;
-i = n - 1;
-
-do
- {
- b2 = b1;
- b1 = b0;
- b0 = x * b1 - b2 + *p++;
- }
-while( --i );
-
-return( 0.5*(b0-b2) );
-}
+++ /dev/null
-/* chdtrf.c
- *
- * Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float df, x, y, chdtrf();
- *
- * y = chdtrf( df, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the left hand tail (from 0 to x)
- * of the Chi square probability density function with
- * v degrees of freedom.
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 3.2e-5 5.0e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrf domain x < 0 or v < 1 0.0
- */
-\f/* chdtrcf()
- *
- * Complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, chdtrcf();
- *
- * y = chdtrcf( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the right hand tail (from x to
- * infinity) of the Chi square probability density function
- * with v degrees of freedom:
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 2.7e-5 3.2e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrc domain x < 0 or v < 1 0.0
- */
-\f/* chdtrif()
- *
- * Inverse of complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float df, x, y, chdtrif();
- *
- * x = chdtrif( df, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Chi-square argument x such that the integral
- * from x to infinity of the Chi-square density is equal
- * to the given cumulative probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * x/2 = igami( df/2, y );
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 10000 2.2e-5 8.5e-7
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtri domain y < 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* chdtr() */
-
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef ANSIC
-float igamcf(float, float), igamf(float, float), igamif(float, float);
-#else
-float igamcf(), igamf(), igamif();
-#endif
-
-float chdtrcf(float dff, float xx)
-{
-float df, x;
-
-df = dff;
-x = xx;
-
-if( (x < 0.0) || (df < 1.0) )
- {
- mtherr( "chdtrcf", DOMAIN );
- return(0.0);
- }
-return( igamcf( 0.5*df, 0.5*x ) );
-}
-
-
-float chdtrf(float dff, float xx)
-{
-float df, x;
-
-df = dff;
-x = xx;
-if( (x < 0.0) || (df < 1.0) )
- {
- mtherr( "chdtrf", DOMAIN );
- return(0.0);
- }
-return( igamf( 0.5*df, 0.5*x ) );
-}
-
-
-float chdtrif( float dff, float yy )
-{
-float y, df, x;
-
-y = yy;
-df = dff;
-if( (y < 0.0) || (y > 1.0) || (df < 1.0) )
- {
- mtherr( "chdtrif", DOMAIN );
- return(0.0);
- }
-
-x = igamif( 0.5 * df, y );
-return( 2.0 * x );
-}
+++ /dev/null
-/* clogf.c
- *
- * Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clogf();
- * cmplxf z, w;
- *
- * clogf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns complex logarithm to the base e (2.718...) of
- * the complex argument x.
- *
- * If z = x + iy, r = sqrt( x**2 + y**2 ),
- * then
- * w = log(r) + i arctan(y/x).
- *
- * The arctangent ranges from -PI to +PI.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.9e-6 6.2e-8
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 3.1e-7.
- *
- */
-\f
-#include <math.h>
-extern float MAXNUMF, MACHEPF, PIF, PIO2F;
-#ifdef ANSIC
-float cabsf(cmplxf *), sqrtf(float), logf(float), atan2f(float, float);
-float expf(float), sinf(float), cosf(float);
-float coshf(float), sinhf(float), asinf(float);
-float ctansf(cmplxf *), redupif(float);
-void cchshf( float, float *, float * );
-void caddf( cmplxf *, cmplxf *, cmplxf * );
-void csqrtf( cmplxf *, cmplxf * );
-#else
-float cabsf(), sqrtf(), logf(), atan2f();
-float expf(), sinf(), cosf();
-float coshf(), sinhf(), asinf();
-float ctansf(), redupif();
-void cchshf(), csqrtf(), caddf();
-#endif
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-void clogf( z, w )
-register cmplxf *z, *w;
-{
-float p, rr;
-
-/*rr = sqrtf( z->r * z->r + z->i * z->i );*/
-rr = cabsf(z);
-p = logf(rr);
-#if ANSIC
-rr = atan2f( z->i, z->r );
-#else
-rr = atan2f( z->r, z->i );
-if( rr > PIF )
- rr -= PIF + PIF;
-#endif
-w->i = rr;
-w->r = p;
-}
-\f/* cexpf()
- *
- * Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexpf();
- * cmplxf z, w;
- *
- * cexpf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the exponential of the complex argument z
- * into the complex result w.
- *
- * If
- * z = x + iy,
- * r = exp(x),
- *
- * then
- *
- * w = r cos y + i r sin y.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.4e-7 4.5e-8
- *
- */
-\f
-void cexpf( z, w )
-register cmplxf *z, *w;
-{
-float r;
-
-r = expf( z->r );
-w->r = r * cosf( z->i );
-w->i = r * sinf( z->i );
-}
-\f/* csinf()
- *
- * Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csinf();
- * cmplxf z, w;
- *
- * csinf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = sin x cosh y + i cos x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.9e-7 5.5e-8
- *
- */
-\f
-void csinf( z, w )
-register cmplxf *z, *w;
-{
-float ch, sh;
-
-cchshf( z->i, &ch, &sh );
-w->r = sinf( z->r ) * ch;
-w->i = cosf( z->r ) * sh;
-}
-
-
-
-/* calculate cosh and sinh */
-
-void cchshf( float xx, float *c, float *s )
-{
-float x, e, ei;
-
-x = xx;
-if( fabsf(x) <= 0.5f )
- {
- *c = coshf(x);
- *s = sinhf(x);
- }
-else
- {
- e = expf(x);
- ei = 0.5f/e;
- e = 0.5f * e;
- *s = e - ei;
- *c = e + ei;
- }
-}
-
-\f/* ccosf()
- *
- * Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccosf();
- * cmplxf z, w;
- *
- * ccosf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = cos x cosh y - i sin x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.8e-7 5.5e-8
- */
-\f
-void ccosf( z, w )
-register cmplxf *z, *w;
-{
-float ch, sh;
-
-cchshf( z->i, &ch, &sh );
-w->r = cosf( z->r ) * ch;
-w->i = -sinf( z->r ) * sh;
-}
-\f/* ctanf()
- *
- * Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctanf();
- * cmplxf z, w;
- *
- * ctanf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x + i sinh 2y
- * w = --------------------.
- * cos 2x + cosh 2y
- *
- * On the real axis the denominator is zero at odd multiples
- * of PI/2. The denominator is evaluated by its Taylor
- * series near these points.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 3.3e-7 5.1e-8
- */
-\f
-void ctanf( z, w )
-register cmplxf *z, *w;
-{
-float d;
-
-d = cosf( 2.0f * z->r ) + coshf( 2.0f * z->i );
-
-if( fabsf(d) < 0.25f )
- d = ctansf(z);
-
-if( d == 0.0f )
- {
- mtherr( "ctanf", OVERFLOW );
- w->r = MAXNUMF;
- w->i = MAXNUMF;
- return;
- }
-
-w->r = sinf( 2.0f * z->r ) / d;
-w->i = sinhf( 2.0f * z->i ) / d;
-}
-\f/* ccotf()
- *
- * Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccotf();
- * cmplxf z, w;
- *
- * ccotf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x - i sinh 2y
- * w = --------------------.
- * cosh 2y - cos 2x
- *
- * On the real axis, the denominator has zeros at even
- * multiples of PI/2. Near these points it is evaluated
- * by a Taylor series.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 3.6e-7 5.7e-8
- * Also tested by ctan * ccot = 1 + i0.
- */
-\f
-void ccotf( z, w )
-register cmplxf *z, *w;
-{
-float d;
-
-
-d = coshf(2.0f * z->i) - cosf(2.0f * z->r);
-
-if( fabsf(d) < 0.25f )
- d = ctansf(z);
-
-if( d == 0.0f )
- {
- mtherr( "ccotf", OVERFLOW );
- w->r = MAXNUMF;
- w->i = MAXNUMF;
- return;
- }
-
-d = 1.0f/d;
-w->r = sinf( 2.0f * z->r ) * d;
-w->i = -sinhf( 2.0f * z->i ) * d;
-}
-\f
-/* Program to subtract nearest integer multiple of PI */
-/* extended precision value of PI: */
-
-static float DP1 = 3.140625;
-static float DP2 = 9.67502593994140625E-4;
-static float DP3 = 1.509957990978376432E-7;
-
-
-float redupif(float xx)
-{
-float x, t;
-long i;
-
-x = xx;
-t = x/PIF;
-if( t >= 0.0f )
- t += 0.5f;
-else
- t -= 0.5f;
-
-i = t; /* the multiple */
-t = i;
-t = ((x - t * DP1) - t * DP2) - t * DP3;
-return(t);
-}
-\f
-/* Taylor series expansion for cosh(2y) - cos(2x) */
-
-float ctansf(z)
-cmplxf *z;
-{
-float f, x, x2, y, y2, rn, t, d;
-
-x = fabsf( 2.0f * z->r );
-y = fabsf( 2.0f * z->i );
-
-x = redupif(x);
-
-x = x * x;
-y = y * y;
-x2 = 1.0f;
-y2 = 1.0f;
-f = 1.0f;
-rn = 0.0f;
-d = 0.0f;
-do
- {
- rn += 1.0f;
- f *= rn;
- rn += 1.0f;
- f *= rn;
- x2 *= x;
- y2 *= y;
- t = y2 + x2;
- t /= f;
- d += t;
-
- rn += 1.0f;
- f *= rn;
- rn += 1.0f;
- f *= rn;
- x2 *= x;
- y2 *= y;
- t = y2 - x2;
- t /= f;
- d += t;
- }
-while( fabsf(t/d) > MACHEPF );
-return(d);
-}
-\f/* casinf()
- *
- * Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casinf();
- * cmplxf z, w;
- *
- * casinf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- * 2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.1e-5 1.5e-6
- * Larger relative error can be observed for z near zero.
- *
- */
-\f
-void casinf( z, w )
-cmplxf *z, *w;
-{
-float x, y;
-static cmplxf ca, ct, zz, z2;
-/*
-float cn, n;
-static float a, b, s, t, u, v, y2;
-static cmplxf sum;
-*/
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0f )
- {
- if( fabsf(x) > 1.0f )
- {
- w->r = PIO2F;
- w->i = 0.0f;
- mtherr( "casinf", DOMAIN );
- }
- else
- {
- w->r = asinf(x);
- w->i = 0.0f;
- }
- return;
- }
-
-/* Power series expansion */
-/*
-b = cabsf(z);
-if( b < 0.125 )
-{
-z2.r = (x - y) * (x + y);
-z2.i = 2.0 * x * y;
-
-cn = 1.0;
-n = 1.0;
-ca.r = x;
-ca.i = y;
-sum.r = x;
-sum.i = y;
-do
- {
- ct.r = z2.r * ca.r - z2.i * ca.i;
- ct.i = z2.r * ca.i + z2.i * ca.r;
- ca.r = ct.r;
- ca.i = ct.i;
-
- cn *= n;
- n += 1.0;
- cn /= n;
- n += 1.0;
- b = cn/n;
-
- ct.r *= b;
- ct.i *= b;
- sum.r += ct.r;
- sum.i += ct.i;
- b = fabsf(ct.r) + fabsf(ct.i);
- }
-while( b > MACHEPF );
-w->r = sum.r;
-w->i = sum.i;
-return;
-}
-*/
-
-
-ca.r = x;
-ca.i = y;
-
-ct.r = -ca.i; /* iz */
-ct.i = ca.r;
-
- /* sqrt( 1 - z*z) */
-/* cmul( &ca, &ca, &zz ) */
-zz.r = (ca.r - ca.i) * (ca.r + ca.i); /*x * x - y * y */
-zz.i = 2.0f * ca.r * ca.i;
-
-zz.r = 1.0f - zz.r;
-zz.i = -zz.i;
-csqrtf( &zz, &z2 );
-
-caddf( &z2, &ct, &zz );
-clogf( &zz, &zz );
-w->r = zz.i; /* mult by 1/i = -i */
-w->i = -zz.r;
-return;
-}
-\f/* cacosf()
- *
- * Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacosf();
- * cmplxf z, w;
- *
- * cacosf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z = PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 9.2e-6 1.2e-6
- *
- */
-\f
-void cacosf( z, w )
-cmplxf *z, *w;
-{
-
-casinf( z, w );
-w->r = PIO2F - w->r;
-w->i = -w->i;
-}
-\f/* catan()
- *
- * Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catan();
- * cmplxf z, w;
- *
- * catan( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- * 1 ( 2x )
- * Re w = - arctan(-----------) + k PI
- * 2 ( 2 2)
- * (1 - x - y )
- *
- * ( 2 2)
- * 1 (x + (y+1) )
- * Im w = - log(------------)
- * 4 ( 2 2)
- * (x + (y-1) )
- *
- * Where k is an arbitrary integer.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 2.3e-6 5.2e-8
- *
- */
-\f
-void catanf( z, w )
-cmplxf *z, *w;
-{
-float a, t, x, x2, y;
-
-x = z->r;
-y = z->i;
-
-if( (x == 0.0f) && (y > 1.0f) )
- goto ovrf;
-
-x2 = x * x;
-a = 1.0f - x2 - (y * y);
-if( a == 0.0f )
- goto ovrf;
-
-#if ANSIC
-t = 0.5f * atan2f( 2.0f * x, a );
-#else
-t = 0.5f * atan2f( a, 2.0f * x );
-#endif
-w->r = redupif( t );
-
-t = y - 1.0f;
-a = x2 + (t * t);
-if( a == 0.0f )
- goto ovrf;
-
-t = y + 1.0f;
-a = (x2 + (t * t))/a;
-w->i = 0.25f*logf(a);
-return;
-
-ovrf:
-mtherr( "catanf", OVERFLOW );
-w->r = MAXNUMF;
-w->i = MAXNUMF;
-}
+++ /dev/null
-/* cmplxf.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * float r; real part
- * float i; imaginary part
- * }cmplxf;
- *
- * cmplxf *a, *b, *c;
- *
- * caddf( a, b, c ); c = b + a
- * csubf( a, b, c ); c = b - a
- * cmulf( a, b, c ); c = b * a
- * cdivf( a, b, c ); c = b / a
- * cnegf( c ); c = -c
- * cmovf( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
-\f * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * IEEE cadd 30000 5.9e-8 2.6e-8
- * IEEE csub 30000 6.0e-8 2.6e-8
- * IEEE cmul 30000 1.1e-7 3.7e-8
- * IEEE cdiv 30000 2.1e-7 5.7e-8
- */
-\f/* cmplx.c
- * complex number arithmetic
- */
-
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-extern float MAXNUMF, MACHEPF, PIF, PIO2F;
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-#ifdef ANSIC
-float sqrtf(float), frexpf(float, int *);
-float ldexpf(float, int);
-float cabsf(cmplxf *), atan2f(float, float), cosf(float), sinf(float);
-#else
-float sqrtf(), frexpf(), ldexpf();
-float cabsf(), atan2f(), cosf(), sinf();
-#endif
-/*
-typedef struct
- {
- float r;
- float i;
- }cmplxf;
-*/
-cmplxf czerof = {0.0, 0.0};
-extern cmplxf czerof;
-cmplxf conef = {1.0, 0.0};
-extern cmplxf conef;
-
-/* c = b + a */
-
-void caddf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-
-c->r = b->r + a->r;
-c->i = b->i + a->i;
-}
-
-
-/* c = b - a */
-
-void csubf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-
-c->r = b->r - a->r;
-c->i = b->i - a->i;
-}
-
-/* c = b * a */
-
-void cmulf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-register float y;
-
-y = b->r * a->r - b->i * a->i;
-c->i = b->r * a->i + b->i * a->r;
-c->r = y;
-}
-
-
-
-/* c = b / a */
-
-void cdivf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-float y, p, q, w;
-
-
-y = a->r * a->r + a->i * a->i;
-p = b->r * a->r + b->i * a->i;
-q = b->i * a->r - b->r * a->i;
-
-if( y < 1.0f )
- {
- w = MAXNUMF * y;
- if( (fabsf(p) > w) || (fabsf(q) > w) || (y == 0.0f) )
- {
- c->r = MAXNUMF;
- c->i = MAXNUMF;
- mtherr( "cdivf", OVERFLOW );
- return;
- }
- }
-c->r = p/y;
-c->i = q/y;
-}
-
-
-/* b = a */
-
-void cmovf( a, b )
-register short *a, *b;
-{
-int i;
-
-
-i = 8;
-do
- *b++ = *a++;
-while( --i );
-}
-
-
-void cnegf( a )
-register cmplxf *a;
-{
-
-a->r = -a->r;
-a->i = -a->i;
-}
-
-/* cabsf()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * float cabsf();
- * cmplxf z;
- * float a;
- *
- * a = cabsf( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.2e-7 3.4e-8
- */
-\f
-
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/*
-typedef struct
- {
- float r;
- float i;
- }cmplxf;
-*/
-/* square root of max and min numbers */
-#define SMAX 1.3043817825332782216E+19
-#define SMIN 7.6664670834168704053E-20
-#define PREC 12
-#define MAXEXPF 128
-
-
-#define SMAXT (2.0f * SMAX)
-#define SMINT (0.5f * SMIN)
-
-float cabsf( z )
-register cmplxf *z;
-{
-float x, y, b, re, im;
-int ex, ey, e;
-
-re = fabsf( z->r );
-im = fabsf( z->i );
-
-if( re == 0.0f )
- {
- return( im );
- }
-if( im == 0.0f )
- {
- return( re );
- }
-
-/* Get the exponents of the numbers */
-x = frexpf( re, &ex );
-y = frexpf( im, &ey );
-
-/* Check if one number is tiny compared to the other */
-e = ex - ey;
-if( e > PREC )
- return( re );
-if( e < -PREC )
- return( im );
-
-/* Find approximate exponent e of the geometric mean. */
-e = (ex + ey) >> 1;
-
-/* Rescale so mean is about 1 */
-x = ldexpf( re, -e );
-y = ldexpf( im, -e );
-
-/* Hypotenuse of the right triangle */
-b = sqrtf( x * x + y * y );
-
-/* Compute the exponent of the answer. */
-y = frexpf( b, &ey );
-ey = e + ey;
-
-/* Check it for overflow and underflow. */
-if( ey > MAXEXPF )
- {
- mtherr( "cabsf", OVERFLOW );
- return( MAXNUMF );
- }
-if( ey < -MAXEXPF )
- return(0.0f);
-
-/* Undo the scaling */
-b = ldexpf( b, e );
-return( b );
-}
-\f/* csqrtf()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrtf();
- * cmplxf z, w;
- *
- * csqrtf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The solution
- * reported is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 100000 1.8e-7 4.2e-8
- *
- */
-\f
-
-void csqrtf( z, w )
-cmplxf *z, *w;
-{
-cmplxf q, s;
-float x, y, r, t;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0f )
- {
- if( x < 0.0f )
- {
- w->r = 0.0f;
- w->i = sqrtf(-x);
- return;
- }
- else
- {
- w->r = sqrtf(x);
- w->i = 0.0f;
- return;
- }
- }
-
-if( x == 0.0f )
- {
- r = fabsf(y);
- r = sqrtf(0.5f*r);
- if( y > 0 )
- w->r = r;
- else
- w->r = -r;
- w->i = r;
- return;
- }
-
-/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
- * The relative error in the first term is approximately y^2/12x^2 .
- */
-if( (fabsf(y) < fabsf(0.015f*x))
- && (x > 0) )
- {
- t = 0.25f*y*(y/x);
- }
-else
- {
- r = cabsf(z);
- t = 0.5f*(r - x);
- }
-
-r = sqrtf(t);
-q.i = r;
-q.r = 0.5f*y/r;
-
-/* Heron iteration in complex arithmetic:
- * q = (q + z/q)/2
- */
-cdivf( &q, z, &s );
-caddf( &q, &s, w );
-w->r *= 0.5f;
-w->i *= 0.5f;
-}
-
+++ /dev/null
-
-#ifdef DEC
-/* MAXNUMF = 2^127 * (1 - 2^-24) */
-float MAXNUMF = 1.7014117331926442990585209174225846272e38;
-float MAXLOGF = 88.02969187150841;
-float MINLOGF = -88.7228391116729996; /* log(2^-128) */
-#else
-/* MAXNUMF = 2^128 * (1 - 2^-24) */
-float MAXNUMF = 3.4028234663852885981170418348451692544e38;
-float MAXLOGF = 88.72283905206835;
-float MINLOGF = -103.278929903431851103; /* log(2^-149) */
-#endif
-
-float LOG2EF = 1.44269504088896341;
-float LOGE2F = 0.693147180559945309;
-float SQRTHF = 0.707106781186547524;
-float PIF = 3.141592653589793238;
-float PIO2F = 1.5707963267948966192;
-float PIO4F = 0.7853981633974483096;
-float MACHEPF = 5.9604644775390625E-8;
+++ /dev/null
-/* coshf.c
- *
- * Hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, coshf();
- *
- * y = coshf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic cosine of argument in the range MINLOGF to
- * MAXLOGF.
- *
- * cosh(x) = ( exp(x) + exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-MAXLOGF 100000 1.2e-7 2.8e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * coshf overflow |x| > MAXLOGF MAXNUMF
- *
- *
- */
-\f
-/* cosh.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1985, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern float MAXLOGF, MAXNUMF;
-
-float expf(float);
-
-float coshf(float xx)
-{
-float x, y;
-
-x = xx;
-if( x < 0 )
- x = -x;
-if( x > MAXLOGF )
- {
- mtherr( "coshf", OVERFLOW );
- return( MAXNUMF );
- }
-y = expf(x);
-y = y + 1.0/y;
-return( 0.5*y );
-}
+++ /dev/null
-/* dawsnf.c
- *
- * Dawson's Integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, dawsnf();
- *
- * y = dawsnf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- * x
- * -
- * 2 | | 2
- * dawsn(x) = exp( -x ) | exp( t ) dt
- * | |
- * -
- * 0
- *
- * Three different rational approximations are employed, for
- * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10 50000 4.4e-7 6.3e-8
- *
- *
- */
-\f
-/* dawsn.c */
-
-
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-/* Dawson's integral, interval 0 to 3.25 */
-static float AN[10] = {
- 1.13681498971755972054E-11,
- 8.49262267667473811108E-10,
- 1.94434204175553054283E-8,
- 9.53151741254484363489E-7,
- 3.07828309874913200438E-6,
- 3.52513368520288738649E-4,
--8.50149846724410912031E-4,
- 4.22618223005546594270E-2,
--9.17480371773452345351E-2,
- 9.99999999999999994612E-1,
-};
-static float AD[11] = {
- 2.40372073066762605484E-11,
- 1.48864681368493396752E-9,
- 5.21265281010541664570E-8,
- 1.27258478273186970203E-6,
- 2.32490249820789513991E-5,
- 3.25524741826057911661E-4,
- 3.48805814657162590916E-3,
- 2.79448531198828973716E-2,
- 1.58874241960120565368E-1,
- 5.74918629489320327824E-1,
- 1.00000000000000000539E0,
-};
-
-/* interval 3.25 to 6.25 */
-static float BN[11] = {
- 5.08955156417900903354E-1,
--2.44754418142697847934E-1,
- 9.41512335303534411857E-2,
--2.18711255142039025206E-2,
- 3.66207612329569181322E-3,
--4.23209114460388756528E-4,
- 3.59641304793896631888E-5,
--2.14640351719968974225E-6,
- 9.10010780076391431042E-8,
--2.40274520828250956942E-9,
- 3.59233385440928410398E-11,
-};
-static float BD[10] = {
-/* 1.00000000000000000000E0,*/
--6.31839869873368190192E-1,
- 2.36706788228248691528E-1,
--5.31806367003223277662E-2,
- 8.48041718586295374409E-3,
--9.47996768486665330168E-4,
- 7.81025592944552338085E-5,
--4.55875153252442634831E-6,
- 1.89100358111421846170E-7,
--4.91324691331920606875E-9,
- 7.18466403235734541950E-11,
-};
-
-/* 6.25 to infinity */
-static float CN[5] = {
--5.90592860534773254987E-1,
- 6.29235242724368800674E-1,
--1.72858975380388136411E-1,
- 1.64837047825189632310E-2,
--4.86827613020462700845E-4,
-};
-static float CD[5] = {
-/* 1.00000000000000000000E0,*/
--2.69820057197544900361E0,
- 1.73270799045947845857E0,
--3.93708582281939493482E-1,
- 3.44278924041233391079E-2,
--9.73655226040941223894E-4,
-};
-
-
-extern float PIF, MACHEPF;
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-#ifdef ANSIC
-float polevlf(float, float *, int);
-float p1evlf(float, float *, int);
-#else
-float polevlf(), p1evlf();
-#endif
-
-float dawsnf( float xxx )
-{
-float xx, x, y;
-int sign;
-
-xx = xxx;
-sign = 1;
-if( xx < 0.0 )
- {
- sign = -1;
- xx = -xx;
- }
-
-if( xx < 3.25 )
- {
- x = xx*xx;
- y = xx * polevlf( x, AN, 9 )/polevlf( x, AD, 10 );
- return( sign * y );
- }
-
-
-x = 1.0/(xx*xx);
-
-if( xx < 6.25 )
- {
- y = 1.0/xx + x * polevlf( x, BN, 10) / (p1evlf( x, BD, 10) * xx);
- return( sign * 0.5 * y );
- }
-
-
-if( xx > 1.0e9 )
- return( (sign * 0.5)/xx );
-
-/* 6.25 to infinity */
-y = 1.0/xx + x * polevlf( x, CN, 4) / (p1evlf( x, CD, 5) * xx);
-return( sign * 0.5 * y );
-}
+++ /dev/null
-/* ellief.c
- *
- * Incomplete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float phi, m, y, ellief();
- *
- * y = ellief( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * phi
- * -
- * | |
- * | 2
- * E(phi\m) = | sqrt( 1 - m sin t ) dt
- * |
- * | |
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random arguments with phi in [0, 2] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,2 10000 4.5e-7 7.4e-8
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Incomplete elliptic integral of second kind */
-
-#include <math.h>
-
-extern float PIF, PIO2F, MACHEPF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float sqrtf(float), logf(float), sinf(float), tanf(float), atanf(float);
-float ellpef(float), ellpkf(float);
-#else
-float sqrtf(), logf(), sinf(), tanf(), atanf();
-float ellpef(), ellpkf();
-#endif
-
-
-float ellief( float phia, float ma )
-{
-float phi, m, a, b, c, e, temp;
-float lphi, t;
-int d, mod;
-
-phi = phia;
-m = ma;
-if( m == 0.0 )
- return( phi );
-if( m == 1.0 )
- return( sinf(phi) );
-lphi = phi;
-if( lphi < 0.0 )
- lphi = -lphi;
-a = 1.0;
-b = 1.0 - m;
-b = sqrtf(b);
-c = sqrtf(m);
-d = 1;
-e = 0.0;
-t = tanf( lphi );
-mod = (lphi + PIO2F)/PIF;
-
-while( fabsf(c/a) > MACHEPF )
- {
- temp = b/a;
- lphi = lphi + atanf(t*temp) + mod * PIF;
- mod = (lphi + PIO2F)/PIF;
- t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
- c = 0.5 * ( a - b );
- temp = sqrtf( a * b );
- a = 0.5 * ( a + b );
- b = temp;
- d += d;
- e += c * sinf(lphi);
- }
-
-b = 1.0 - m;
-temp = ellpef(b)/ellpkf(b);
-temp *= (atanf(t) + mod * PIF)/(d * a);
-temp += e;
-if( phi < 0.0 )
- temp = -temp;
-return( temp );
-}
+++ /dev/null
-/* ellikf.c
- *
- * Incomplete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float phi, m, y, ellikf();
- *
- * y = ellikf( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * phi
- * -
- * | |
- * | dt
- * F(phi\m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points with phi in [0, 2] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,2 10000 2.9e-7 5.8e-8
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Incomplete elliptic integral of first kind */
-
-#include <math.h>
-extern float PIF, PIO2F, MACHEPF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float sqrtf(float), logf(float), sinf(float), tanf(float), atanf(float);
-#else
-float sqrtf(), logf(), sinf(), tanf(), atanf();
-#endif
-
-
-float ellikf( float phia, float ma )
-{
-float phi, m, a, b, c, temp;
-float t;
-int d, mod, sign;
-
-phi = phia;
-m = ma;
-if( m == 0.0 )
- return( phi );
-if( phi < 0.0 )
- {
- phi = -phi;
- sign = -1;
- }
-else
- sign = 0;
-a = 1.0;
-b = 1.0 - m;
-if( b == 0.0 )
- return( logf( tanf( 0.5*(PIO2F + phi) ) ) );
-b = sqrtf(b);
-c = sqrtf(m);
-d = 1;
-t = tanf( phi );
-mod = (phi + PIO2F)/PIF;
-
-while( fabsf(c/a) > MACHEPF )
- {
- temp = b/a;
- phi = phi + atanf(t*temp) + mod * PIF;
- mod = (phi + PIO2F)/PIF;
- t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
- c = ( a - b )/2.0;
- temp = sqrtf( a * b );
- a = ( a + b )/2.0;
- b = temp;
- d += d;
- }
-
-temp = (atanf(t) + mod * PIF)/(d * a);
-if( sign < 0 )
- temp = -temp;
-return( temp );
-}
+++ /dev/null
-/* ellpef.c
- *
- * Complete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float m1, y, ellpef();
- *
- * y = ellpef( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * pi/2
- * -
- * | | 2
- * E(m) = | sqrt( 1 - m sin t ) dt
- * | |
- * -
- * 0
- *
- * Where m = 1 - m1, using the approximation
- *
- * P(x) - x log x Q(x).
- *
- * Though there are no singularities, the argument m1 is used
- * rather than m for compatibility with ellpk().
- *
- * E(1) = 1; E(0) = pi/2.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 1 30000 1.1e-7 3.9e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpef domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpe.c */
-
-/* Elliptic integral of second kind */
-
-/*
-Cephes Math Library, Release 2.1: February, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-
-static float P[] = {
- 1.53552577301013293365E-4,
- 2.50888492163602060990E-3,
- 8.68786816565889628429E-3,
- 1.07350949056076193403E-2,
- 7.77395492516787092951E-3,
- 7.58395289413514708519E-3,
- 1.15688436810574127319E-2,
- 2.18317996015557253103E-2,
- 5.68051945617860553470E-2,
- 4.43147180560990850618E-1,
- 1.00000000000000000299E0
-};
-static float Q[] = {
- 3.27954898576485872656E-5,
- 1.00962792679356715133E-3,
- 6.50609489976927491433E-3,
- 1.68862163993311317300E-2,
- 2.61769742454493659583E-2,
- 3.34833904888224918614E-2,
- 4.27180926518931511717E-2,
- 5.85936634471101055642E-2,
- 9.37499997197644278445E-2,
- 2.49999999999888314361E-1
-};
-
-float polevlf(float, float *, int), logf(float);
-float ellpef( float xx)
-{
-float x;
-
-x = xx;
-if( (x <= 0.0) || (x > 1.0) )
- {
- if( x == 0.0 )
- return( 1.0 );
- mtherr( "ellpef", DOMAIN );
- return( 0.0 );
- }
-return( polevlf(x,P,10) - logf(x) * (x * polevlf(x,Q,9)) );
-}
+++ /dev/null
-/* ellpjf.c
- *
- * Jacobian Elliptic Functions
- *
- *
- *
- * SYNOPSIS:
- *
- * float u, m, sn, cn, dn, phi;
- * int ellpj();
- *
- * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
- * and dn(u|m) of parameter m between 0 and 1, and real
- * argument u.
- *
- * These functions are periodic, with quarter-period on the
- * real axis equal to the complete elliptic integral
- * ellpk(1.0-m).
- *
- * Relation to incomplete elliptic integral:
- * If u = ellik(phi,m), then sn(u|m) = sin(phi),
- * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
- *
- * Computation is by means of the arithmetic-geometric mean
- * algorithm, except when m is within 1e-9 of 0 or 1. In the
- * latter case with m close to 1, the approximation applies
- * only for phi < pi/2.
- *
- * ACCURACY:
- *
- * Tested at random points with u between 0 and 10, m between
- * 0 and 1.
- *
- * Absolute error (* = relative error):
- * arithmetic function # trials peak rms
- * IEEE sn 10000 1.7e-6 2.2e-7
- * IEEE cn 10000 1.6e-6 2.2e-7
- * IEEE dn 10000 1.4e-3 1.9e-5
- * IEEE phi 10000 3.9e-7* 6.7e-8*
- *
- * Peak error observed in consistency check using addition
- * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
- * the above relation to the incomplete elliptic integral.
- * Accuracy deteriorates when u is large.
- *
- */
-\f
-/* ellpj.c */
-
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern float PIO2F, MACHEPF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float sqrtf(float), sinf(float), cosf(float), asinf(float), tanhf(float);
-float sinhf(float), coshf(float), atanf(float), expf(float);
-#else
-float sqrtf(), sinf(), cosf(), asinf(), tanhf();
-float sinhf(), coshf(), atanf(), expf();
-#endif
-
-int ellpjf( float uu, float mm,
- float *sn, float *cn, float *dn, float *ph )
-{
-float u, m, ai, b, phi, t, twon;
-float a[10], c[10];
-int i;
-
-u = uu;
-m = mm;
-/* Check for special cases */
-
-if( m < 0.0 || m > 1.0 )
- {
- mtherr( "ellpjf", DOMAIN );
- return(-1);
- }
-if( m < 1.0e-5 )
- {
- t = sinf(u);
- b = cosf(u);
- ai = 0.25 * m * (u - t*b);
- *sn = t - ai*b;
- *cn = b + ai*t;
- *ph = u - ai;
- *dn = 1.0 - 0.5*m*t*t;
- return(0);
- }
-
-if( m >= 0.99999 )
- {
- ai = 0.25 * (1.0-m);
- b = coshf(u);
- t = tanhf(u);
- phi = 1.0/b;
- twon = b * sinhf(u);
- *sn = t + ai * (twon - u)/(b*b);
- *ph = 2.0*atanf(expf(u)) - PIO2F + ai*(twon - u)/b;
- ai *= t * phi;
- *cn = phi - ai * (twon - u);
- *dn = phi + ai * (twon + u);
- return(0);
- }
-
-
-/* A. G. M. scale */
-a[0] = 1.0;
-b = sqrtf(1.0 - m);
-c[0] = sqrtf(m);
-twon = 1.0;
-i = 0;
-
-while( fabsf( (c[i]/a[i]) ) > MACHEPF )
- {
- if( i > 8 )
- {
-/* mtherr( "ellpjf", OVERFLOW );*/
- break;
- }
- ai = a[i];
- ++i;
- c[i] = 0.5 * ( ai - b );
- t = sqrtf( ai * b );
- a[i] = 0.5 * ( ai + b );
- b = t;
- twon += twon;
- }
-
-
-/* backward recurrence */
-phi = twon * a[i] * u;
-do
- {
- t = c[i] * sinf(phi) / a[i];
- b = phi;
- phi = 0.5 * (asinf(t) + phi);
- }
-while( --i );
-
-*sn = sinf(phi);
-t = cosf(phi);
-*cn = t;
-*dn = t/cosf(phi-b);
-*ph = phi;
-return(0);
-}
+++ /dev/null
-/* ellpkf.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float m1, y, ellpkf();
- *
- * y = ellpkf( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * pi/2
- * -
- * | |
- * | dt
- * K(m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * where m = 1 - m1, using the approximation
- *
- * P(x) - log x Q(x).
- *
- * The argument m1 is used rather than m so that the logarithmic
- * singularity at m = 1 will be shifted to the origin; this
- * preserves maximum accuracy.
- *
- * K(0) = pi/2.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 30000 1.3e-7 3.4e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpkf domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpk.c */
-
-
-/*
-Cephes Math Library, Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-static float P[] =
-{
- 1.37982864606273237150E-4,
- 2.28025724005875567385E-3,
- 7.97404013220415179367E-3,
- 9.85821379021226008714E-3,
- 6.87489687449949877925E-3,
- 6.18901033637687613229E-3,
- 8.79078273952743772254E-3,
- 1.49380448916805252718E-2,
- 3.08851465246711995998E-2,
- 9.65735902811690126535E-2,
- 1.38629436111989062502E0
-};
-
-static float Q[] =
-{
- 2.94078955048598507511E-5,
- 9.14184723865917226571E-4,
- 5.94058303753167793257E-3,
- 1.54850516649762399335E-2,
- 2.39089602715924892727E-2,
- 3.01204715227604046988E-2,
- 3.73774314173823228969E-2,
- 4.88280347570998239232E-2,
- 7.03124996963957469739E-2,
- 1.24999999999870820058E-1,
- 4.99999999999999999821E-1
-};
-static float C1 = 1.3862943611198906188E0; /* log(4) */
-
-extern float MACHEPF, MAXNUMF;
-
-float polevlf(float, float *, int);
-float p1evlf(float, float *, int);
-float logf(float);
-float ellpkf(float xx)
-{
-float x;
-
-x = xx;
-if( (x < 0.0) || (x > 1.0) )
- {
- mtherr( "ellpkf", DOMAIN );
- return( 0.0 );
- }
-
-if( x > MACHEPF )
- {
- return( polevlf(x,P,10) - logf(x) * polevlf(x,Q,10) );
- }
-else
- {
- if( x == 0.0 )
- {
- mtherr( "ellpkf", SING );
- return( MAXNUMF );
- }
- else
- {
- return( C1 - 0.5 * logf(x) );
- }
- }
-}
+++ /dev/null
-/* exp10f.c
- *
- * Base 10 exponential function
- * (Common antilogarithm)
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, exp10f();
- *
- * y = exp10f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 10 raised to the x power.
- *
- * Range reduction is accomplished by expressing the argument
- * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
- * A polynomial approximates 10**f.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -38,+38 100000 9.8e-8 2.8e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp10 underflow x < -MAXL10 0.0
- * exp10 overflow x > MAXL10 MAXNUM
- *
- * IEEE single arithmetic: MAXL10 = 38.230809449325611792.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-static float P[] = {
- 2.063216740311022E-001,
- 5.420251702225484E-001,
- 1.171292686296281E+000,
- 2.034649854009453E+000,
- 2.650948748208892E+000,
- 2.302585167056758E+000
-};
-
-/*static float LOG102 = 3.01029995663981195214e-1;*/
-static float LOG210 = 3.32192809488736234787e0;
-static float LG102A = 3.00781250000000000000E-1;
-static float LG102B = 2.48745663981195213739E-4;
-static float MAXL10 = 38.230809449325611792;
-
-
-
-
-extern float MAXNUMF;
-
-float floorf(float), ldexpf(float, int), polevlf(float, float *, int);
-
-float exp10f(float xx)
-{
-float x, px, qx;
-short n;
-
-x = xx;
-if( x > MAXL10 )
- {
- mtherr( "exp10f", OVERFLOW );
- return( MAXNUMF );
- }
-
-if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
- {
- mtherr( "exp10f", UNDERFLOW );
- return(0.0);
- }
-
-/* The following is necessary because range reduction blows up: */
-if( x == 0 )
- return(1.0);
-
-/* Express 10**x = 10**g 2**n
- * = 10**g 10**( n log10(2) )
- * = 10**( g + n log10(2) )
- */
-px = x * LOG210;
-qx = floorf( px + 0.5 );
-n = qx;
-x -= qx * LG102A;
-x -= qx * LG102B;
-
-/* rational approximation for exponential
- * of the fractional part:
- * 10**x - 1 = 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
-px = 1.0 + x * polevlf( x, P, 5 );
-
-/* multiply by power of 2 */
-x = ldexpf( px, n );
-
-return(x);
-}
+++ /dev/null
-/* exp2f.c
- *
- * Base 2 exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, exp2f();
- *
- * y = exp2f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 2 raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- * x k f
- * 2 = 2 2.
- *
- * A polynomial approximates 2**x in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -127,+127 100000 1.7e-7 2.8e-8
- *
- *
- * See exp.c for comments on error amplification.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < -MAXL2 0.0
- * exp overflow x > MAXL2 MAXNUMF
- *
- * For IEEE arithmetic, MAXL2 = 127.
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-
-#include <math.h>
-static char fname[] = {"exp2f"};
-
-static float P[] = {
- 1.535336188319500E-004,
- 1.339887440266574E-003,
- 9.618437357674640E-003,
- 5.550332471162809E-002,
- 2.402264791363012E-001,
- 6.931472028550421E-001
-};
-#define MAXL2 127.0
-#define MINL2 -127.0
-
-
-
-extern float MAXNUMF;
-
-float polevlf(float, float *, int), floorf(float), ldexpf(float, int);
-
-float exp2f( float xx )
-{
-float x, px;
-int i0;
-
-x = xx;
-if( x > MAXL2)
- {
- mtherr( fname, OVERFLOW );
- return( MAXNUMF );
- }
-
-if( x < MINL2 )
- {
- mtherr( fname, UNDERFLOW );
- return(0.0);
- }
-
-/* The following is necessary because range reduction blows up: */
-if( x == 0 )
- return(1.0);
-
-/* separate into integer and fractional parts */
-px = floorf(x);
-i0 = px;
-x = x - px;
-
-if( x > 0.5 )
- {
- i0 += 1;
- x -= 1.0;
- }
-
-/* rational approximation
- * exp2(x) = 1.0 + xP(x)
- */
-px = 1.0 + x * polevlf( x, P, 5 );
-
-/* scale by power of 2 */
-px = ldexpf( px, i0 );
-return(px);
-}
+++ /dev/null
-/* expf.c
- *
- * Exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, expf();
- *
- * y = expf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns e (2.71828...) raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- *
- * x k f
- * e = 2 e.
- *
- * A polynomial is used to approximate exp(f)
- * in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +- MAXLOG 100000 1.7e-7 2.8e-8
- *
- *
- * Error amplification in the exponential function can be
- * a serious matter. The error propagation involves
- * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
- * which shows that a 1 lsb error in representing X produces
- * a relative error of X times 1 lsb in the function.
- * While the routine gives an accurate result for arguments
- * that are exactly represented by a double precision
- * computer number, the result contains amplified roundoff
- * error for large arguments not exactly represented.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * expf underflow x < MINLOGF 0.0
- * expf overflow x > MAXLOGF MAXNUMF
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision exponential function.
- * test interval: [-0.5, +0.5]
- * trials: 80000
- * peak relative error: 7.6e-8
- * rms relative error: 2.8e-8
- */
-#include <math.h>
-extern float LOG2EF, MAXLOGF, MINLOGF, MAXNUMF;
-
-static float C1 = 0.693359375;
-static float C2 = -2.12194440e-4;
-
-
-
-float floorf( float ), ldexpf( float, int );
-
-float expf( float xx )
-{
-float x, z;
-int n;
-
-x = xx;
-
-
-if( x > MAXLOGF)
- {
- mtherr( "expf", OVERFLOW );
- return( MAXNUMF );
- }
-
-if( x < MINLOGF )
- {
- mtherr( "expf", UNDERFLOW );
- return(0.0);
- }
-
-/* Express e**x = e**g 2**n
- * = e**g e**( n loge(2) )
- * = e**( g + n loge(2) )
- */
-z = floorf( LOG2EF * x + 0.5 ); /* floor() truncates toward -infinity. */
-x -= z * C1;
-x -= z * C2;
-n = z;
-
-z = x * x;
-/* Theoretical peak relative error in [-0.5, +0.5] is 4.2e-9. */
-z =
-((((( 1.9875691500E-4 * x
- + 1.3981999507E-3) * x
- + 8.3334519073E-3) * x
- + 4.1665795894E-2) * x
- + 1.6666665459E-1) * x
- + 5.0000001201E-1) * z
- + x
- + 1.0;
-
-/* multiply by power of 2 */
-x = ldexpf( z, n );
-
-return( x );
-}
+++ /dev/null
-/* expnf.c
- *
- * Exponential integral En
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * float x, y, expnf();
- *
- * y = expnf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the exponential integral
- *
- * inf.
- * -
- * | | -xt
- * | e
- * E (x) = | ---- dt.
- * n | n
- * | | t
- * -
- * 1
- *
- *
- * Both n and x must be nonnegative.
- *
- * The routine employs either a power series, a continued
- * fraction, or an asymptotic formula depending on the
- * relative values of n and x.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 10000 5.6e-7 1.2e-7
- *
- */
-\f
-/* expn.c */
-
-/* Cephes Math Library Release 2.2: July, 1992
- * Copyright 1985, 1992 by Stephen L. Moshier
- * Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */
-
-#include <math.h>
-
-#define EUL 0.57721566490153286060
-#define BIG 16777216.
-extern float MAXNUMF, MACHEPF, MAXLOGF;
-#ifdef ANSIC
-float powf(float, float), gammaf(float), logf(float), expf(float);
-#else
-float powf(), gammaf(), logf(), expf();
-#endif
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-
-float expnf( int n, float xx )
-{
-float x, ans, r, t, yk, xk;
-float pk, pkm1, pkm2, qk, qkm1, qkm2;
-float psi, z;
-int i, k;
-static float big = BIG;
-
-
-x = xx;
-if( n < 0 )
- goto domerr;
-
-if( x < 0 )
- {
-domerr: mtherr( "expnf", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x > MAXLOGF )
- return( 0.0 );
-
-if( x == 0.0 )
- {
- if( n < 2 )
- {
- mtherr( "expnf", SING );
- return( MAXNUMF );
- }
- else
- return( 1.0/(n-1.0) );
- }
-
-if( n == 0 )
- return( expf(-x)/x );
-\f
-/* expn.c */
-/* Expansion for large n */
-
-if( n > 5000 )
- {
- xk = x + n;
- yk = 1.0 / (xk * xk);
- t = n;
- ans = yk * t * (6.0 * x * x - 8.0 * t * x + t * t);
- ans = yk * (ans + t * (t - 2.0 * x));
- ans = yk * (ans + t);
- ans = (ans + 1.0) * expf( -x ) / xk;
- goto done;
- }
-
-if( x > 1.0 )
- goto cfrac;
-\f
-/* expn.c */
-
-/* Power series expansion */
-
-psi = -EUL - logf(x);
-for( i=1; i<n; i++ )
- psi = psi + 1.0/i;
-
-z = -x;
-xk = 0.0;
-yk = 1.0;
-pk = 1.0 - n;
-if( n == 1 )
- ans = 0.0;
-else
- ans = 1.0/pk;
-do
- {
- xk += 1.0;
- yk *= z/xk;
- pk += 1.0;
- if( pk != 0.0 )
- {
- ans += yk/pk;
- }
- if( ans != 0.0 )
- t = fabsf(yk/ans);
- else
- t = 1.0;
- }
-while( t > MACHEPF );
-k = xk;
-t = n;
-r = n - 1;
-ans = (powf(z, r) * psi / gammaf(t)) - ans;
-goto done;
-\f
-/* expn.c */
-/* continued fraction */
-cfrac:
-k = 1;
-pkm2 = 1.0;
-qkm2 = x;
-pkm1 = 1.0;
-qkm1 = x + n;
-ans = pkm1/qkm1;
-
-do
- {
- k += 1;
- if( k & 1 )
- {
- yk = 1.0;
- xk = n + (k-1)/2;
- }
- else
- {
- yk = x;
- xk = k/2;
- }
- pk = pkm1 * yk + pkm2 * xk;
- qk = qkm1 * yk + qkm2 * xk;
- if( qk != 0 )
- {
- r = pk/qk;
- t = fabsf( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-if( fabsf(pk) > big )
- {
- pkm2 *= MACHEPF;
- pkm1 *= MACHEPF;
- qkm2 *= MACHEPF;
- qkm1 *= MACHEPF;
- }
- }
-while( t > MACHEPF );
-
-ans *= expf( -x );
-
-done:
-return( ans );
-}
-
+++ /dev/null
-/* facf.c
- *
- * Factorial function
- *
- *
- *
- * SYNOPSIS:
- *
- * float y, facf();
- * int i;
- *
- * y = facf( i );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns factorial of i = 1 * 2 * 3 * ... * i.
- * fac(0) = 1.0.
- *
- * Due to machine arithmetic bounds the largest value of
- * i accepted is 33 in single precision arithmetic.
- * Greater values, or negative ones,
- * produce an error message and return MAXNUM.
- *
- *
- *
- * ACCURACY:
- *
- * For i < 34 the values are simply tabulated, and have
- * full machine accuracy.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Factorials of integers from 0 through 33 */
-static float factbl[] = {
- 1.00000000000000000000E0,
- 1.00000000000000000000E0,
- 2.00000000000000000000E0,
- 6.00000000000000000000E0,
- 2.40000000000000000000E1,
- 1.20000000000000000000E2,
- 7.20000000000000000000E2,
- 5.04000000000000000000E3,
- 4.03200000000000000000E4,
- 3.62880000000000000000E5,
- 3.62880000000000000000E6,
- 3.99168000000000000000E7,
- 4.79001600000000000000E8,
- 6.22702080000000000000E9,
- 8.71782912000000000000E10,
- 1.30767436800000000000E12,
- 2.09227898880000000000E13,
- 3.55687428096000000000E14,
- 6.40237370572800000000E15,
- 1.21645100408832000000E17,
- 2.43290200817664000000E18,
- 5.10909421717094400000E19,
- 1.12400072777760768000E21,
- 2.58520167388849766400E22,
- 6.20448401733239439360E23,
- 1.55112100433309859840E25,
- 4.03291461126605635584E26,
- 1.0888869450418352160768E28,
- 3.04888344611713860501504E29,
- 8.841761993739701954543616E30,
- 2.6525285981219105863630848E32,
- 8.22283865417792281772556288E33,
- 2.6313083693369353016721801216E35,
- 8.68331761881188649551819440128E36
-};
-#define MAXFACF 33
-
-extern float MAXNUMF;
-
-#ifdef ANSIC
-float facf( int i )
-#else
-float facf(i)
-int i;
-#endif
-{
-
-if( i < 0 )
- {
- mtherr( "facf", SING );
- return( MAXNUMF );
- }
-
-if( i > MAXFACF )
- {
- mtherr( "facf", OVERFLOW );
- return( MAXNUMF );
- }
-
-/* Get answer from table for small i. */
-return( factbl[i] );
-}
+++ /dev/null
-/* fdtrf.c
- *
- * F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * float x, y, fdtrf();
- *
- * y = fdtrf( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density). This is the density
- * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
- * variables having Chi square distributions with df1
- * and df2 degrees of freedom, respectively.
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
- *
- *
- * The arguments a and b are greater than zero, and x
- * x is nonnegative.
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 2.2e-5 1.1e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrf domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrcf()
- *
- * Complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * float x, y, fdtrcf();
- *
- * y = fdtrcf( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from x to infinity under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density).
- *
- *
- * inf.
- * -
- * 1 | | a-1 b-1
- * 1-P(x) = ------ | t (1-t) dt
- * B(a,b) | |
- * -
- * x
- *
- * (See fdtr.c.)
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 7.3e-5 1.2e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrcf domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrif()
- *
- * Inverse of complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float df1, df2, x, y, fdtrif();
- *
- * x = fdtrif( df1, df2, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the F density argument x such that the integral
- * from x to infinity of the F density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relations
- *
- * z = incbi( df2/2, df1/2, y )
- * x = df2 (1-z) / (df1 z).
- *
- * Note: the following relations hold for the inverse of
- * the uncomplemented F distribution:
- *
- * z = incbi( df1/2, df2/2, y )
- * x = df2 z / (df1 (1-z)).
- *
- *
- *
- * ACCURACY:
- *
- * arithmetic domain # trials peak rms
- * Absolute error:
- * IEEE 0,100 5000 4.0e-5 3.2e-6
- * Relative error:
- * IEEE 0,100 5000 1.2e-3 1.8e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrif domain y <= 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-#ifdef ANSIC
-float incbetf(float, float, float);
-float incbif(float, float, float);
-#else
-float incbetf(), incbif();
-#endif
-
-float fdtrcf( int ia, int ib, float xx )
-{
-float x, a, b, w;
-
-x = xx;
-if( (ia < 1) || (ib < 1) || (x < 0.0) )
- {
- mtherr( "fdtrcf", DOMAIN );
- return( 0.0 );
- }
-a = ia;
-b = ib;
-w = b / (b + a * x);
-return( incbetf( 0.5*b, 0.5*a, w ) );
-}
-
-
-
-float fdtrf( int ia, int ib, int xx )
-{
-float x, a, b, w;
-
-x = xx;
-if( (ia < 1) || (ib < 1) || (x < 0.0) )
- {
- mtherr( "fdtrf", DOMAIN );
- return( 0.0 );
- }
-a = ia;
-b = ib;
-w = a * x;
-w = w / (b + w);
-return( incbetf( 0.5*a, 0.5*b, w) );
-}
-
-
-float fdtrif( int ia, int ib, float yy )
-{
-float y, a, b, w, x;
-
-y = yy;
-if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
- {
- mtherr( "fdtrif", DOMAIN );
- return( 0.0 );
- }
-a = ia;
-b = ib;
-w = incbif( 0.5*b, 0.5*a, y );
-x = (b - b*w)/(a*w);
-return(x);
-}
+++ /dev/null
-/* ceilf()
- * floorf()
- * frexpf()
- * ldexpf()
- * signbitf()
- * isnanf()
- * isfinitef()
- *
- * Single precision floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y;
- * float ceilf(), floorf(), frexpf(), ldexpf();
- * int signbit(), isnan(), isfinite();
- * int expnt, n;
- *
- * y = floorf(x);
- * y = ceilf(x);
- * y = frexpf( x, &expnt );
- * y = ldexpf( x, n );
- * n = signbit(x);
- * n = isnan(x);
- * n = isfinite(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * All four routines return a single precision floating point
- * result.
- *
- * sfloor() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * sceil() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * sfrexp() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * ldexpf() multiplies x by 2**n.
- *
- * signbit(x) returns 1 if the sign bit of x is 1, else 0.
- *
- * These functions are part of the standard C run time library
- * for many but not all C compilers. The ones supplied are
- * written in C for either DEC or IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-#ifdef DEC
-#undef DENORMAL
-#define DENORMAL 0
-#endif
-
-#ifdef UNK
-#undef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-/*
-char *unkmsg = "ceil(), floor(), frexp(), ldexp() must be rewritten!\n";
-*/
-#endif
-
-#define EXPMSK 0x807f
-#define MEXP 255
-#define NBITS 24
-
-
-extern float MAXNUMF; /* (2^24 - 1) * 2^103 */
-#ifdef ANSIC
-float floorf(float);
-#else
-float floorf();
-#endif
-
-float ceilf( float x )
-{
-float y;
-
-#ifdef UNK
-printf( "%s\n", unkmsg );
-return(0.0);
-#endif
-
-y = floorf( (float )x );
-if( y < x )
- y += 1.0;
-return(y);
-}
-
-
-
-
-/* Bit clearing masks: */
-
-static unsigned short bmask[] = {
-0xffff,
-0xfffe,
-0xfffc,
-0xfff8,
-0xfff0,
-0xffe0,
-0xffc0,
-0xff80,
-0xff00,
-0xfe00,
-0xfc00,
-0xf800,
-0xf000,
-0xe000,
-0xc000,
-0x8000,
-0x0000,
-};
-
-
-
-float floorf( float x )
-{
-unsigned short *p;
-union
- {
- float y;
- unsigned short i[2];
- } u;
-int e;
-
-#ifdef UNK
-printf( "%s\n", unkmsg );
-return(0.0);
-#endif
-
-u.y = x;
-/* find the exponent (power of 2) */
-#ifdef DEC
-p = &u.i[0];
-e = (( *p >> 7) & 0377) - 0201;
-p += 3;
-#endif
-
-#ifdef IBMPC
-p = &u.i[1];
-e = (( *p >> 7) & 0xff) - 0x7f;
-p -= 1;
-#endif
-
-#ifdef MIEEE
-p = &u.i[0];
-e = (( *p >> 7) & 0xff) - 0x7f;
-p += 1;
-#endif
-
-if( e < 0 )
- {
- if( u.y < 0 )
- return( -1.0 );
- else
- return( 0.0 );
- }
-
-e = (NBITS -1) - e;
-/* clean out 16 bits at a time */
-while( e >= 16 )
- {
-#ifdef IBMPC
- *p++ = 0;
-#endif
-
-#ifdef DEC
- *p-- = 0;
-#endif
-
-#ifdef MIEEE
- *p-- = 0;
-#endif
- e -= 16;
- }
-
-/* clear the remaining bits */
-if( e > 0 )
- *p &= bmask[e];
-
-if( (x < 0) && (u.y != x) )
- u.y -= 1.0;
-
-return(u.y);
-}
-
-
-
-float frexpf( float x, int *pw2 )
-{
-union
- {
- float y;
- unsigned short i[2];
- } u;
-int i, k;
-short *q;
-
-u.y = x;
-
-#ifdef UNK
-printf( "%s\n", unkmsg );
-return(0.0);
-#endif
-
-#ifdef IBMPC
-q = &u.i[1];
-#endif
-
-#ifdef DEC
-q = &u.i[0];
-#endif
-
-#ifdef MIEEE
-q = &u.i[0];
-#endif
-
-/* find the exponent (power of 2) */
-
-i = ( *q >> 7) & 0xff;
-if( i == 0 )
- {
- if( u.y == 0.0 )
- {
- *pw2 = 0;
- return(0.0);
- }
-/* Number is denormal or zero */
-#if DENORMAL
-/* Handle denormal number. */
- do
- {
- u.y *= 2.0;
- i -= 1;
- k = ( *q >> 7) & 0xff;
- }
- while( k == 0 );
- i = i + k;
-#else
- *pw2 = 0;
- return( 0.0 );
-#endif /* DENORMAL */
- }
-i -= 0x7e;
-*pw2 = i;
-*q &= 0x807f; /* strip all exponent bits */
-*q |= 0x3f00; /* mantissa between 0.5 and 1 */
-return( u.y );
-}
-
-
-
-
-
-float ldexpf( float x, int pw2 )
-{
-union
- {
- float y;
- unsigned short i[2];
- } u;
-short *q;
-int e;
-
-#ifdef UNK
-printf( "%s\n", unkmsg );
-return(0.0);
-#endif
-
-u.y = x;
-#ifdef DEC
-q = &u.i[0];
-#endif
-
-#ifdef IBMPC
-q = &u.i[1];
-#endif
-#ifdef MIEEE
-q = &u.i[0];
-#endif
-while( (e = ( *q >> 7) & 0xff) == 0 )
- {
- if( u.y == (float )0.0 )
- {
- return( 0.0 );
- }
-/* Input is denormal. */
- if( pw2 > 0 )
- {
- u.y *= 2.0;
- pw2 -= 1;
- }
- if( pw2 < 0 )
- {
- if( pw2 < -24 )
- return( 0.0 );
- u.y *= 0.5;
- pw2 += 1;
- }
- if( pw2 == 0 )
- return(u.y);
- }
-
-e += pw2;
-
-/* Handle overflow */
-if( e > MEXP )
- {
- return( MAXNUMF );
- }
-
-*q &= 0x807f;
-
-/* Handle denormalized results */
-if( e < 1 )
- {
-#if DENORMAL
- if( e < -24 )
- return( 0.0 );
- *q |= 0x80; /* Set LSB of exponent. */
- /* For denormals, significant bits may be lost even
- when dividing by 2. Construct 2^-(1-e) so the result
- is obtained with only one multiplication. */
- u.y *= ldexpf(1.0f, e - 1);
- return(u.y);
-#else
- return( 0.0 );
-#endif
- }
-*q |= (e & 0xff) << 7;
-return(u.y);
-}
-
-
-/* Return 1 if the sign bit of x is 1, else 0. */
-
-int signbitf(x)
-float x;
-{
-union
- {
- float f;
- short s[4];
- int i;
- } u;
-
-u.f = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- return( u.i < 0 );
-#endif
-#ifdef DEC
- return( u.s[1] < 0 );
-#endif
-#ifdef MIEEE
- return( u.i < 0 );
-#endif
- }
-else
- {
-#ifdef IBMPC
- return( u.s[1] < 0 );
-#endif
-#ifdef DEC
- return( u.s[1] < 0 );
-#endif
-#ifdef MIEEE
- return( u.s[0] < 0 );
-#endif
- }
-}
-
-
-/* Return 1 if x is a number that is Not a Number, else return 0. */
-
-int isnanf(x)
-float x;
-{
-#ifdef NANS
-union
- {
- float f;
- unsigned short s[2];
- unsigned int i;
- } u;
-
-u.f = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- if( ((u.i & 0x7f800000) == 0x7f800000)
- && ((u.i & 0x007fffff) != 0) )
- return 1;
-#endif
-#ifdef DEC
- if( (u.s[1] & 0x7f80) == 0)
- {
- if( (u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( ((u.i & 0x7f800000) == 0x7f800000)
- && ((u.i & 0x007fffff) != 0) )
- return 1;
-#endif
- return(0);
- }
-else
- { /* size int not 4 */
-#ifdef IBMPC
- if( (u.s[1] & 0x7f80) == 0x7f80)
- {
- if( ((u.s[1] & 0x007f) | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef DEC
- if( (u.s[1] & 0x7f80) == 0)
- {
- if( (u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( (u.s[0] & 0x7f80) == 0x7f80)
- {
- if( ((u.s[0] & 0x000f) | u.s[1]) != 0 )
- return(1);
- }
-#endif
- return(0);
- } /* size int not 4 */
-
-#else
-/* No NANS. */
-return(0);
-#endif
-}
-
-
-/* Return 1 if x is not infinite and is not a NaN. */
-
-int isfinitef(x)
-float x;
-{
-#ifdef INFINITIES
-union
- {
- float f;
- unsigned short s[2];
- unsigned int i;
- } u;
-
-u.f = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- if( (u.i & 0x7f800000) != 0x7f800000)
- return 1;
-#endif
-#ifdef DEC
- if( (u.s[1] & 0x7f80) == 0)
- {
- if( (u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( (u.i & 0x7f800000) != 0x7f800000)
- return 1;
-#endif
- return(0);
- }
-else
- {
-#ifdef IBMPC
- if( (u.s[1] & 0x7f80) != 0x7f80)
- return 1;
-#endif
-#ifdef DEC
- if( (u.s[1] & 0x7f80) == 0)
- {
- if( (u.s[1] | u.s[0]) != 0 )
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( (u.s[0] & 0x7f80) != 0x7f80)
- return 1;
-#endif
- return(0);
- }
-#else
-/* No INFINITY. */
-return(1);
-#endif
-}
+++ /dev/null
-/* fresnlf.c
- *
- * Fresnel integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, S, C;
- * void fresnlf();
- *
- * fresnlf( x, _&S, _&C );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the Fresnel integrals
- *
- * x
- * -
- * | |
- * C(x) = | cos(pi/2 t**2) dt,
- * | |
- * -
- * 0
- *
- * x
- * -
- * | |
- * S(x) = | sin(pi/2 t**2) dt.
- * | |
- * -
- * 0
- *
- *
- * The integrals are evaluated by power series for small x.
- * For x >= 1 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
- * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
- *
- *
- *
- * ACCURACY:
- *
- * Relative error.
- *
- * Arithmetic function domain # trials peak rms
- * IEEE S(x) 0, 10 30000 1.1e-6 1.9e-7
- * IEEE C(x) 0, 10 30000 1.1e-6 2.0e-7
- */
-\f
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* S(x) for small x */
-static float sn[7] = {
- 1.647629463788700E-009,
--1.522754752581096E-007,
- 8.424748808502400E-006,
--3.120693124703272E-004,
- 7.244727626597022E-003,
--9.228055941124598E-002,
- 5.235987735681432E-001
-};
-
-/* C(x) for small x */
-static float cn[7] = {
- 1.416802502367354E-008,
--1.157231412229871E-006,
- 5.387223446683264E-005,
--1.604381798862293E-003,
- 2.818489036795073E-002,
--2.467398198317899E-001,
- 9.999999760004487E-001
-};
-
-
-/* Auxiliary function f(x) */
-static float fn[8] = {
--1.903009855649792E+012,
- 1.355942388050252E+011,
--4.158143148511033E+009,
- 7.343848463587323E+007,
--8.732356681548485E+005,
- 8.560515466275470E+003,
--1.032877601091159E+002,
- 2.999401847870011E+000
-};
-
-/* Auxiliary function g(x) */
-static float gn[8] = {
--1.860843997624650E+011,
- 1.278350673393208E+010,
--3.779387713202229E+008,
- 6.492611570598858E+006,
--7.787789623358162E+004,
- 8.602931494734327E+002,
--1.493439396592284E+001,
- 9.999841934744914E-001
-};
-
-
-extern float PIF, PIO2F;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float polevlf( float, float *, int );
-float cosf(float), sinf(float);
-#else
-float polevlf(), cosf(), sinf();
-#endif
-
-void fresnlf( float xxa, float *ssa, float *cca )
-{
-float f, g, cc, ss, c, s, t, u, x, x2;
-
-x = xxa;
-x = fabsf(x);
-x2 = x * x;
-if( x2 < 2.5625 )
- {
- t = x2 * x2;
- ss = x * x2 * polevlf( t, sn, 6);
- cc = x * polevlf( t, cn, 6);
- goto done;
- }
-
-if( x > 36974.0 )
- {
- cc = 0.5;
- ss = 0.5;
- goto done;
- }
-
-
-/* Asymptotic power series auxiliary functions
- * for large argument
- */
- x2 = x * x;
- t = PIF * x2;
- u = 1.0/(t * t);
- t = 1.0/t;
- f = 1.0 - u * polevlf( u, fn, 7);
- g = t * polevlf( u, gn, 7);
-
- t = PIO2F * x2;
- c = cosf(t);
- s = sinf(t);
- t = PIF * x;
- cc = 0.5 + (f * s - g * c)/t;
- ss = 0.5 - (f * c + g * s)/t;
-
-done:
-if( xxa < 0.0 )
- {
- cc = -cc;
- ss = -ss;
- }
-
-*cca = cc;
-*ssa = ss;
-#if !ANSIC
-return 0;
-#endif
-}
+++ /dev/null
-/* gammaf.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, gammaf();
- * extern int sgngamf;
- *
- * y = gammaf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngamf.
- * This same variable is also filled in by the logarithmic
- * gamma function lgam().
- *
- * Arguments between 0 and 10 are reduced by recurrence and the
- * function is approximated by a polynomial function covering
- * the interval (2,3). Large arguments are handled by Stirling's
- * formula. Negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,-33 100,000 5.7e-7 1.0e-7
- * IEEE -33,0 100,000 6.1e-7 1.2e-7
- *
- *
- */\f
-/* lgamf()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, lgamf();
- * extern int sgngamf;
- *
- * y = lgamf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngamf.
- *
- * For arguments greater than 6.5, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula. Arguments between 0 and +6.5 are reduced by
- * by recurrence to the interval [.75,1.25] or [1.5,2.5] of a rational
- * approximation. The cosecant reflection formula is employed for
- * arguments less than zero.
- *
- * Arguments greater than MAXLGM = 2.035093e36 return MAXNUM and an
- * error message.
- *
- *
- *
- * ACCURACY:
- *
- *
- *
- * arithmetic domain # trials peak rms
- * IEEE -100,+100 500,000 7.4e-7 6.8e-8
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- * The routine has low relative error for positive arguments.
- *
- * The following test used the relative error criterion.
- * IEEE -2, +3 100000 4.0e-7 5.6e-8
- *
- */
-\f
-/* gamma.c */
-/* gamma function */
-
-/*
-Cephes Math Library Release 2.7: July, 1998
-Copyright 1984, 1987, 1989, 1992, 1998 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-/* define MAXGAM 34.84425627277176174 */
-
-/* Stirling's formula for the gamma function
- * gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) ( 1 + 1/x P(1/x) )
- * .028 < 1/x < .1
- * relative error < 1.9e-11
- */
-static float STIR[] = {
--2.705194986674176E-003,
- 3.473255786154910E-003,
- 8.333331788340907E-002,
-};
-static float MAXSTIR = 26.77;
-static float SQTPIF = 2.50662827463100050242; /* sqrt( 2 pi ) */
-
-int sgngamf = 0;
-extern int sgngamf;
-extern float MAXLOGF, MAXNUMF, PIF;
-
-#ifdef ANSIC
-float expf(float);
-float logf(float);
-float powf( float, float );
-float sinf(float);
-float gammaf(float);
-float floorf(float);
-static float stirf(float);
-float polevlf( float, float *, int );
-float p1evlf( float, float *, int );
-#else
-float expf(), logf(), powf(), sinf(), floorf();
-float polevlf(), p1evlf();
-static float stirf();
-#endif
-
-/* Gamma function computed by Stirling's formula,
- * sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
- * The polynomial STIR is valid for 33 <= x <= 172.
- */
-static float stirf( float xx )
-{
-float x, y, w, v;
-
-x = xx;
-w = 1.0/x;
-w = 1.0 + w * polevlf( w, STIR, 2 );
-y = expf( -x );
-if( x > MAXSTIR )
- { /* Avoid overflow in pow() */
- v = powf( x, 0.5 * x - 0.25 );
- y *= v;
- y *= v;
- }
-else
- {
- y = powf( x, x - 0.5 ) * y;
- }
-y = SQTPIF * y * w;
-return( y );
-}
-
-
-/* gamma(x+2), 0 < x < 1 */
-static float P[] = {
- 1.536830450601906E-003,
- 5.397581592950993E-003,
- 4.130370201859976E-003,
- 7.232307985516519E-002,
- 8.203960091619193E-002,
- 4.117857447645796E-001,
- 4.227867745131584E-001,
- 9.999999822945073E-001,
-};
-
-float gammaf( float xx )
-{
-float p, q, x, z, nz;
-int i, direction, negative;
-
-x = xx;
-sgngamf = 1;
-negative = 0;
-nz = 0.0;
-if( x < 0.0 )
- {
- negative = 1;
- q = -x;
- p = floorf(q);
- if( p == q )
- goto goverf;
- i = p;
- if( (i & 1) == 0 )
- sgngamf = -1;
- nz = q - p;
- if( nz > 0.5 )
- {
- p += 1.0;
- nz = q - p;
- }
- nz = q * sinf( PIF * nz );
- if( nz == 0.0 )
- {
-goverf:
- mtherr( "gamma", OVERFLOW );
- return( sgngamf * MAXNUMF);
- }
- if( nz < 0 )
- nz = -nz;
- x = q;
- }
-if( x >= 10.0 )
- {
- z = stirf(x);
- }
-if( x < 2.0 )
- direction = 1;
-else
- direction = 0;
-z = 1.0;
-while( x >= 3.0 )
- {
- x -= 1.0;
- z *= x;
- }
-/*
-while( x < 0.0 )
- {
- if( x > -1.E-4 )
- goto small;
- z *=x;
- x += 1.0;
- }
-*/
-while( x < 2.0 )
- {
- if( x < 1.e-4 )
- goto small;
- z *=x;
- x += 1.0;
- }
-
-if( direction )
- z = 1.0/z;
-
-if( x == 2.0 )
- return(z);
-
-x -= 2.0;
-p = z * polevlf( x, P, 7 );
-
-gdone:
-
-if( negative )
- {
- p = sgngamf * PIF/(nz * p );
- }
-return(p);
-
-small:
-if( x == 0.0 )
- {
- mtherr( "gamma", SING );
- return( MAXNUMF );
- }
-else
- {
- p = z / ((1.0 + 0.5772156649015329 * x) * x);
- goto gdone;
- }
-}
-
-
-
-
-/* log gamma(x+2), -.5 < x < .5 */
-static float B[] = {
- 6.055172732649237E-004,
--1.311620815545743E-003,
- 2.863437556468661E-003,
--7.366775108654962E-003,
- 2.058355474821512E-002,
--6.735323259371034E-002,
- 3.224669577325661E-001,
- 4.227843421859038E-001
-};
-
-/* log gamma(x+1), -.25 < x < .25 */
-static float C[] = {
- 1.369488127325832E-001,
--1.590086327657347E-001,
- 1.692415923504637E-001,
--2.067882815621965E-001,
- 2.705806208275915E-001,
--4.006931650563372E-001,
- 8.224670749082976E-001,
--5.772156501719101E-001
-};
-
-/* log( sqrt( 2*pi ) ) */
-static float LS2PI = 0.91893853320467274178;
-#define MAXLGM 2.035093e36
-static float PIINV = 0.318309886183790671538;
-
-/* Logarithm of gamma function */
-
-
-float lgamf( float xx )
-{
-float p, q, w, z, x;
-float nx, tx;
-int i, direction;
-
-sgngamf = 1;
-
-x = xx;
-if( x < 0.0 )
- {
- q = -x;
- w = lgamf(q); /* note this modifies sgngam! */
- p = floorf(q);
- if( p == q )
- goto loverf;
- i = p;
- if( (i & 1) == 0 )
- sgngamf = -1;
- else
- sgngamf = 1;
- z = q - p;
- if( z > 0.5 )
- {
- p += 1.0;
- z = p - q;
- }
- z = q * sinf( PIF * z );
- if( z == 0.0 )
- goto loverf;
- z = -logf( PIINV*z ) - w;
- return( z );
- }
-
-if( x < 6.5 )
- {
- direction = 0;
- z = 1.0;
- tx = x;
- nx = 0.0;
- if( x >= 1.5 )
- {
- while( tx > 2.5 )
- {
- nx -= 1.0;
- tx = x + nx;
- z *=tx;
- }
- x += nx - 2.0;
-iv1r5:
- p = x * polevlf( x, B, 7 );
- goto cont;
- }
- if( x >= 1.25 )
- {
- z *= x;
- x -= 1.0; /* x + 1 - 2 */
- direction = 1;
- goto iv1r5;
- }
- if( x >= 0.75 )
- {
- x -= 1.0;
- p = x * polevlf( x, C, 7 );
- q = 0.0;
- goto contz;
- }
- while( tx < 1.5 )
- {
- if( tx == 0.0 )
- goto loverf;
- z *=tx;
- nx += 1.0;
- tx = x + nx;
- }
- direction = 1;
- x += nx - 2.0;
- p = x * polevlf( x, B, 7 );
-
-cont:
- if( z < 0.0 )
- {
- sgngamf = -1;
- z = -z;
- }
- else
- {
- sgngamf = 1;
- }
- q = logf(z);
- if( direction )
- q = -q;
-contz:
- return( p + q );
- }
-
-if( x > MAXLGM )
- {
-loverf:
- mtherr( "lgamf", OVERFLOW );
- return( sgngamf * MAXNUMF );
- }
-
-/* Note, though an asymptotic formula could be used for x >= 3,
- * there is cancellation error in the following if x < 6.5. */
-q = LS2PI - x;
-q += ( x - 0.5 ) * logf(x);
-
-if( x <= 1.0e4 )
- {
- z = 1.0/x;
- p = z * z;
- q += (( 6.789774945028216E-004 * p
- - 2.769887652139868E-003 ) * p
- + 8.333316229807355E-002 ) * z;
- }
-return( q );
-}
+++ /dev/null
-/* gdtrf.c
- *
- * Gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, gdtrf();
- *
- * y = gdtrf( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from zero to x of the gamma probability
- * density function:
- *
- *
- * x
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * 0
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igam( b, ax ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 5.8e-5 3.0e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrf domain x < 0 0.0
- *
- */
-\f/* gdtrcf.c
- *
- * Complemented gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, gdtrcf();
- *
- * y = gdtrcf( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from x to infinity of the gamma
- * probability density function:
- *
- *
- * inf.
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * x
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igamc( b, ax ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 9.1e-5 1.5e-5
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrcf domain x < 0 0.0
- *
- */
-\f
-/* gdtr() */
-
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-#ifdef ANSIC
-float igamf(float, float), igamcf(float, float);
-#else
-float igamf(), igamcf();
-#endif
-
-
-
-float gdtrf( float aa, float bb, float xx )
-{
-float a, b, x;
-
-a = aa;
-b = bb;
-x = xx;
-
-
-if( x < 0.0 )
- {
- mtherr( "gdtrf", DOMAIN );
- return( 0.0 );
- }
-return( igamf( b, a * x ) );
-}
-
-
-
-float gdtrcf( float aa, float bb, float xx )
-{
-float a, b, x;
-
-a = aa;
-b = bb;
-x = xx;
-if( x < 0.0 )
- {
- mtherr( "gdtrcf", DOMAIN );
- return( 0.0 );
- }
-return( igamcf( b, a * x ) );
-}
+++ /dev/null
-/* hyp2f1f.c
- *
- * Gauss hypergeometric function F
- * 2 1
- *
- *
- * SYNOPSIS:
- *
- * float a, b, c, x, y, hyp2f1f();
- *
- * y = hyp2f1f( a, b, c, x );
- *
- *
- * DESCRIPTION:
- *
- *
- * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
- * 2 1
- *
- * inf.
- * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
- * = 1 + > ----------------------------- x .
- * - c(c+1)...(c+k) (k+1)!
- * k = 0
- *
- * Cases addressed are
- * Tests and escapes for negative integer a, b, or c
- * Linear transformation if c - a or c - b negative integer
- * Special case c = a or c = b
- * Linear transformation for x near +1
- * Transformation for x < -0.5
- * Psi function expansion if x > 0.5 and c - a - b integer
- * Conditionally, a recurrence on c to make c-a-b > 0
- *
- * |x| > 1 is rejected.
- *
- * The parameters a, b, c are considered to be integer
- * valued if they are within 1.0e-6 of the nearest integer.
- *
- * ACCURACY:
- *
- * Relative error (-1 < x < 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,3 30000 5.8e-4 4.3e-6
- */
-\f
-/* hyp2f1 */
-
-
-/*
-Cephes Math Library Release 2.2: November, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-#define EPS 1.0e-5
-#define EPS2 1.0e-5
-#define ETHRESH 1.0e-5
-
-extern float MAXNUMF, MACHEPF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float powf(float, float);
-static float hys2f1f(float, float, float, float, float *);
-static float hyt2f1f(float, float, float, float, float *);
-float gammaf(float), logf(float), expf(float), psif(float);
-float floorf(float);
-#else
-float powf(), gammaf(), logf(), expf(), psif();
-float floorf();
-static float hyt2f1f(), hys2f1f();
-#endif
-
-#define roundf(x) (floorf((x)+(float )0.5))
-
-
-
-
-float hyp2f1f( float aa, float bb, float cc, float xx )
-{
-float a, b, c, x;
-float d, d1, d2, e;
-float p, q, r, s, y, ax;
-float ia, ib, ic, id, err;
-int flag, i, aid;
-
-a = aa;
-b = bb;
-c = cc;
-x = xx;
-err = 0.0;
-ax = fabsf(x);
-s = 1.0 - x;
-flag = 0;
-ia = roundf(a); /* nearest integer to a */
-ib = roundf(b);
-
-if( a <= 0 )
- {
- if( fabsf(a-ia) < EPS ) /* a is a negative integer */
- flag |= 1;
- }
-
-if( b <= 0 )
- {
- if( fabsf(b-ib) < EPS ) /* b is a negative integer */
- flag |= 2;
- }
-
-if( ax < 1.0 )
- {
- if( fabsf(b-c) < EPS ) /* b = c */
- {
- y = powf( s, -a ); /* s to the -a power */
- goto hypdon;
- }
- if( fabsf(a-c) < EPS ) /* a = c */
- {
- y = powf( s, -b ); /* s to the -b power */
- goto hypdon;
- }
- }
-
-
-
-if( c <= 0.0 )
- {
- ic = roundf(c); /* nearest integer to c */
- if( fabsf(c-ic) < EPS ) /* c is a negative integer */
- {
- /* check if termination before explosion */
- if( (flag & 1) && (ia > ic) )
- goto hypok;
- if( (flag & 2) && (ib > ic) )
- goto hypok;
- goto hypdiv;
- }
- }
-
-if( flag ) /* function is a polynomial */
- goto hypok;
-
-if( ax > 1.0 ) /* series diverges */
- goto hypdiv;
-
-p = c - a;
-ia = roundf(p);
-if( (ia <= 0.0) && (fabsf(p-ia) < EPS) ) /* negative int c - a */
- flag |= 4;
-
-r = c - b;
-ib = roundf(r); /* nearest integer to r */
-if( (ib <= 0.0) && (fabsf(r-ib) < EPS) ) /* negative int c - b */
- flag |= 8;
-
-d = c - a - b;
-id = roundf(d); /* nearest integer to d */
-q = fabsf(d-id);
-
-if( fabsf(ax-1.0) < EPS ) /* |x| == 1.0 */
- {
- if( x > 0.0 )
- {
- if( flag & 12 ) /* negative int c-a or c-b */
- {
- if( d >= 0.0 )
- goto hypf;
- else
- goto hypdiv;
- }
- if( d <= 0.0 )
- goto hypdiv;
- y = gammaf(c)*gammaf(d)/(gammaf(p)*gammaf(r));
- goto hypdon;
- }
-
- if( d <= -1.0 )
- goto hypdiv;
- }
-
-/* Conditionally make d > 0 by recurrence on c
- * AMS55 #15.2.27
- */
-if( d < 0.0 )
- {
-/* Try the power series first */
- y = hyt2f1f( a, b, c, x, &err );
- if( err < ETHRESH )
- goto hypdon;
-/* Apply the recurrence if power series fails */
- err = 0.0;
- aid = 2 - id;
- e = c + aid;
- d2 = hyp2f1f(a,b,e,x);
- d1 = hyp2f1f(a,b,e+1.0,x);
- q = a + b + 1.0;
- for( i=0; i<aid; i++ )
- {
- r = e - 1.0;
- y = (e*(r-(2.0*e-q)*x)*d2 + (e-a)*(e-b)*x*d1)/(e*r*s);
- e = r;
- d1 = d2;
- d2 = y;
- }
- goto hypdon;
- }
-
-
-if( flag & 12 )
- goto hypf; /* negative integer c-a or c-b */
-
-hypok:
-y = hyt2f1f( a, b, c, x, &err );
-
-hypdon:
-if( err > ETHRESH )
- {
- mtherr( "hyp2f1", PLOSS );
-/* printf( "Estimated err = %.2e\n", err );*/
- }
-return(y);
-
-/* The transformation for c-a or c-b negative integer
- * AMS55 #15.3.3
- */
-hypf:
-y = powf( s, d ) * hys2f1f( c-a, c-b, c, x, &err );
-goto hypdon;
-
-/* The alarm exit */
-hypdiv:
-mtherr( "hyp2f1f", OVERFLOW );
-return( MAXNUMF );
-}
-
-
-
-
-/* Apply transformations for |x| near 1
- * then call the power series
- */
-static float hyt2f1f( float aa, float bb, float cc, float xx, float *loss )
-{
-float a, b, c, x;
-float p, q, r, s, t, y, d, err, err1;
-float ax, id, d1, d2, e, y1;
-int i, aid;
-
-a = aa;
-b = bb;
-c = cc;
-x = xx;
-err = 0.0;
-s = 1.0 - x;
-if( x < -0.5 )
- {
- if( b > a )
- y = powf( s, -a ) * hys2f1f( a, c-b, c, -x/s, &err );
-
- else
- y = powf( s, -b ) * hys2f1f( c-a, b, c, -x/s, &err );
-
- goto done;
- }
-
-
-
-d = c - a - b;
-id = roundf(d); /* nearest integer to d */
-
-if( x > 0.8 )
-{
-
-if( fabsf(d-id) > EPS2 ) /* test for integer c-a-b */
- {
-/* Try the power series first */
- y = hys2f1f( a, b, c, x, &err );
- if( err < ETHRESH )
- goto done;
-/* If power series fails, then apply AMS55 #15.3.6 */
- q = hys2f1f( a, b, 1.0-d, s, &err );
- q *= gammaf(d) /(gammaf(c-a) * gammaf(c-b));
- r = powf(s,d) * hys2f1f( c-a, c-b, d+1.0, s, &err1 );
- r *= gammaf(-d)/(gammaf(a) * gammaf(b));
- y = q + r;
-
- q = fabsf(q); /* estimate cancellation error */
- r = fabsf(r);
- if( q > r )
- r = q;
- err += err1 + (MACHEPF*r)/y;
-
- y *= gammaf(c);
- goto done;
- }
-else
- {
-/* Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12 */
- if( id >= 0.0 )
- {
- e = d;
- d1 = d;
- d2 = 0.0;
- aid = id;
- }
- else
- {
- e = -d;
- d1 = 0.0;
- d2 = d;
- aid = -id;
- }
-
- ax = logf(s);
-
- /* sum for t = 0 */
- y = psif(1.0) + psif(1.0+e) - psif(a+d1) - psif(b+d1) - ax;
- y /= gammaf(e+1.0);
-
- p = (a+d1) * (b+d1) * s / gammaf(e+2.0); /* Poch for t=1 */
- t = 1.0;
- do
- {
- r = psif(1.0+t) + psif(1.0+t+e) - psif(a+t+d1)
- - psif(b+t+d1) - ax;
- q = p * r;
- y += q;
- p *= s * (a+t+d1) / (t+1.0);
- p *= (b+t+d1) / (t+1.0+e);
- t += 1.0;
- }
- while( fabsf(q/y) > EPS );
-
-
- if( id == 0.0 )
- {
- y *= gammaf(c)/(gammaf(a)*gammaf(b));
- goto psidon;
- }
-
- y1 = 1.0;
-
- if( aid == 1 )
- goto nosum;
-
- t = 0.0;
- p = 1.0;
- for( i=1; i<aid; i++ )
- {
- r = 1.0-e+t;
- p *= s * (a+t+d2) * (b+t+d2) / r;
- t += 1.0;
- p /= t;
- y1 += p;
- }
-
-
-nosum:
- p = gammaf(c);
- y1 *= gammaf(e) * p / (gammaf(a+d1) * gammaf(b+d1));
- y *= p / (gammaf(a+d2) * gammaf(b+d2));
- if( (aid & 1) != 0 )
- y = -y;
-
- q = powf( s, id ); /* s to the id power */
- if( id > 0.0 )
- y *= q;
- else
- y1 *= q;
-
- y += y1;
-psidon:
- goto done;
- }
-}
-
-
-/* Use defining power series if no special cases */
-y = hys2f1f( a, b, c, x, &err );
-
-done:
-*loss = err;
-return(y);
-}
-
-
-
-
-
-/* Defining power series expansion of Gauss hypergeometric function */
-
-static float hys2f1f( float aa, float bb, float cc, float xx, float *loss )
-{
-int i;
-float a, b, c, x;
-float f, g, h, k, m, s, u, umax;
-
-
-a = aa;
-b = bb;
-c = cc;
-x = xx;
-i = 0;
-umax = 0.0;
-f = a;
-g = b;
-h = c;
-k = 0.0;
-s = 1.0;
-u = 1.0;
-
-do
- {
- if( fabsf(h) < EPS )
- return( MAXNUMF );
- m = k + 1.0;
- u = u * ((f+k) * (g+k) * x / ((h+k) * m));
- s += u;
- k = fabsf(u); /* remember largest term summed */
- if( k > umax )
- umax = k;
- k = m;
- if( ++i > 10000 ) /* should never happen */
- {
- *loss = 1.0;
- return(s);
- }
- }
-while( fabsf(u/s) > MACHEPF );
-
-/* return estimated relative error */
-*loss = (MACHEPF*umax)/fabsf(s) + (MACHEPF*i);
-
-return(s);
-}
-
-
+++ /dev/null
-/* hypergf.c
- *
- * Confluent hypergeometric function
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, hypergf();
- *
- * y = hypergf( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the confluent hypergeometric function
- *
- * 1 2
- * a x a(a+1) x
- * F ( a,b;x ) = 1 + ---- + --------- + ...
- * 1 1 b 1! b(b+1) 2!
- *
- * Many higher transcendental functions are special cases of
- * this power series.
- *
- * As is evident from the formula, b must not be a negative
- * integer or zero unless a is an integer with 0 >= a > b.
- *
- * The routine attempts both a direct summation of the series
- * and an asymptotic expansion. In each case error due to
- * roundoff, cancellation, and nonconvergence is estimated.
- * The result with smaller estimated error is returned.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (a, b, x), all three variables
- * ranging from 0 to 30.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,5 10000 6.6e-7 1.3e-7
- * IEEE 0,30 30000 1.1e-5 6.5e-7
- *
- * Larger errors can be observed when b is near a negative
- * integer or zero. Certain combinations of arguments yield
- * serious cancellation error in the power series summation
- * and also are not in the region of near convergence of the
- * asymptotic series. An error message is printed if the
- * self-estimated relative error is greater than 1.0e-3.
- *
- */
-\f
-/* hyperg.c */
-
-
-/*
-Cephes Math Library Release 2.1: November, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-extern float MAXNUMF, MACHEPF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float expf(float);
-float hyp2f0f(float, float, float, int, float *);
-static float hy1f1af(float, float, float, float *);
-static float hy1f1pf(float, float, float, float *);
-float logf(float), gammaf(float), lgamf(float);
-#else
-float expf(), hyp2f0f();
-float logf(), gammaf(), lgamf();
-static float hy1f1pf(), hy1f1af();
-#endif
-
-float hypergf( float aa, float bb, float xx )
-{
-float a, b, x, asum, psum, acanc, pcanc, temp;
-
-
-a = aa;
-b = bb;
-x = xx;
-/* See if a Kummer transformation will help */
-temp = b - a;
-if( fabsf(temp) < 0.001 * fabsf(a) )
- return( expf(x) * hypergf( temp, b, -x ) );
-
-psum = hy1f1pf( a, b, x, &pcanc );
-if( pcanc < 1.0e-6 )
- goto done;
-
-
-/* try asymptotic series */
-
-asum = hy1f1af( a, b, x, &acanc );
-
-
-/* Pick the result with less estimated error */
-
-if( acanc < pcanc )
- {
- pcanc = acanc;
- psum = asum;
- }
-
-done:
-if( pcanc > 1.0e-3 )
- mtherr( "hyperg", PLOSS );
-
-return( psum );
-}
-
-
-
-
-/* Power series summation for confluent hypergeometric function */
-
-
-static float hy1f1pf( float aa, float bb, float xx, float *err )
-{
-float a, b, x, n, a0, sum, t, u, temp;
-float an, bn, maxt, pcanc;
-
-a = aa;
-b = bb;
-x = xx;
-/* set up for power series summation */
-an = a;
-bn = b;
-a0 = 1.0;
-sum = 1.0;
-n = 1.0;
-t = 1.0;
-maxt = 0.0;
-
-
-while( t > MACHEPF )
- {
- if( bn == 0 ) /* check bn first since if both */
- {
- mtherr( "hypergf", SING );
- return( MAXNUMF ); /* an and bn are zero it is */
- }
- if( an == 0 ) /* a singularity */
- return( sum );
- if( n > 200 )
- goto pdone;
- u = x * ( an / (bn * n) );
-
- /* check for blowup */
- temp = fabsf(u);
- if( (temp > 1.0 ) && (maxt > (MAXNUMF/temp)) )
- {
- pcanc = 1.0; /* estimate 100% error */
- goto blowup;
- }
-
- a0 *= u;
- sum += a0;
- t = fabsf(a0);
- if( t > maxt )
- maxt = t;
-/*
- if( (maxt/fabsf(sum)) > 1.0e17 )
- {
- pcanc = 1.0;
- goto blowup;
- }
-*/
- an += 1.0;
- bn += 1.0;
- n += 1.0;
- }
-
-pdone:
-
-/* estimate error due to roundoff and cancellation */
-if( sum != 0.0 )
- maxt /= fabsf(sum);
-maxt *= MACHEPF; /* this way avoids multiply overflow */
-pcanc = fabsf( MACHEPF * n + maxt );
-
-blowup:
-
-*err = pcanc;
-
-return( sum );
-}
-
-
-/* hy1f1a() */
-/* asymptotic formula for hypergeometric function:
- *
- * ( -a
- * -- ( |z|
- * | (b) ( -------- 2f0( a, 1+a-b, -1/x )
- * ( --
- * ( | (b-a)
- *
- *
- * x a-b )
- * e |x| )
- * + -------- 2f0( b-a, 1-a, 1/x ) )
- * -- )
- * | (a) )
- */
-
-static float hy1f1af( float aa, float bb, float xx, float *err )
-{
-float a, b, x, h1, h2, t, u, temp, acanc, asum, err1, err2;
-
-a = aa;
-b = bb;
-x = xx;
-if( x == 0 )
- {
- acanc = 1.0;
- asum = MAXNUMF;
- goto adone;
- }
-temp = logf( fabsf(x) );
-t = x + temp * (a-b);
-u = -temp * a;
-
-if( b > 0 )
- {
- temp = lgamf(b);
- t += temp;
- u += temp;
- }
-
-h1 = hyp2f0f( a, a-b+1, -1.0/x, 1, &err1 );
-
-temp = expf(u) / gammaf(b-a);
-h1 *= temp;
-err1 *= temp;
-
-h2 = hyp2f0f( b-a, 1.0-a, 1.0/x, 2, &err2 );
-
-if( a < 0 )
- temp = expf(t) / gammaf(a);
-else
- temp = expf( t - lgamf(a) );
-
-h2 *= temp;
-err2 *= temp;
-
-if( x < 0.0 )
- asum = h1;
-else
- asum = h2;
-
-acanc = fabsf(err1) + fabsf(err2);
-
-
-if( b < 0 )
- {
- temp = gammaf(b);
- asum *= temp;
- acanc *= fabsf(temp);
- }
-
-
-if( asum != 0.0 )
- acanc /= fabsf(asum);
-
-acanc *= 30.0; /* fudge factor, since error of asymptotic formula
- * often seems this much larger than advertised */
-
-adone:
-
-
-*err = acanc;
-return( asum );
-}
-\f
-/* hyp2f0() */
-
-float hyp2f0f(float aa, float bb, float xx, int type, float *err)
-{
-float a, b, x, a0, alast, t, tlast, maxt;
-float n, an, bn, u, sum, temp;
-
-a = aa;
-b = bb;
-x = xx;
-an = a;
-bn = b;
-a0 = 1.0;
-alast = 1.0;
-sum = 0.0;
-n = 1.0;
-t = 1.0;
-tlast = 1.0e9;
-maxt = 0.0;
-
-do
- {
- if( an == 0 )
- goto pdone;
- if( bn == 0 )
- goto pdone;
-
- u = an * (bn * x / n);
-
- /* check for blowup */
- temp = fabsf(u);
- if( (temp > 1.0 ) && (maxt > (MAXNUMF/temp)) )
- goto error;
-
- a0 *= u;
- t = fabsf(a0);
-
- /* terminating condition for asymptotic series */
- if( t > tlast )
- goto ndone;
-
- tlast = t;
- sum += alast; /* the sum is one term behind */
- alast = a0;
-
- if( n > 200 )
- goto ndone;
-
- an += 1.0;
- bn += 1.0;
- n += 1.0;
- if( t > maxt )
- maxt = t;
- }
-while( t > MACHEPF );
-
-
-pdone: /* series converged! */
-
-/* estimate error due to roundoff and cancellation */
-*err = fabsf( MACHEPF * (n + maxt) );
-
-alast = a0;
-goto done;
-
-ndone: /* series did not converge */
-
-/* The following "Converging factors" are supposed to improve accuracy,
- * but do not actually seem to accomplish very much. */
-
-n -= 1.0;
-x = 1.0/x;
-
-switch( type ) /* "type" given as subroutine argument */
-{
-case 1:
- alast *= ( 0.5 + (0.125 + 0.25*b - 0.5*a + 0.25*x - 0.25*n)/x );
- break;
-
-case 2:
- alast *= 2.0/3.0 - b + 2.0*a + x - n;
- break;
-
-default:
- ;
-}
-
-/* estimate error due to roundoff, cancellation, and nonconvergence */
-*err = MACHEPF * (n + maxt) + fabsf( a0 );
-
-
-done:
-sum += alast;
-return( sum );
-
-/* series blew up: */
-error:
-*err = MAXNUMF;
-mtherr( "hypergf", TLOSS );
-return( sum );
-}
+++ /dev/null
-/* i0f.c
- *
- * Modified Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i0();
- *
- * y = i0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order zero of the
- * argument.
- *
- * The function is defined as i0(x) = j0( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 100000 4.0e-7 7.9e-8
- *
- */
-\f/* i0ef.c
- *
- * Modified Bessel function of order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i0ef();
- *
- * y = i0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order zero of the argument.
- *
- * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 100000 3.7e-7 7.0e-8
- * See i0f().
- *
- */
-\f
-/* i0.c */
-
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for exp(-x) I0(x)
- * in the interval [0,8].
- *
- * lim(x->0){ exp(-x) I0(x) } = 1.
- */
-
-static float A[] =
-{
--1.30002500998624804212E-8f,
- 6.04699502254191894932E-8f,
--2.67079385394061173391E-7f,
- 1.11738753912010371815E-6f,
--4.41673835845875056359E-6f,
- 1.64484480707288970893E-5f,
--5.75419501008210370398E-5f,
- 1.88502885095841655729E-4f,
--5.76375574538582365885E-4f,
- 1.63947561694133579842E-3f,
--4.32430999505057594430E-3f,
- 1.05464603945949983183E-2f,
--2.37374148058994688156E-2f,
- 4.93052842396707084878E-2f,
--9.49010970480476444210E-2f,
- 1.71620901522208775349E-1f,
--3.04682672343198398683E-1f,
- 6.76795274409476084995E-1f
-};
-
-
-/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
- * in the inverted interval [8,infinity].
- *
- * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
- */
-
-static float B[] =
-{
- 3.39623202570838634515E-9f,
- 2.26666899049817806459E-8f,
- 2.04891858946906374183E-7f,
- 2.89137052083475648297E-6f,
- 6.88975834691682398426E-5f,
- 3.36911647825569408990E-3f,
- 8.04490411014108831608E-1f
-};
-
-
-float chbevlf(float, float *, int), expf(float), sqrtf(float);
-
-float i0f( float x )
-{
-float y;
-
-if( x < 0 )
- x = -x;
-if( x <= 8.0f )
- {
- y = 0.5f*x - 2.0f;
- return( expf(x) * chbevlf( y, A, 18 ) );
- }
-
-return( expf(x) * chbevlf( 32.0f/x - 2.0f, B, 7 ) / sqrtf(x) );
-}
-
-
-
-float chbevlf(float, float *, int), expf(float), sqrtf(float);
-
-float i0ef( float x )
-{
-float y;
-
-if( x < 0 )
- x = -x;
-if( x <= 8.0f )
- {
- y = 0.5f*x - 2.0f;
- return( chbevlf( y, A, 18 ) );
- }
-
-return( chbevlf( 32.0f/x - 2.0f, B, 7 ) / sqrtf(x) );
-}
+++ /dev/null
-/* i1f.c
- *
- * Modified Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i1f();
- *
- * y = i1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order one of the
- * argument.
- *
- * The function is defined as i1(x) = -i j1( ix ).
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 100000 1.5e-6 1.6e-7
- *
- *
- */
-\f/* i1ef.c
- *
- * Modified Bessel function of order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i1ef();
- *
- * y = i1ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order one of the argument.
- *
- * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.5e-6 1.5e-7
- * See i1().
- *
- */
-\f
-/* i1.c 2 */
-
-
-/*
-Cephes Math Library Release 2.0: March, 1987
-Copyright 1985, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for exp(-x) I1(x) / x
- * in the interval [0,8].
- *
- * lim(x->0){ exp(-x) I1(x) / x } = 1/2.
- */
-
-static float A[] =
-{
- 9.38153738649577178388E-9f,
--4.44505912879632808065E-8f,
- 2.00329475355213526229E-7f,
--8.56872026469545474066E-7f,
- 3.47025130813767847674E-6f,
--1.32731636560394358279E-5f,
- 4.78156510755005422638E-5f,
--1.61760815825896745588E-4f,
- 5.12285956168575772895E-4f,
--1.51357245063125314899E-3f,
- 4.15642294431288815669E-3f,
--1.05640848946261981558E-2f,
- 2.47264490306265168283E-2f,
--5.29459812080949914269E-2f,
- 1.02643658689847095384E-1f,
--1.76416518357834055153E-1f,
- 2.52587186443633654823E-1f
-};
-
-
-/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
- * in the inverted interval [8,infinity].
- *
- * lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
- */
-
-static float B[] =
-{
--3.83538038596423702205E-9f,
--2.63146884688951950684E-8f,
--2.51223623787020892529E-7f,
--3.88256480887769039346E-6f,
--1.10588938762623716291E-4f,
--9.76109749136146840777E-3f,
- 7.78576235018280120474E-1f
-};
-\f
-/* i1.c */
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float chbevlf(float, float *, int);
-float expf(float), sqrtf(float);
-#else
-float chbevlf(), expf(), sqrtf();
-#endif
-
-
-float i1f(float xx)
-{
-float x, y, z;
-
-x = xx;
-z = fabsf(x);
-if( z <= 8.0f )
- {
- y = 0.5f*z - 2.0f;
- z = chbevlf( y, A, 17 ) * z * expf(z);
- }
-else
- {
- z = expf(z) * chbevlf( 32.0f/z - 2.0f, B, 7 ) / sqrtf(z);
- }
-if( x < 0.0f )
- z = -z;
-return( z );
-}
-\f
-/* i1e() */
-
-float i1ef( float xx )
-{
-float x, y, z;
-
-x = xx;
-z = fabsf(x);
-if( z <= 8.0f )
- {
- y = 0.5f*z - 2.0f;
- z = chbevlf( y, A, 17 ) * z;
- }
-else
- {
- z = chbevlf( 32.0f/z - 2.0f, B, 7 ) / sqrtf(z);
- }
-if( x < 0.0f )
- z = -z;
-return( z );
-}
+++ /dev/null
-/* igamf.c
- *
- * Incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, x, y, igamf();
- *
- * y = igamf( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 20000 7.8e-6 5.9e-7
- *
- */
-\f/* igamcf()
- *
- * Complemented incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, x, y, igamcf();
- *
- * y = igamcf( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 7.8e-6 5.9e-7
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1985, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* BIG = 1/MACHEPF */
-#define BIG 16777216.
-
-extern float MACHEPF, MAXLOGF;
-
-#ifdef ANSIC
-float lgamf(float), expf(float), logf(float), igamf(float, float);
-#else
-float lgamf(), expf(), logf(), igamf();
-#endif
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-
-
-float igamcf( float aa, float xx )
-{
-float a, x, ans, c, yc, ax, y, z;
-float pk, pkm1, pkm2, qk, qkm1, qkm2;
-float r, t;
-static float big = BIG;
-
-a = aa;
-x = xx;
-if( (x <= 0) || ( a <= 0) )
- return( 1.0 );
-
-if( (x < 1.0) || (x < a) )
- return( 1.0 - igamf(a,x) );
-
-ax = a * logf(x) - x - lgamf(a);
-if( ax < -MAXLOGF )
- {
- mtherr( "igamcf", UNDERFLOW );
- return( 0.0 );
- }
-ax = expf(ax);
-
-/* continued fraction */
-y = 1.0 - a;
-z = x + y + 1.0;
-c = 0.0;
-pkm2 = 1.0;
-qkm2 = x;
-pkm1 = x + 1.0;
-qkm1 = z * x;
-ans = pkm1/qkm1;
-
-do
- {
- c += 1.0;
- y += 1.0;
- z += 2.0;
- yc = y * c;
- pk = pkm1 * z - pkm2 * yc;
- qk = qkm1 * z - qkm2 * yc;
- if( qk != 0 )
- {
- r = pk/qk;
- t = fabsf( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
- if( fabsf(pk) > big )
- {
- pkm2 *= MACHEPF;
- pkm1 *= MACHEPF;
- qkm2 *= MACHEPF;
- qkm1 *= MACHEPF;
- }
- }
-while( t > MACHEPF );
-
-return( ans * ax );
-}
-
-
-
-/* left tail of incomplete gamma function:
- *
- * inf. k
- * a -x - x
- * x e > ----------
- * - -
- * k=0 | (a+k+1)
- *
- */
-
-float igamf( float aa, float xx )
-{
-float a, x, ans, ax, c, r;
-
-a = aa;
-x = xx;
-if( (x <= 0) || ( a <= 0) )
- return( 0.0 );
-
-if( (x > 1.0) && (x > a ) )
- return( 1.0 - igamcf(a,x) );
-
-/* Compute x**a * exp(-x) / gamma(a) */
-ax = a * logf(x) - x - lgamf(a);
-if( ax < -MAXLOGF )
- {
- mtherr( "igamf", UNDERFLOW );
- return( 0.0 );
- }
-ax = expf(ax);
-
-/* power series */
-r = a;
-c = 1.0;
-ans = 1.0;
-
-do
- {
- r += 1.0;
- c *= x/r;
- ans += c;
- }
-while( c/ans > MACHEPF );
-
-return( ans * ax/a );
-}
+++ /dev/null
-/* igamif()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, x, y, igamif();
- *
- * x = igamif( a, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * igamc( a, x ) = y.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(y) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Tested for a ranging from 0 to 100 and x from 0 to 1.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 1.0e-5 1.5e-6
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-extern float MACHEPF, MAXLOGF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float igamcf(float, float);
-float ndtrif(float), expf(float), logf(float), sqrtf(float), lgamf(float);
-#else
-float igamcf();
-float ndtrif(), expf(), logf(), sqrtf(), lgamf();
-#endif
-
-
-float igamif( float aa, float yy0 )
-{
-float a, y0, d, y, x0, lgm;
-int i;
-
-a = aa;
-y0 = yy0;
-/* approximation to inverse function */
-d = 1.0/(9.0*a);
-y = ( 1.0 - d - ndtrif(y0) * sqrtf(d) );
-x0 = a * y * y * y;
-
-lgm = lgamf(a);
-
-for( i=0; i<10; i++ )
- {
- if( x0 <= 0.0 )
- {
- mtherr( "igamif", UNDERFLOW );
- return(0.0);
- }
- y = igamcf(a,x0);
-/* compute the derivative of the function at this point */
- d = (a - 1.0) * logf(x0) - x0 - lgm;
- if( d < -MAXLOGF )
- {
- mtherr( "igamif", UNDERFLOW );
- goto done;
- }
- d = -expf(d);
-/* compute the step to the next approximation of x */
- if( d == 0.0 )
- goto done;
- d = (y - y0)/d;
- x0 = x0 - d;
- if( i < 3 )
- continue;
- if( fabsf(d/x0) < (2.0 * MACHEPF) )
- goto done;
- }
-
-done:
-return( x0 );
-}
+++ /dev/null
-/* incbetf.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, incbetf();
- *
- * y = incbetf( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion.
- * If a < 1, the function calls itself recursively after a
- * transformation to increase a to a+1.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) with a and b in the indicated
- * interval and x between 0 and 1.
- *
- * arithmetic domain # trials peak rms
- * Relative error:
- * IEEE 0,30 10000 3.7e-5 5.1e-6
- * IEEE 0,100 10000 1.7e-4 2.5e-5
- * The useful domain for relative error is limited by underflow
- * of the single precision exponential function.
- * Absolute error:
- * IEEE 0,30 100000 2.2e-5 9.6e-7
- * IEEE 0,100 10000 6.5e-5 3.7e-6
- *
- * Larger errors may occur for extreme ratios of a and b.
- *
- * ERROR MESSAGES:
- * message condition value returned
- * incbetf domain x<0, x>1 0.0
- */
-\f
-
-/*
-Cephes Math Library, Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef ANSIC
-float lgamf(float), expf(float), logf(float);
-static float incbdf(float, float, float);
-static float incbcff(float, float, float);
-float incbpsf(float, float, float);
-#else
-float lgamf(), expf(), logf();
-float incbpsf();
-static float incbcff(), incbdf();
-#endif
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-/* BIG = 1/MACHEPF */
-#define BIG 16777216.
-extern float MACHEPF, MAXLOGF;
-#define MINLOGF (-MAXLOGF)
-
-float incbetf( float aaa, float bbb, float xxx )
-{
-float aa, bb, xx, ans, a, b, t, x, onemx;
-int flag;
-
-aa = aaa;
-bb = bbb;
-xx = xxx;
-if( (xx <= 0.0) || ( xx >= 1.0) )
- {
- if( xx == 0.0 )
- return(0.0);
- if( xx == 1.0 )
- return( 1.0 );
- mtherr( "incbetf", DOMAIN );
- return( 0.0 );
- }
-
-onemx = 1.0 - xx;
-
-
-/* transformation for small aa */
-
-if( aa <= 1.0 )
- {
- ans = incbetf( aa+1.0, bb, xx );
- t = aa*logf(xx) + bb*logf( 1.0-xx )
- + lgamf(aa+bb) - lgamf(aa+1.0) - lgamf(bb);
- if( t > MINLOGF )
- ans += expf(t);
- return( ans );
- }
-
-
-/* see if x is greater than the mean */
-
-if( xx > (aa/(aa+bb)) )
- {
- flag = 1;
- a = bb;
- b = aa;
- t = xx;
- x = onemx;
- }
-else
- {
- flag = 0;
- a = aa;
- b = bb;
- t = onemx;
- x = xx;
- }
-
-/* transformation for small aa */
-/*
-if( a <= 1.0 )
- {
- ans = a*logf(x) + b*logf( onemx )
- + lgamf(a+b) - lgamf(a+1.0) - lgamf(b);
- t = incbetf( a+1.0, b, x );
- if( ans > MINLOGF )
- t += expf(ans);
- goto bdone;
- }
-*/
-/* Choose expansion for optimal convergence */
-
-
-if( b > 10.0 )
- {
-if( fabsf(b*x/a) < 0.3 )
- {
- t = incbpsf( a, b, x );
- goto bdone;
- }
- }
-
-ans = x * (a+b-2.0)/(a-1.0);
-if( ans < 1.0 )
- {
- ans = incbcff( a, b, x );
- t = b * logf( t );
- }
-else
- {
- ans = incbdf( a, b, x );
- t = (b-1.0) * logf(t);
- }
-
-t += a*logf(x) + lgamf(a+b) - lgamf(a) - lgamf(b);
-t += logf( ans/a );
-
-if( t < MINLOGF )
- {
- t = 0.0;
- if( flag == 0 )
- {
- mtherr( "incbetf", UNDERFLOW );
- }
- }
-else
- {
- t = expf(t);
- }
-bdone:
-
-if( flag )
- t = 1.0 - t;
-
-return( t );
-}
-\f
-/* Continued fraction expansion #1
- * for incomplete beta integral
- */
-
-static float incbcff( float aa, float bb, float xx )
-{
-float a, b, x, xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
-float k1, k2, k3, k4, k5, k6, k7, k8;
-float r, t, ans;
-static float big = BIG;
-int n;
-
-a = aa;
-b = bb;
-x = xx;
-k1 = a;
-k2 = a + b;
-k3 = a;
-k4 = a + 1.0;
-k5 = 1.0;
-k6 = b - 1.0;
-k7 = k4;
-k8 = a + 2.0;
-
-pkm2 = 0.0;
-qkm2 = 1.0;
-pkm1 = 1.0;
-qkm1 = 1.0;
-ans = 1.0;
-r = 0.0;
-n = 0;
-do
- {
-
- xk = -( x * k1 * k2 )/( k3 * k4 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = ( x * k5 * k6 )/( k7 * k8 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if( qk != 0 )
- r = pk/qk;
- if( r != 0 )
- {
- t = fabsf( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
-
- if( t < MACHEPF )
- goto cdone;
-
- k1 += 1.0;
- k2 += 1.0;
- k3 += 2.0;
- k4 += 2.0;
- k5 += 1.0;
- k6 -= 1.0;
- k7 += 2.0;
- k8 += 2.0;
-
- if( (fabsf(qk) + fabsf(pk)) > big )
- {
- pkm2 *= MACHEPF;
- pkm1 *= MACHEPF;
- qkm2 *= MACHEPF;
- qkm1 *= MACHEPF;
- }
- if( (fabsf(qk) < MACHEPF) || (fabsf(pk) < MACHEPF) )
- {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- }
-while( ++n < 100 );
-
-cdone:
-return(ans);
-}
-
-\f
-/* Continued fraction expansion #2
- * for incomplete beta integral
- */
-
-static float incbdf( float aa, float bb, float xx )
-{
-float a, b, x, xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
-float k1, k2, k3, k4, k5, k6, k7, k8;
-float r, t, ans, z;
-static float big = BIG;
-int n;
-
-a = aa;
-b = bb;
-x = xx;
-k1 = a;
-k2 = b - 1.0;
-k3 = a;
-k4 = a + 1.0;
-k5 = 1.0;
-k6 = a + b;
-k7 = a + 1.0;;
-k8 = a + 2.0;
-
-pkm2 = 0.0;
-qkm2 = 1.0;
-pkm1 = 1.0;
-qkm1 = 1.0;
-z = x / (1.0-x);
-ans = 1.0;
-r = 0.0;
-n = 0;
-do
- {
-
- xk = -( z * k1 * k2 )/( k3 * k4 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = ( z * k5 * k6 )/( k7 * k8 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if( qk != 0 )
- r = pk/qk;
- if( r != 0 )
- {
- t = fabsf( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
-
- if( t < MACHEPF )
- goto cdone;
-
- k1 += 1.0;
- k2 -= 1.0;
- k3 += 2.0;
- k4 += 2.0;
- k5 += 1.0;
- k6 += 1.0;
- k7 += 2.0;
- k8 += 2.0;
-
- if( (fabsf(qk) + fabsf(pk)) > big )
- {
- pkm2 *= MACHEPF;
- pkm1 *= MACHEPF;
- qkm2 *= MACHEPF;
- qkm1 *= MACHEPF;
- }
- if( (fabsf(qk) < MACHEPF) || (fabsf(pk) < MACHEPF) )
- {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- }
-while( ++n < 100 );
-
-cdone:
-return(ans);
-}
-
-
-/* power series */
-float incbpsf( float aa, float bb, float xx )
-{
-float a, b, x, t, u, y, s;
-
-a = aa;
-b = bb;
-x = xx;
-
-y = a * logf(x) + (b-1.0)*logf(1.0-x) - logf(a);
-y -= lgamf(a) + lgamf(b);
-y += lgamf(a+b);
-
-
-t = x / (1.0 - x);
-s = 0.0;
-u = 1.0;
-do
- {
- b -= 1.0;
- if( b == 0.0 )
- break;
- a += 1.0;
- u *= t*b/a;
- s += u;
- }
-while( fabsf(u) > MACHEPF );
-
-if( y < MINLOGF )
- {
- mtherr( "incbetf", UNDERFLOW );
- s = 0.0;
- }
-else
- s = expf(y) * (1.0 + s);
-/*printf( "incbpsf: %.4e\n", s );*/
-return(s);
-}
+++ /dev/null
-/* incbif()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, incbif();
- *
- * x = incbif( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y.
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 0,100 5000 2.8e-4 8.3e-6
- *
- * Overflow and larger errors may occur for one of a or b near zero
- * and the other large.
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-extern float MACHEPF, MINLOGF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float incbetf(float, float, float);
-float ndtrif(float), expf(float), logf(float), sqrtf(float), lgamf(float);
-#else
-float incbetf();
-float ndtrif(), expf(), logf(), sqrtf(), lgamf();
-#endif
-
-float incbif( float aaa, float bbb, float yyy0 )
-{
-float aa, bb, yy0, a, b, y0;
-float d, y, x, x0, x1, lgm, yp, di;
-int i, rflg;
-
-
-aa = aaa;
-bb = bbb;
-yy0 = yyy0;
-if( yy0 <= 0 )
- return(0.0);
-if( yy0 >= 1.0 )
- return(1.0);
-
-/* approximation to inverse function */
-
-yp = -ndtrif(yy0);
-
-if( yy0 > 0.5 )
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0 - yy0;
- yp = -yp;
- }
-else
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
-
-
-if( (aa <= 1.0) || (bb <= 1.0) )
- {
- y = 0.5 * yp * yp;
- }
-else
- {
- lgm = (yp * yp - 3.0)* 0.16666666666666667;
- x0 = 2.0/( 1.0/(2.0*a-1.0) + 1.0/(2.0*b-1.0) );
- y = yp * sqrtf( x0 + lgm ) / x0
- - ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
- * (lgm + 0.833333333333333333 - 2.0/(3.0*x0));
- y = 2.0 * y;
- if( y < MINLOGF )
- {
- x0 = 1.0;
- goto under;
- }
- }
-
-x = a/( a + b * expf(y) );
-y = incbetf( a, b, x );
-yp = (y - y0)/y0;
-if( fabsf(yp) < 0.1 )
- goto newt;
-
-/* Resort to interval halving if not close enough */
-x0 = 0.0;
-x1 = 1.0;
-di = 0.5;
-
-for( i=0; i<20; i++ )
- {
- if( i != 0 )
- {
- x = di * x1 + (1.0-di) * x0;
- y = incbetf( a, b, x );
- yp = (y - y0)/y0;
- if( fabsf(yp) < 1.0e-3 )
- goto newt;
- }
-
- if( y < y0 )
- {
- x0 = x;
- di = 0.5;
- }
- else
- {
- x1 = x;
- di *= di;
- if( di == 0.0 )
- di = 0.5;
- }
- }
-
-if( x0 == 0.0 )
- {
-under:
- mtherr( "incbif", UNDERFLOW );
- goto done;
- }
-
-newt:
-
-x0 = x;
-lgm = lgamf(a+b) - lgamf(a) - lgamf(b);
-
-for( i=0; i<10; i++ )
- {
-/* compute the function at this point */
- if( i != 0 )
- y = incbetf(a,b,x0);
-/* compute the derivative of the function at this point */
- d = (a - 1.0) * logf(x0) + (b - 1.0) * logf(1.0-x0) + lgm;
- if( d < MINLOGF )
- {
- x0 = 0.0;
- goto under;
- }
- d = expf(d);
-/* compute the step to the next approximation of x */
- d = (y - y0)/d;
- x = x0;
- x0 = x0 - d;
- if( x0 <= 0.0 )
- {
- x0 = 0.0;
- goto under;
- }
- if( x0 >= 1.0 )
- {
- x0 = 1.0;
- goto under;
- }
- if( i < 2 )
- continue;
- if( fabsf(d/x0) < 256.0 * MACHEPF )
- goto done;
- }
-
-done:
-if( rflg )
- x0 = 1.0 - x0;
-return( x0 );
-}
+++ /dev/null
-/* ivf.c
- *
- * Modified Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, ivf();
- *
- * y = ivf( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of order v of the
- * argument. If x is negative, v must be integer valued.
- *
- * The function is defined as Iv(x) = Jv( ix ). It is
- * here computed in terms of the confluent hypergeometric
- * function, according to the formula
- *
- * v -x
- * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
- *
- * If v is a negative integer, then v is replaced by -v.
- *
- *
- * ACCURACY:
- *
- * Tested at random points (v, x), with v between 0 and
- * 30, x between 0 and 28.
- * arithmetic domain # trials peak rms
- * Relative error:
- * IEEE 0,15 3000 4.7e-6 5.4e-7
- * Absolute error (relative when function > 1)
- * IEEE 0,30 5000 8.5e-6 1.3e-6
- *
- * Accuracy is diminished if v is near a negative integer.
- * The useful domain for relative error is limited by overflow
- * of the single precision exponential function.
- *
- * See also hyperg.c.
- *
- */
-\f/* iv.c */
-/* Modified Bessel function of noninteger order */
-/* If x < 0, then v must be an integer. */
-
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-extern float MAXNUMF;
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-float hypergf(float, float, float);
-float expf(float), gammaf(float), logf(float), floorf(float);
-
-float ivf( float v, float x )
-{
-int sign;
-float t, ax;
-
-/* If v is a negative integer, invoke symmetry */
-t = floorf(v);
-if( v < 0.0 )
- {
- if( t == v )
- {
- v = -v; /* symmetry */
- t = -t;
- }
- }
-/* If x is negative, require v to be an integer */
-sign = 1;
-if( x < 0.0 )
- {
- if( t != v )
- {
- mtherr( "ivf", DOMAIN );
- return( 0.0 );
- }
- if( v != 2.0 * floorf(v/2.0) )
- sign = -1;
- }
-
-/* Avoid logarithm singularity */
-if( x == 0.0 )
- {
- if( v == 0.0 )
- return( 1.0 );
- if( v < 0.0 )
- {
- mtherr( "ivf", OVERFLOW );
- return( MAXNUMF );
- }
- else
- return( 0.0 );
- }
-
-ax = fabsf(x);
-t = v * logf( 0.5 * ax ) - x;
-t = sign * expf(t) / gammaf( v + 1.0 );
-ax = v + 0.5;
-return( t * hypergf( ax, 2.0 * ax, 2.0 * x ) );
-}
+++ /dev/null
-/* j0f.c
- *
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j0f();
- *
- * y = j0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval the following polynomial
- * approximation is used:
- *
- *
- * 2 2 2
- * (w - r ) (w - r ) (w - r ) P(w)
- * 1 2 3
- *
- * 2
- * where w = x and the three r's are zeros of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.3e-7 3.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.4e-8
- *
- */
-\f/* y0f.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, y0f();
- *
- * y = y0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2 2 2
- * y0(x) = (w - r ) (w - r ) (w - r ) R(x) + 2/pi ln(x) j0(x).
- * 1 2 3
- *
- * Thus a call to j0() is required. The three zeros are removed
- * from R(x) to improve its numerical stability.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.4e-7 3.4e-8
- * IEEE 2, 32 100000 1.8e-7 5.3e-8
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-static float MO[8] = {
--6.838999669318810E-002f,
- 1.864949361379502E-001f,
--2.145007480346739E-001f,
- 1.197549369473540E-001f,
--3.560281861530129E-003f,
--4.969382655296620E-002f,
--3.355424622293709E-006f,
- 7.978845717621440E-001f
-};
-
-static float PH[8] = {
- 3.242077816988247E+001f,
--3.630592630518434E+001f,
- 1.756221482109099E+001f,
--4.974978466280903E+000f,
- 1.001973420681837E+000f,
--1.939906941791308E-001f,
- 6.490598792654666E-002f,
--1.249992184872738E-001f
-};
-
-static float YP[5] = {
- 9.454583683980369E-008f,
--9.413212653797057E-006f,
- 5.344486707214273E-004f,
--1.584289289821316E-002f,
- 1.707584643733568E-001f
-};
-
-float YZ1 = 0.43221455686510834878f;
-float YZ2 = 22.401876406482861405f;
-float YZ3 = 64.130620282338755553f;
-
-static float DR1 = 5.78318596294678452118f;
-/*
-static float DR2 = 30.4712623436620863991;
-static float DR3 = 74.887006790695183444889;
-*/
-
-static float JP[5] = {
--6.068350350393235E-008f,
- 6.388945720783375E-006f,
--3.969646342510940E-004f,
- 1.332913422519003E-002f,
--1.729150680240724E-001f
-};
-extern float PIO4F;
-
-
-float polevlf(float, float *, int);
-float logf(float), sinf(float), cosf(float), sqrtf(float);
-
-float j0f( float xx )
-{
-float x, w, z, p, q, xn;
-
-
-if( xx < 0 )
- x = -xx;
-else
- x = xx;
-
-if( x <= 2.0f )
- {
- z = x * x;
- if( x < 1.0e-3f )
- return( 1.0f - 0.25f*z );
-
- p = (z-DR1) * polevlf( z, JP, 4);
- return( p );
- }
-
-q = 1.0f/x;
-w = sqrtf(q);
-
-p = w * polevlf( q, MO, 7);
-w = q*q;
-xn = q * polevlf( w, PH, 7) - PIO4F;
-p = p * cosf(xn + x);
-return(p);
-}
-\f
-/* y0() 2 */
-/* Bessel function of second kind, order zero */
-
-/* Rational approximation coefficients YP[] are used for x < 6.5.
- * The function computed is y0(x) - 2 ln(x) j0(x) / pi,
- * whose value at x = 0 is 2 * ( log(0.5) + EUL ) / pi
- * = 0.073804295108687225 , EUL is Euler's constant.
- */
-
-static float TWOOPI = 0.636619772367581343075535f; /* 2/pi */
-extern float MAXNUMF;
-
-float y0f( float xx )
-{
-float x, w, z, p, q, xn;
-
-
-x = xx;
-if( x <= 2.0f )
- {
- if( x <= 0.0f )
- {
- mtherr( "y0f", DOMAIN );
- return( -MAXNUMF );
- }
- z = x * x;
-/* w = (z-YZ1)*(z-YZ2)*(z-YZ3) * polevlf( z, YP, 4);*/
- w = (z-YZ1) * polevlf( z, YP, 4);
- w += TWOOPI * logf(x) * j0f(x);
- return( w );
- }
-
-q = 1.0f/x;
-w = sqrtf(q);
-
-p = w * polevlf( q, MO, 7);
-w = q*q;
-xn = q * polevlf( w, PH, 7) - PIO4F;
-p = p * sinf(xn + x);
-return( p );
-}
+++ /dev/null
-float z[20] = {
-2.4048254489898681641,
-5.5200781822204589844,
-8.6537275314331054687,
-11.791533470153808594,
-14.930917739868164062,
-18.071063995361328125,
-21.211637496948242188,
-24.352472305297851563,
-27.493478775024414062,
-30.634607315063476562,
-33.775821685791015625,
-36.9170989990234375,
-40.0584259033203125,
-43.19979095458984375,
-46.3411865234375,
-49.482608795166015625,
-52.624050140380859375,
-55.76551055908203125,
-58.906982421875,
-62.04846954345703125,
-};
-
-/* #if ANSIC */
-#if __STDC__
-float j0f(float);
-#else
-float j0f();
-#endif
-
-int main()
-{
-float y;
-int i;
-
-for (i = 0; i< 20; i++)
- {
- y = j0f(z[i]);
- printf("%.9e\n", y);
- }
-exit(0);
-}
-
+++ /dev/null
-/* j1f.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j1f();
- *
- * y = j1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a polynomial approximation
- * 2
- * (w - r ) x P(w)
- * 1
- * 2
- * is used, where w = x and r is the first zero of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.2e-7 2.5e-8
- * IEEE 2, 32 100000 2.0e-7 5.3e-8
- *
- *
- */
-\f/* y1.c
- *
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2
- * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
- * 1
- *
- * Thus a call to j1() is required.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.2e-7 4.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.3e-8
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-
-static float JP[5] = {
--4.878788132172128E-009f,
- 6.009061827883699E-007f,
--4.541343896997497E-005f,
- 1.937383947804541E-003f,
--3.405537384615824E-002f
-};
-
-static float YP[5] = {
- 8.061978323326852E-009f,
--9.496460629917016E-007f,
- 6.719543806674249E-005f,
--2.641785726447862E-003f,
- 4.202369946500099E-002f
-};
-
-static float MO1[8] = {
- 6.913942741265801E-002f,
--2.284801500053359E-001f,
- 3.138238455499697E-001f,
--2.102302420403875E-001f,
- 5.435364690523026E-003f,
- 1.493389585089498E-001f,
- 4.976029650847191E-006f,
- 7.978845453073848E-001f
-};
-
-static float PH1[8] = {
--4.497014141919556E+001f,
- 5.073465654089319E+001f,
--2.485774108720340E+001f,
- 7.222973196770240E+000f,
--1.544842782180211E+000f,
- 3.503787691653334E-001f,
--1.637986776941202E-001f,
- 3.749989509080821E-001f
-};
-
-static float YO1 = 4.66539330185668857532f;
-static float Z1 = 1.46819706421238932572E1f;
-
-static float THPIO4F = 2.35619449019234492885f; /* 3*pi/4 */
-static float TWOOPI = 0.636619772367581343075535f; /* 2/pi */
-extern float PIO4;
-
-
-float polevlf(float, float *, int);
-float logf(float), sinf(float), cosf(float), sqrtf(float);
-
-float j1f( float xx )
-{
-float x, w, z, p, q, xn;
-
-
-x = xx;
-if( x < 0 )
- x = -xx;
-
-if( x <= 2.0f )
- {
- z = x * x;
- p = (z-Z1) * x * polevlf( z, JP, 4 );
- return( p );
- }
-
-q = 1.0f/x;
-w = sqrtf(q);
-
-p = w * polevlf( q, MO1, 7);
-w = q*q;
-xn = q * polevlf( w, PH1, 7) - THPIO4F;
-p = p * cosf(xn + x);
-return(p);
-}
-
-
-
-
-extern float MAXNUMF;
-
-float y1f( float xx )
-{
-float x, w, z, p, q, xn;
-
-
-x = xx;
-if( x <= 2.0f )
- {
- if( x <= 0.0f )
- {
- mtherr( "y1f", DOMAIN );
- return( -MAXNUMF );
- }
- z = x * x;
- w = (z - YO1) * x * polevlf( z, YP, 4 );
- w += TWOOPI * ( j1f(x) * logf(x) - 1.0f/x );
- return( w );
- }
-
-q = 1.0f/x;
-w = sqrtf(q);
-
-p = w * polevlf( q, MO1, 7);
-w = q*q;
-xn = q * polevlf( w, PH1, 7) - THPIO4F;
-p = p * sinf(xn + x);
-return(p);
-}
+++ /dev/null
-/* jnf.c
- *
- * Bessel function of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * float x, y, jnf();
- *
- * y = jnf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The ratio of jn(x) to j0(x) is computed by backward
- * recurrence. First the ratio jn/jn-1 is found by a
- * continued fraction expansion. Then the recurrence
- * relating successive orders is applied until j0 or j1 is
- * reached.
- *
- * If n = 0 or 1 the routine for j0 or j1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic range # trials peak rms
- * IEEE 0, 15 30000 3.6e-7 3.6e-8
- *
- *
- * Not suitable for large n or x. Use jvf() instead.
- *
- */
-\f
-/* jn.c
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-#include <math.h>
-
-extern float MACHEPF;
-
-float j0f(float), j1f(float);
-
-float jnf( int n, float xx )
-{
-float x, pkm2, pkm1, pk, xk, r, ans, xinv, sign;
-int k;
-
-x = xx;
-sign = 1.0;
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) != 0 ) /* -1**n */
- sign = -1.0;
- }
-
-if( n == 0 )
- return( sign * j0f(x) );
-if( n == 1 )
- return( sign * j1f(x) );
-if( n == 2 )
- return( sign * (2.0 * j1f(x) / x - j0f(x)) );
-
-/*
-if( x < MACHEPF )
- return( 0.0 );
-*/
-
-/* continued fraction */
-k = 24;
-pk = 2 * (n + k);
-ans = pk;
-xk = x * x;
-
-do
- {
- pk -= 2.0;
- ans = pk - (xk/ans);
- }
-while( --k > 0 );
-/*ans = x/ans;*/
-
-/* backward recurrence */
-
-pk = 1.0;
-/*pkm1 = 1.0/ans;*/
-xinv = 1.0/x;
-pkm1 = ans * xinv;
-k = n-1;
-r = (float )(2 * k);
-
-do
- {
- pkm2 = (pkm1 * r - pk * x) * xinv;
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0;
- }
-while( --k > 0 );
-
-r = pk;
-if( r < 0 )
- r = -r;
-ans = pkm1;
-if( ans < 0 )
- ans = -ans;
-
-if( r > ans ) /* if( fabs(pk) > fabs(pkm1) ) */
- ans = sign * j1f(x)/pk;
-else
- ans = sign * j0f(x)/pkm1;
-return( ans );
-}
+++ /dev/null
-/* jvf.c
- *
- * Bessel function of noninteger order
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, jvf();
- *
- * y = jvf( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order v of the argument,
- * where v is real. Negative x is allowed if v is an integer.
- *
- * Several expansions are included: the ascending power
- * series, the Hankel expansion, and two transitional
- * expansions for large v. If v is not too large, it
- * is reduced by recurrence to a region of best accuracy.
- *
- * The single precision routine accepts negative v, but with
- * reduced accuracy.
- *
- *
- *
- * ACCURACY:
- * Results for integer v are indicated by *.
- * Error criterion is absolute, except relative when |jv()| > 1.
- *
- * arithmetic domain # trials peak rms
- * v x
- * IEEE 0,125 0,125 30000 2.0e-6 2.0e-7
- * IEEE -17,0 0,125 30000 1.1e-5 4.0e-7
- * IEEE -100,0 0,125 3000 1.5e-4 7.8e-6
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-#define DEBUG 0
-
-extern float MAXNUMF, MACHEPF, MINLOGF, MAXLOGF, PIF;
-extern int sgngamf;
-
-/* BIG = 1/MACHEPF */
-#define BIG 16777216.
-
-#ifdef ANSIC
-float floorf(float), j0f(float), j1f(float);
-static float jnxf(float, float);
-static float jvsf(float, float);
-static float hankelf(float, float);
-static float jntf(float, float);
-static float recurf( float *, float, float * );
-float sqrtf(float), sinf(float), cosf(float);
-float lgamf(float), expf(float), logf(float), powf(float, float);
-float gammaf(float), cbrtf(float), acosf(float);
-int airyf(float, float *, float *, float *, float *);
-float polevlf(float, float *, int);
-#else
-float floorf(), j0f(), j1f();
-float sqrtf(), sinf(), cosf();
-float lgamf(), expf(), logf(), powf(), gammaf();
-float cbrtf(), polevlf(), acosf();
-void airyf();
-static float recurf(), jvsf(), hankelf(), jnxf(), jntf(), jvsf();
-#endif
-
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-float jvf( float nn, float xx )
-{
-float n, x, k, q, t, y, an, sign;
-int i, nint;
-
-n = nn;
-x = xx;
-nint = 0; /* Flag for integer n */
-sign = 1.0; /* Flag for sign inversion */
-an = fabsf( n );
-y = floorf( an );
-if( y == an )
- {
- nint = 1;
- i = an - 16384.0 * floorf( an/16384.0 );
- if( n < 0.0 )
- {
- if( i & 1 )
- sign = -sign;
- n = an;
- }
- if( x < 0.0 )
- {
- if( i & 1 )
- sign = -sign;
- x = -x;
- }
- if( n == 0.0 )
- return( j0f(x) );
- if( n == 1.0 )
- return( sign * j1f(x) );
- }
-
-if( (x < 0.0) && (y != an) )
- {
- mtherr( "jvf", DOMAIN );
- y = 0.0;
- goto done;
- }
-
-y = fabsf(x);
-
-if( y < MACHEPF )
- goto underf;
-
-/* Easy cases - x small compared to n */
-t = 3.6 * sqrtf(an);
-if( y < t )
- return( sign * jvsf(n,x) );
-
-/* x large compared to n */
-k = 3.6 * sqrtf(y);
-if( (an < k) && (y > 6.0) )
- return( sign * hankelf(n,x) );
-
-if( (n > -100) && (n < 14.0) )
- {
-/* Note: if x is too large, the continued
- * fraction will fail; but then the
- * Hankel expansion can be used.
- */
- if( nint != 0 )
- {
- k = 0.0;
- q = recurf( &n, x, &k );
- if( k == 0.0 )
- {
- y = j0f(x)/q;
- goto done;
- }
- if( k == 1.0 )
- {
- y = j1f(x)/q;
- goto done;
- }
- }
-
- if( n >= 0.0 )
- {
-/* Recur backwards from a larger value of n
- */
- if( y > 1.3 * an )
- goto recurdwn;
- if( an > 1.3 * y )
- goto recurdwn;
- k = n;
- y = 2.0*(y+an+1.0);
- if( (y - n) > 33.0 )
- y = n + 33.0;
- y = n + floorf(y-n);
- q = recurf( &y, x, &k );
- y = jvsf(y,x) * q;
- goto done;
- }
-recurdwn:
- if( an > (k + 3.0) )
- {
-/* Recur backwards from n to k
- */
- if( n < 0.0 )
- k = -k;
- q = n - floorf(n);
- k = floorf(k) + q;
- if( n > 0.0 )
- q = recurf( &n, x, &k );
- else
- {
- t = k;
- k = n;
- q = recurf( &t, x, &k );
- k = t;
- }
- if( q == 0.0 )
- {
-underf:
- y = 0.0;
- goto done;
- }
- }
- else
- {
- k = n;
- q = 1.0;
- }
-
-/* boundary between convergence of
- * power series and Hankel expansion
- */
- t = fabsf(k);
- if( t < 26.0 )
- t = (0.0083*t + 0.09)*t + 12.9;
- else
- t = 0.9 * t;
-
- if( y > t ) /* y = |x| */
- y = hankelf(k,x);
- else
- y = jvsf(k,x);
-#if DEBUG
-printf( "y = %.16e, q = %.16e\n", y, q );
-#endif
- if( n > 0.0 )
- y /= q;
- else
- y *= q;
- }
-
-else
- {
-/* For large positive n, use the uniform expansion
- * or the transitional expansion.
- * But if x is of the order of n**2,
- * these may blow up, whereas the
- * Hankel expansion will then work.
- */
- if( n < 0.0 )
- {
- mtherr( "jvf", TLOSS );
- y = 0.0;
- goto done;
- }
- t = y/an;
- t /= an;
- if( t > 0.3 )
- y = hankelf(n,x);
- else
- y = jnxf(n,x);
- }
-
-done: return( sign * y);
-}
-\f
-/* Reduce the order by backward recurrence.
- * AMS55 #9.1.27 and 9.1.73.
- */
-
-static float recurf( float *n, float xx, float *newn )
-{
-float x, pkm2, pkm1, pk, pkp1, qkm2, qkm1;
-float k, ans, qk, xk, yk, r, t, kf, xinv;
-static float big = BIG;
-int nflag, ctr;
-
-x = xx;
-/* continued fraction for Jn(x)/Jn-1(x) */
-if( *n < 0.0 )
- nflag = 1;
-else
- nflag = 0;
-
-fstart:
-
-#if DEBUG
-printf( "n = %.6e, newn = %.6e, cfrac = ", *n, *newn );
-#endif
-
-pkm2 = 0.0;
-qkm2 = 1.0;
-pkm1 = x;
-qkm1 = *n + *n;
-xk = -x * x;
-yk = qkm1;
-ans = 1.0;
-ctr = 0;
-do
- {
- yk += 2.0;
- pk = pkm1 * yk + pkm2 * xk;
- qk = qkm1 * yk + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
- if( qk != 0 )
- r = pk/qk;
- else
- r = 0.0;
- if( r != 0 )
- {
- t = fabsf( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0;
-
- if( t < MACHEPF )
- goto done;
-
- if( fabsf(pk) > big )
- {
- pkm2 *= MACHEPF;
- pkm1 *= MACHEPF;
- qkm2 *= MACHEPF;
- qkm1 *= MACHEPF;
- }
- }
-while( t > MACHEPF );
-
-done:
-
-#if DEBUG
-printf( "%.6e\n", ans );
-#endif
-
-/* Change n to n-1 if n < 0 and the continued fraction is small
- */
-if( nflag > 0 )
- {
- if( fabsf(ans) < 0.125 )
- {
- nflag = -1;
- *n = *n - 1.0;
- goto fstart;
- }
- }
-
-
-kf = *newn;
-
-/* backward recurrence
- * 2k
- * J (x) = --- J (x) - J (x)
- * k-1 x k k+1
- */
-
-pk = 1.0;
-pkm1 = 1.0/ans;
-k = *n - 1.0;
-r = 2 * k;
-xinv = 1.0/x;
-do
- {
- pkm2 = (pkm1 * r - pk * x) * xinv;
- pkp1 = pk;
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0;
-#if 0
- t = fabsf(pkp1) + fabsf(pk);
- if( (k > (kf + 2.5)) && (fabsf(pkm1) < 0.25*t) )
- {
- k -= 1.0;
- t = x*x;
- pkm2 = ( (r*(r+2.0)-t)*pk - r*x*pkp1 )/t;
- pkp1 = pk;
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0;
- }
-#endif
- k -= 1.0;
- }
-while( k > (kf + 0.5) );
-
-#if 0
-/* Take the larger of the last two iterates
- * on the theory that it may have less cancellation error.
- */
-if( (kf >= 0.0) && (fabsf(pk) > fabsf(pkm1)) )
- {
- k += 1.0;
- pkm2 = pk;
- }
-#endif
-
-*newn = k;
-#if DEBUG
-printf( "newn %.6e\n", k );
-#endif
-return( pkm2 );
-}
-
-
-
-/* Ascending power series for Jv(x).
- * AMS55 #9.1.10.
- */
-
-static float jvsf( float nn, float xx )
-{
-float n, x, t, u, y, z, k, ay;
-
-#if DEBUG
-printf( "jvsf: " );
-#endif
-n = nn;
-x = xx;
-z = -0.25 * x * x;
-u = 1.0;
-y = u;
-k = 1.0;
-t = 1.0;
-
-while( t > MACHEPF )
- {
- u *= z / (k * (n+k));
- y += u;
- k += 1.0;
- t = fabsf(u);
- if( (ay = fabsf(y)) > 1.0 )
- t /= ay;
- }
-
-if( x < 0.0 )
- {
- y = y * powf( 0.5 * x, n ) / gammaf( n + 1.0 );
- }
-else
- {
- t = n * logf(0.5*x) - lgamf(n + 1.0);
- if( t < -MAXLOGF )
- {
- return( 0.0 );
- }
- if( t > MAXLOGF )
- {
- t = logf(y) + t;
- if( t > MAXLOGF )
- {
- mtherr( "jvf", OVERFLOW );
- return( MAXNUMF );
- }
- else
- {
- y = sgngamf * expf(t);
- return(y);
- }
- }
- y = sgngamf * y * expf( t );
- }
-#if DEBUG
-printf( "y = %.8e\n", y );
-#endif
-return(y);
-}
-\f
-/* Hankel's asymptotic expansion
- * for large x.
- * AMS55 #9.2.5.
- */
-static float hankelf( float nn, float xx )
-{
-float n, x, t, u, z, k, sign, conv;
-float p, q, j, m, pp, qq;
-int flag;
-
-#if DEBUG
-printf( "hankelf: " );
-#endif
-n = nn;
-x = xx;
-m = 4.0*n*n;
-j = 1.0;
-z = 8.0 * x;
-k = 1.0;
-p = 1.0;
-u = (m - 1.0)/z;
-q = u;
-sign = 1.0;
-conv = 1.0;
-flag = 0;
-t = 1.0;
-pp = 1.0e38;
-qq = 1.0e38;
-
-while( t > MACHEPF )
- {
- k += 2.0;
- j += 1.0;
- sign = -sign;
- u *= (m - k * k)/(j * z);
- p += sign * u;
- k += 2.0;
- j += 1.0;
- u *= (m - k * k)/(j * z);
- q += sign * u;
- t = fabsf(u/p);
- if( t < conv )
- {
- conv = t;
- qq = q;
- pp = p;
- flag = 1;
- }
-/* stop if the terms start getting larger */
- if( (flag != 0) && (t > conv) )
- {
-#if DEBUG
- printf( "Hankel: convergence to %.4E\n", conv );
-#endif
- goto hank1;
- }
- }
-
-hank1:
-u = x - (0.5*n + 0.25) * PIF;
-t = sqrtf( 2.0/(PIF*x) ) * ( pp * cosf(u) - qq * sinf(u) );
-return( t );
-}
-\f
-
-/* Asymptotic expansion for large n.
- * AMS55 #9.3.35.
- */
-
-static float lambda[] = {
- 1.0,
- 1.041666666666666666666667E-1,
- 8.355034722222222222222222E-2,
- 1.282265745563271604938272E-1,
- 2.918490264641404642489712E-1,
- 8.816272674437576524187671E-1,
- 3.321408281862767544702647E+0,
- 1.499576298686255465867237E+1,
- 7.892301301158651813848139E+1,
- 4.744515388682643231611949E+2,
- 3.207490090890661934704328E+3
-};
-static float mu[] = {
- 1.0,
- -1.458333333333333333333333E-1,
- -9.874131944444444444444444E-2,
- -1.433120539158950617283951E-1,
- -3.172272026784135480967078E-1,
- -9.424291479571202491373028E-1,
- -3.511203040826354261542798E+0,
- -1.572726362036804512982712E+1,
- -8.228143909718594444224656E+1,
- -4.923553705236705240352022E+2,
- -3.316218568547972508762102E+3
-};
-static float P1[] = {
- -2.083333333333333333333333E-1,
- 1.250000000000000000000000E-1
-};
-static float P2[] = {
- 3.342013888888888888888889E-1,
- -4.010416666666666666666667E-1,
- 7.031250000000000000000000E-2
-};
-static float P3[] = {
- -1.025812596450617283950617E+0,
- 1.846462673611111111111111E+0,
- -8.912109375000000000000000E-1,
- 7.324218750000000000000000E-2
-};
-static float P4[] = {
- 4.669584423426247427983539E+0,
- -1.120700261622299382716049E+1,
- 8.789123535156250000000000E+0,
- -2.364086914062500000000000E+0,
- 1.121520996093750000000000E-1
-};
-static float P5[] = {
- -2.8212072558200244877E1,
- 8.4636217674600734632E1,
- -9.1818241543240017361E1,
- 4.2534998745388454861E1,
- -7.3687943594796316964E0,
- 2.27108001708984375E-1
-};
-static float P6[] = {
- 2.1257013003921712286E2,
- -7.6525246814118164230E2,
- 1.0599904525279998779E3,
- -6.9957962737613254123E2,
- 2.1819051174421159048E2,
- -2.6491430486951555525E1,
- 5.7250142097473144531E-1
-};
-static float P7[] = {
- -1.9194576623184069963E3,
- 8.0617221817373093845E3,
- -1.3586550006434137439E4,
- 1.1655393336864533248E4,
- -5.3056469786134031084E3,
- 1.2009029132163524628E3,
- -1.0809091978839465550E2,
- 1.7277275025844573975E0
-};
-
-
-static float jnxf( float nn, float xx )
-{
-float n, x, zeta, sqz, zz, zp, np;
-float cbn, n23, t, z, sz;
-float pp, qq, z32i, zzi;
-float ak, bk, akl, bkl;
-int sign, doa, dob, nflg, k, s, tk, tkp1, m;
-static float u[8];
-static float ai, aip, bi, bip;
-
-n = nn;
-x = xx;
-/* Test for x very close to n.
- * Use expansion for transition region if so.
- */
-cbn = cbrtf(n);
-z = (x - n)/cbn;
-if( (fabsf(z) <= 0.7) || (n < 0.0) )
- return( jntf(n,x) );
-z = x/n;
-zz = 1.0 - z*z;
-if( zz == 0.0 )
- return(0.0);
-
-if( zz > 0.0 )
- {
- sz = sqrtf( zz );
- t = 1.5 * (logf( (1.0+sz)/z ) - sz ); /* zeta ** 3/2 */
- zeta = cbrtf( t * t );
- nflg = 1;
- }
-else
- {
- sz = sqrtf(-zz);
- t = 1.5 * (sz - acosf(1.0/z));
- zeta = -cbrtf( t * t );
- nflg = -1;
- }
-z32i = fabsf(1.0/t);
-sqz = cbrtf(t);
-
-/* Airy function */
-n23 = cbrtf( n * n );
-t = n23 * zeta;
-
-#if DEBUG
-printf("zeta %.5E, Airyf(%.5E)\n", zeta, t );
-#endif
-airyf( t, &ai, &aip, &bi, &bip );
-
-/* polynomials in expansion */
-u[0] = 1.0;
-zzi = 1.0/zz;
-u[1] = polevlf( zzi, P1, 1 )/sz;
-u[2] = polevlf( zzi, P2, 2 )/zz;
-u[3] = polevlf( zzi, P3, 3 )/(sz*zz);
-pp = zz*zz;
-u[4] = polevlf( zzi, P4, 4 )/pp;
-u[5] = polevlf( zzi, P5, 5 )/(pp*sz);
-pp *= zz;
-u[6] = polevlf( zzi, P6, 6 )/pp;
-u[7] = polevlf( zzi, P7, 7 )/(pp*sz);
-
-#if DEBUG
-for( k=0; k<=7; k++ )
- printf( "u[%d] = %.5E\n", k, u[k] );
-#endif
-
-pp = 0.0;
-qq = 0.0;
-np = 1.0;
-/* flags to stop when terms get larger */
-doa = 1;
-dob = 1;
-akl = MAXNUMF;
-bkl = MAXNUMF;
-
-for( k=0; k<=3; k++ )
- {
- tk = 2 * k;
- tkp1 = tk + 1;
- zp = 1.0;
- ak = 0.0;
- bk = 0.0;
- for( s=0; s<=tk; s++ )
- {
- if( doa )
- {
- if( (s & 3) > 1 )
- sign = nflg;
- else
- sign = 1;
- ak += sign * mu[s] * zp * u[tk-s];
- }
-
- if( dob )
- {
- m = tkp1 - s;
- if( ((m+1) & 3) > 1 )
- sign = nflg;
- else
- sign = 1;
- bk += sign * lambda[s] * zp * u[m];
- }
- zp *= z32i;
- }
-
- if( doa )
- {
- ak *= np;
- t = fabsf(ak);
- if( t < akl )
- {
- akl = t;
- pp += ak;
- }
- else
- doa = 0;
- }
-
- if( dob )
- {
- bk += lambda[tkp1] * zp * u[0];
- bk *= -np/sqz;
- t = fabsf(bk);
- if( t < bkl )
- {
- bkl = t;
- qq += bk;
- }
- else
- dob = 0;
- }
-#if DEBUG
- printf("a[%d] %.5E, b[%d] %.5E\n", k, ak, k, bk );
-#endif
- if( np < MACHEPF )
- break;
- np /= n*n;
- }
-
-/* normalizing factor ( 4*zeta/(1 - z**2) )**1/4 */
-t = 4.0 * zeta/zz;
-t = sqrtf( sqrtf(t) );
-
-t *= ai*pp/cbrtf(n) + aip*qq/(n23*n);
-return(t);
-}
-\f
-/* Asymptotic expansion for transition region,
- * n large and x close to n.
- * AMS55 #9.3.23.
- */
-
-static float PF2[] = {
- -9.0000000000000000000e-2,
- 8.5714285714285714286e-2
-};
-static float PF3[] = {
- 1.3671428571428571429e-1,
- -5.4920634920634920635e-2,
- -4.4444444444444444444e-3
-};
-static float PF4[] = {
- 1.3500000000000000000e-3,
- -1.6036054421768707483e-1,
- 4.2590187590187590188e-2,
- 2.7330447330447330447e-3
-};
-static float PG1[] = {
- -2.4285714285714285714e-1,
- 1.4285714285714285714e-2
-};
-static float PG2[] = {
- -9.0000000000000000000e-3,
- 1.9396825396825396825e-1,
- -1.1746031746031746032e-2
-};
-static float PG3[] = {
- 1.9607142857142857143e-2,
- -1.5983694083694083694e-1,
- 6.3838383838383838384e-3
-};
-
-
-static float jntf( float nn, float xx )
-{
-float n, x, z, zz, z3;
-float cbn, n23, cbtwo;
-float ai, aip, bi, bip; /* Airy functions */
-float nk, fk, gk, pp, qq;
-float F[5], G[4];
-int k;
-
-n = nn;
-x = xx;
-cbn = cbrtf(n);
-z = (x - n)/cbn;
-cbtwo = cbrtf( 2.0 );
-
-/* Airy function */
-zz = -cbtwo * z;
-airyf( zz, &ai, &aip, &bi, &bip );
-
-/* polynomials in expansion */
-zz = z * z;
-z3 = zz * z;
-F[0] = 1.0;
-F[1] = -z/5.0;
-F[2] = polevlf( z3, PF2, 1 ) * zz;
-F[3] = polevlf( z3, PF3, 2 );
-F[4] = polevlf( z3, PF4, 3 ) * z;
-G[0] = 0.3 * zz;
-G[1] = polevlf( z3, PG1, 1 );
-G[2] = polevlf( z3, PG2, 2 ) * z;
-G[3] = polevlf( z3, PG3, 2 ) * zz;
-#if DEBUG
-for( k=0; k<=4; k++ )
- printf( "F[%d] = %.5E\n", k, F[k] );
-for( k=0; k<=3; k++ )
- printf( "G[%d] = %.5E\n", k, G[k] );
-#endif
-pp = 0.0;
-qq = 0.0;
-nk = 1.0;
-n23 = cbrtf( n * n );
-
-for( k=0; k<=4; k++ )
- {
- fk = F[k]*nk;
- pp += fk;
- if( k != 4 )
- {
- gk = G[k]*nk;
- qq += gk;
- }
-#if DEBUG
- printf("fk[%d] %.5E, gk[%d] %.5E\n", k, fk, k, gk );
-#endif
- nk /= n23;
- }
-
-fk = cbtwo * ai * pp/cbn + cbrtf(4.0) * aip * qq/n;
-return(fk);
-}
+++ /dev/null
-/* k0f.c
- *
- * Modified Bessel function, third kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0f();
- *
- * y = k0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order zero of the argument.
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at 2000 random points between 0 and 8. Peak absolute
- * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-7 8.5e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * K0 domain x <= 0 MAXNUM
- *
- */
-\f/* k0ef()
- *
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0ef();
- *
- * y = k0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 8.1e-7 7.8e-8
- * See k0().
- *
- */
-\f
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for K0(x) + log(x/2) I0(x)
- * in the interval [0,2]. The odd order coefficients are all
- * zero; only the even order coefficients are listed.
- *
- * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL.
- */
-
-static float A[] =
-{
- 1.90451637722020886025E-9f,
- 2.53479107902614945675E-7f,
- 2.28621210311945178607E-5f,
- 1.26461541144692592338E-3f,
- 3.59799365153615016266E-2f,
- 3.44289899924628486886E-1f,
--5.35327393233902768720E-1f
-};
-
-
-
-/* Chebyshev coefficients for exp(x) sqrt(x) K0(x)
- * in the inverted interval [2,infinity].
- *
- * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2).
- */
-
-static float B[] = {
--1.69753450938905987466E-9f,
- 8.57403401741422608519E-9f,
--4.66048989768794782956E-8f,
- 2.76681363944501510342E-7f,
--1.83175552271911948767E-6f,
- 1.39498137188764993662E-5f,
--1.28495495816278026384E-4f,
- 1.56988388573005337491E-3f,
--3.14481013119645005427E-2f,
- 2.44030308206595545468E0f
-};
-
-/* k0.c */
-
-extern float MAXNUMF;
-
-#ifdef ANSIC
-float chbevlf(float, float *, int);
-float expf(float), i0f(float), logf(float), sqrtf(float);
-#else
-float chbevlf(), expf(), i0f(), logf(), sqrtf();
-#endif
-
-
-float k0f( float xx )
-{
-float x, y, z;
-
-x = xx;
-if( x <= 0.0f )
- {
- mtherr( "k0f", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x <= 2.0f )
- {
- y = x * x - 2.0f;
- y = chbevlf( y, A, 7 ) - logf( 0.5f * x ) * i0f(x);
- return( y );
- }
-z = 8.0f/x - 2.0f;
-y = expf(-x) * chbevlf( z, B, 10 ) / sqrtf(x);
-return(y);
-}
-
-
-
-float k0ef( float xx )
-{
-float x, y;
-
-
-x = xx;
-if( x <= 0.0f )
- {
- mtherr( "k0ef", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x <= 2.0f )
- {
- y = x * x - 2.0f;
- y = chbevlf( y, A, 7 ) - logf( 0.5f * x ) * i0f(x);
- return( y * expf(x) );
- }
-
-y = chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x);
-return(y);
-}
+++ /dev/null
-/* k1f.c
- *
- * Modified Bessel function, third kind, order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1f();
- *
- * y = k1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the modified Bessel function of the third kind
- * of order one of the argument.
- *
- * The range is partitioned into the two intervals [0,2] and
- * (2, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.6e-7 7.6e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * k1 domain x <= 0 MAXNUM
- *
- */
-\f/* k1ef.c
- *
- * Modified Bessel function, third kind, order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1ef();
- *
- * y = k1ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order one of the argument:
- *
- * k1e(x) = exp(x) * k1(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.9e-7 6.7e-8
- * See k1().
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
- * in the interval [0,2].
- *
- * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
- */
-
-#define MINNUMF 6.0e-39
-static float A[] =
-{
--2.21338763073472585583E-8f,
--2.43340614156596823496E-6f,
--1.73028895751305206302E-4f,
--6.97572385963986435018E-3f,
--1.22611180822657148235E-1f,
--3.53155960776544875667E-1f,
- 1.52530022733894777053E0f
-};
-
-
-
-
-/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
- * in the interval [2,infinity].
- *
- * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
- */
-
-static float B[] =
-{
- 2.01504975519703286596E-9f,
--1.03457624656780970260E-8f,
- 5.74108412545004946722E-8f,
--3.50196060308781257119E-7f,
- 2.40648494783721712015E-6f,
--1.93619797416608296024E-5f,
- 1.95215518471351631108E-4f,
--2.85781685962277938680E-3f,
- 1.03923736576817238437E-1f,
- 2.72062619048444266945E0f
-};
-
-
-
-extern float MAXNUMF;
-#ifdef ANSIC
-float chbevlf(float, float *, int);
-float expf(float), i1f(float), logf(float), sqrtf(float);
-#else
-float chbevlf(), expf(), i1f(), logf(), sqrtf();
-#endif
-
-float k1f(float xx)
-{
-float x, y;
-
-x = xx;
-if( x <= MINNUMF )
- {
- mtherr( "k1f", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x <= 2.0f )
- {
- y = x * x - 2.0f;
- y = logf( 0.5f * x ) * i1f(x) + chbevlf( y, A, 7 ) / x;
- return( y );
- }
-
-return( expf(-x) * chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x) );
-
-}
-
-
-
-float k1ef( float xx )
-{
-float x, y;
-
-x = xx;
-if( x <= 0.0f )
- {
- mtherr( "k1ef", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x <= 2.0f )
- {
- y = x * x - 2.0f;
- y = logf( 0.5f * x ) * i1f(x) + chbevlf( y, A, 7 ) / x;
- return( y * expf(x) );
- }
-
-return( chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x) );
-
-}
+++ /dev/null
-/* knf.c
- *
- * Modified Bessel function, third kind, integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, knf();
- * int n;
- *
- * y = knf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order n of the argument.
- *
- * The range is partitioned into the two intervals [0,9.55] and
- * (9.55, infinity). An ascending power series is used in the
- * low range, and an asymptotic expansion in the high range.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, relative when function > 1:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 10000 2.0e-4 3.8e-6
- *
- * Error is high only near the crossover point x = 9.55
- * between the two expansions used.
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-
-*/
-
-
-/*
-Algorithm for Kn.
- n-1
- -n - (n-k-1)! 2 k
-K (x) = 0.5 (x/2) > -------- (-x /4)
- n - k!
- k=0
-
- inf. 2 k
- n n - (x /4)
- + (-1) 0.5(x/2) > {p(k+1) + p(n+k+1) - 2log(x/2)} ---------
- - k! (n+k)!
- k=0
-
-where p(m) is the psi function: p(1) = -EUL and
-
- m-1
- -
- p(m) = -EUL + > 1/k
- -
- k=1
-
-For large x,
- 2 2 2
- u-1 (u-1 )(u-3 )
-K (z) = sqrt(pi/2z) exp(-z) { 1 + ------- + ------------ + ...}
- v 1 2
- 1! (8z) 2! (8z)
-asymptotically, where
-
- 2
- u = 4 v .
-
-*/
-\f
-#include <math.h>
-
-#define EUL 5.772156649015328606065e-1
-#define MAXFAC 31
-extern float MACHEPF, MAXNUMF, MAXLOGF, PIF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-float expf(float), logf(float), sqrtf(float);
-
-float knf( int nnn, float xx )
-{
-float x, k, kf, nk1f, nkf, zn, t, s, z0, z;
-float ans, fn, pn, pk, zmn, tlg, tox;
-int i, n, nn;
-
-nn = nnn;
-x = xx;
-if( nn < 0 )
- n = -nn;
-else
- n = nn;
-
-if( n > MAXFAC )
- {
-overf:
- mtherr( "knf", OVERFLOW );
- return( MAXNUMF );
- }
-
-if( x <= 0.0 )
- {
- if( x < 0.0 )
- mtherr( "knf", DOMAIN );
- else
- mtherr( "knf", SING );
- return( MAXNUMF );
- }
-
-
-if( x > 9.55 )
- goto asymp;
-
-ans = 0.0;
-z0 = 0.25 * x * x;
-fn = 1.0;
-pn = 0.0;
-zmn = 1.0;
-tox = 2.0/x;
-
-if( n > 0 )
- {
- /* compute factorial of n and psi(n) */
- pn = -EUL;
- k = 1.0;
- for( i=1; i<n; i++ )
- {
- pn += 1.0/k;
- k += 1.0;
- fn *= k;
- }
-
- zmn = tox;
-
- if( n == 1 )
- {
- ans = 1.0/x;
- }
- else
- {
- nk1f = fn/n;
- kf = 1.0;
- s = nk1f;
- z = -z0;
- zn = 1.0;
- for( i=1; i<n; i++ )
- {
- nk1f = nk1f/(n-i);
- kf = kf * i;
- zn *= z;
- t = nk1f * zn / kf;
- s += t;
- if( (MAXNUMF - fabsf(t)) < fabsf(s) )
- goto overf;
- if( (tox > 1.0) && ((MAXNUMF/tox) < zmn) )
- goto overf;
- zmn *= tox;
- }
- s *= 0.5;
- t = fabsf(s);
- if( (zmn > 1.0) && ((MAXNUMF/zmn) < t) )
- goto overf;
- if( (t > 1.0) && ((MAXNUMF/t) < zmn) )
- goto overf;
- ans = s * zmn;
- }
- }
-
-
-tlg = 2.0 * logf( 0.5 * x );
-pk = -EUL;
-if( n == 0 )
- {
- pn = pk;
- t = 1.0;
- }
-else
- {
- pn = pn + 1.0/n;
- t = 1.0/fn;
- }
-s = (pk+pn-tlg)*t;
-k = 1.0;
-do
- {
- t *= z0 / (k * (k+n));
- pk += 1.0/k;
- pn += 1.0/(k+n);
- s += (pk+pn-tlg)*t;
- k += 1.0;
- }
-while( fabsf(t/s) > MACHEPF );
-
-s = 0.5 * s / zmn;
-if( n & 1 )
- s = -s;
-ans += s;
-
-return(ans);
-
-
-
-/* Asymptotic expansion for Kn(x) */
-/* Converges to 1.4e-17 for x > 18.4 */
-
-asymp:
-
-if( x > MAXLOGF )
- {
- mtherr( "knf", UNDERFLOW );
- return(0.0);
- }
-k = n;
-pn = 4.0 * k * k;
-pk = 1.0;
-z0 = 8.0 * x;
-fn = 1.0;
-t = 1.0;
-s = t;
-nkf = MAXNUMF;
-i = 0;
-do
- {
- z = pn - pk * pk;
- t = t * z /(fn * z0);
- nk1f = fabsf(t);
- if( (i >= n) && (nk1f > nkf) )
- {
- goto adone;
- }
- nkf = nk1f;
- s += t;
- fn += 1.0;
- pk += 2.0;
- i += 1;
- }
-while( fabsf(t/s) > MACHEPF );
-
-adone:
-ans = expf(-x) * sqrtf( PIF/(2.0*x) ) * s;
-return(ans);
-}
+++ /dev/null
-/* log10f.c
- *
- * Common logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, log10f();
- *
- * y = log10f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns logarithm to the base 10 of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. The logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 100000 1.3e-7 3.4e-8
- * IEEE 0, MAXNUMF 100000 1.3e-7 2.6e-8
- *
- * In the tests over the interval [0, MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [-MAXL10, MAXL10].
- *
- * ERROR MESSAGES:
- *
- * log10f singularity: x = 0; returns -MAXL10
- * log10f domain: x < 0; returns -MAXL10
- * MAXL10 = 38.230809449325611792
- */
-\f
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-static char fname[] = {"log10"};
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-static float P[] = {
- 7.0376836292E-2,
--1.1514610310E-1,
- 1.1676998740E-1,
--1.2420140846E-1,
- 1.4249322787E-1,
--1.6668057665E-1,
- 2.0000714765E-1,
--2.4999993993E-1,
- 3.3333331174E-1
-};
-
-
-#define SQRTH 0.70710678118654752440
-#define L102A 3.0078125E-1
-#define L102B 2.48745663981195213739E-4
-#define L10EA 4.3359375E-1
-#define L10EB 7.00731903251827651129E-4
-
-static float MAXL10 = 38.230809449325611792;
-
-float frexpf(float, int *), polevlf(float, float *, int);
-
-float log10f(float xx)
-{
-float x, y, z;
-int e;
-
-x = xx;
-/* Test for domain */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- mtherr( fname, SING );
- else
- mtherr( fname, DOMAIN );
- return( -MAXL10 );
- }
-
-/* separate mantissa from exponent */
-
-x = frexpf( x, &e );
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = 2.0*x - 1.0;
- }
-else
- {
- x = x - 1.0;
- }
-
-
-/* rational form */
-z = x*x;
-y = x * ( z * polevlf( x, P, 8 ) );
-y = y - 0.5 * z; /* y - 0.5 * x**2 */
-
-/* multiply log of fraction by log10(e)
- * and base 2 exponent by log10(2)
- */
-z = (x + y) * L10EB; /* accumulate terms in order of size */
-z += y * L10EA;
-z += x * L10EA;
-x = e;
-z += x * L102B;
-z += x * L102A;
-
-
-return( z );
-}
+++ /dev/null
-/* log2f.c
- *
- * Base 2 logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, log2f();
- *
- * y = log2f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 2 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the base e
- * logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE exp(+-88) 100000 1.1e-7 2.4e-8
- * IEEE 0.5, 2.0 100000 1.1e-7 3.0e-8
- *
- * In the tests over the interval [exp(+-88)], the logarithms
- * of the random arguments were uniformly distributed.
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns MINLOGF/log(2)
- * log domain: x < 0; returns MINLOGF/log(2)
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-static char fname[] = {"log2"};
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)
- * 1/sqrt(2) <= x < sqrt(2)
- */
-
-static float P[] = {
- 7.0376836292E-2,
--1.1514610310E-1,
- 1.1676998740E-1,
--1.2420140846E-1,
- 1.4249322787E-1,
--1.6668057665E-1,
- 2.0000714765E-1,
--2.4999993993E-1,
- 3.3333331174E-1
-};
-
-#define LOG2EA 0.44269504088896340735992
-#define SQRTH 0.70710678118654752440
-extern float MINLOGF, LOGE2F;
-
-float frexpf(float, int *), polevlf(float, float *, int);
-
-float log2f(float xx)
-{
-float x, y, z;
-int e;
-
-x = xx;
-/* Test for domain */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- mtherr( fname, SING );
- else
- mtherr( fname, DOMAIN );
- return( MINLOGF/LOGE2F );
- }
-
-/* separate mantissa from exponent */
-x = frexpf( x, &e );
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = 2.0*x - 1.0;
- }
-else
- {
- x = x - 1.0;
- }
-
-z = x*x;
-y = x * ( z * polevlf( x, P, 8 ) );
-y = y - 0.5 * z; /* y - 0.5 * x**2 */
-
-
-/* Multiply log of fraction by log2(e)
- * and base 2 exponent by 1
- *
- * ***CAUTION***
- *
- * This sequence of operations is critical and it may
- * be horribly defeated by some compiler optimizers.
- */
-z = y * LOG2EA;
-z += x * LOG2EA;
-z += y;
-z += x;
-z += (float )e;
-return( z );
-}
+++ /dev/null
-/* logf.c
- *
- * Natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, logf();
- *
- * y = logf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 100000 7.6e-8 2.7e-8
- * IEEE 1, MAXNUMF 100000 2.6e-8
- *
- * In the tests over the interval [1, MAXNUM], the logarithms
- * of the random arguments were uniformly distributed over
- * [0, MAXLOGF].
- *
- * ERROR MESSAGES:
- *
- * logf singularity: x = 0; returns MINLOG
- * logf domain: x < 0; returns MINLOG
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision natural logarithm
- * test interval: [sqrt(2)/2, sqrt(2)]
- * trials: 10000
- * peak relative error: 7.1e-8
- * rms relative error: 2.7e-8
- */
-
-#include <math.h>
-extern float MINLOGF, SQRTHF;
-
-
-float frexpf( float, int * );
-
-float logf( float xx )
-{
-register float y;
-float x, z, fe;
-int e;
-
-x = xx;
-fe = 0.0;
-/* Test for domain */
-if( x <= 0.0 )
- {
- if( x == 0.0 )
- mtherr( "logf", SING );
- else
- mtherr( "logf", DOMAIN );
- return( MINLOGF );
- }
-
-x = frexpf( x, &e );
-if( x < SQRTHF )
- {
- e -= 1;
- x = x + x - 1.0; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0;
- }
-z = x * x;
-/* 3.4e-9 */
-/*
-p = logfcof;
-y = *p++ * x;
-for( i=0; i<8; i++ )
- {
- y += *p++;
- y *= x;
- }
-y *= z;
-*/
-
-y =
-(((((((( 7.0376836292E-2 * x
-- 1.1514610310E-1) * x
-+ 1.1676998740E-1) * x
-- 1.2420140846E-1) * x
-+ 1.4249322787E-1) * x
-- 1.6668057665E-1) * x
-+ 2.0000714765E-1) * x
-- 2.4999993993E-1) * x
-+ 3.3333331174E-1) * x * z;
-
-if( e )
- {
- fe = e;
- y += -2.12194440e-4 * fe;
- }
-
-y += -0.5 * z; /* y - 0.5 x^2 */
-z = x + y; /* ... + x */
-
-if( e )
- z += 0.693359375 * fe;
-
-return( z );
-}
+++ /dev/null
-/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * void mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file math.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * math.h
- *
- */
-\f
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Notice: the order of appearance of the following
- * messages is bound to the error codes defined
- * in math.h.
- */
-static char *ermsg[7] = {
-"unknown", /* error code 0 */
-"domain", /* error code 1 */
-"singularity", /* et seq. */
-"overflow",
-"underflow",
-"total loss of precision",
-"partial loss of precision"
-};
-
-
-void printf();
-
-int mtherr( name, code )
-char *name;
-int code;
-{
-
-/* Display string passed by calling program,
- * which is supposed to be the name of the
- * function in which the error occurred:
- */
-printf( "\n%s ", name );
- /* exit(2); */
-
-/* Display error message defined
- * by the code argument.
- */
-if( (code <= 0) || (code >= 6) )
- code = 0;
-printf( "%s error\n", ermsg[code] );
-
-/* Return to calling
- * program
- */
-return 0;
-}
+++ /dev/null
-float inf = 1.0f/0.0f;
-float nnn = 1.0f/0.0f - 1.0f/0.0f;
-float fin = 1.0f;
-float neg = -1.0f;
-float nn2;
-
-int isnanf(), isfinitef(), signbitf();
-
-void pvalue (char *str, float x)
-{
-union
- {
- float f;
- unsigned int i;
- }u;
-
-printf("%s ", str);
-u.f = x;
-printf("%08x\n", u.i);
-}
-
-
-int
-main()
-{
-
-if (!isnanf(nnn))
- abort();
-pvalue("nnn", nnn);
-pvalue("inf", inf);
-nn2 = inf - inf;
-pvalue("inf - inf", nn2);
-if (isnanf(fin))
- abort();
-if (isnanf(inf))
- abort();
-if (!isfinitef(fin))
- abort();
-if (isfinitef(nnn))
- abort();
-if (isfinitef(inf))
- abort();
-if (!signbitf(neg))
- abort();
-if (signbitf(fin))
- abort();
-if (signbitf(inf))
- abort();
-/*
-if (signbitf(nnn))
- abort();
- */
-exit (0);
-}
+++ /dev/null
-/* nbdtrf.c
- *
- * Negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, nbdtrf();
- *
- * y = nbdtrf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the negative
- * binomial distribution:
- *
- * k
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * In a sequence of Bernoulli trials, this is the probability
- * that k or fewer failures precede the nth success.
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 1.5e-4 1.9e-5
- *
- */
-\f/* nbdtrcf.c
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * float p, y, nbdtrcf();
- *
- * y = nbdtrcf( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 1.4e-4 2.0e-5
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef ANSIC
-float incbetf(float, float, float);
-#else
-float incbetf();
-#endif
-
-
-float nbdtrcf( int k, int n, float pp )
-{
-float dk, dn, p;
-
-p = pp;
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtrf", DOMAIN );
- return( 0.0 );
- }
-
-dk = k+1;
-dn = n;
-return( incbetf( dk, dn, 1.0 - p ) );
-}
-
-
-
-float nbdtrf( int k, int n, float pp )
-{
-float dk, dn, p;
-
-p = pp;
-if( (p < 0.0) || (p > 1.0) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtrf", DOMAIN );
- return( 0.0 );
- }
-dk = k+1;
-dn = n;
-return( incbetf( dn, dk, p ) );
-}
+++ /dev/null
-/* ndtrf.c
- *
- * Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, ndtrf();
- *
- * y = ndtrf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the Gaussian probability density
- * function, integrated from minus infinity to x:
- *
- * x
- * -
- * 1 | | 2
- * ndtr(x) = --------- | exp( - t /2 ) dt
- * sqrt(2pi) | |
- * -
- * -inf.
- *
- * = ( 1 + erf(z) ) / 2
- * = erfc(z) / 2
- *
- * where z = x/sqrt(2). Computation is via the functions
- * erf and erfc.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -13,0 50000 1.5e-5 2.6e-6
- *
- *
- * ERROR MESSAGES:
- *
- * See erfcf().
- *
- */
-\f/* erff.c
- *
- * Error function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, erff();
- *
- * y = erff( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The integral is
- *
- * x
- * -
- * 2 | | 2
- * erf(x) = -------- | exp( - t ) dt.
- * sqrt(pi) | |
- * -
- * 0
- *
- * The magnitude of x is limited to 9.231948545 for DEC
- * arithmetic; 1 or -1 is returned outside this range.
- *
- * For 0 <= |x| < 1, erf(x) = x * P(x**2); otherwise
- * erf(x) = 1 - erfc(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -9.3,9.3 50000 1.7e-7 2.8e-8
- *
- */
-\f/* erfcf.c
- *
- * Complementary error function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, erfcf();
- *
- * y = erfcf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * 1 - erf(x) =
- *
- * inf.
- * -
- * 2 | | 2
- * erfc(x) = -------- | exp( - t ) dt
- * sqrt(pi) | |
- * -
- * x
- *
- *
- * For small x, erfc(x) = 1 - erf(x); otherwise polynomial
- * approximations 1/x P(1/x**2) are computed.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -9.3,9.3 50000 3.9e-6 7.2e-7
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfcf underflow x**2 > MAXLOGF 0.0
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-extern float MAXLOGF, SQRTHF;
-
-
-/* erfc(x) = exp(-x^2) P(1/x), 1 < x < 2 */
-static float P[] = {
- 2.326819970068386E-002,
--1.387039388740657E-001,
- 3.687424674597105E-001,
--5.824733027278666E-001,
- 6.210004621745983E-001,
--4.944515323274145E-001,
- 3.404879937665872E-001,
--2.741127028184656E-001,
- 5.638259427386472E-001
-};
-
-/* erfc(x) = exp(-x^2) 1/x P(1/x^2), 2 < x < 14 */
-static float R[] = {
--1.047766399936249E+001,
- 1.297719955372516E+001,
--7.495518717768503E+000,
- 2.921019019210786E+000,
--1.015265279202700E+000,
- 4.218463358204948E-001,
--2.820767439740514E-001,
- 5.641895067754075E-001
-};
-
-/* erf(x) = x P(x^2), 0 < x < 1 */
-static float T[] = {
- 7.853861353153693E-005,
--8.010193625184903E-004,
- 5.188327685732524E-003,
--2.685381193529856E-002,
- 1.128358514861418E-001,
--3.761262582423300E-001,
- 1.128379165726710E+000
-};
-
-/*#define UTHRESH 37.519379347*/
-
-#define UTHRESH 14.0
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float polevlf(float, float *, int);
-float expf(float), logf(float), erff(float), erfcf(float);
-#else
-float polevlf(), expf(), logf(), erff(), erfcf();
-#endif
-
-
-
-float ndtrf(float aa)
-{
-float x, y, z;
-
-x = aa;
-x *= SQRTHF;
-z = fabsf(x);
-
-if( z < SQRTHF )
- y = 0.5 + 0.5 * erff(x);
-else
- {
- y = 0.5 * erfcf(z);
-
- if( x > 0 )
- y = 1.0 - y;
- }
-
-return(y);
-}
-
-
-float erfcf(float aa)
-{
-float a, p,q,x,y,z;
-
-
-a = aa;
-x = fabsf(a);
-
-if( x < 1.0 )
- return( 1.0 - erff(a) );
-
-z = -a * a;
-
-if( z < -MAXLOGF )
- {
-under:
- mtherr( "erfcf", UNDERFLOW );
- if( a < 0 )
- return( 2.0 );
- else
- return( 0.0 );
- }
-
-z = expf(z);
-q = 1.0/x;
-y = q * q;
-if( x < 2.0 )
- {
- p = polevlf( y, P, 8 );
- }
-else
- {
- p = polevlf( y, R, 7 );
- }
-
-y = z * q * p;
-
-if( a < 0 )
- y = 2.0 - y;
-
-if( y == 0.0 )
- goto under;
-
-return(y);
-}
-
-
-float erff(float xx)
-{
-float x, y, z;
-
-x = xx;
-if( fabsf(x) > 1.0 )
- return( 1.0 - erfcf(x) );
-
-z = x * x;
-y = x * polevlf( z, T, 6 );
-return( y );
-
-}
+++ /dev/null
-/* ndtrif.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, ndtrif();
- *
- * x = ndtrif( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2.0 * log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
- * There are two rational functions P/Q, one for 0 < y < exp(-32)
- * and the other for y up to exp(-2). For larger arguments,
- * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1e-38, 1 30000 3.6e-7 5.0e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtrif domain x <= 0 -MAXNUM
- * ndtrif domain x >= 1 MAXNUM
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern float MAXNUMF;
-
-/* sqrt(2pi) */
-static float s2pi = 2.50662827463100050242;
-
-/* approximation for 0 <= |y - 0.5| <= 3/8 */
-static float P0[5] = {
--5.99633501014107895267E1,
- 9.80010754185999661536E1,
--5.66762857469070293439E1,
- 1.39312609387279679503E1,
--1.23916583867381258016E0,
-};
-static float Q0[8] = {
-/* 1.00000000000000000000E0,*/
- 1.95448858338141759834E0,
- 4.67627912898881538453E0,
- 8.63602421390890590575E1,
--2.25462687854119370527E2,
- 2.00260212380060660359E2,
--8.20372256168333339912E1,
- 1.59056225126211695515E1,
--1.18331621121330003142E0,
-};
-
-/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
- * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
- */
-static float P1[9] = {
- 4.05544892305962419923E0,
- 3.15251094599893866154E1,
- 5.71628192246421288162E1,
- 4.40805073893200834700E1,
- 1.46849561928858024014E1,
- 2.18663306850790267539E0,
--1.40256079171354495875E-1,
--3.50424626827848203418E-2,
--8.57456785154685413611E-4,
-};
-static float Q1[8] = {
-/* 1.00000000000000000000E0,*/
- 1.57799883256466749731E1,
- 4.53907635128879210584E1,
- 4.13172038254672030440E1,
- 1.50425385692907503408E1,
- 2.50464946208309415979E0,
--1.42182922854787788574E-1,
--3.80806407691578277194E-2,
--9.33259480895457427372E-4,
-};
-
-
-/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
- * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
- */
-
-static float P2[9] = {
- 3.23774891776946035970E0,
- 6.91522889068984211695E0,
- 3.93881025292474443415E0,
- 1.33303460815807542389E0,
- 2.01485389549179081538E-1,
- 1.23716634817820021358E-2,
- 3.01581553508235416007E-4,
- 2.65806974686737550832E-6,
- 6.23974539184983293730E-9,
-};
-static float Q2[8] = {
-/* 1.00000000000000000000E0,*/
- 6.02427039364742014255E0,
- 3.67983563856160859403E0,
- 1.37702099489081330271E0,
- 2.16236993594496635890E-1,
- 1.34204006088543189037E-2,
- 3.28014464682127739104E-4,
- 2.89247864745380683936E-6,
- 6.79019408009981274425E-9,
-};
-
-#ifdef ANSIC
-float polevlf(float, float *, int);
-float p1evlf(float, float *, int);
-float logf(float), sqrtf(float);
-#else
-float polevlf(), p1evlf(), logf(), sqrtf();
-#endif
-
-
-float ndtrif(float yy0)
-{
-float y0, x, y, z, y2, x0, x1;
-int code;
-
-y0 = yy0;
-if( y0 <= 0.0 )
- {
- mtherr( "ndtrif", DOMAIN );
- return( -MAXNUMF );
- }
-if( y0 >= 1.0 )
- {
- mtherr( "ndtrif", DOMAIN );
- return( MAXNUMF );
- }
-code = 1;
-y = y0;
-if( y > (1.0 - 0.13533528323661269189) ) /* 0.135... = exp(-2) */
- {
- y = 1.0 - y;
- code = 0;
- }
-
-if( y > 0.13533528323661269189 )
- {
- y = y - 0.5;
- y2 = y * y;
- x = y + y * (y2 * polevlf( y2, P0, 4)/p1evlf( y2, Q0, 8 ));
- x = x * s2pi;
- return(x);
- }
-
-x = sqrtf( -2.0 * logf(y) );
-x0 = x - logf(x)/x;
-
-z = 1.0/x;
-if( x < 8.0 ) /* y > exp(-32) = 1.2664165549e-14 */
- x1 = z * polevlf( z, P1, 8 )/p1evlf( z, Q1, 8 );
-else
- x1 = z * polevlf( z, P2, 8 )/p1evlf( z, Q2, 8 );
-x = x0 - x1;
-if( code != 0 )
- x = -x;
-return( x );
-}
+++ /dev/null
-/* pdtrf.c
- *
- * Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * float m, y, pdtrf();
- *
- * y = pdtrf( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the first k terms of the Poisson
- * distribution:
- *
- * k j
- * -- -m m
- * > e --
- * -- j!
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the relation
- *
- * y = pdtr( k, m ) = igamc( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 6.9e-5 8.0e-6
- *
- */
-\f/* pdtrcf()
- *
- * Complemented poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * float m, y, pdtrcf();
- *
- * y = pdtrcf( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the Poisson
- * distribution:
- *
- * inf. j
- * -- -m m
- * > e --
- * -- j!
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the formula
- *
- * y = pdtrc( k, m ) = igam( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 8.4e-5 1.2e-5
- *
- */
-\f/* pdtrif()
- *
- * Inverse Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * float m, y, pdtrf();
- *
- * m = pdtrif( k, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Poisson variable x such that the integral
- * from 0 to x of the Poisson density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * m = igami( k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100 5000 8.7e-6 1.4e-6
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pdtri domain y < 0 or y >= 1 0.0
- * k < 0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-#ifdef ANSIC
-float igamf(float, float), igamcf(float, float), igamif(float, float);
-#else
-float igamf(), igamcf(), igamif();
-#endif
-
-
-float pdtrcf( int k, float mm )
-{
-float v, m;
-
-m = mm;
-if( (k < 0) || (m <= 0.0) )
- {
- mtherr( "pdtrcf", DOMAIN );
- return( 0.0 );
- }
-v = k+1;
-return( igamf( v, m ) );
-}
-
-
-
-float pdtrf( int k, float mm )
-{
-float v, m;
-
-m = mm;
-if( (k < 0) || (m <= 0.0) )
- {
- mtherr( "pdtr", DOMAIN );
- return( 0.0 );
- }
-v = k+1;
-return( igamcf( v, m ) );
-}
-
-
-float pdtrif( int k, float yy )
-{
-float v, y;
-
-y = yy;
-if( (k < 0) || (y < 0.0) || (y >= 1.0) )
- {
- mtherr( "pdtrif", DOMAIN );
- return( 0.0 );
- }
-v = k+1;
-v = igamif( v, y );
-return( v );
-}
+++ /dev/null
-/* polevlf.c
- * p1evlf.c
- *
- * Evaluate polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * float x, y, coef[N+1], polevlf[];
- *
- * y = polevlf( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates polynomial of degree N:
- *
- * 2 N
- * y = C + C x + C x +...+ C x
- * 0 1 2 N
- *
- * Coefficients are stored in reverse order:
- *
- * coef[0] = C , ..., coef[N] = C .
- * N 0
- *
- * The function p1evl() assumes that coef[N] = 1.0 and is
- * omitted from the array. Its calling arguments are
- * otherwise the same as polevl().
- *
- *
- * SPEED:
- *
- * In the interest of speed, there are no checks for out
- * of bounds arithmetic. This routine is used by most of
- * the functions in the library. Depending on available
- * equipment features, the user may wish to rewrite the
- * program in microcode or assembly language.
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-float polevlf( float xx, float *coef, int N )
-{
-float ans, x;
-float *p;
-int i;
-
-x = xx;
-p = coef;
-ans = *p++;
-
-/*
-for( i=0; i<N; i++ )
- ans = ans * x + *p++;
-*/
-
-i = N;
-do
- ans = ans * x + *p++;
-while( --i );
-
-return( ans );
-}
-
-/* p1evl() */
-/* N
- * Evaluate polynomial when coefficient of x is 1.0.
- * Otherwise same as polevl.
- */
-
-float p1evlf( float xx, float *coef, int N )
-{
-float ans, x;
-float *p;
-int i;
-
-x = xx;
-p = coef;
-ans = x + *p++;
-i = N-1;
-
-do
- ans = ans * x + *p++;
-while( --i );
-
-return( ans );
-}
+++ /dev/null
-/* polynf.c
- * polyrf.c
- * Arithmetic operations on polynomials
- *
- * In the following descriptions a, b, c are polynomials of degree
- * na, nb, nc respectively. The degree of a polynomial cannot
- * exceed a run-time value MAXPOLF. An operation that attempts
- * to use or generate a polynomial of higher degree may produce a
- * result that suffers truncation at degree MAXPOL. The value of
- * MAXPOL is set by calling the function
- *
- * polinif( maxpol );
- *
- * where maxpol is the desired maximum degree. This must be
- * done prior to calling any of the other functions in this module.
- * Memory for internal temporary polynomial storage is allocated
- * by polinif().
- *
- * Each polynomial is represented by an array containing its
- * coefficients, together with a separately declared integer equal
- * to the degree of the polynomial. The coefficients appear in
- * ascending order; that is,
- *
- * 2 na
- * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
- *
- *
- *
- * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
- * polprtf( a, na, D ); Print the coefficients of a to D digits.
- * polclrf( a, na ); Set a identically equal to zero, up to a[na].
- * polmovf( a, na, b ); Set b = a.
- * poladdf( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
- * polsubf( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
- * polmulf( a, na, b, nb, c ); c = b * a, nc = na+nb
- *
- *
- * Division:
- *
- * i = poldivf( a, na, b, nb, c ); c = b / a, nc = MAXPOL
- *
- * returns i = the degree of the first nonzero coefficient of a.
- * The computed quotient c must be divided by x^i. An error message
- * is printed if a is identically zero.
- *
- *
- * Change of variables:
- * If a and b are polynomials, and t = a(x), then
- * c(t) = b(a(x))
- * is a polynomial found by substituting a(x) for t. The
- * subroutine call for this is
- *
- * polsbtf( a, na, b, nb, c );
- *
- *
- * Notes:
- * poldivf() is an integer routine; polevaf() is float.
- * Any of the arguments a, b, c may refer to the same array.
- *
- */
-
-#ifndef NULL
-#define NULL 0
-#endif
-#include <math.h>
-
-#ifdef ANSIC
-void printf(), sprintf(), exit();
-void free(void *);
-void *malloc(int);
-#else
-void printf(), sprintf(), free(), exit();
-void *malloc();
-#endif
-/* near pointer version of malloc() */
-/*#define malloc _nmalloc*/
-/*#define free _nfree*/
-
-/* Pointers to internal arrays. Note poldiv() allocates
- * and deallocates some temporary arrays every time it is called.
- */
-static float *pt1 = 0;
-static float *pt2 = 0;
-static float *pt3 = 0;
-
-/* Maximum degree of polynomial. */
-int MAXPOLF = 0;
-extern int MAXPOLF;
-
-/* Number of bytes (chars) in maximum size polynomial. */
-static int psize = 0;
-
-
-/* Initialize max degree of polynomials
- * and allocate temporary storage.
- */
-#ifdef ANSIC
-void polinif( int maxdeg )
-#else
-int polinif( maxdeg )
-int maxdeg;
-#endif
-{
-
-MAXPOLF = maxdeg;
-psize = (maxdeg + 1) * sizeof(float);
-
-/* Release previously allocated memory, if any. */
-if( pt3 )
- free(pt3);
-if( pt2 )
- free(pt2);
-if( pt1 )
- free(pt1);
-
-/* Allocate new arrays */
-pt1 = (float * )malloc(psize); /* used by polsbtf */
-pt2 = (float * )malloc(psize); /* used by polsbtf */
-pt3 = (float * )malloc(psize); /* used by polmul */
-
-/* Report if failure */
-if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
- {
- mtherr( "polinif", ERANGE );
- exit(1);
- }
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-
-/* Print the coefficients of a, with d decimal precision.
- */
-static char *form = "abcdefghijk";
-
-#ifdef ANSIC
-void polprtf( float *a, int na, int d )
-#else
-int polprtf( a, na, d )
-float a[];
-int na, d;
-#endif
-{
-int i, j, d1;
-char *p;
-
-/* Create format descriptor string for the printout.
- * Do this partly by hand, since sprintf() may be too
- * bug-ridden to accomplish this feat by itself.
- */
-p = form;
-*p++ = '%';
-d1 = d + 8;
-(void )sprintf( p, "%d ", d1 );
-p += 1;
-if( d1 >= 10 )
- p += 1;
-*p++ = '.';
-(void )sprintf( p, "%d ", d );
-p += 1;
-if( d >= 10 )
- p += 1;
-*p++ = 'e';
-*p++ = ' ';
-*p++ = '\0';
-
-
-/* Now do the printing.
- */
-d1 += 1;
-j = 0;
-for( i=0; i<=na; i++ )
- {
-/* Detect end of available line */
- j += d1;
- if( j >= 78 )
- {
- printf( "\n" );
- j = d1;
- }
- printf( form, a[i] );
- }
-printf( "\n" );
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-
-/* Set a = 0.
- */
-#ifdef ANSIC
-void polclrf( register float *a, int n )
-#else
-int polclrf( a, n )
-register float *a;
-int n;
-#endif
-{
-int i;
-
-if( n > MAXPOLF )
- n = MAXPOLF;
-for( i=0; i<=n; i++ )
- *a++ = 0.0;
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-
-/* Set b = a.
- */
-#ifdef ANSIC
-void polmovf( register float *a, int na, register float *b )
-#else
-int polmovf( a, na, b )
-register float *a, *b;
-int na;
-#endif
-{
-int i;
-
-if( na > MAXPOLF )
- na = MAXPOLF;
-
-for( i=0; i<= na; i++ )
- {
- *b++ = *a++;
- }
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-/* c = b * a.
- */
-#ifdef ANSIC
-void polmulf( float a[], int na, float b[], int nb, float c[] )
-#else
-int polmulf( a, na, b, nb, c )
-float a[], b[], c[];
-int na, nb;
-#endif
-{
-int i, j, k, nc;
-float x;
-
-nc = na + nb;
-polclrf( pt3, MAXPOLF );
-
-for( i=0; i<=na; i++ )
- {
- x = a[i];
- for( j=0; j<=nb; j++ )
- {
- k = i + j;
- if( k > MAXPOLF )
- break;
- pt3[k] += x * b[j];
- }
- }
-
-if( nc > MAXPOLF )
- nc = MAXPOLF;
-for( i=0; i<=nc; i++ )
- c[i] = pt3[i];
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-
-
-/* c = b + a.
- */
-#ifdef ANSIC
-void poladdf( float a[], int na, float b[], int nb, float c[] )
-#else
-int poladdf( a, na, b, nb, c )
-float a[], b[], c[];
-int na, nb;
-#endif
-{
-int i, n;
-
-
-if( na > nb )
- n = na;
-else
- n = nb;
-
-if( n > MAXPOLF )
- n = MAXPOLF;
-
-for( i=0; i<=n; i++ )
- {
- if( i > na )
- c[i] = b[i];
- else if( i > nb )
- c[i] = a[i];
- else
- c[i] = b[i] + a[i];
- }
-#if !ANSIC
-return 0;
-#endif
-}
-
-/* c = b - a.
- */
-#ifdef ANSIC
-void polsubf( float a[], int na, float b[], int nb, float c[] )
-#else
-int polsubf( a, na, b, nb, c )
-float a[], b[], c[];
-int na, nb;
-#endif
-{
-int i, n;
-
-
-if( na > nb )
- n = na;
-else
- n = nb;
-
-if( n > MAXPOLF )
- n = MAXPOLF;
-
-for( i=0; i<=n; i++ )
- {
- if( i > na )
- c[i] = b[i];
- else if( i > nb )
- c[i] = -a[i];
- else
- c[i] = b[i] - a[i];
- }
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-
-/* c = b/a
- */
-#ifdef ANSIC
-int poldivf( float a[], int na, float b[], int nb, float c[] )
-#else
-int poldivf( a, na, b, nb, c )
-float a[], b[], c[];
-int na, nb;
-#endif
-{
-float quot;
-float *ta, *tb, *tq;
-int i, j, k, sing;
-
-sing = 0;
-
-/* Allocate temporary arrays. This would be quicker
- * if done automatically on the stack, but stack space
- * may be hard to obtain on a small computer.
- */
-ta = (float * )malloc( psize );
-polclrf( ta, MAXPOLF );
-polmovf( a, na, ta );
-
-tb = (float * )malloc( psize );
-polclrf( tb, MAXPOLF );
-polmovf( b, nb, tb );
-
-tq = (float * )malloc( psize );
-polclrf( tq, MAXPOLF );
-
-/* What to do if leading (constant) coefficient
- * of denominator is zero.
- */
-if( a[0] == 0.0 )
- {
- for( i=0; i<=na; i++ )
- {
- if( ta[i] != 0.0 )
- goto nzero;
- }
- mtherr( "poldivf", SING );
- goto done;
-
-nzero:
-/* Reduce the degree of the denominator. */
- for( i=0; i<na; i++ )
- ta[i] = ta[i+1];
- ta[na] = 0.0;
-
- if( b[0] != 0.0 )
- {
-/* Optional message:
- printf( "poldivf singularity, divide quotient by x\n" );
-*/
- sing += 1;
- }
- else
- {
-/* Reduce degree of numerator. */
- for( i=0; i<nb; i++ )
- tb[i] = tb[i+1];
- tb[nb] = 0.0;
- }
-/* Call self, using reduced polynomials. */
- sing += poldivf( ta, na, tb, nb, c );
- goto done;
- }
-
-/* Long division algorithm. ta[0] is nonzero.
- */
-for( i=0; i<=MAXPOLF; i++ )
- {
- quot = tb[i]/ta[0];
- for( j=0; j<=MAXPOLF; j++ )
- {
- k = j + i;
- if( k > MAXPOLF )
- break;
- tb[k] -= quot * ta[j];
- }
- tq[i] = quot;
- }
-/* Send quotient to output array. */
-polmovf( tq, MAXPOLF, c );
-
-done:
-
-/* Restore allocated memory. */
-free(tq);
-free(tb);
-free(ta);
-return( sing );
-}
-
-
-
-
-/* Change of variables
- * Substitute a(y) for the variable x in b(x).
- * x = a(y)
- * c(x) = b(x) = b(a(y)).
- */
-
-#ifdef ANSIC
-void polsbtf( float a[], int na, float b[], int nb, float c[] )
-#else
-int polsbtf( a, na, b, nb, c )
-float a[], b[], c[];
-int na, nb;
-#endif
-{
-int i, j, k, n2;
-float x;
-
-/* 0th degree term:
- */
-polclrf( pt1, MAXPOLF );
-pt1[0] = b[0];
-
-polclrf( pt2, MAXPOLF );
-pt2[0] = 1.0;
-n2 = 0;
-
-for( i=1; i<=nb; i++ )
- {
-/* Form ith power of a. */
- polmulf( a, na, pt2, n2, pt2 );
- n2 += na;
- x = b[i];
-/* Add the ith coefficient of b times the ith power of a. */
- for( j=0; j<=n2; j++ )
- {
- if( j > MAXPOLF )
- break;
- pt1[j] += x * pt2[j];
- }
- }
-
-k = n2 + nb;
-if( k > MAXPOLF )
- k = MAXPOLF;
-for( i=0; i<=k; i++ )
- c[i] = pt1[i];
-#if !ANSIC
-return 0;
-#endif
-}
-
-
-
-
-/* Evaluate polynomial a(t) at t = x.
- */
-float polevaf( float *a, int na, float xx )
-{
-float x, s;
-int i;
-
-x = xx;
-s = a[na];
-for( i=na-1; i>=0; i-- )
- {
- s = s * x + a[i];
- }
-return(s);
-}
-
+++ /dev/null
-/* powf.c
- *
- * Power function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, z, powf();
- *
- * z = powf( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/16 and pseudo extended precision arithmetic to
- * obtain an extra three bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 100,000 1.4e-7 3.6e-8
- * 1/10 < x < 10, x uniformly distributed.
- * -10 < y < 10, y uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * powf overflow x**y > MAXNUMF MAXNUMF
- * powf underflow x**y < 1/MAXNUMF 0.0
- * powf domain x<0 and y noninteger 0.0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-static char fname[] = {"powf"};
-
-
-/* 2^(-i/16)
- * The decimal values are rounded to 24-bit precision
- */
-static float A[] = {
- 1.00000000000000000000E0,
- 9.57603275775909423828125E-1,
- 9.17004048824310302734375E-1,
- 8.78126084804534912109375E-1,
- 8.40896427631378173828125E-1,
- 8.05245161056518554687500E-1,
- 7.71105408668518066406250E-1,
- 7.38413095474243164062500E-1,
- 7.07106769084930419921875E-1,
- 6.77127778530120849609375E-1,
- 6.48419797420501708984375E-1,
- 6.20928883552551269531250E-1,
- 5.94603538513183593750000E-1,
- 5.69394290447235107421875E-1,
- 5.45253872871398925781250E-1,
- 5.22136867046356201171875E-1,
- 5.00000000000000000000E-1
-};
-/* continuation, for even i only
- * 2^(i/16) = A[i] + B[i/2]
- */
-static float B[] = {
- 0.00000000000000000000E0,
--5.61963907099083340520586E-9,
--1.23776636307969995237668E-8,
- 4.03545234539989593104537E-9,
- 1.21016171044789693621048E-8,
--2.00949968760174979411038E-8,
- 1.89881769396087499852802E-8,
--6.53877009617774467211965E-9,
- 0.00000000000000000000E0
-};
-
-/* 1 / A[i]
- * The decimal values are full precision
- */
-static float Ainv[] = {
- 1.00000000000000000000000E0,
- 1.04427378242741384032197E0,
- 1.09050773266525765920701E0,
- 1.13878863475669165370383E0,
- 1.18920711500272106671750E0,
- 1.24185781207348404859368E0,
- 1.29683955465100966593375E0,
- 1.35425554693689272829801E0,
- 1.41421356237309504880169E0,
- 1.47682614593949931138691E0,
- 1.54221082540794082361229E0,
- 1.61049033194925430817952E0,
- 1.68179283050742908606225E0,
- 1.75625216037329948311216E0,
- 1.83400808640934246348708E0,
- 1.91520656139714729387261E0,
- 2.00000000000000000000000E0
-};
-
-#ifdef DEC
-#define MEXP 2032.0
-#define MNEXP -2032.0
-#else
-#define MEXP 2048.0
-#define MNEXP -2400.0
-#endif
-
-/* log2(e) - 1 */
-#define LOG2EA 0.44269504088896340736F
-extern float MAXNUMF;
-
-#define F W
-#define Fa Wa
-#define Fb Wb
-#define G W
-#define Ga Wa
-#define Gb u
-#define H W
-#define Ha Wb
-#define Hb Wb
-
-
-#ifdef ANSIC
-float floorf( float );
-float frexpf( float, int *);
-float ldexpf( float, int );
-float powif( float, int );
-#else
-float floorf(), frexpf(), ldexpf(), powif();
-#endif
-
-/* Find a multiple of 1/16 that is within 1/16 of x. */
-#define reduc(x) 0.0625 * floorf( 16 * (x) )
-
-#ifdef ANSIC
-float powf( float x, float y )
-#else
-float powf( x, y )
-float x, y;
-#endif
-{
-float u, w, z, W, Wa, Wb, ya, yb;
-/* float F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
-int e, i, nflg;
-
-
-nflg = 0; /* flag = 1 if x<0 raised to integer power */
-w = floorf(y);
-if( w < 0 )
- z = -w;
-else
- z = w;
-if( (w == y) && (z < 32768.0) )
- {
- i = w;
- w = powif( x, i );
- return( w );
- }
-
-
-if( x <= 0.0F )
- {
- if( x == 0.0 )
- {
- if( y == 0.0 )
- return( 1.0 ); /* 0**0 */
- else
- return( 0.0 ); /* 0**y */
- }
- else
- {
- if( w != y )
- { /* noninteger power of negative number */
- mtherr( fname, DOMAIN );
- return(0.0);
- }
- nflg = 1;
- if( x < 0 )
- x = -x;
- }
- }
-
-/* separate significand from exponent */
-x = frexpf( x, &e );
-
-/* find significand in antilog table A[] */
-i = 1;
-if( x <= A[9] )
- i = 9;
-if( x <= A[i+4] )
- i += 4;
-if( x <= A[i+2] )
- i += 2;
-if( x >= A[1] )
- i = -1;
-i += 1;
-
-
-/* Find (x - A[i])/A[i]
- * in order to compute log(x/A[i]):
- *
- * log(x) = log( a x/a ) = log(a) + log(x/a)
- *
- * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
- */
-x -= A[i];
-x -= B[ i >> 1 ];
-x *= Ainv[i];
-
-
-/* rational approximation for log(1+v):
- *
- * log(1+v) = v - 0.5 v^2 + v^3 P(v)
- * Theoretical relative error of the approximation is 3.5e-11
- * on the interval 2^(1/16) - 1 > v > 2^(-1/16) - 1
- */
-z = x*x;
-w = (((-0.1663883081054895 * x
- + 0.2003770364206271) * x
- - 0.2500006373383951) * x
- + 0.3333331095506474) * x * z;
-w -= 0.5 * z;
-
-/* Convert to base 2 logarithm:
- * multiply by log2(e)
- */
-w = w + LOG2EA * w;
-/* Note x was not yet added in
- * to above rational approximation,
- * so do it now, while multiplying
- * by log2(e).
- */
-z = w + LOG2EA * x;
-z = z + x;
-
-/* Compute exponent term of the base 2 logarithm. */
-w = -i;
-w *= 0.0625; /* divide by 16 */
-w += e;
-/* Now base 2 log of x is w + z. */
-
-/* Multiply base 2 log by y, in extended precision. */
-
-/* separate y into large part ya
- * and small part yb less than 1/16
- */
-ya = reduc(y);
-yb = y - ya;
-
-
-F = z * y + w * yb;
-Fa = reduc(F);
-Fb = F - Fa;
-
-G = Fa + w * ya;
-Ga = reduc(G);
-Gb = G - Ga;
-
-H = Fb + Gb;
-Ha = reduc(H);
-w = 16 * (Ga + Ha);
-
-/* Test the power of 2 for overflow */
-if( w > MEXP )
- {
- mtherr( fname, OVERFLOW );
- return( MAXNUMF );
- }
-
-if( w < MNEXP )
- {
- mtherr( fname, UNDERFLOW );
- return( 0.0 );
- }
-
-e = w;
-Hb = H - Ha;
-
-if( Hb > 0.0 )
- {
- e += 1;
- Hb -= 0.0625;
- }
-
-/* Now the product y * log2(x) = Hb + e/16.0.
- *
- * Compute base 2 exponential of Hb,
- * where -0.0625 <= Hb <= 0.
- * Theoretical relative error of the approximation is 2.8e-12.
- */
-/* z = 2**Hb - 1 */
-z = ((( 9.416993633606397E-003 * Hb
- + 5.549356188719141E-002) * Hb
- + 2.402262883964191E-001) * Hb
- + 6.931471791490764E-001) * Hb;
-
-/* Express e/16 as an integer plus a negative number of 16ths.
- * Find lookup table entry for the fractional power of 2.
- */
-if( e < 0 )
- i = -( -e >> 4 );
-else
- i = (e >> 4) + 1;
-e = (i << 4) - e;
-w = A[e];
-z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
-z = ldexpf( z, i ); /* multiply by integer power of 2 */
-
-if( nflg )
- {
-/* For negative x,
- * find out if the integer exponent
- * is odd or even.
- */
- w = 2 * floorf( (float) 0.5 * w );
- if( w != y )
- z = -z; /* odd exponent */
- }
-
-return( z );
-}
+++ /dev/null
-/* powif.c
- *
- * Real raised to integer power
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, powif();
- * int n;
- *
- * y = powif( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns argument x raised to the nth power.
- * The routine efficiently decomposes n as a sum of powers of
- * two. The desired power is a product of two-to-the-kth
- * powers of x. Thus to compute the 32767 power of x requires
- * 28 multiplications instead of 32767 multiplications.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic x domain n domain # trials peak rms
- * IEEE .04,26 -26,26 100000 1.1e-6 2.0e-7
- * IEEE 1,2 -128,128 100000 1.1e-5 1.0e-6
- *
- * Returns MAXNUMF on overflow, zero on underflow.
- *
- */
-\f
-/* powi.c */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern float MAXNUMF, MAXLOGF, MINLOGF, LOGE2F;
-
-float frexpf( float, int * );
-
-float powif( float x, int nn )
-{
-int n, e, sign, asign, lx;
-float w, y, s;
-
-if( x == 0.0 )
- {
- if( nn == 0 )
- return( 1.0 );
- else if( nn < 0 )
- return( MAXNUMF );
- else
- return( 0.0 );
- }
-
-if( nn == 0 )
- return( 1.0 );
-
-
-if( x < 0.0 )
- {
- asign = -1;
- x = -x;
- }
-else
- asign = 0;
-
-
-if( nn < 0 )
- {
- sign = -1;
- n = -nn;
-/*
- x = 1.0/x;
-*/
- }
-else
- {
- sign = 0;
- n = nn;
- }
-
-/* Overflow detection */
-
-/* Calculate approximate logarithm of answer */
-s = frexpf( x, &lx );
-e = (lx - 1)*n;
-if( (e == 0) || (e > 64) || (e < -64) )
- {
- s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
- s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2F;
- }
-else
- {
- s = LOGE2F * e;
- }
-
-if( s > MAXLOGF )
- {
- mtherr( "powi", OVERFLOW );
- y = MAXNUMF;
- goto done;
- }
-
-if( s < MINLOGF )
- return(0.0);
-
-/* Handle tiny denormal answer, but with less accuracy
- * since roundoff error in 1.0/x will be amplified.
- * The precise demarcation should be the gradual underflow threshold.
- */
-if( s < (-MAXLOGF+2.0) )
- {
- x = 1.0/x;
- sign = 0;
- }
-
-/* First bit of the power */
-if( n & 1 )
- y = x;
-
-else
- {
- y = 1.0;
- asign = 0;
- }
-
-w = x;
-n >>= 1;
-while( n )
- {
- w = w * w; /* arg to the 2-to-the-kth power */
- if( n & 1 ) /* if that bit is set, then include in product */
- y *= w;
- n >>= 1;
- }
-
-
-done:
-
-if( asign )
- y = -y; /* odd power of negative number */
-if( sign )
- y = 1.0/y;
-return(y);
-}
+++ /dev/null
-#include <stdio.h>
-#include <math.h>
-extern float MAXNUMF, MAXLOGF, MINLOGF;
-
-int
-main()
-{
-float exp1, minnum, x, y, z, e;
-exp1 = expf(1.0F);
-
-minnum = powif(2.0F,-149);
-
-x = exp1;
-y = MINLOGF + logf(0.501);
-/*y = MINLOGF - 0.405;*/
-z = powf(x,y);
-e = (z - minnum) / minnum;
-printf("%.16e %.16e\n", z, e);
-
-x = exp1;
-y = MAXLOGF;
-z = powf(x,y);
-e = (z - MAXNUMF) / MAXNUMF;
-printf("%.16e %.16e\n", z, e);
-
-x = MAXNUMF;
-y = 1.0F/MAXLOGF;
-z = powf(x,y);
-e = (z - exp1) / exp1;
-printf("%.16e %.16e\n", z, e);
-
-
-x = exp1;
-y = MINLOGF;
-z = powf(x,y);
-e = (z - minnum) / minnum;
-printf("%.16e %.16e\n", z, e);
-
-
-exit(0);
-}
+++ /dev/null
-/* psif.c
- *
- * Psi (digamma) function
- *
- *
- * SYNOPSIS:
- *
- * float x, y, psif();
- *
- * y = psif( x );
- *
- *
- * DESCRIPTION:
- *
- * d -
- * psi(x) = -- ln | (x)
- * dx
- *
- * is the logarithmic derivative of the gamma function.
- * For integer x,
- * n-1
- * -
- * psi(n) = -EUL + > 1/k.
- * -
- * k=1
- *
- * This formula is used for 0 < n <= 10. If x is negative, it
- * is transformed to a positive argument by the reflection
- * formula psi(1-x) = psi(x) + pi cot(pi x).
- * For general positive x, the argument is made greater than 10
- * using the recurrence psi(x+1) = psi(x) + 1/x.
- * Then the following asymptotic expansion is applied:
- *
- * inf. B
- * - 2k
- * psi(x) = log(x) - 1/2x - > -------
- * - 2k
- * k=1 2k x
- *
- * where the B2k are Bernoulli numbers.
- *
- * ACCURACY:
- * Absolute error, relative when |psi| > 1 :
- * arithmetic domain # trials peak rms
- * IEEE -33,0 30000 8.2e-7 1.2e-7
- * IEEE 0,33 100000 7.3e-7 7.7e-8
- *
- * ERROR MESSAGES:
- * message condition value returned
- * psi singularity x integer <=0 MAXNUMF
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-
-static float A[] = {
--4.16666666666666666667E-3,
- 3.96825396825396825397E-3,
--8.33333333333333333333E-3,
- 8.33333333333333333333E-2
-};
-
-
-#define EUL 0.57721566490153286061
-
-extern float PIF, MAXNUMF;
-
-
-
-float floorf(float), logf(float), tanf(float);
-float polevlf(float, float *, int);
-
-float psif(float xx)
-{
-float p, q, nz, x, s, w, y, z;
-int i, n, negative;
-
-
-x = xx;
-nz = 0.0;
-negative = 0;
-if( x <= 0.0 )
- {
- negative = 1;
- q = x;
- p = floorf(q);
- if( p == q )
- {
- mtherr( "psif", SING );
- return( MAXNUMF );
- }
- nz = q - p;
- if( nz != 0.5 )
- {
- if( nz > 0.5 )
- {
- p += 1.0;
- nz = q - p;
- }
- nz = PIF/tanf(PIF*nz);
- }
- else
- {
- nz = 0.0;
- }
- x = 1.0 - x;
- }
-
-/* check for positive integer up to 10 */
-if( (x <= 10.0) && (x == floorf(x)) )
- {
- y = 0.0;
- n = x;
- for( i=1; i<n; i++ )
- {
- w = i;
- y += 1.0/w;
- }
- y -= EUL;
- goto done;
- }
-
-s = x;
-w = 0.0;
-while( s < 10.0 )
- {
- w += 1.0/s;
- s += 1.0;
- }
-
-if( s < 1.0e8 )
- {
- z = 1.0/(s * s);
- y = z * polevlf( z, A, 3 );
- }
-else
- y = 0.0;
-
-y = logf(s) - (0.5/s) - y - w;
-
-done:
-if( negative )
- {
- y -= nz;
- }
-return(y);
-}
+++ /dev/null
-/* rgammaf.c
- *
- * Reciprocal gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, rgammaf();
- *
- * y = rgammaf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns one divided by the gamma function of the argument.
- *
- * The function is approximated by a Chebyshev expansion in
- * the interval [0,1]. Range reduction is by recurrence
- * for arguments between -34.034 and +34.84425627277176174.
- * 1/MAXNUMF is returned for positive arguments outside this
- * range.
- *
- * The reciprocal gamma function has no singularities,
- * but overflow and underflow may occur for large arguments.
- * These conditions return either MAXNUMF or 1/MAXNUMF with
- * appropriate sign.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -34,+34 100000 8.9e-7 1.1e-7
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1985, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for reciprocal gamma function
- * in interval 0 to 1. Function is 1/(x gamma(x)) - 1
- */
-
-static float R[] = {
- 1.08965386454418662084E-9,
--3.33964630686836942556E-8,
- 2.68975996440595483619E-7,
- 2.96001177518801696639E-6,
--8.04814124978471142852E-5,
- 4.16609138709688864714E-4,
- 5.06579864028608725080E-3,
--6.41925436109158228810E-2,
--4.98558728684003594785E-3,
- 1.27546015610523951063E-1
-};
-
-
-static char name[] = "rgammaf";
-
-extern float PIF, MAXLOGF, MAXNUMF;
-
-
-
-float chbevlf(float, float *, int);
-float expf(float), logf(float), sinf(float), lgamf(float);
-
-float rgammaf(float xx)
-{
-float x, w, y, z;
-int sign;
-
-x = xx;
-if( x > 34.84425627277176174)
- {
- mtherr( name, UNDERFLOW );
- return(1.0/MAXNUMF);
- }
-if( x < -34.034 )
- {
- w = -x;
- z = sinf( PIF*w );
- if( z == 0.0 )
- return(0.0);
- if( z < 0.0 )
- {
- sign = 1;
- z = -z;
- }
- else
- sign = -1;
-
- y = logf( w * z / PIF ) + lgamf(w);
- if( y < -MAXLOGF )
- {
- mtherr( name, UNDERFLOW );
- return( sign * 1.0 / MAXNUMF );
- }
- if( y > MAXLOGF )
- {
- mtherr( name, OVERFLOW );
- return( sign * MAXNUMF );
- }
- return( sign * expf(y));
- }
-z = 1.0;
-w = x;
-
-while( w > 1.0 ) /* Downward recurrence */
- {
- w -= 1.0;
- z *= w;
- }
-while( w < 0.0 ) /* Upward recurrence */
- {
- z /= w;
- w += 1.0;
- }
-if( w == 0.0 ) /* Nonpositive integer */
- return(0.0);
-if( w == 1.0 ) /* Other integer */
- return( 1.0/z );
-
-y = w * ( 1.0 + chbevlf( 4.0*w-2.0, R, 10 ) ) / z;
-return(y);
-}
+++ /dev/null
-/* Null stubs for coprocessor precision settings */
-
-int
-sprec() {return 0; }
-
-int
-dprec() {return 0; }
-
-int
-ldprec() {return 0; }
+++ /dev/null
-/* shichif.c
- *
- * Hyperbolic sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, Chi, Shi;
- *
- * shichi( x, &Chi, &Shi );
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integrals
- *
- * x
- * -
- * | | cosh t - 1
- * Chi(x) = eul + ln x + | ----------- dt,
- * | | t
- * -
- * 0
- *
- * x
- * -
- * | | sinh t
- * Shi(x) = | ------ dt
- * | | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are evaluated by power series for x < 8
- * and by Chebyshev expansions for x between 8 and 88.
- * For large x, both functions approach exp(x)/2x.
- * Arguments greater than 88 in magnitude return MAXNUM.
- *
- *
- * ACCURACY:
- *
- * Test interval 0 to 88.
- * Relative error:
- * arithmetic function # trials peak rms
- * IEEE Shi 20000 3.5e-7 7.0e-8
- * Absolute error, except relative when |Chi| > 1:
- * IEEE Chi 20000 3.8e-7 7.6e-8
- */
-\f
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-/* x exp(-x) shi(x), inverted interval 8 to 18 */
-static float S1[] = {
--3.56699611114982536845E-8,
- 1.44818877384267342057E-7,
- 7.82018215184051295296E-7,
--5.39919118403805073710E-6,
--3.12458202168959833422E-5,
- 8.90136741950727517826E-5,
- 2.02558474743846862168E-3,
- 2.96064440855633256972E-2,
- 1.11847751047257036625E0
-};
-
-/* x exp(-x) shi(x), inverted interval 18 to 88 */
-static float S2[] = {
- 1.69050228879421288846E-8,
- 1.25391771228487041649E-7,
- 1.16229947068677338732E-6,
- 1.61038260117376323993E-5,
- 3.49810375601053973070E-4,
- 1.28478065259647610779E-2,
- 1.03665722588798326712E0
-};
-
-
-/* x exp(-x) chin(x), inverted interval 8 to 18 */
-static float C1[] = {
- 1.31458150989474594064E-8,
--4.75513930924765465590E-8,
--2.21775018801848880741E-7,
- 1.94635531373272490962E-6,
- 4.33505889257316408893E-6,
--6.13387001076494349496E-5,
--3.13085477492997465138E-4,
- 4.97164789823116062801E-4,
- 2.64347496031374526641E-2,
- 1.11446150876699213025E0
-};
-
-/* x exp(-x) chin(x), inverted interval 18 to 88 */
-static float C2[] = {
--3.00095178028681682282E-9,
- 7.79387474390914922337E-8,
- 1.06942765566401507066E-6,
- 1.59503164802313196374E-5,
- 3.49592575153777996871E-4,
- 1.28475387530065247392E-2,
- 1.03665693917934275131E0
-};
-
-
-
-/* Sine and cosine integrals */
-
-#define EUL 0.57721566490153286061
-extern float MACHEPF, MAXNUMF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float logf(float ), expf(float), chbevlf(float, float *, int);
-#else
-float logf(), expf(), chbevlf();
-#endif
-
-
-
-int shichif( float xx, float *si, float *ci )
-{
-float x, k, z, c, s, a;
-short sign;
-
-x = xx;
-if( x < 0.0 )
- {
- sign = -1;
- x = -x;
- }
-else
- sign = 0;
-
-
-if( x == 0.0 )
- {
- *si = 0.0;
- *ci = -MAXNUMF;
- return( 0 );
- }
-
-if( x >= 8.0 )
- goto chb;
-
-z = x * x;
-
-/* Direct power series expansion */
-
-a = 1.0;
-s = 1.0;
-c = 0.0;
-k = 2.0;
-
-do
- {
- a *= z/k;
- c += a/k;
- k += 1.0;
- a /= k;
- s += a/k;
- k += 1.0;
- }
-while( fabsf(a/s) > MACHEPF );
-
-s *= x;
-goto done;
-
-
-chb:
-
-if( x < 18.0 )
- {
- a = (576.0/x - 52.0)/10.0;
- k = expf(x) / x;
- s = k * chbevlf( a, S1, 9 );
- c = k * chbevlf( a, C1, 10 );
- goto done;
- }
-
-if( x <= 88.0 )
- {
- a = (6336.0/x - 212.0)/70.0;
- k = expf(x) / x;
- s = k * chbevlf( a, S2, 7 );
- c = k * chbevlf( a, C2, 7 );
- goto done;
- }
-else
- {
- if( sign )
- *si = -MAXNUMF;
- else
- *si = MAXNUMF;
- *ci = MAXNUMF;
- return(0);
- }
-done:
-if( sign )
- s = -s;
-
-*si = s;
-
-*ci = EUL + logf(x) + c;
-return(0);
-}
+++ /dev/null
-/* sicif.c
- *
- * Sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, Ci, Si;
- *
- * sicif( x, &Si, &Ci );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the integrals
- *
- * x
- * -
- * | cos t - 1
- * Ci(x) = eul + ln x + | --------- dt,
- * | t
- * -
- * 0
- * x
- * -
- * | sin t
- * Si(x) = | ----- dt
- * | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are approximated by rational functions.
- * For x > 8 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * Ci(x) = f(x) sin(x) - g(x) cos(x)
- * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
- *
- *
- * ACCURACY:
- * Test interval = [0,50].
- * Absolute error, except relative when > 1:
- * arithmetic function # trials peak rms
- * IEEE Si 30000 2.1e-7 4.3e-8
- * IEEE Ci 30000 3.9e-7 2.2e-8
- */
-\f
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-static float SN[] = {
--8.39167827910303881427E-11,
- 4.62591714427012837309E-8,
--9.75759303843632795789E-6,
- 9.76945438170435310816E-4,
--4.13470316229406538752E-2,
- 1.00000000000000000302E0,
-};
-static float SD[] = {
- 2.03269266195951942049E-12,
- 1.27997891179943299903E-9,
- 4.41827842801218905784E-7,
- 9.96412122043875552487E-5,
- 1.42085239326149893930E-2,
- 9.99999999999999996984E-1,
-};
-
-static float CN[] = {
- 2.02524002389102268789E-11,
--1.35249504915790756375E-8,
- 3.59325051419993077021E-6,
--4.74007206873407909465E-4,
- 2.89159652607555242092E-2,
--1.00000000000000000080E0,
-};
-static float CD[] = {
- 4.07746040061880559506E-12,
- 3.06780997581887812692E-9,
- 1.23210355685883423679E-6,
- 3.17442024775032769882E-4,
- 5.10028056236446052392E-2,
- 4.00000000000000000080E0,
-};
-
-
-static float FN4[] = {
- 4.23612862892216586994E0,
- 5.45937717161812843388E0,
- 1.62083287701538329132E0,
- 1.67006611831323023771E-1,
- 6.81020132472518137426E-3,
- 1.08936580650328664411E-4,
- 5.48900223421373614008E-7,
-};
-static float FD4[] = {
-/* 1.00000000000000000000E0,*/
- 8.16496634205391016773E0,
- 7.30828822505564552187E0,
- 1.86792257950184183883E0,
- 1.78792052963149907262E-1,
- 7.01710668322789753610E-3,
- 1.10034357153915731354E-4,
- 5.48900252756255700982E-7,
-};
-
-
-static float FN8[] = {
- 4.55880873470465315206E-1,
- 7.13715274100146711374E-1,
- 1.60300158222319456320E-1,
- 1.16064229408124407915E-2,
- 3.49556442447859055605E-4,
- 4.86215430826454749482E-6,
- 3.20092790091004902806E-8,
- 9.41779576128512936592E-11,
- 9.70507110881952024631E-14,
-};
-static float FD8[] = {
-/* 1.00000000000000000000E0,*/
- 9.17463611873684053703E-1,
- 1.78685545332074536321E-1,
- 1.22253594771971293032E-2,
- 3.58696481881851580297E-4,
- 4.92435064317881464393E-6,
- 3.21956939101046018377E-8,
- 9.43720590350276732376E-11,
- 9.70507110881952025725E-14,
-};
-
-static float GN4[] = {
- 8.71001698973114191777E-2,
- 6.11379109952219284151E-1,
- 3.97180296392337498885E-1,
- 7.48527737628469092119E-2,
- 5.38868681462177273157E-3,
- 1.61999794598934024525E-4,
- 1.97963874140963632189E-6,
- 7.82579040744090311069E-9,
-};
-static float GD4[] = {
-/* 1.00000000000000000000E0,*/
- 1.64402202413355338886E0,
- 6.66296701268987968381E-1,
- 9.88771761277688796203E-2,
- 6.22396345441768420760E-3,
- 1.73221081474177119497E-4,
- 2.02659182086343991969E-6,
- 7.82579218933534490868E-9,
-};
-
-static float GN8[] = {
- 6.97359953443276214934E-1,
- 3.30410979305632063225E-1,
- 3.84878767649974295920E-2,
- 1.71718239052347903558E-3,
- 3.48941165502279436777E-5,
- 3.47131167084116673800E-7,
- 1.70404452782044526189E-9,
- 3.85945925430276600453E-12,
- 3.14040098946363334640E-15,
-};
-static float GD8[] = {
-/* 1.00000000000000000000E0,*/
- 1.68548898811011640017E0,
- 4.87852258695304967486E-1,
- 4.67913194259625806320E-2,
- 1.90284426674399523638E-3,
- 3.68475504442561108162E-5,
- 3.57043223443740838771E-7,
- 1.72693748966316146736E-9,
- 3.87830166023954706752E-12,
- 3.14040098946363335242E-15,
-};
-
-#define EUL 0.57721566490153286061
-extern float MAXNUMF, PIO2F, MACHEPF;
-
-
-
-#ifdef ANSIC
-float logf(float), sinf(float), cosf(float);
-float polevlf(float, float *, int);
-float p1evlf(float, float *, int);
-#else
-float logf(), sinf(), cosf(), polevlf(), p1evlf();
-#endif
-
-
-int sicif( float xx, float *si, float *ci )
-{
-float x, z, c, s, f, g;
-int sign;
-
-x = xx;
-if( x < 0.0 )
- {
- sign = -1;
- x = -x;
- }
-else
- sign = 0;
-
-
-if( x == 0.0 )
- {
- *si = 0.0;
- *ci = -MAXNUMF;
- return( 0 );
- }
-
-
-if( x > 1.0e9 )
- {
- *si = PIO2F - cosf(x)/x;
- *ci = sinf(x)/x;
- return( 0 );
- }
-
-
-
-if( x > 4.0 )
- goto asympt;
-
-z = x * x;
-s = x * polevlf( z, SN, 5 ) / polevlf( z, SD, 5 );
-c = z * polevlf( z, CN, 5 ) / polevlf( z, CD, 5 );
-
-if( sign )
- s = -s;
-*si = s;
-*ci = EUL + logf(x) + c; /* real part if x < 0 */
-return(0);
-
-
-
-/* The auxiliary functions are:
- *
- *
- * *si = *si - PIO2;
- * c = cos(x);
- * s = sin(x);
- *
- * t = *ci * s - *si * c;
- * a = *ci * c + *si * s;
- *
- * *si = t;
- * *ci = -a;
- */
-
-
-asympt:
-
-s = sinf(x);
-c = cosf(x);
-z = 1.0/(x*x);
-if( x < 8.0 )
- {
- f = polevlf( z, FN4, 6 ) / (x * p1evlf( z, FD4, 7 ));
- g = z * polevlf( z, GN4, 7 ) / p1evlf( z, GD4, 7 );
- }
-else
- {
- f = polevlf( z, FN8, 8 ) / (x * p1evlf( z, FD8, 8 ));
- g = z * polevlf( z, GN8, 8 ) / p1evlf( z, GD8, 9 );
- }
-*si = PIO2F - f * c - g * s;
-if( sign )
- *si = -( *si );
-*ci = f * s - g * c;
-
-return(0);
-}
+++ /dev/null
-/* sindgf.c
- *
- * Circular sine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sindgf();
- *
- * y = sindgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 Q(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-3600 100,000 1.2e-7 3.0e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 2^24 0.0
- *
- */
-\f
-/* cosdgf.c
- *
- * Circular cosine of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cosdgf();
- *
- * y = cosdgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 Q(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1985, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/* Single precision circular sine
- * test interval: [-pi/4, +pi/4]
- * trials: 10000
- * peak relative error: 6.8e-8
- * rms relative error: 2.6e-8
- */
-#include <math.h>
-
-
-/*static float FOPI = 1.27323954473516;*/
-
-extern float PIO4F;
-
-/* These are for a 24-bit significand: */
-static float T24M1 = 16777215.;
-
-static float PI180 = 0.0174532925199432957692; /* pi/180 */
-
-float sindgf( float xx )
-{
-float x, y, z;
-long j;
-int sign;
-
-sign = 1;
-x = xx;
-if( xx < 0 )
- {
- sign = -1;
- x = -xx;
- }
-if( x > T24M1 )
- {
- mtherr( "sindgf", TLOSS );
- return(0.0);
- }
-j = 0.022222222222222222222 * x; /* integer part of x/45 */
-y = j;
-/* map zeros to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-j &= 7; /* octant modulo 360 degrees */
-/* reflect in x axis */
-if( j > 3)
- {
- sign = -sign;
- j -= 4;
- }
-
-x = x - y * 45.0;
-x *= PI180; /* multiply by pi/180 to convert to radians */
-
-z = x * x;
-if( (j==1) || (j==2) )
- {
-/*
- y = ((( 2.4462803166E-5 * z
- - 1.3887580023E-3) * z
- + 4.1666650433E-2) * z
- - 4.9999999968E-1) * z
- + 1.0;
-*/
-
-/* measured relative error in +/- pi/4 is 7.8e-8 */
- y = (( 2.443315711809948E-005 * z
- - 1.388731625493765E-003) * z
- + 4.166664568298827E-002) * z * z;
- y -= 0.5 * z;
- y += 1.0;
- }
-else
- {
-/* Theoretical relative error = 3.8e-9 in [-pi/4, +pi/4] */
- y = ((-1.9515295891E-4 * z
- + 8.3321608736E-3) * z
- - 1.6666654611E-1) * z * x;
- y += x;
- }
-
-if(sign < 0)
- y = -y;
-return( y);
-}
-
-
-/* Single precision circular cosine
- * test interval: [-pi/4, +pi/4]
- * trials: 10000
- * peak relative error: 8.3e-8
- * rms relative error: 2.2e-8
- */
-
-float cosdgf( float xx )
-{
-register float x, y, z;
-int j, sign;
-
-/* make argument positive */
-sign = 1;
-x = xx;
-if( x < 0 )
- x = -x;
-
-if( x > T24M1 )
- {
- mtherr( "cosdgf", TLOSS );
- return(0.0);
- }
-
-j = 0.02222222222222222222222 * x; /* integer part of x/PIO4 */
-y = j;
-/* integer and fractional part modulo one octant */
-if( j & 1 ) /* map zeros to origin */
- {
- j += 1;
- y += 1.0;
- }
-j &= 7;
-if( j > 3)
- {
- j -=4;
- sign = -sign;
- }
-
-if( j > 1 )
- sign = -sign;
-
-x = x - y * 45.0; /* x mod 45 degrees */
-x *= PI180; /* multiply by pi/180 to convert to radians */
-
-z = x * x;
-
-if( (j==1) || (j==2) )
- {
- y = (((-1.9515295891E-4 * z
- + 8.3321608736E-3) * z
- - 1.6666654611E-1) * z * x)
- + x;
- }
-else
- {
- y = (( 2.443315711809948E-005 * z
- - 1.388731625493765E-003) * z
- + 4.166664568298827E-002) * z * z;
- y -= 0.5 * z;
- y += 1.0;
- }
-if(sign < 0)
- y = -y;
-return( y );
-}
-
+++ /dev/null
-/* sinf.c
- *
- * Circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sinf();
- *
- * y = sinf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by
- * x + x**3 P(x**2).
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - x**2 Q(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -4096,+4096 100,000 1.2e-7 3.0e-8
- * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 2^24 0.0
- *
- * Partial loss of accuracy begins to occur at x = 2^13
- * = 8192. Results may be meaningless for x >= 2^24
- * The routine as implemented flags a TLOSS error
- * for x >= 2^24 and returns 0.0.
- */
-\f
-/* cosf.c
- *
- * Circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cosf();
- *
- * y = cosf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - x**2 Q(x**2).
- * Between pi/4 and pi/2 the sine is represented as
- * x + x**3 P(x**2).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1985, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/* Single precision circular sine
- * test interval: [-pi/4, +pi/4]
- * trials: 10000
- * peak relative error: 6.8e-8
- * rms relative error: 2.6e-8
- */
-#include <math.h>
-
-
-static float FOPI = 1.27323954473516;
-
-extern float PIO4F;
-/* Note, these constants are for a 32-bit significand: */
-/*
-static float DP1 = 0.7853851318359375;
-static float DP2 = 1.30315311253070831298828125e-5;
-static float DP3 = 3.03855025325309630e-11;
-static float lossth = 65536.;
-*/
-
-/* These are for a 24-bit significand: */
-static float DP1 = 0.78515625;
-static float DP2 = 2.4187564849853515625e-4;
-static float DP3 = 3.77489497744594108e-8;
-static float lossth = 8192.;
-static float T24M1 = 16777215.;
-
-static float sincof[] = {
--1.9515295891E-4,
- 8.3321608736E-3,
--1.6666654611E-1
-};
-static float coscof[] = {
- 2.443315711809948E-005,
--1.388731625493765E-003,
- 4.166664568298827E-002
-};
-
-float sinf( float xx )
-{
-float *p;
-float x, y, z;
-register unsigned long j;
-register int sign;
-
-sign = 1;
-x = xx;
-if( xx < 0 )
- {
- sign = -1;
- x = -xx;
- }
-if( x > T24M1 )
- {
- mtherr( "sinf", TLOSS );
- return(0.0);
- }
-j = FOPI * x; /* integer part of x/(PI/4) */
-y = j;
-/* map zeros to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-j &= 7; /* octant modulo 360 degrees */
-/* reflect in x axis */
-if( j > 3)
- {
- sign = -sign;
- j -= 4;
- }
-
-if( x > lossth )
- {
- mtherr( "sinf", PLOSS );
- x = x - y * PIO4F;
- }
-else
- {
-/* Extended precision modular arithmetic */
- x = ((x - y * DP1) - y * DP2) - y * DP3;
- }
-/*einits();*/
-z = x * x;
-if( (j==1) || (j==2) )
- {
-/* measured relative error in +/- pi/4 is 7.8e-8 */
-/*
- y = (( 2.443315711809948E-005 * z
- - 1.388731625493765E-003) * z
- + 4.166664568298827E-002) * z * z;
-*/
- p = coscof;
- y = *p++;
- y = y * z + *p++;
- y = y * z + *p++;
- y *= z * z;
- y -= 0.5 * z;
- y += 1.0;
- }
-else
- {
-/* Theoretical relative error = 3.8e-9 in [-pi/4, +pi/4] */
-/*
- y = ((-1.9515295891E-4 * z
- + 8.3321608736E-3) * z
- - 1.6666654611E-1) * z * x;
- y += x;
-*/
- p = sincof;
- y = *p++;
- y = y * z + *p++;
- y = y * z + *p++;
- y *= z * x;
- y += x;
- }
-/*einitd();*/
-if(sign < 0)
- y = -y;
-return( y);
-}
-
-
-/* Single precision circular cosine
- * test interval: [-pi/4, +pi/4]
- * trials: 10000
- * peak relative error: 8.3e-8
- * rms relative error: 2.2e-8
- */
-
-float cosf( float xx )
-{
-float x, y, z;
-int j, sign;
-
-/* make argument positive */
-sign = 1;
-x = xx;
-if( x < 0 )
- x = -x;
-
-if( x > T24M1 )
- {
- mtherr( "cosf", TLOSS );
- return(0.0);
- }
-
-j = FOPI * x; /* integer part of x/PIO4 */
-y = j;
-/* integer and fractional part modulo one octant */
-if( j & 1 ) /* map zeros to origin */
- {
- j += 1;
- y += 1.0;
- }
-j &= 7;
-if( j > 3)
- {
- j -=4;
- sign = -sign;
- }
-
-if( j > 1 )
- sign = -sign;
-
-if( x > lossth )
- {
- mtherr( "cosf", PLOSS );
- x = x - y * PIO4F;
- }
-else
-/* Extended precision modular arithmetic */
- x = ((x - y * DP1) - y * DP2) - y * DP3;
-
-z = x * x;
-
-if( (j==1) || (j==2) )
- {
- y = (((-1.9515295891E-4 * z
- + 8.3321608736E-3) * z
- - 1.6666654611E-1) * z * x)
- + x;
- }
-else
- {
- y = (( 2.443315711809948E-005 * z
- - 1.388731625493765E-003) * z
- + 4.166664568298827E-002) * z * z;
- y -= 0.5 * z;
- y += 1.0;
- }
-if(sign < 0)
- y = -y;
-return( y );
-}
-
+++ /dev/null
-/* sinhf.c
- *
- * Hyperbolic sine
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sinhf();
- *
- * y = sinhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic sine of argument in the range MINLOGF to
- * MAXLOGF.
- *
- * The range is partitioned into two segments. If |x| <= 1, a
- * polynomial approximation is used.
- * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-MAXLOG 100000 1.1e-7 2.9e-8
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision hyperbolic sine
- * test interval: [-1, +1]
- * trials: 10000
- * peak relative error: 9.0e-8
- * rms relative error: 3.0e-8
- */
-#include <math.h>
-extern float MAXLOGF, MAXNUMF;
-
-float expf( float );
-
-float sinhf( float xx )
-{
-register float z;
-float x;
-
-x = xx;
-if( xx < 0 )
- z = -x;
-else
- z = x;
-
-if( z > MAXLOGF )
- {
- mtherr( "sinhf", DOMAIN );
- if( x > 0 )
- return( MAXNUMF );
- else
- return( -MAXNUMF );
- }
-if( z > 1.0 )
- {
- z = expf(z);
- z = 0.5*z - (0.5/z);
- if( x < 0 )
- z = -z;
- }
-else
- {
- z = x * x;
- z =
- (( 2.03721912945E-4 * z
- + 8.33028376239E-3) * z
- + 1.66667160211E-1) * z * x
- + x;
- }
-return( z );
-}
+++ /dev/null
-/* spencef.c
- *
- * Dilogarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, spencef();
- *
- * y = spencef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral
- *
- * x
- * -
- * | | log t
- * spence(x) = - | ----- dt
- * | | t - 1
- * -
- * 1
- *
- * for x >= 0. A rational approximation gives the integral in
- * the interval (0.5, 1.5). Transformation formulas for 1/x
- * and 1-x are employed outside the basic expansion range.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,4 30000 4.4e-7 6.3e-8
- *
- *
- */
-\f
-/* spence.c */
-
-
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1985, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-static float A[8] = {
- 4.65128586073990045278E-5,
- 7.31589045238094711071E-3,
- 1.33847639578309018650E-1,
- 8.79691311754530315341E-1,
- 2.71149851196553469920E0,
- 4.25697156008121755724E0,
- 3.29771340985225106936E0,
- 1.00000000000000000126E0,
-};
-static float B[8] = {
- 6.90990488912553276999E-4,
- 2.54043763932544379113E-2,
- 2.82974860602568089943E-1,
- 1.41172597751831069617E0,
- 3.63800533345137075418E0,
- 5.03278880143316990390E0,
- 3.54771340985225096217E0,
- 9.99999999999999998740E-1,
-};
-
-extern float PIF, MACHEPF;
-
-/* pi * pi / 6 */
-#define PIFS 1.64493406684822643647
-
-
-float logf(float), polevlf(float, float *, int);
-float spencef(float xx)
-{
-float x, w, y, z;
-int flag;
-
-x = xx;
-if( x < 0.0 )
- {
- mtherr( "spencef", DOMAIN );
- return(0.0);
- }
-
-if( x == 1.0 )
- return( 0.0 );
-
-if( x == 0.0 )
- return( PIFS );
-
-flag = 0;
-
-if( x > 2.0 )
- {
- x = 1.0/x;
- flag |= 2;
- }
-
-if( x > 1.5 )
- {
- w = (1.0/x) - 1.0;
- flag |= 2;
- }
-
-else if( x < 0.5 )
- {
- w = -x;
- flag |= 1;
- }
-
-else
- w = x - 1.0;
-
-
-y = -w * polevlf( w, A, 7) / polevlf( w, B, 7 );
-
-if( flag & 1 )
- y = PIFS - logf(x) * logf(1.0-x) - y;
-
-if( flag & 2 )
- {
- z = logf(x);
- y = -0.5 * z * z - y;
- }
-
-return( y );
-}
+++ /dev/null
-/* sqrtf.c
- *
- * Square root
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, sqrtf();
- *
- * y = sqrtf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the square root of x.
- *
- * Range reduction involves isolating the power of two of the
- * argument and using a polynomial approximation to obtain
- * a rough value for the square root. Then Heron's iteration
- * is used three times to converge to an accurate value.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1.e38 100000 8.7e-8 2.9e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sqrtf domain x < 0 0.0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision square root
- * test interval: [sqrt(2)/2, sqrt(2)]
- * trials: 30000
- * peak relative error: 8.8e-8
- * rms relative error: 3.3e-8
- *
- * test interval: [0.01, 100.0]
- * trials: 50000
- * peak relative error: 8.7e-8
- * rms relative error: 3.3e-8
- *
- * Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
- */
-#include <math.h>
-
-#ifdef ANSIC
-float frexpf( float, int * );
-float ldexpf( float, int );
-
-float sqrtf( float xx )
-#else
-float frexpf(), ldexpf();
-
-float sqrtf(xx)
-float xx;
-#endif
-{
-float f, x, y;
-int e;
-
-f = xx;
-if( f <= 0.0 )
- {
- if( f < 0.0 )
- mtherr( "sqrtf", DOMAIN );
- return( 0.0 );
- }
-
-x = frexpf( f, &e ); /* f = x * 2**e, 0.5 <= x < 1.0 */
-/* If power of 2 is odd, double x and decrement the power of 2. */
-if( e & 1 )
- {
- x = x + x;
- e -= 1;
- }
-
-e >>= 1; /* The power of 2 of the square root. */
-
-if( x > 1.41421356237 )
- {
-/* x is between sqrt(2) and 2. */
- x = x - 2.0;
- y =
- ((((( -9.8843065718E-4 * x
- + 7.9479950957E-4) * x
- - 3.5890535377E-3) * x
- + 1.1028809744E-2) * x
- - 4.4195203560E-2) * x
- + 3.5355338194E-1) * x
- + 1.41421356237E0;
- goto sqdon;
- }
-
-if( x > 0.707106781187 )
- {
-/* x is between sqrt(2)/2 and sqrt(2). */
- x = x - 1.0;
- y =
- ((((( 1.35199291026E-2 * x
- - 2.26657767832E-2) * x
- + 2.78720776889E-2) * x
- - 3.89582788321E-2) * x
- + 6.24811144548E-2) * x
- - 1.25001503933E-1) * x * x
- + 0.5 * x
- + 1.0;
- goto sqdon;
- }
-
-/* x is between 0.5 and sqrt(2)/2. */
-x = x - 0.5;
-y =
-((((( -3.9495006054E-1 * x
- + 5.1743034569E-1) * x
- - 4.3214437330E-1) * x
- + 3.5310730460E-1) * x
- - 3.5354581892E-1) * x
- + 7.0710676017E-1) * x
- + 7.07106781187E-1;
-
-sqdon:
-y = ldexpf( y, e ); /* y = y * 2**e */
-return( y);
-}
+++ /dev/null
-/* stdtrf.c
- *
- * Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * float t, stdtrf();
- * short k;
- *
- * y = stdtrf( k, t );
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral from minus infinity to t of the Student
- * t distribution with integer k > 0 degrees of freedom:
- *
- * t
- * -
- * | |
- * - | 2 -(k+1)/2
- * | ( (k+1)/2 ) | ( x )
- * ---------------------- | ( 1 + --- ) dx
- * - | ( k )
- * sqrt( k pi ) | ( k/2 ) |
- * | |
- * -
- * -inf.
- *
- * Relation to incomplete beta integral:
- *
- * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
- * where
- * z = k/(k + t**2).
- *
- * For t < -1, this is the method of computation. For higher t,
- * a direct method is derived from integration by parts.
- * Since the function is symmetric about t=0, the area under the
- * right tail of the density is found by calling the function
- * with -t instead of t.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +/- 100 5000 2.3e-5 2.9e-6
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-extern float PIF, MACHEPF;
-
-#ifdef ANSIC
-float sqrtf(float), atanf(float), incbetf(float, float, float);
-#else
-float sqrtf(), atanf(), incbetf();
-#endif
-
-
-
-float stdtrf( int k, float tt )
-{
-float t, x, rk, z, f, tz, p, xsqk;
-int j;
-
-t = tt;
-if( k <= 0 )
- {
- mtherr( "stdtrf", DOMAIN );
- return(0.0);
- }
-
-if( t == 0 )
- return( 0.5 );
-
-if( t < -1.0 )
- {
- rk = k;
- z = rk / (rk + t * t);
- p = 0.5 * incbetf( 0.5*rk, 0.5, z );
- return( p );
- }
-
-/* compute integral from -t to + t */
-
-if( t < 0 )
- x = -t;
-else
- x = t;
-
-rk = k; /* degrees of freedom */
-z = 1.0 + ( x * x )/rk;
-
-/* test if k is odd or even */
-if( (k & 1) != 0)
- {
-
- /* computation for odd k */
-
- xsqk = x/sqrtf(rk);
- p = atanf( xsqk );
- if( k > 1 )
- {
- f = 1.0;
- tz = 1.0;
- j = 3;
- while( (j<=(k-2)) && ( (tz/f) > MACHEPF ) )
- {
- tz *= (j-1)/( z * j );
- f += tz;
- j += 2;
- }
- p += f * xsqk/z;
- }
- p *= 2.0/PIF;
- }
-
-
-else
- {
-
- /* computation for even k */
-
- f = 1.0;
- tz = 1.0;
- j = 2;
-
- while( ( j <= (k-2) ) && ( (tz/f) > MACHEPF ) )
- {
- tz *= (j - 1)/( z * j );
- f += tz;
- j += 2;
- }
- p = f * x/sqrtf(z*rk);
- }
-
-/* common exit */
-
-
-if( t < 0 )
- p = -p; /* note destruction of relative accuracy */
-
- p = 0.5 + 0.5 * p;
-return(p);
-}
+++ /dev/null
-/* struvef.c
- *
- * Struve function
- *
- *
- *
- * SYNOPSIS:
- *
- * float v, x, y, struvef();
- *
- * y = struvef( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the Struve function Hv(x) of order v, argument x.
- * Negative x is rejected unless v is an integer.
- *
- * This module also contains the hypergeometric functions 1F2
- * and 3F0 and a routine for the Bessel function Yv(x) with
- * noninteger v.
- *
- *
- *
- * ACCURACY:
- *
- * v varies from 0 to 10.
- * Absolute error (relative error when |Hv(x)| > 1):
- * arithmetic domain # trials peak rms
- * IEEE -10,10 100000 9.0e-5 4.0e-6
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-#define DEBUG 0
-
-extern float MACHEPF, MAXNUMF, PIF;
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-#ifdef ANSIC
-float gammaf(float), powf(float, float), sqrtf(float);
-float yvf(float, float);
-float floorf(float), ynf(int, float);
-float jvf(float, float);
-float sinf(float), cosf(float);
-#else
-float gammaf(), powf(), sqrtf(), yvf();
-float floorf(), ynf(), jvf(), sinf(), cosf();
-#endif
-
-float onef2f( float aa, float bb, float cc, float xx, float *err )
-{
-float a, b, c, x, n, a0, sum, t;
-float an, bn, cn, max, z;
-
-a = aa;
-b = bb;
-c = cc;
-x = xx;
-an = a;
-bn = b;
-cn = c;
-a0 = 1.0;
-sum = 1.0;
-n = 1.0;
-t = 1.0;
-max = 0.0;
-
-do
- {
- if( an == 0 )
- goto done;
- if( bn == 0 )
- goto error;
- if( cn == 0 )
- goto error;
- if( (a0 > 1.0e34) || (n > 200) )
- goto error;
- a0 *= (an * x) / (bn * cn * n);
- sum += a0;
- an += 1.0;
- bn += 1.0;
- cn += 1.0;
- n += 1.0;
- z = fabsf( a0 );
- if( z > max )
- max = z;
- if( sum != 0 )
- t = fabsf( a0 / sum );
- else
- t = z;
- }
-while( t > MACHEPF );
-
-done:
-
-*err = fabsf( MACHEPF*max /sum );
-
-#if DEBUG
- printf(" onef2f cancellation error %.5E\n", *err );
-#endif
-
-goto xit;
-
-error:
-#if DEBUG
-printf("onef2f does not converge\n");
-#endif
-*err = MAXNUMF;
-
-xit:
-
-#if DEBUG
-printf("onef2( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
-#endif
-return(sum);
-}
-
-
-
-float threef0f( float aa, float bb, float cc, float xx, float *err )
-{
-float a, b, c, x, n, a0, sum, t, conv, conv1;
-float an, bn, cn, max, z;
-
-a = aa;
-b = bb;
-c = cc;
-x = xx;
-an = a;
-bn = b;
-cn = c;
-a0 = 1.0;
-sum = 1.0;
-n = 1.0;
-t = 1.0;
-max = 0.0;
-conv = 1.0e38;
-conv1 = conv;
-
-do
- {
- if( an == 0.0 )
- goto done;
- if( bn == 0.0 )
- goto done;
- if( cn == 0.0 )
- goto done;
- if( (a0 > 1.0e34) || (n > 200) )
- goto error;
- a0 *= (an * bn * cn * x) / n;
- an += 1.0;
- bn += 1.0;
- cn += 1.0;
- n += 1.0;
- z = fabsf( a0 );
- if( z > max )
- max = z;
- if( z >= conv )
- {
- if( (z < max) && (z > conv1) )
- goto done;
- }
- conv1 = conv;
- conv = z;
- sum += a0;
- if( sum != 0 )
- t = fabsf( a0 / sum );
- else
- t = z;
- }
-while( t > MACHEPF );
-
-done:
-
-t = fabsf( MACHEPF*max/sum );
-#if DEBUG
- printf(" threef0f cancellation error %.5E\n", t );
-#endif
-
-max = fabsf( conv/sum );
-if( max > t )
- t = max;
-#if DEBUG
- printf(" threef0f convergence %.5E\n", max );
-#endif
-
-goto xit;
-
-error:
-#if DEBUG
-printf("threef0f does not converge\n");
-#endif
-t = MAXNUMF;
-
-xit:
-
-#if DEBUG
-printf("threef0f( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
-#endif
-
-*err = t;
-return(sum);
-}
-
-
-
-
-float struvef( float vv, float xx )
-{
-float v, x, y, ya, f, g, h, t;
-float onef2err, threef0err;
-
-v = vv;
-x = xx;
-f = floorf(v);
-if( (v < 0) && ( v-f == 0.5 ) )
- {
- y = jvf( -v, x );
- f = 1.0 - f;
- g = 2.0 * floorf(0.5*f);
- if( g != f )
- y = -y;
- return(y);
- }
-t = 0.25*x*x;
-f = fabsf(x);
-g = 1.5 * fabsf(v);
-if( (f > 30.0) && (f > g) )
- {
- onef2err = MAXNUMF;
- y = 0.0;
- }
-else
- {
- y = onef2f( 1.0, 1.5, 1.5+v, -t, &onef2err );
- }
-
-if( (f < 18.0) || (x < 0.0) )
- {
- threef0err = MAXNUMF;
- ya = 0.0;
- }
-else
- {
- ya = threef0f( 1.0, 0.5, 0.5-v, -1.0/t, &threef0err );
- }
-
-f = sqrtf( PIF );
-h = powf( 0.5*x, v-1.0 );
-
-if( onef2err <= threef0err )
- {
- g = gammaf( v + 1.5 );
- y = y * h * t / ( 0.5 * f * g );
- return(y);
- }
-else
- {
- g = gammaf( v + 0.5 );
- ya = ya * h / ( f * g );
- ya = ya + yvf( v, x );
- return(ya);
- }
-}
-
-
-
-
-/* Bessel function of noninteger order
- */
-
-float yvf( float vv, float xx )
-{
-float v, x, y, t;
-int n;
-
-v = vv;
-x = xx;
-y = floorf( v );
-if( y == v )
- {
- n = v;
- y = ynf( n, x );
- return( y );
- }
-t = PIF * v;
-y = (cosf(t) * jvf( v, x ) - jvf( -v, x ))/sinf(t);
-return( y );
-}
-
-/* Crossover points between ascending series and asymptotic series
- * for Struve function
- *
- * v x
- *
- * 0 19.2
- * 1 18.95
- * 2 19.15
- * 3 19.3
- * 5 19.7
- * 10 21.35
- * 20 26.35
- * 30 32.31
- * 40 40.0
- */
+++ /dev/null
-/* tandgf.c
- *
- * Circular tangent of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, tandgf();
- *
- * y = tandgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is into intervals of 45 degrees.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-2^24 50000 2.4e-7 4.8e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tanf total loss x > 2^24 0.0
- *
- */
-\f/* cotdgf.c
- *
- * Circular cotangent of angle in degrees
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cotdgf();
- *
- * y = cotdgf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of 45 degrees.
- * A common routine computes either the tangent or cotangent.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-2^24 50000 2.4e-7 4.8e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 2^24 0.0
- * cot singularity x = 0 MAXNUMF
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision circular tangent
- * test interval: [-pi/4, +pi/4]
- * trials: 10000
- * peak relative error: 8.7e-8
- * rms relative error: 2.8e-8
- */
-#include <math.h>
-
-extern float MAXNUMF;
-
-static float T24M1 = 16777215.;
-static float PI180 = 0.0174532925199432957692; /* pi/180 */
-
-static float tancotf( float xx, int cotflg )
-{
-float x, y, z, zz;
-long j;
-int sign;
-
-
-/* make argument positive but save the sign */
-if( xx < 0.0 )
- {
- x = -xx;
- sign = -1;
- }
-else
- {
- x = xx;
- sign = 1;
- }
-
-if( x > T24M1 )
- {
- if( cotflg )
- mtherr( "cotdgf", TLOSS );
- else
- mtherr( "tandgf", TLOSS );
- return(0.0);
- }
-
-/* compute x mod PIO4 */
-j = 0.022222222222222222222 * x; /* integer part of x/45 */
-y = j;
-
-/* map zeros and singularities to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-
-z = x - y * 45.0;
-z *= PI180; /* multiply by pi/180 to convert to radians */
-
-zz = z * z;
-
-if( x > 1.0e-4 )
- {
-/* 1.7e-8 relative error in [-pi/4, +pi/4] */
- y =
- ((((( 9.38540185543E-3 * zz
- + 3.11992232697E-3) * zz
- + 2.44301354525E-2) * zz
- + 5.34112807005E-2) * zz
- + 1.33387994085E-1) * zz
- + 3.33331568548E-1) * zz * z
- + z;
- }
-else
- {
- y = z;
- }
-
-if( j & 2 )
- {
- if( cotflg )
- y = -y;
- else
- {
- if( y != 0.0 )
- {
- y = -1.0/y;
- }
- else
- {
- mtherr( "tandgf", SING );
- y = MAXNUMF;
- }
- }
- }
-else
- {
- if( cotflg )
- {
- if( y != 0.0 )
- y = 1.0/y;
- else
- {
- mtherr( "cotdgf", SING );
- y = MAXNUMF;
- }
- }
- }
-
-if( sign < 0 )
- y = -y;
-
-return( y );
-}
-
-
-float tandgf( float x )
-{
-
-return( tancotf(x,0) );
-}
-
-float cotdgf( float x )
-{
-
-if( x == 0.0 )
- {
- mtherr( "cotdgf", SING );
- return( MAXNUMF );
- }
-return( tancotf(x,1) );
-}
-
+++ /dev/null
-/* tanf.c
- *
- * Circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, tanf();
- *
- * y = tanf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A polynomial approximation
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-4096 100000 3.3e-7 4.5e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tanf total loss x > 2^24 0.0
- *
- */
-\f/* cotf.c
- *
- * Circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, cotf();
- *
- * y = cotf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the radian argument x.
- * A common routine computes either the tangent or cotangent.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-4096 100000 3.0e-7 4.5e-8
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 2^24 0.0
- * cot singularity x = 0 MAXNUMF
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision circular tangent
- * test interval: [-pi/4, +pi/4]
- * trials: 10000
- * peak relative error: 8.7e-8
- * rms relative error: 2.8e-8
- */
-#include <math.h>
-
-extern float MAXNUMF;
-
-static float DP1 = 0.78515625;
-static float DP2 = 2.4187564849853515625e-4;
-static float DP3 = 3.77489497744594108e-8;
-float FOPI = 1.27323954473516; /* 4/pi */
-static float lossth = 8192.;
-/*static float T24M1 = 16777215.;*/
-
-
-static float tancotf( float xx, int cotflg )
-{
-float x, y, z, zz;
-long j;
-int sign;
-
-
-/* make argument positive but save the sign */
-if( xx < 0.0 )
- {
- x = -xx;
- sign = -1;
- }
-else
- {
- x = xx;
- sign = 1;
- }
-
-if( x > lossth )
- {
- if( cotflg )
- mtherr( "cotf", TLOSS );
- else
- mtherr( "tanf", TLOSS );
- return(0.0);
- }
-
-/* compute x mod PIO4 */
-j = FOPI * x; /* integer part of x/(PI/4) */
-y = j;
-
-/* map zeros and singularities to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0;
- }
-
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-
-if( x > 1.0e-4 )
- {
-/* 1.7e-8 relative error in [-pi/4, +pi/4] */
- y =
- ((((( 9.38540185543E-3 * zz
- + 3.11992232697E-3) * zz
- + 2.44301354525E-2) * zz
- + 5.34112807005E-2) * zz
- + 1.33387994085E-1) * zz
- + 3.33331568548E-1) * zz * z
- + z;
- }
-else
- {
- y = z;
- }
-
-if( j & 2 )
- {
- if( cotflg )
- y = -y;
- else
- y = -1.0/y;
- }
-else
- {
- if( cotflg )
- y = 1.0/y;
- }
-
-if( sign < 0 )
- y = -y;
-
-return( y );
-}
-
-
-float tanf( float x )
-{
-
-return( tancotf(x,0) );
-}
-
-float cotf( float x )
-{
-
-if( x == 0.0 )
- {
- mtherr( "cotf", SING );
- return( MAXNUMF );
- }
-return( tancotf(x,1) );
-}
-
+++ /dev/null
-/* tanhf.c
- *
- * Hyperbolic tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, tanhf();
- *
- * y = tanhf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic tangent of argument in the range MINLOG to
- * MAXLOG.
- *
- * A polynomial approximation is used for |x| < 0.625.
- * Otherwise,
- *
- * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -2,2 100000 1.3e-7 2.6e-8
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-/* Single precision hyperbolic tangent
- * test interval: [-0.625, +0.625]
- * trials: 10000
- * peak relative error: 7.2e-8
- * rms relative error: 2.6e-8
- */
-#include <math.h>
-
-extern float MAXLOGF;
-
-float expf( float );
-
-float tanhf( float xx )
-{
-float x, z;
-
-if( xx < 0 )
- x = -xx;
-else
- x = xx;
-
-if( x > 0.5 * MAXLOGF )
- {
- if( xx > 0 )
- return( 1.0 );
- else
- return( -1.0 );
- }
-if( x >= 0.625 )
- {
- x = expf(x+x);
- z = 1.0 - 2.0/(x + 1.0);
- if( xx < 0 )
- z = -z;
- }
-else
- {
- z = x * x;
- z =
- (((( -5.70498872745E-3 * z
- + 2.06390887954E-2) * z
- - 5.37397155531E-2) * z
- + 1.33314422036E-1) * z
- - 3.33332819422E-1) * z * xx
- + xx;
- }
-return( z );
-}
+++ /dev/null
-/* ynf.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, ynf();
- * int n;
- *
- * y = ynf( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0() and y1().
- *
- * If n = 0 or 1 the routine for y0 or y1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative when y > 1:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 10000 2.3e-6 3.4e-7
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * yn singularity x = 0 MAXNUMF
- * yn overflow MAXNUMF
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern float MAXNUMF, MAXLOGF;
-
-float y0f(float), y1f(float), logf(float);
-
-float ynf( int nn, float xx )
-{
-float x, an, anm1, anm2, r, xinv;
-int k, n, sign;
-
-x = xx;
-n = nn;
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) == 0 ) /* -1**n */
- sign = 1;
- else
- sign = -1;
- }
-else
- sign = 1;
-
-
-if( n == 0 )
- return( sign * y0f(x) );
-if( n == 1 )
- return( sign * y1f(x) );
-
-/* test for overflow */
-if( x <= 0.0 )
- {
- mtherr( "ynf", SING );
- return( -MAXNUMF );
- }
-if( (x < 1.0) || (n > 29) )
- {
- an = (float )n;
- r = an * logf( an/x );
- if( r > MAXLOGF )
- {
- mtherr( "ynf", OVERFLOW );
- return( -MAXNUMF );
- }
- }
-
-/* forward recurrence on n */
-
-anm2 = y0f(x);
-anm1 = y1f(x);
-k = 1;
-r = 2 * k;
-xinv = 1.0/x;
-do
- {
- an = r * anm1 * xinv - anm2;
- anm2 = anm1;
- anm1 = an;
- r += 2.0;
- ++k;
- }
-while( k < n );
-
-
-return( sign * an );
-}
+++ /dev/null
- /* zetacf.c
- *
- * Riemann zeta function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, zetacf();
- *
- * y = zetacf( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zetac(x) = > k , x > 1,
- * -
- * k=2
- *
- * is related to the Riemann zeta function by
- *
- * Riemann zeta(x) = zetac(x) + 1.
- *
- * Extension of the function definition for x < 1 is implemented.
- * Zero is returned for x > log2(MAXNUM).
- *
- * An overflow error may occur for large negative x, due to the
- * gamma function in the reflection formula.
- *
- * ACCURACY:
- *
- * Tabulated values have full machine accuracy.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,50 30000 5.5e-7 7.5e-8
- *
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-
-/* Riemann zeta(x) - 1
- * for integer arguments between 0 and 30.
- */
-static float azetacf[] = {
--1.50000000000000000000E0,
- 1.70141183460469231730E38, /* infinity. */
- 6.44934066848226436472E-1,
- 2.02056903159594285400E-1,
- 8.23232337111381915160E-2,
- 3.69277551433699263314E-2,
- 1.73430619844491397145E-2,
- 8.34927738192282683980E-3,
- 4.07735619794433937869E-3,
- 2.00839282608221441785E-3,
- 9.94575127818085337146E-4,
- 4.94188604119464558702E-4,
- 2.46086553308048298638E-4,
- 1.22713347578489146752E-4,
- 6.12481350587048292585E-5,
- 3.05882363070204935517E-5,
- 1.52822594086518717326E-5,
- 7.63719763789976227360E-6,
- 3.81729326499983985646E-6,
- 1.90821271655393892566E-6,
- 9.53962033872796113152E-7,
- 4.76932986787806463117E-7,
- 2.38450502727732990004E-7,
- 1.19219925965311073068E-7,
- 5.96081890512594796124E-8,
- 2.98035035146522801861E-8,
- 1.49015548283650412347E-8,
- 7.45071178983542949198E-9,
- 3.72533402478845705482E-9,
- 1.86265972351304900640E-9,
- 9.31327432419668182872E-10
-};
-
-
-/* 2**x (1 - 1/x) (zeta(x) - 1) = P(1/x)/Q(1/x), 1 <= x <= 10 */
-static float P[9] = {
- 5.85746514569725319540E11,
- 2.57534127756102572888E11,
- 4.87781159567948256438E10,
- 5.15399538023885770696E9,
- 3.41646073514754094281E8,
- 1.60837006880656492731E7,
- 5.92785467342109522998E5,
- 1.51129169964938823117E4,
- 2.01822444485997955865E2,
-};
-static float Q[8] = {
-/* 1.00000000000000000000E0,*/
- 3.90497676373371157516E11,
- 5.22858235368272161797E10,
- 5.64451517271280543351E9,
- 3.39006746015350418834E8,
- 1.79410371500126453702E7,
- 5.66666825131384797029E5,
- 1.60382976810944131506E4,
- 1.96436237223387314144E2,
-};
-
-/* log(zeta(x) - 1 - 2**-x), 10 <= x <= 50 */
-static float A[11] = {
- 8.70728567484590192539E6,
- 1.76506865670346462757E8,
- 2.60889506707483264896E10,
- 5.29806374009894791647E11,
- 2.26888156119238241487E13,
- 3.31884402932705083599E14,
- 5.13778997975868230192E15,
--1.98123688133907171455E15,
--9.92763810039983572356E16,
- 7.82905376180870586444E16,
- 9.26786275768927717187E16,
-};
-static float B[10] = {
-/* 1.00000000000000000000E0,*/
--7.92625410563741062861E6,
--1.60529969932920229676E8,
--2.37669260975543221788E10,
--4.80319584350455169857E11,
--2.07820961754173320170E13,
--2.96075404507272223680E14,
--4.86299103694609136686E15,
- 5.34589509675789930199E15,
- 5.71464111092297631292E16,
--1.79915597658676556828E16,
-};
-
-/* (1-x) (zeta(x) - 1), 0 <= x <= 1 */
-
-static float R[6] = {
--3.28717474506562731748E-1,
- 1.55162528742623950834E1,
--2.48762831680821954401E2,
- 1.01050368053237678329E3,
- 1.26726061410235149405E4,
--1.11578094770515181334E5,
-};
-static float S[5] = {
-/* 1.00000000000000000000E0,*/
- 1.95107674914060531512E1,
- 3.17710311750646984099E2,
- 3.03835500874445748734E3,
- 2.03665876435770579345E4,
- 7.43853965136767874343E4,
-};
-
-
-#define MAXL2 127
-
-/*
- * Riemann zeta function, minus one
- */
-
-extern float MACHEPF, PIO2F, MAXNUMF, PIF;
-
-#ifdef ANSIC
-extern float sinf ( float xx );
-extern float floorf ( float x );
-extern float gammaf ( float xx );
-extern float powf ( float x, float y );
-extern float expf ( float xx );
-extern float polevlf ( float xx, float *coef, int N );
-extern float p1evlf ( float xx, float *coef, int N );
-#else
-float sinf(), floorf(), gammaf(), powf(), expf();
-float polevlf(), p1evlf();
-#endif
-
-float zetacf(float xx)
-{
-int i;
-float x, a, b, s, w;
-
-x = xx;
-if( x < 0.0 )
- {
- if( x < -30.8148 )
- {
- mtherr( "zetacf", OVERFLOW );
- return(0.0);
- }
- s = 1.0 - x;
- w = zetacf( s );
- b = sinf(PIO2F*x) * powf(2.0*PIF, x) * gammaf(s) * (1.0 + w) / PIF;
- return(b - 1.0);
- }
-
-if( x >= MAXL2 )
- return(0.0); /* because first term is 2**-x */
-
-/* Tabulated values for integer argument */
-w = floorf(x);
-if( w == x )
- {
- i = x;
- if( i < 31 )
- {
- return( azetacf[i] );
- }
- }
-
-
-if( x < 1.0 )
- {
- w = 1.0 - x;
- a = polevlf( x, R, 5 ) / ( w * p1evlf( x, S, 5 ));
- return( a );
- }
-
-if( x == 1.0 )
- {
- mtherr( "zetacf", SING );
- return( MAXNUMF );
- }
-
-if( x <= 10.0 )
- {
- b = powf( 2.0, x ) * (x - 1.0);
- w = 1.0/x;
- s = (x * polevlf( w, P, 8 )) / (b * p1evlf( w, Q, 8 ));
- return( s );
- }
-
-if( x <= 50.0 )
- {
- b = powf( 2.0, -x );
- w = polevlf( x, A, 10 ) / p1evlf( x, B, 10 );
- w = expf(w) + b;
- return(w);
- }
-
-
-/* Basic sum of inverse powers */
-
-
-s = 0.0;
-a = 1.0;
-do
- {
- a += 2.0;
- b = powf( a, -x );
- s += b;
- }
-while( b/s > MACHEPF );
-
-b = powf( 2.0, -x );
-s = (s + b)/(1.0-b);
-return(s);
-}
+++ /dev/null
-/* zetaf.c
- *
- * Riemann zeta function of two arguments
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, q, y, zetaf();
- *
- * y = zetaf( x, q );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=0
- *
- * where x > 1 and q is not a negative integer or zero.
- * The Euler-Maclaurin summation formula is used to obtain
- * the expansion
- *
- * n
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=1
- *
- * 1-x inf. B x(x+1)...(x+2j)
- * (n+q) 1 - 2j
- * + --------- - ------- + > --------------------
- * x-1 x - x+2j+1
- * 2(n+q) j=1 (2j)! (n+q)
- *
- * where the B2j are Bernoulli numbers. Note that (see zetac.c)
- * zeta(x,1) = zetac(x) + 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,25 10000 6.9e-7 1.0e-7
- *
- * Large arguments may produce underflow in powf(), in which
- * case the results are inaccurate.
- *
- * REFERENCE:
- *
- * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
- * Series, and Products, p. 1073; Academic Press, 1980.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern float MAXNUMF, MACHEPF;
-
-/* Expansion coefficients
- * for Euler-Maclaurin summation formula
- * (2k)! / B2k
- * where B2k are Bernoulli numbers
- */
-static float A[] = {
-12.0,
--720.0,
-30240.0,
--1209600.0,
-47900160.0,
--1.8924375803183791606e9, /*1.307674368e12/691*/
-7.47242496e10,
--2.950130727918164224e12, /*1.067062284288e16/3617*/
-1.1646782814350067249e14, /*5.109094217170944e18/43867*/
--4.5979787224074726105e15, /*8.028576626982912e20/174611*/
-1.8152105401943546773e17, /*1.5511210043330985984e23/854513*/
--7.1661652561756670113e18 /*1.6938241367317436694528e27/236364091*/
-};
-/* 30 Nov 86 -- error in third coefficient fixed */
-
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-
-float powf( float, float );
-float zetaf(float xx, float qq)
-{
-int i;
-float x, q, a, b, k, s, w, t;
-
-x = xx;
-q = qq;
-if( x == 1.0 )
- return( MAXNUMF );
-
-if( x < 1.0 )
- {
- mtherr( "zetaf", DOMAIN );
- return(0.0);
- }
-
-
-/* Euler-Maclaurin summation formula */
-/*
-if( x < 25.0 )
-{
-*/
-w = 9.0;
-s = powf( q, -x );
-a = q;
-for( i=0; i<9; i++ )
- {
- a += 1.0;
- b = powf( a, -x );
- s += b;
- if( b/s < MACHEPF )
- goto done;
- }
-
-w = a;
-s += b*w/(x-1.0);
-s -= 0.5 * b;
-a = 1.0;
-k = 0.0;
-for( i=0; i<12; i++ )
- {
- a *= x + k;
- b /= w;
- t = a*b/A[i];
- s = s + t;
- t = fabsf(t/s);
- if( t < MACHEPF )
- goto done;
- k += 1.0;
- a *= x + k;
- b /= w;
- k += 1.0;
- }
-done:
-return(s);
-/*
-}
-*/
-
-
-/* Basic sum of inverse powers */
-/*
-pseres:
-
-s = powf( q, -x );
-a = q;
-do
- {
- a += 2.0;
- b = powf( a, -x );
- s += b;
- }
-while( b/s > MACHEPF );
-
-b = powf( 2.0, -x );
-s = (s + b)/(1.0-b);
-return(s);
-*/
-}
--- /dev/null
+/*******************************************************************************
+* *
+* File fp_private.h, *
+* All pack 4 dependencies for the MathLib elems plus some defines used *
+* throughout MathLib. *
+* *
+* Copyright © 1991 Apple Computer, Inc. All rights reserved. *
+* *
+* Written by Ali Sazegari, started on October 1991, *
+* *
+* W A R N I N G: This routine expects a 64 bit double model. *
+* *
+*******************************************************************************/
+
+#define NoException 0
+
+/*******************************************************************************
+* Values of constants. *
+*******************************************************************************/
+
+//#define SgnMask 0x8000
+#define dSgnMask 0x80000000
+#define sSgnMask 0x7FFFFFFF
+
+//#define ExpMask 0x7FFF
+#define dExpMask 0x7FF00000
+#define sExpMask 0xFF000000
+
+ /* according to rounding BIG & SMALL are: */
+#define BIG 1.1e+300 /* used to deliver ±° or largest number, */
+#define SMALL 1.1e-300 /* used to deliver ±0 or smallest number. */
+#define InfExp 0x7FF
+#define dMaxExp 0x7FF00000
+
+#define MaxExpP1 1024
+#define MaxExp 1023
+
+#define DenormLimit -52
+
+//#define ManMask 0x80000000
+#define dManMask 0x00080000
+
+//#define IsItDenorm 0x80000000
+#define dIsItDenorm 0x00080000
+
+//#define xIsItSNaN 0x40000000
+#define dIsItSNaN 0x00080000
+
+#define dHighMan 0x000FFFFF
+#define dFirstBitSet 0x00080000
+#define BIAS 0x3FF
+
+//#define GetSign 0x8000
+#define dGetSign 0x80000000
+#define sGetSign 0x80000000
+
+//#define Infinity(x) ( x.hex.exponent & ExpMask ) == ExpMask
+#define dInfinity(x) ( x.hex.high & dExpMask ) == dExpMask
+#define sInfinity(x) ( ( x.hexsgl << 1 ) & sExpMask ) == sExpMask
+
+//#define Exponent(x) x.hex.exponent & ExpMask
+#define dExponent(x) x.hex.high & dExpMask
+#define sExponent(x) ( ( x.hexsgl << 1 ) & sExpMask )
+
+#define sZero(x) ( x.hexsgl & sSgnMask ) == 0
+//#define Sign(x) ( x.hex.exponent & SgnMask ) == SgnMask
+
+/*******************************************************************************
+* Types used in the auxiliary functions. *
+*******************************************************************************/
+
+typedef struct /* Hex representation of a double. */
+ {
+#if defined(__BIG_ENDIAN__)
+ unsigned long int high;
+ unsigned long int low;
+#else
+ unsigned long int low;
+ unsigned long int high;
+#endif
+ } dHexParts;
+
+typedef union
+ {
+ unsigned char byties[8];
+ double dbl;
+ } DblInHex;
+
+//enum boolean { FALSE, TRUE };
+
+/*******************************************************************************
+* Macros to access long subfields of a double value. *
+*******************************************************************************/
+
+#define highpartd(x) *((long *) &x)
+#define lowpartd(x) *((long *) &x + 1)
+
+enum {
+ FP_SNAN = 0, /* signaling NaN
+ */
+ FP_QNAN = 1, /* quiet NaN
+ */
+ FP_INFINITE = 2, /* + or - infinity
+ */
+ FP_ZERO = 3, /* + or - zero
+ */
+ FP_NORMAL = 4, /* all normal numbers
+ */
+ FP_SUBNORMAL = 5 /* denormal numbers
+ */
+};
+
--- /dev/null
+/***********************************************************************
+** File: fpmacros.c
+**
+** Contains: C source code for implementations of floating-point
+** functions which involve float format numbers, as
+** defined in header <fp.h>. In particular, this file
+** contains implementations of functions
+** __fpclassify(d,f), __isnormal(d,f), __isfinite(d,f),
+** __isnan(d,f), and __signbit(d,f). This file targets
+** PowerPC platforms.
+**
+** Written by: Robert A. Murley, Ali Sazegari
+**
+** Copyright: c 2001 by Apple Computer, Inc., all rights reserved
+**
+** Change History (most recent first):
+**
+** 07 Jul 01 ram First created from fpfloatfunc.c, fp.c,
+** classify.c and sign.c in MathLib v3 Mac OS9.
+**
+***********************************************************************/
+
+#include "fp_private.h"
+
+#define SIGN_MASK 0x80000000
+#define NSIGN_MASK 0x7fffffff
+#define FEXP_MASK 0x7f800000
+#define FFRAC_MASK 0x007fffff
+
+/***********************************************************************
+ long int __fpclassifyf(float x) returns the classification code of the
+ argument x, as defined in <fp.h>.
+
+ Exceptions: INVALID signaled if x is a signaling NaN; in this case,
+ the FP_QNAN code is returned.
+
+ Calls: none
+***********************************************************************/
+
+long int __fpclassifyf ( float x )
+{
+ unsigned long int iexp;
+
+ union {
+ unsigned long int lval;
+ float fval;
+ } z;
+
+ z.fval = x;
+ iexp = z.lval & FEXP_MASK; /* isolate float exponent */
+
+ if (iexp == FEXP_MASK) { /* NaN or INF case */
+ if ((z.lval & 0x007fffff) == 0)
+ return (long int) FP_INFINITE;
+ else if ((z.lval & 0x00400000) != 0)
+ return (long int) FP_QNAN;
+ else
+ return (long int) FP_SNAN;
+ }
+
+ if (iexp != 0) /* normal float */
+ return (long int) FP_NORMAL;
+
+ if (x == 0.0)
+ return (long int) FP_ZERO; /* zero */
+ else
+ return (long int) FP_SUBNORMAL; /* must be subnormal */
+}
+
+
+/***********************************************************************
+ Function __fpclassify,
+ Implementation of classify of a double number for the PowerPC.
+
+ Exceptions: INVALID signaled if x is a signaling NaN; in this case,
+ the FP_QNAN code is returned.
+
+ Calls: none
+***********************************************************************/
+
+long int __fpclassify ( double arg )
+{
+ register unsigned long int exponent;
+ union
+ {
+ dHexParts hex;
+ double dbl;
+ } x;
+
+ x.dbl = arg;
+
+ exponent = x.hex.high & dExpMask;
+ if ( exponent == dExpMask )
+ {
+ if ( ( ( x.hex.high & dHighMan ) | x.hex.low ) == 0 )
+ return (long int) FP_INFINITE;
+ else
+ return ( x.hex.high & 0x00080000 ) ? FP_QNAN : FP_SNAN;
+ }
+ else if ( exponent != 0)
+ return (long int) FP_NORMAL;
+ else {
+ if ( arg == 0.0 )
+ return (long int) FP_ZERO;
+ else
+ return (long int) FP_SUBNORMAL;
+ }
+}
+
+
+/***********************************************************************
+ long int __isnormalf(float x) returns nonzero if and only if x is a
+ normalized float number and zero otherwise.
+
+ Exceptions: INVALID is raised if x is a signaling NaN; in this case,
+ zero is returned.
+
+ Calls: none
+***********************************************************************/
+
+long int __isnormalf ( float x )
+{
+ unsigned long int iexp;
+ union {
+ unsigned long int lval;
+ float fval;
+ } z;
+
+ z.fval = x;
+ iexp = z.lval & FEXP_MASK; /* isolate float exponent */
+ return ((iexp != FEXP_MASK) && (iexp != 0));
+}
+
+
+long int __isnorma ( double x )
+{
+ return ( __fpclassify ( x ) == FP_NORMAL );
+}
+
+
+/***********************************************************************
+ long int __isfinitef(float x) returns nonzero if and only if x is a
+ finite (normal, subnormal, or zero) float number and zero otherwise.
+
+ Exceptions: INVALID is raised if x is a signaling NaN; in this case,
+ zero is returned.
+
+ Calls: none
+***********************************************************************/
+
+long int __isfinitef ( float x )
+{
+ union {
+ unsigned long int lval;
+ float fval;
+ } z;
+
+ z.fval = x;
+ return ((z.lval & FEXP_MASK) != FEXP_MASK);
+}
+
+long int __isfinite ( double x )
+{
+ return ( __fpclassify ( x ) >= FP_ZERO );
+}
+
+
+
+/***********************************************************************
+ long int __isnanf(float x) returns nonzero if and only if x is a
+ NaN and zero otherwise.
+
+ Exceptions: INVALID is raised if x is a signaling NaN; in this case,
+ nonzero is returned.
+
+ Calls: none
+***********************************************************************/
+
+long int __isnanf ( float x )
+{
+ union {
+ unsigned long int lval;
+ float fval;
+ } z;
+
+ z.fval = x;
+ return (((z.lval&FEXP_MASK) == FEXP_MASK) && ((z.lval&FFRAC_MASK) != 0));
+}
+
+long int __isnan ( double x )
+{
+ long int class = __fpclassify(x);
+ return ( ( class == FP_SNAN ) || ( class == FP_QNAN ) );
+}
+
+
+/***********************************************************************
+ long int __signbitf(float x) returns nonzero if and only if the sign
+ bit of x is set and zero otherwise.
+
+ Exceptions: INVALID is raised if x is a signaling NaN.
+
+ Calls: none
+***********************************************************************/
+
+long int __signbitf ( float x )
+{
+ union {
+ unsigned long int lval;
+ float fval;
+ } z;
+
+ z.fval = x;
+ return ((z.lval & SIGN_MASK) != 0);
+}
+
+
+/***********************************************************************
+ Function sign of a double.
+ Implementation of sign bit for the PowerPC.
+
+ Calls: none
+***********************************************************************/
+
+long int __signbit ( double arg )
+{
+ union
+ {
+ dHexParts hex;
+ double dbl;
+ } x;
+ long int sign;
+
+ x.dbl = arg;
+ sign = ( ( x.hex.high & dSgnMask ) == dSgnMask ) ? 1 : 0;
+ return sign;
+}
+
+
--- /dev/null
+#if defined(__ppc__)
+/*******************************************************************************
+* *
+* File frexpldexp.c, *
+* Functions frexp(x) and ldexp(x), *
+* Implementation of frexp and ldexp functions for the PowerPC. *
+* *
+* Copyright © 1991 Apple Computer, Inc. All rights reserved. *
+* *
+* Written by Ali Sazegari, started on January 1991, *
+* *
+* W A R N I N G: This routine expects a 64 bit double model. *
+* *
+* December03 1992: first rs6000 implementation. *
+* October 05 1993: added special cases for NaN and ° in frexp. *
+* May 27 1997: improved the performance of frexp by eliminating the *
+* switch statement. *
+* June 13 2001: (ram) rewrote frexp to eliminate calls to scalb and *
+* logb. *
+* *
+*******************************************************************************/
+
+#include <limits.h>
+#include <math.h>
+
+static const double two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
+
+typedef union
+ {
+ struct {
+#if defined(__BIG_ENDIAN__)
+ unsigned long int hi;
+ unsigned long int lo;
+#else
+ unsigned long int lo;
+ unsigned long int hi;
+#endif
+ } words;
+ double dbl;
+ } DblInHex;
+
+double ldexp ( double value, int exp )
+ {
+ if ( exp > SHRT_MAX )
+ exp = SHRT_MAX;
+ else if ( exp < -SHRT_MAX )
+ exp = -SHRT_MAX;
+ return scalb ( value, exp );
+ }
+
+double frexp ( double value, int *eptr )
+ {
+ DblInHex argument;
+ unsigned long int valueHead;
+
+ argument.dbl = value;
+ valueHead = argument.words.hi & 0x7fffffffUL; // valueHead <- |x|
+
+ *eptr = 0;
+ if ( valueHead >= 0x7ff00000 || ( valueHead | argument.words.lo ) == 0 )
+ return value; // 0, inf, or NaN
+
+ if ( valueHead < 0x00100000 )
+ { // denorm
+ argument.dbl = two54 * value;
+ valueHead = argument.words.hi &0x7fffffff;
+ *eptr = -54;
+ }
+ *eptr += ( valueHead >> 20 ) - 1022;
+ argument.words.hi = ( argument.words.hi & 0x800fffff ) | 0x3fe00000;
+ return argument.dbl;
+ }
+#endif /* __ppc__ */
--- /dev/null
+/* @(#)k_cos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
+#endif
+
+/*
+ * __kernel_cos( x, y )
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ *
+ * Algorithm
+ * 1. Since cos(-x) = cos(x), we need only to consider positive x.
+ * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+ * 3. cos(x) is approximated by a polynomial of degree 14 on
+ * [0,pi/4]
+ * 4 14
+ * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+ * where the remez error is
+ *
+ * | 2 4 6 8 10 12 14 | -58
+ * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
+ * | |
+ *
+ * 4 6 8 10 12 14
+ * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
+ * cos(x) = 1 - x*x/2 + r
+ * since cos(x+y) ~ cos(x) - sin(x)*y
+ * ~ cos(x) - x*y,
+ * a correction term is necessary in cos(x) and hence
+ * cos(x+y) = 1 - (x*x/2 - (r - x*y))
+ * For better accuracy when x > 0.3, let qx = |x|/4 with
+ * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
+ * Then
+ * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
+ * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
+ * magnitude of the latter is at least a quarter of x*x/2,
+ * thus, reducing the rounding error in the subtraction.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
+C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
+C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
+C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
+C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
+C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
+
+#ifdef __STDC__
+ double __kernel_cos(double x, double y)
+#else
+ double __kernel_cos(x, y)
+ double x,y;
+#endif
+{
+ double a,hz,z,r,qx;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff; /* ix = |x|'s high word*/
+ if(ix<0x3e400000) { /* if x < 2**27 */
+ if(((int)x)==0) return one; /* generate inexact */
+ }
+ z = x*x;
+ r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
+ if(ix < 0x3FD33333) /* if |x| < 0.3 */
+ return one - (0.5*z - (z*r - x*y));
+ else {
+ if(ix > 0x3fe90000) { /* x > 0.78125 */
+ qx = 0.28125;
+ } else {
+ INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
+ }
+ hz = 0.5*z-qx;
+ a = one-qx;
+ return a - (hz - (z*r-x*y));
+ }
+}
--- /dev/null
+/* @(#)k_rem_pio2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
+#endif
+
+/*
+ * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
+ * double x[],y[]; int e0,nx,prec; int ipio2[];
+ *
+ * __kernel_rem_pio2 return the last three digits of N with
+ * y = x - N*pi/2
+ * so that |y| < pi/2.
+ *
+ * The method is to compute the integer (mod 8) and fraction parts of
+ * (2/pi)*x without doing the full multiplication. In general we
+ * skip the part of the product that are known to be a huge integer (
+ * more accurately, = 0 mod 8 ). Thus the number of operations are
+ * independent of the exponent of the input.
+ *
+ * (2/pi) is represented by an array of 24-bit integers in ipio2[].
+ *
+ * Input parameters:
+ * x[] The input value (must be positive) is broken into nx
+ * pieces of 24-bit integers in double precision format.
+ * x[i] will be the i-th 24 bit of x. The scaled exponent
+ * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
+ * match x's up to 24 bits.
+ *
+ * Example of breaking a double positive z into x[0]+x[1]+x[2]:
+ * e0 = ilogb(z)-23
+ * z = scalbn(z,-e0)
+ * for i = 0,1,2
+ * x[i] = floor(z)
+ * z = (z-x[i])*2**24
+ *
+ *
+ * y[] ouput result in an array of double precision numbers.
+ * The dimension of y[] is:
+ * 24-bit precision 1
+ * 53-bit precision 2
+ * 64-bit precision 2
+ * 113-bit precision 3
+ * The actual value is the sum of them. Thus for 113-bit
+ * precison, one may have to do something like:
+ *
+ * long double t,w,r_head, r_tail;
+ * t = (long double)y[2] + (long double)y[1];
+ * w = (long double)y[0];
+ * r_head = t+w;
+ * r_tail = w - (r_head - t);
+ *
+ * e0 The exponent of x[0]
+ *
+ * nx dimension of x[]
+ *
+ * prec an integer indicating the precision:
+ * 0 24 bits (single)
+ * 1 53 bits (double)
+ * 2 64 bits (extended)
+ * 3 113 bits (quad)
+ *
+ * ipio2[]
+ * integer array, contains the (24*i)-th to (24*i+23)-th
+ * bit of 2/pi after binary point. The corresponding
+ * floating value is
+ *
+ * ipio2[i] * 2^(-24(i+1)).
+ *
+ * External function:
+ * double scalbn(), floor();
+ *
+ *
+ * Here is the description of some local variables:
+ *
+ * jk jk+1 is the initial number of terms of ipio2[] needed
+ * in the computation. The recommended value is 2,3,4,
+ * 6 for single, double, extended,and quad.
+ *
+ * jz local integer variable indicating the number of
+ * terms of ipio2[] used.
+ *
+ * jx nx - 1
+ *
+ * jv index for pointing to the suitable ipio2[] for the
+ * computation. In general, we want
+ * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
+ * is an integer. Thus
+ * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
+ * Hence jv = max(0,(e0-3)/24).
+ *
+ * jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
+ *
+ * q[] double array with integral value, representing the
+ * 24-bits chunk of the product of x and 2/pi.
+ *
+ * q0 the corresponding exponent of q[0]. Note that the
+ * exponent for q[i] would be q0-24*i.
+ *
+ * PIo2[] double precision array, obtained by cutting pi/2
+ * into 24 bits chunks.
+ *
+ * f[] ipio2[] in floating point
+ *
+ * iq[] integer array by breaking up q[] in 24-bits chunk.
+ *
+ * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
+ *
+ * ih integer. If >0 it indicates q[] is >= 0.5, hence
+ * it also indicates the *sign* of the result.
+ *
+ */
+
+
+/*
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
+#else
+static int init_jk[] = {2,3,4,6};
+#endif
+
+#ifdef __STDC__
+static const double PIo2[] = {
+#else
+static double PIo2[] = {
+#endif
+ 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
+ 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
+ 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
+ 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
+ 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
+ 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
+ 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
+ 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
+};
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+zero = 0.0,
+one = 1.0,
+two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
+
+#ifdef __STDC__
+ int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
+#else
+ int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
+ double x[], y[]; int e0,nx,prec; int32_t ipio2[];
+#endif
+{
+ int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
+ double z,fw,f[20],fq[20],q[20];
+
+ /* initialize jk*/
+ jk = init_jk[prec];
+ jp = jk;
+
+ /* determine jx,jv,q0, note that 3>q0 */
+ jx = nx-1;
+ jv = (e0-3)/24; if(jv<0) jv=0;
+ q0 = e0-24*(jv+1);
+
+ /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+ j = jv-jx; m = jx+jk;
+ for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
+
+ /* compute q[0],q[1],...q[jk] */
+ for (i=0;i<=jk;i++) {
+ for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
+ }
+
+ jz = jk;
+recompute:
+ /* distill q[] into iq[] reversingly */
+ for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
+ fw = (double)((int32_t)(twon24* z));
+ iq[i] = (int32_t)(z-two24*fw);
+ z = q[j-1]+fw;
+ }
+
+ /* compute n */
+ z = scalbn(z,q0); /* actual value of z */
+ z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
+ n = (int32_t) z;
+ z -= (double)n;
+ ih = 0;
+ if(q0>0) { /* need iq[jz-1] to determine n */
+ i = (iq[jz-1]>>(24-q0)); n += i;
+ iq[jz-1] -= i<<(24-q0);
+ ih = iq[jz-1]>>(23-q0);
+ }
+ else if(q0==0) ih = iq[jz-1]>>23;
+ else if(z>=0.5) ih=2;
+
+ if(ih>0) { /* q > 0.5 */
+ n += 1; carry = 0;
+ for(i=0;i<jz ;i++) { /* compute 1-q */
+ j = iq[i];
+ if(carry==0) {
+ if(j!=0) {
+ carry = 1; iq[i] = 0x1000000- j;
+ }
+ } else iq[i] = 0xffffff - j;
+ }
+ if(q0>0) { /* rare case: chance is 1 in 12 */
+ switch(q0) {
+ case 1:
+ iq[jz-1] &= 0x7fffff; break;
+ case 2:
+ iq[jz-1] &= 0x3fffff; break;
+ }
+ }
+ if(ih==2) {
+ z = one - z;
+ if(carry!=0) z -= scalbn(one,q0);
+ }
+ }
+
+ /* check if recomputation is needed */
+ if(z==zero) {
+ j = 0;
+ for (i=jz-1;i>=jk;i--) j |= iq[i];
+ if(j==0) { /* need recomputation */
+ for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
+
+ for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
+ f[jx+i] = (double) ipio2[jv+i];
+ for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
+ q[i] = fw;
+ }
+ jz += k;
+ goto recompute;
+ }
+ }
+
+ /* chop off zero terms */
+ if(z==0.0) {
+ jz -= 1; q0 -= 24;
+ while(iq[jz]==0) { jz--; q0-=24;}
+ } else { /* break z into 24-bit if necessary */
+ z = scalbn(z,-q0);
+ if(z>=two24) {
+ fw = (double)((int32_t)(twon24*z));
+ iq[jz] = (int32_t)(z-two24*fw);
+ jz += 1; q0 += 24;
+ iq[jz] = (int32_t) fw;
+ } else iq[jz] = (int32_t) z ;
+ }
+
+ /* convert integer "bit" chunk to floating-point value */
+ fw = scalbn(one,q0);
+ for(i=jz;i>=0;i--) {
+ q[i] = fw*(double)iq[i]; fw*=twon24;
+ }
+
+ /* compute PIo2[0,...,jp]*q[jz,...,0] */
+ for(i=jz;i>=0;i--) {
+ for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
+ fq[jz-i] = fw;
+ }
+
+ /* compress fq[] into y[] */
+ switch(prec) {
+ case 0:
+ fw = 0.0;
+ for (i=jz;i>=0;i--) fw += fq[i];
+ y[0] = (ih==0)? fw: -fw;
+ break;
+ case 1:
+ case 2:
+ fw = 0.0;
+ for (i=jz;i>=0;i--) fw += fq[i];
+ y[0] = (ih==0)? fw: -fw;
+ fw = fq[0]-fw;
+ for (i=1;i<=jz;i++) fw += fq[i];
+ y[1] = (ih==0)? fw: -fw;
+ break;
+ case 3: /* painful */
+ for (i=jz;i>0;i--) {
+ fw = fq[i-1]+fq[i];
+ fq[i] += fq[i-1]-fw;
+ fq[i-1] = fw;
+ }
+ for (i=jz;i>1;i--) {
+ fw = fq[i-1]+fq[i];
+ fq[i] += fq[i-1]-fw;
+ fq[i-1] = fw;
+ }
+ for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
+ if(ih==0) {
+ y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
+ } else {
+ y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
+ }
+ }
+ return n&7;
+}
--- /dev/null
+/* @(#)k_sin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
+#endif
+
+/* __kernel_sin( x, y, iy)
+ * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
+ *
+ * Algorithm
+ * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
+ * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
+ * 3. sin(x) is approximated by a polynomial of degree 13 on
+ * [0,pi/4]
+ * 3 13
+ * sin(x) ~ x + S1*x + ... + S6*x
+ * where
+ *
+ * |sin(x) 2 4 6 8 10 12 | -58
+ * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
+ * | x |
+ *
+ * 4. sin(x+y) = sin(x) + sin'(x')*y
+ * ~ sin(x) + (1-x*x/2)*y
+ * For better accuracy, let
+ * 3 2 2 2 2
+ * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
+ * then 3 2
+ * sin(x) = x + (S1*x + (x *(r-y/2)+y))
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
+S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
+S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
+S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
+S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
+S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
+
+#ifdef __STDC__
+ double __kernel_sin(double x, double y, int iy)
+#else
+ double __kernel_sin(x, y, iy)
+ double x,y; int iy; /* iy=0 if y is zero */
+#endif
+{
+ double z,r,v;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff; /* high word of x */
+ if(ix<0x3e400000) /* |x| < 2**-27 */
+ {if((int)x==0) return x;} /* generate inexact */
+ z = x*x;
+ v = z*x;
+ r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
+ if(iy==0) return x+v*(S1+z*r);
+ else return x-((z*(half*y-v*r)-y)-v*S1);
+}
--- /dev/null
+/* @(#)k_standard.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_standard.c,v 1.6 1995/05/10 20:46:35 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+#include <errno.h>
+
+#ifndef _USE_WRITE
+#include <stdio.h> /* fputs(), stderr */
+#define WRITE2(u,v) fputs(u, stderr)
+#else /* !defined(_USE_WRITE) */
+#include <unistd.h> /* write */
+#define WRITE2(u,v) write(2, u, v)
+#undef fflush
+#endif /* !defined(_USE_WRITE) */
+
+#ifdef __STDC__
+static const double zero = 0.0; /* used as const */
+#else
+static double zero = 0.0; /* used as const */
+#endif
+
+/*
+ * Standard conformance (non-IEEE) on exception cases.
+ * Mapping:
+ * 1 -- acos(|x|>1)
+ * 2 -- asin(|x|>1)
+ * 3 -- atan2(+-0,+-0)
+ * 4 -- hypot overflow
+ * 5 -- cosh overflow
+ * 6 -- exp overflow
+ * 7 -- exp underflow
+ * 8 -- y0(0)
+ * 9 -- y0(-ve)
+ * 10-- y1(0)
+ * 11-- y1(-ve)
+ * 12-- yn(0)
+ * 13-- yn(-ve)
+ * 14-- lgamma(finite) overflow
+ * 15-- lgamma(-integer)
+ * 16-- log(0)
+ * 17-- log(x<0)
+ * 18-- log10(0)
+ * 19-- log10(x<0)
+ * 20-- pow(0.0,0.0)
+ * 21-- pow(x,y) overflow
+ * 22-- pow(x,y) underflow
+ * 23-- pow(0,negative)
+ * 24-- pow(neg,non-integral)
+ * 25-- sinh(finite) overflow
+ * 26-- sqrt(negative)
+ * 27-- fmod(x,0)
+ * 28-- remainder(x,0)
+ * 29-- acosh(x<1)
+ * 30-- atanh(|x|>1)
+ * 31-- atanh(|x|=1)
+ * 32-- scalb overflow
+ * 33-- scalb underflow
+ * 34-- j0(|x|>X_TLOSS)
+ * 35-- y0(x>X_TLOSS)
+ * 36-- j1(|x|>X_TLOSS)
+ * 37-- y1(x>X_TLOSS)
+ * 38-- jn(|x|>X_TLOSS, n)
+ * 39-- yn(x>X_TLOSS, n)
+ * 40-- gamma(finite) overflow
+ * 41-- gamma(-integer)
+ * 42-- pow(NaN,0.0)
+ */
+
+
+#ifdef __STDC__
+ double __kernel_standard(double x, double y, int type)
+#else
+ double __kernel_standard(x,y,type)
+ double x,y; int type;
+#endif
+{
+ struct exception exc;
+#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
+#define HUGE_VAL inf
+ double inf = 0.0;
+
+ SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
+#endif
+
+#ifdef _USE_WRITE
+ (void) fflush(stdout);
+#endif
+ exc.arg1 = x;
+ exc.arg2 = y;
+ switch(type) {
+ case 1:
+ case 101:
+ /* acos(|x|>1) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "acos" : "acosf";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if(_LIB_VERSION == _SVID_) {
+ (void) WRITE2("acos: DOMAIN error\n", 19);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 2:
+ case 102:
+ /* asin(|x|>1) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "asin" : "asinf";
+ exc.retval = zero;
+ if(_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if(_LIB_VERSION == _SVID_) {
+ (void) WRITE2("asin: DOMAIN error\n", 19);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 3:
+ case 103:
+ /* atan2(+-0,+-0) */
+ exc.arg1 = y;
+ exc.arg2 = x;
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "atan2" : "atan2f";
+ exc.retval = zero;
+ if(_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if(_LIB_VERSION == _SVID_) {
+ (void) WRITE2("atan2: DOMAIN error\n", 20);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 4:
+ case 104:
+ /* hypot(finite,finite) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "hypot" : "hypotf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 5:
+ case 105:
+ /* cosh(finite) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "cosh" : "coshf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 6:
+ case 106:
+ /* exp(finite) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "exp" : "expf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 7:
+ case 107:
+ /* exp(finite) underflow */
+ exc.type = UNDERFLOW;
+ exc.name = type < 100 ? "exp" : "expf";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 8:
+ case 108:
+ /* y0(0) = -inf */
+ exc.type = DOMAIN; /* should be SING for IEEE */
+ exc.name = type < 100 ? "y0" : "y0f";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("y0: DOMAIN error\n", 17);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 9:
+ case 109:
+ /* y0(x<0) = NaN */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "y0" : "y0f";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("y0: DOMAIN error\n", 17);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 10:
+ case 110:
+ /* y1(0) = -inf */
+ exc.type = DOMAIN; /* should be SING for IEEE */
+ exc.name = type < 100 ? "y1" : "y1f";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("y1: DOMAIN error\n", 17);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 11:
+ case 111:
+ /* y1(x<0) = NaN */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "y1" : "y1f";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("y1: DOMAIN error\n", 17);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 12:
+ case 112:
+ /* yn(n,0) = -inf */
+ exc.type = DOMAIN; /* should be SING for IEEE */
+ exc.name = type < 100 ? "yn" : "ynf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("yn: DOMAIN error\n", 17);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 13:
+ case 113:
+ /* yn(x<0) = NaN */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "yn" : "ynf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("yn: DOMAIN error\n", 17);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 14:
+ case 114:
+ /* lgamma(finite) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "lgamma" : "lgammaf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 15:
+ case 115:
+ /* lgamma(-integer) or lgamma(0) */
+ exc.type = SING;
+ exc.name = type < 100 ? "lgamma" : "lgammaf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("lgamma: SING error\n", 19);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 16:
+ case 116:
+ /* log(0) */
+ exc.type = SING;
+ exc.name = type < 100 ? "log" : "logf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("log: SING error\n", 16);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 17:
+ case 117:
+ /* log(x<0) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "log" : "logf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("log: DOMAIN error\n", 18);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 18:
+ case 118:
+ /* log10(0) */
+ exc.type = SING;
+ exc.name = type < 100 ? "log10" : "log10f";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("log10: SING error\n", 18);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 19:
+ case 119:
+ /* log10(x<0) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "log10" : "log10f";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = -HUGE;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("log10: DOMAIN error\n", 20);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 20:
+ case 120:
+ /* pow(0.0,0.0) */
+ /* error only if _LIB_VERSION == _SVID_ */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "pow" : "powf";
+ exc.retval = zero;
+ if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
+ else if (!matherr(&exc)) {
+ (void) WRITE2("pow(0,0): DOMAIN error\n", 23);
+ errno = EDOM;
+ }
+ break;
+ case 21:
+ case 121:
+ /* pow(x,y) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "pow" : "powf";
+ if (_LIB_VERSION == _SVID_) {
+ exc.retval = HUGE;
+ y *= 0.5;
+ if(x<zero&&rint(y)!=y) exc.retval = -HUGE;
+ } else {
+ exc.retval = HUGE_VAL;
+ y *= 0.5;
+ if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL;
+ }
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 22:
+ case 122:
+ /* pow(x,y) underflow */
+ exc.type = UNDERFLOW;
+ exc.name = type < 100 ? "pow" : "powf";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 23:
+ case 123:
+ /* 0**neg */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "pow" : "powf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = zero;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 24:
+ case 124:
+ /* neg**non-integral */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "pow" : "powf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = zero;
+ else
+ exc.retval = zero/zero; /* X/Open allow NaN */
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 25:
+ case 125:
+ /* sinh(finite) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "sinh" : "sinhf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = ( (x>zero) ? HUGE : -HUGE);
+ else
+ exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 26:
+ case 126:
+ /* sqrt(x<0) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "sqrt" : "sqrtf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = zero;
+ else
+ exc.retval = zero/zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("sqrt: DOMAIN error\n", 19);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 27:
+ case 127:
+ /* fmod(x,0) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "fmod" : "fmodf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = x;
+ else
+ exc.retval = zero/zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("fmod: DOMAIN error\n", 20);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 28:
+ case 128:
+ /* remainder(x,0) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "remainder" : "remainderf";
+ exc.retval = zero/zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("remainder: DOMAIN error\n", 24);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 29:
+ case 129:
+ /* acosh(x<1) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "acosh" : "acoshf";
+ exc.retval = zero/zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("acosh: DOMAIN error\n", 20);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 30:
+ case 130:
+ /* atanh(|x|>1) */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "atanh" : "atanhf";
+ exc.retval = zero/zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("atanh: DOMAIN error\n", 20);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 31:
+ case 131:
+ /* atanh(|x|=1) */
+ exc.type = SING;
+ exc.name = type < 100 ? "atanh" : "atanhf";
+ exc.retval = x/zero; /* sign(x)*inf */
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("atanh: SING error\n", 18);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 32:
+ case 132:
+ /* scalb overflow; SVID also returns +-HUGE_VAL */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "scalb" : "scalbf";
+ exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 33:
+ case 133:
+ /* scalb underflow */
+ exc.type = UNDERFLOW;
+ exc.name = type < 100 ? "scalb" : "scalbf";
+ exc.retval = copysign(zero,x);
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 34:
+ case 134:
+ /* j0(|x|>X_TLOSS) */
+ exc.type = TLOSS;
+ exc.name = type < 100 ? "j0" : "j0f";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2(exc.name, 2);
+ (void) WRITE2(": TLOSS error\n", 14);
+ }
+ errno = ERANGE;
+ }
+ break;
+ case 35:
+ case 135:
+ /* y0(x>X_TLOSS) */
+ exc.type = TLOSS;
+ exc.name = type < 100 ? "y0" : "y0f";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2(exc.name, 2);
+ (void) WRITE2(": TLOSS error\n", 14);
+ }
+ errno = ERANGE;
+ }
+ break;
+ case 36:
+ case 136:
+ /* j1(|x|>X_TLOSS) */
+ exc.type = TLOSS;
+ exc.name = type < 100 ? "j1" : "j1f";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2(exc.name, 2);
+ (void) WRITE2(": TLOSS error\n", 14);
+ }
+ errno = ERANGE;
+ }
+ break;
+ case 37:
+ case 137:
+ /* y1(x>X_TLOSS) */
+ exc.type = TLOSS;
+ exc.name = type < 100 ? "y1" : "y1f";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2(exc.name, 2);
+ (void) WRITE2(": TLOSS error\n", 14);
+ }
+ errno = ERANGE;
+ }
+ break;
+ case 38:
+ case 138:
+ /* jn(|x|>X_TLOSS) */
+ exc.type = TLOSS;
+ exc.name = type < 100 ? "jn" : "jnf";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2(exc.name, 2);
+ (void) WRITE2(": TLOSS error\n", 14);
+ }
+ errno = ERANGE;
+ }
+ break;
+ case 39:
+ case 139:
+ /* yn(x>X_TLOSS) */
+ exc.type = TLOSS;
+ exc.name = type < 100 ? "yn" : "ynf";
+ exc.retval = zero;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2(exc.name, 2);
+ (void) WRITE2(": TLOSS error\n", 14);
+ }
+ errno = ERANGE;
+ }
+ break;
+ case 40:
+ case 140:
+ /* gamma(finite) overflow */
+ exc.type = OVERFLOW;
+ exc.name = type < 100 ? "gamma" : "gammaf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ break;
+ case 41:
+ case 141:
+ /* gamma(-integer) or gamma(0) */
+ exc.type = SING;
+ exc.name = type < 100 ? "gamma" : "gammaf";
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = HUGE;
+ else
+ exc.retval = HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ if (_LIB_VERSION == _SVID_) {
+ (void) WRITE2("gamma: SING error\n", 18);
+ }
+ errno = EDOM;
+ }
+ break;
+ case 42:
+ case 142:
+ /* pow(NaN,0.0) */
+ /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
+ exc.type = DOMAIN;
+ exc.name = type < 100 ? "pow" : "powf";
+ exc.retval = x;
+ if (_LIB_VERSION == _IEEE_ ||
+ _LIB_VERSION == _POSIX_) exc.retval = 1.0;
+ else if (!matherr(&exc)) {
+ errno = EDOM;
+ }
+ break;
+ }
+ return exc.retval;
+}
--- /dev/null
+/* @(#)k_tan.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 jtc Exp $";
+#endif
+
+/* __kernel_tan( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k=1) or
+ * -1/tan (if k= -1) is returned.
+ *
+ * Algorithm
+ * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
+ * 3. tan(x) is approximated by a odd polynomial of degree 27 on
+ * [0,0.67434]
+ * 3 27
+ * tan(x) ~ x + T1*x + ... + T13*x
+ * where
+ *
+ * |tan(x) 2 4 26 | -59.2
+ * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
+ * | x |
+ *
+ * Note: tan(x+y) = tan(x) + tan'(x)*y
+ * ~ tan(x) + (1+x*x)*y
+ * Therefore, for better accuracy in computing tan(x+y), let
+ * 3 2 2 2 2
+ * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
+ * then
+ * 3 2
+ * tan(x+y) = x + (T1*x + (x *(r+y)+y))
+ *
+ * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
+ * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include "math.h"
+#include "math_private.h"
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
+T[] = {
+ 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
+ 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
+ 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
+ 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
+ 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
+ 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
+ 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
+ 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
+ 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
+ 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
+ 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
+ -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
+ 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
+};
+
+#ifdef __STDC__
+ double __kernel_tan(double x, double y, int iy)
+#else
+ double __kernel_tan(x, y, iy)
+ double x,y; int iy;
+#endif
+{
+ double z,r,v,w,s;
+ int32_t ix,hx;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff; /* high word of |x| */
+ if(ix<0x3e300000) /* x < 2**-28 */
+ {if((int)x==0) { /* generate inexact */
+ u_int32_t low;
+ GET_LOW_WORD(low,x);
+ if(((ix|low)|(iy+1))==0) return one/fabs(x);
+ else return (iy==1)? x: -one/x;
+ }
+ }
+ if(ix>=0x3FE59428) { /* |x|>=0.6744 */
+ if(hx<0) {x = -x; y = -y;}
+ z = pio4-x;
+ w = pio4lo-y;
+ x = z+w; y = 0.0;
+ }
+ z = x*x;
+ w = z*z;
+ /* Break x^5*(T[1]+x^2*T[2]+...) into
+ * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+ * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+ */
+ r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
+ v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
+ s = z*x;
+ r = y + z*(s*(r+v)+y);
+ r += T[0]*s;
+ w = x+r;
+ if(ix>=0x3FE59428) {
+ v = (double)iy;
+ return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
+ }
+ if(iy==1) return w;
+ else { /* if allow error up to 2 ulp,
+ simply return -1.0/(x+r) here */
+ /* compute -1.0/(x+r) accurately */
+ double a,t;
+ z = w;
+ SET_LOW_WORD(z,0);
+ v = r-(z - x); /* z+v = r+x */
+ t = a = -1.0/w; /* a = -1.0/w */
+ SET_LOW_WORD(t,0);
+ s = 1.0+t*z;
+ return t+a*(s+t*v);
+ }
+}
+++ /dev/null
-# Makefile for uClibc's math library
-# Copyright (C) 2001 by Lineo, inc.
-#
-# This math library is derived primarily from the Cephes Math Library,
-# copyright by Stephen L. Moshier <moshier@world.std.com>
-#
-# This program is free software; you can redistribute it and/or modify it under
-# the terms of the GNU Library General Public License as published by the Free
-# Software Foundation; either version 2 of the License, or (at your option) any
-# later version.
-#
-# This program is distributed in the hope that it will be useful, but WITHOUT
-# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
-# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
-# details.
-#
-# You should have received a copy of the GNU Library General Public License
-# along with this program; if not, write to the Free Software Foundation, Inc.,
-# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-#
-
-TOPDIR=../../
-include $(TOPDIR)Rules.mak
-
-LIBM=../libm.a
-TARGET_CC= $(TOPDIR)/extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
-
-CSRC=acoshl.c asinhl.c asinl.c atanhl.c atanl.c bdtrl.c btdtrl.c cbrtl.c \
- chdtrl.c coshl.c ellpel.c ellpkl.c elliel.c ellikl.c ellpjl.c \
- exp10l.c exp2l.c expl.c fdtrl.c gammal.c gdtrl.c igamil.c igaml.c \
- incbetl.c incbil.c isnanl.c j0l.c j1l.c jnl.c ldrand.c log10l.c log2l.c \
- logl.c nbdtrl.c ndtril.c ndtrl.c pdtrl.c powl.c powil.c sinhl.c sinl.c \
- sqrtl.c stdtrl.c tanhl.c tanl.c unityl.c ynl.c \
- floorl.c polevll.c mtherr.c #cmplxl.c clogl.c
-COBJS=$(patsubst %.c,%.o, $(CSRC))
-
-
-OBJS=$(COBJS)
-
-all: $(OBJS) $(LIBM)
-
-$(LIBM): ar-target
-
-ar-target: $(OBJS)
- $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
-
-$(COBJS): %.o : %.c
- $(TARGET_CC) $(TARGET_CFLAGS) -c $< -o $@
- $(STRIPTOOL) -x -R .note -R .comment $*.o
-
-$(OBJ): Makefile
-
-clean:
- rm -f *.[oa] *~ core
-
-
-
-#-----------------------------------------
-
-
-#all: mtstl lparanoi lcalc fltestl nantst testvect monotl libml.a
-
-mtstl: libml.a mtstl.o $(OBJS)
- $(TARGET_CC) $(TARGET_CFLAGS) -o mtstl mtstl.o libml.a $(LIBS)
-
-mtstl.o: mtstl.c
-
-lparanoi: libml.a lparanoi.o setprec.o ieee.o econst.o $(OBJS)
- $(TARGET_CC) $(TARGET_CFLAGS) -o lparanoi lparanoi.o setprec.o ieee.o econst.o libml.a $(LIBS)
-
-lparanoi.o: lparanoi.c
- $(TARGET_CC) $(TARGET_CFLAGS) -Wno-implicit -c lparanoi.c
-
-econst.o: econst.c ehead.h
-
-lcalc: libml.a lcalc.o ieee.o econst.o $(OBJS)
- $(TARGET_CC) $(TARGET_CFLAGS) -o lcalc lcalc.o ieee.o econst.o libml.a $(LIBS)
-
-lcalc.o: lcalc.c lcalc.h ehead.h
-
-ieee.o: ieee.c ehead.h
-
-# Use $(OBJS) in ar command for libml.a if possible; else *.o
-libml.a: $(OBJS) mconf.h
- ar -rv libml.a $(OBJS)
- ranlib libml.a
-
-
-fltestl: fltestl.c libml.a
- $(TARGET_CC) $(TARGET_CFLAGS) -o fltestl fltestl.c libml.a
-
-fltestl.o: fltestl.c
-
-flrtstl: flrtstl.c libml.a
- $(TARGET_CC) $(TARGET_CFLAGS) -o flrtstl flrtstl.c libml.a
-
-flrtstl.o: flrtstl.c
-
-nantst: nantst.c libml.a
- $(TARGET_CC) $(TARGET_CFLAGS) -o nantst nantst.c libml.a
-
-nantst.o: nantst.c
-
-testvect: testvect.o libml.a
- $(TARGET_CC) $(TARGET_CFLAGS) -o testvect testvect.o libml.a
-
-testvect.o: testvect.c
- $(TARGET_CC) -g -c -o testvect.o testvect.c
-
-monotl: monotl.o libml.a
- $(TARGET_CC) $(TARGET_CFLAGS) -o monotl monotl.o libml.a
-
-monotl.o: monotl.c
- $(TARGET_CC) -g -c -o monotl.o monotl.c
-
-# Run test programs
-check: mtstl fltestl testvect monotl libml.a
- -mtstl
- -fltestl
- -testvect
- -monotl
-
+++ /dev/null
-/* acoshl.c
- *
- * Inverse hyperbolic cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, acoshl();
- *
- * y = acoshl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a rational approximation
- *
- * sqrt(2z) * P(z)/Q(z)
- *
- * where z = x-1, is used. Otherwise,
- *
- * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,3 30000 2.0e-19 3.9e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acoshl domain |x| < 1 0.0
- *
- */
-\f
-/* asinhl.c
- *
- * Inverse hyperbolic sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, asinhl();
- *
- * y = asinhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic sine of argument.
- *
- * If |x| < 0.5, the function is approximated by a rational
- * form x + x**3 P(x)/Q(x). Otherwise,
- *
- * asinh(x) = log( x + sqrt(1 + x*x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -3,3 30000 1.7e-19 3.5e-20
- *
- */
-\f
-/* asinl.c
- *
- * Inverse circular sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, asinl();
- *
- * y = asinl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
- *
- * A rational function of the form x + x**3 P(x**2)/Q(x**2)
- * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
- * transformed by the identity
- *
- * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 30000 2.7e-19 4.8e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 0.0
- *
- */
-\f/* acosl()
- *
- * Inverse circular cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acosl();
- *
- * y = acosl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 30000 1.4e-19 3.5e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asin domain |x| > 1 0.0
- */
-\f
-/* atanhl.c
- *
- * Inverse hyperbolic tangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, atanhl();
- *
- * y = atanhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic tangent of argument in the range
- * MINLOGL to MAXLOGL.
- *
- * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
- * employed. Otherwise,
- * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1,1 30000 1.1e-19 3.3e-20
- *
- */
-\f
-/* atanl.c
- *
- * Inverse circular tangent, long double precision
- * (arctangent)
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, atanl();
- *
- * y = atanl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose tangent
- * is x.
- *
- * Range reduction is from four intervals into the interval
- * from zero to tan( pi/8 ). The approximant uses a rational
- * function of degree 3/4 of the form x + x**3 P(x)/Q(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 150000 1.3e-19 3.0e-20
- *
- */
-\f/* atan2l()
- *
- * Quadrant correct inverse circular tangent,
- * long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, z, atan2l();
- *
- * z = atan2l( y, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle whose tangent is y/x.
- * Define compile time symbol ANSIC = 1 for ANSI standard,
- * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
- * 0 to 2PI, args (x,y).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 60000 1.7e-19 3.2e-20
- * See atan.c.
- *
- */
-\f
-/* bdtrl.c
- *
- * Binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, bdtrl();
- *
- * y = bdtrl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the Binomial
- * probability density:
- *
- * k
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (k,n,p) with a and b between 0
- * and 10000 and p between 0 and 1.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10000 3000 1.6e-14 2.2e-15
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrl domain k < 0 0.0
- * n < k
- * x < 0, x > 1
- *
- */
-\f/* bdtrcl()
- *
- * Complemented binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, bdtrcl();
- *
- * y = bdtrcl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 through n of the Binomial
- * probability density:
- *
- * n
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * See incbet.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrcl domain x<0, x>1, n<k 0.0
- */
-\f/* bdtril()
- *
- * Inverse binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, bdtril();
- *
- * p = bdtril( k, n, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the event probability p such that the sum of the
- * terms 0 through k of the Binomial probability density
- * is equal to the given cumulative probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relation
- *
- * 1 - p = incbi( n-k, k+1, y ).
- *
- * ACCURACY:
- *
- * See incbi.c.
- * Tested at random k, n between 1 and 10000. The "domain" refers to p:
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 3500 2.0e-15 8.2e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtril domain k < 0, n <= k 0.0
- * x < 0, x > 1
- */
-\f
-
-/* btdtrl.c
- *
- * Beta distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, btdtrl();
- *
- * y = btdtrl( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the beta density
- * function:
- *
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * P(x) = ---------- | t (1-t) dt
- * - - | |
- * | (a) | (b) -
- * 0
- *
- *
- * The mean value of this distribution is a/(a+b). The variance
- * is ab/[(a+b)^2 (a+b+1)].
- *
- * This function is identical to the incomplete beta integral
- * function, incbetl(a, b, x).
- *
- * The complemented function is
- *
- * 1 - P(1-x) = incbetl( b, a, x );
- *
- *
- * ACCURACY:
- *
- * See incbetl.c.
- *
- */
-\f
-/* cbrtl.c
- *
- * Cube root, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, cbrtl();
- *
- * y = cbrtl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the cube root of the argument, which may be negative.
- *
- * Range reduction involves determining the power of 2 of
- * the argument. A polynomial of degree 2 applied to the
- * mantissa, and multiplication by the cube root of 1, 2, or 4
- * approximates the root to within about 0.1%. Then Newton's
- * iteration is used three times to converge to an accurate
- * result.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE .125,8 80000 7.0e-20 2.2e-20
- * IEEE exp(+-707) 100000 7.0e-20 2.4e-20
- *
- */
-\f
-/* chdtrl.c
- *
- * Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double df, x, y, chdtrl();
- *
- * y = chdtrl( df, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the left hand tail (from 0 to x)
- * of the Chi square probability density function with
- * v degrees of freedom.
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtr domain x < 0 or v < 1 0.0
- */
-\f/* chdtrcl()
- *
- * Complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double v, x, y, chdtrcl();
- *
- * y = chdtrcl( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the right hand tail (from x to
- * infinity) of the Chi square probability density function
- * with v degrees of freedom:
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrc domain x < 0 or v < 1 0.0
- */
-\f/* chdtril()
- *
- * Inverse of complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double df, x, y, chdtril();
- *
- * x = chdtril( df, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Chi-square argument x such that the integral
- * from x to infinity of the Chi-square density is equal
- * to the given cumulative probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * x/2 = igami( df/2, y );
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtri domain y < 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* clogl.c
- *
- * Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clogl();
- * cmplxl z, w;
- *
- * clogl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns complex logarithm to the base e (2.718...) of
- * the complex argument x.
- *
- * If z = x + iy, r = sqrt( x**2 + y**2 ),
- * then
- * w = log(r) + i arctan(y/x).
- *
- * The arctangent ranges from -PI to +PI.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 7000 8.5e-17 1.9e-17
- * IEEE -10,+10 30000 5.0e-15 1.1e-16
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
- * absolute error 1.0e-16.
- */
-\f
-\f/* cexpl()
- *
- * Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexpl();
- * cmplxl z, w;
- *
- * cexpl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the exponential of the complex argument z
- * into the complex result w.
- *
- * If
- * z = x + iy,
- * r = exp(x),
- *
- * then
- *
- * w = r cos y + i r sin y.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8700 3.7e-17 1.1e-17
- * IEEE -10,+10 30000 3.0e-16 8.7e-17
- *
- */
-\f/* csinl()
- *
- * Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csinl();
- * cmplxl z, w;
- *
- * csinl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = sin x cosh y + i cos x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 5.3e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- * Also tested by csin(casin(z)) = z.
- *
- */
-\f/* ccosl()
- *
- * Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccosl();
- * cmplxl z, w;
- *
- * ccosl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = cos x cosh y - i sin x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 4.5e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- */
-\f/* ctanl()
- *
- * Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctanl();
- * cmplxl z, w;
- *
- * ctanl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x + i sinh 2y
- * w = --------------------.
- * cos 2x + cosh 2y
- *
- * On the real axis the denominator is zero at odd multiples
- * of PI/2. The denominator is evaluated by its Taylor
- * series near these points.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 7.1e-17 1.6e-17
- * IEEE -10,+10 30000 7.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
- */
-\f/* ccotl()
- *
- * Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccotl();
- * cmplxl z, w;
- *
- * ccotl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x - i sinh 2y
- * w = --------------------.
- * cosh 2y - cos 2x
- *
- * On the real axis, the denominator has zeros at even
- * multiples of PI/2. Near these points it is evaluated
- * by a Taylor series.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 3000 6.5e-17 1.6e-17
- * IEEE -10,+10 30000 9.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 + i0.
- */
-\f
-\f/* casinl()
- *
- * Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casinl();
- * cmplxl z, w;
- *
- * casinl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- * 2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 10100 2.1e-15 3.4e-16
- * IEEE -10,+10 30000 2.2e-14 2.7e-15
- * Larger relative error can be observed for z near zero.
- * Also tested by csin(casin(z)) = z.
- */
-\f/* cacosl()
- *
- * Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacosl();
- * cmplxl z, w;
- *
- * cacosl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z = PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 1.6e-15 2.8e-16
- * IEEE -10,+10 30000 1.8e-14 2.2e-15
- */
-\f
-\f/* catanl()
- *
- * Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catanl();
- * cmplxl z, w;
- *
- * catanl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- * 1 ( 2x )
- * Re w = - arctan(-----------) + k PI
- * 2 ( 2 2)
- * (1 - x - y )
- *
- * ( 2 2)
- * 1 (x + (y+1) )
- * Im w = - log(------------)
- * 4 ( 2 2)
- * (x + (y-1) )
- *
- * Where k is an arbitrary integer.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5900 1.3e-16 7.8e-18
- * IEEE -10,+10 30000 2.3e-15 8.5e-17
- * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
- * had peak relative error 1.5e-16, rms relative error
- * 2.9e-17. See also clog().
- */
-\f
-/* cmplxl.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * long double r; real part
- * long double i; imaginary part
- * }cmplxl;
- *
- * cmplxl *a, *b, *c;
- *
- * caddl( a, b, c ); c = b + a
- * csubl( a, b, c ); c = b - a
- * cmull( a, b, c ); c = b * a
- * cdivl( a, b, c ); c = b / a
- * cnegl( c ); c = -c
- * cmovl( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
- * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * DEC cadd 10000 1.4e-17 3.4e-18
- * IEEE cadd 100000 1.1e-16 2.7e-17
- * DEC csub 10000 1.4e-17 4.5e-18
- * IEEE csub 100000 1.1e-16 3.4e-17
- * DEC cmul 3000 2.3e-17 8.7e-18
- * IEEE cmul 100000 2.1e-16 6.9e-17
- * DEC cdiv 18000 4.9e-17 1.3e-17
- * IEEE cdiv 100000 3.7e-16 1.1e-16
- */
-\f
-/* cabsl()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * long double cabsl();
- * cmplxl z;
- * long double a;
- *
- * a = cabs( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -30,+30 30000 3.2e-17 9.2e-18
- * IEEE -10,+10 100000 2.7e-16 6.9e-17
- */
-\f/* csqrtl()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrtl();
- * cmplxl z, w;
- *
- * csqrtl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The root chosen
- * is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 25000 3.2e-17 9.6e-18
- * IEEE -10,+10 100000 3.2e-16 7.7e-17
- *
- * 2
- * Also tested by csqrt( z ) = z, and tested by arguments
- * close to the real axis.
- */
-\f
-/* coshl.c
- *
- * Hyperbolic cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, coshl();
- *
- * y = coshl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic cosine of argument in the range MINLOGL to
- * MAXLOGL.
- *
- * cosh(x) = ( exp(x) + exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-10000 30000 1.1e-19 2.8e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cosh overflow |x| > MAXLOGL MAXNUML
- *
- *
- */
-\f
-/* elliel.c
- *
- * Incomplete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double phi, m, y, elliel();
- *
- * y = elliel( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * phi
- * -
- * | |
- * | 2
- * E(phi_\m) = | sqrt( 1 - m sin t ) dt
- * |
- * | |
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random arguments with phi in [-10, 10] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 50000 2.7e-18 2.3e-19
- *
- *
- */
-\f
-/* ellikl.c
- *
- * Incomplete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double phi, m, y, ellikl();
- *
- * y = ellikl( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * phi
- * -
- * | |
- * | dt
- * F(phi_\m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points with m in [0, 1] and phi as indicated.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 30000 3.6e-18 4.1e-19
- *
- *
- */
-\f
-/* ellpel.c
- *
- * Complete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double m1, y, ellpel();
- *
- * y = ellpel( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * pi/2
- * -
- * | | 2
- * E(m) = | sqrt( 1 - m sin t ) dt
- * | |
- * -
- * 0
- *
- * Where m = 1 - m1, using the approximation
- *
- * P(x) - x log x Q(x).
- *
- * Though there are no singularities, the argument m1 is used
- * rather than m for compatibility with ellpk().
- *
- * E(1) = 1; E(0) = pi/2.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 1 10000 1.1e-19 3.5e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpel domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpjl.c
- *
- * Jacobian Elliptic Functions
- *
- *
- *
- * SYNOPSIS:
- *
- * long double u, m, sn, cn, dn, phi;
- * int ellpjl();
- *
- * ellpjl( u, m, _&sn, _&cn, _&dn, _&phi );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
- * and dn(u|m) of parameter m between 0 and 1, and real
- * argument u.
- *
- * These functions are periodic, with quarter-period on the
- * real axis equal to the complete elliptic integral
- * ellpk(1.0-m).
- *
- * Relation to incomplete elliptic integral:
- * If u = ellik(phi,m), then sn(u|m) = sin(phi),
- * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
- *
- * Computation is by means of the arithmetic-geometric mean
- * algorithm, except when m is within 1e-12 of 0 or 1. In the
- * latter case with m close to 1, the approximation applies
- * only for phi < pi/2.
- *
- * ACCURACY:
- *
- * Tested at random points with u between 0 and 10, m between
- * 0 and 1.
- *
- * Absolute error (* = relative error):
- * arithmetic function # trials peak rms
- * IEEE sn 10000 1.7e-18 2.3e-19
- * IEEE cn 20000 1.6e-18 2.2e-19
- * IEEE dn 10000 4.7e-15 2.7e-17
- * IEEE phi 10000 4.0e-19* 6.6e-20*
- *
- * Accuracy deteriorates when u is large.
- *
- */
-\f
-/* ellpkl.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double m1, y, ellpkl();
- *
- * y = ellpkl( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * pi/2
- * -
- * | |
- * | dt
- * K(m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * where m = 1 - m1, using the approximation
- *
- * P(x) - log x Q(x).
- *
- * The argument m1 is used rather than m so that the logarithmic
- * singularity at m = 1 will be shifted to the origin; this
- * preserves maximum accuracy.
- *
- * K(0) = pi/2.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 10000 1.1e-19 3.3e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpkl domain x<0, x>1 0.0
- *
- */
-\f
-/* exp10l.c
- *
- * Base 10 exponential function, long double precision
- * (Common antilogarithm)
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, exp10l()
- *
- * y = exp10l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 10 raised to the x power.
- *
- * Range reduction is accomplished by expressing the argument
- * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
- * The Pade' form
- *
- * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- *
- * is used to approximate 10**f.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-4900 30000 1.0e-19 2.7e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp10l underflow x < -MAXL10 0.0
- * exp10l overflow x > MAXL10 MAXNUM
- *
- * IEEE arithmetic: MAXL10 = 4932.0754489586679023819
- *
- */
-\f
-/* exp2l.c
- *
- * Base 2 exponential function, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, exp2l();
- *
- * y = exp2l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 2 raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- * x k f
- * 2 = 2 2.
- *
- * A Pade' form
- *
- * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
- *
- * approximates 2**x in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-16300 300000 9.1e-20 2.6e-20
- *
- *
- * See exp.c for comments on error amplification.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp2l underflow x < -16382 0.0
- * exp2l overflow x >= 16384 MAXNUM
- *
- */
-\f
-/* expl.c
- *
- * Exponential function, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, expl();
- *
- * y = expl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns e (2.71828...) raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- *
- * x k f
- * e = 2 e.
- *
- * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
- * in the basic range [-0.5 ln 2, 0.5 ln 2].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-10000 50000 1.12e-19 2.81e-20
- *
- *
- * Error amplification in the exponential function can be
- * a serious matter. The error propagation involves
- * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
- * which shows that a 1 lsb error in representing X produces
- * a relative error of X times 1 lsb in the function.
- * While the routine gives an accurate result for arguments
- * that are exactly represented by a long double precision
- * computer number, the result contains amplified roundoff
- * error for large arguments not exactly represented.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < MINLOG 0.0
- * exp overflow x > MAXLOG MAXNUM
- *
- */
-\f
-/* fabsl.c
- *
- * Absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y;
- *
- * y = fabsl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the absolute value of the argument.
- *
- */
-\f
-/* fdtrl.c
- *
- * F distribution, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * long double x, y, fdtrl();
- *
- * y = fdtrl( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density). This is the density
- * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
- * variables having Chi square distributions with df1
- * and df2 degrees of freedom, respectively.
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbetl( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
- *
- *
- * The arguments a and b are greater than zero, and x
- * x is nonnegative.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) in the indicated intervals.
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 1,100 10000 9.3e-18 2.9e-19
- * IEEE 0,1 1,10000 10000 1.9e-14 2.9e-15
- * IEEE 1,5 1,10000 10000 5.8e-15 1.4e-16
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrl domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrcl()
- *
- * Complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * long double x, y, fdtrcl();
- *
- * y = fdtrcl( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from x to infinity under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density).
- *
- *
- * inf.
- * -
- * 1 | | a-1 b-1
- * 1-P(x) = ------ | t (1-t) dt
- * B(a,b) | |
- * -
- * x
- *
- * (See fdtr.c.)
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
- *
- *
- * ACCURACY:
- *
- * See incbet.c.
- * Tested at random points (a,b,x).
- *
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 0,100 10000 4.2e-18 3.3e-19
- * IEEE 0,1 1,10000 10000 7.2e-15 2.6e-16
- * IEEE 1,5 1,10000 10000 1.7e-14 3.0e-15
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrcl domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtril()
- *
- * Inverse of complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * long double x, p, fdtril();
- *
- * x = fdtril( df1, df2, p );
- *
- * DESCRIPTION:
- *
- * Finds the F density argument x such that the integral
- * from x to infinity of the F density is equal to the
- * given probability p.
- *
- * This is accomplished using the inverse beta integral
- * function and the relations
- *
- * z = incbi( df2/2, df1/2, p )
- * x = df2 (1-z) / (df1 z).
- *
- * Note: the following relations hold for the inverse of
- * the uncomplemented F distribution:
- *
- * z = incbi( df1/2, df2/2, p )
- * x = df2 z / (df1 (1-z)).
- *
- * ACCURACY:
- *
- * See incbi.c.
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between .001 and 1:
- * IEEE 1,100 40000 4.6e-18 2.7e-19
- * IEEE 1,10000 30000 1.7e-14 1.4e-16
- * For p between 10^-6 and .001:
- * IEEE 1,100 20000 1.9e-15 3.9e-17
- * IEEE 1,10000 30000 2.7e-15 4.0e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtril domain p <= 0 or p > 1 0.0
- * v < 1
- */
-\f
-/* ceill()
- * floorl()
- * frexpl()
- * ldexpl()
- * fabsl()
- *
- * Floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y;
- * long double ceill(), floorl(), frexpl(), ldexpl(), fabsl();
- * int expnt, n;
- *
- * y = floorl(x);
- * y = ceill(x);
- * y = frexpl( x, &expnt );
- * y = ldexpl( x, n );
- * y = fabsl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * All four routines return a long double precision floating point
- * result.
- *
- * floorl() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * ceill() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * frexpl() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * ldexpl() multiplies x by 2**n.
- *
- * fabsl() returns the absolute value of its argument.
- *
- * These functions are part of the standard C run time library
- * for some but not all C compilers. The ones supplied are
- * written in C for IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-/* gammal.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, gammal();
- * extern int sgngam;
- *
- * y = gammal( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
- *
- * Arguments |x| <= 13 are reduced by recurrence and the function
- * approximated by a rational function of degree 7/8 in the
- * interval (2,3). Large arguments are handled by Stirling's
- * formula. Large negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -40,+40 10000 3.6e-19 7.9e-20
- * IEEE -1755,+1755 10000 4.8e-18 6.5e-19
- *
- * Accuracy for large arguments is dominated by error in powl().
- *
- */\f
-/* lgaml()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, lgaml();
- * extern int sgngam;
- *
- * y = lgaml( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
- *
- * For arguments greater than 33, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula using a polynomial approximation of
- * degree 4. Arguments between -33 and +33 are reduced by
- * recurrence to the interval [2,3] of a rational approximation.
- * The cosecant reflection formula is employed for arguments
- * less than -33.
- *
- * Arguments greater than MAXLGML (10^4928) return MAXNUML.
- *
- *
- *
- * ACCURACY:
- *
- *
- * arithmetic domain # trials peak rms
- * IEEE -40, 40 100000 2.2e-19 4.6e-20
- * IEEE 10^-2000,10^+2000 20000 1.6e-19 3.3e-20
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- *
- */
-\f
-/* gdtrl.c
- *
- * Gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, gdtrl();
- *
- * y = gdtrl( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from zero to x of the gamma probability
- * density function:
- *
- *
- * x
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * 0
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igam( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrl domain x < 0 0.0
- *
- */
-\f/* gdtrcl.c
- *
- * Complemented gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, gdtrcl();
- *
- * y = gdtrcl( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from x to infinity of the gamma
- * probability density function:
- *
- *
- * inf.
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * x
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igamc( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrcl domain x < 0 0.0
- *
- */
-\f
-/*
-C
-C ..................................................................
-C
-C SUBROUTINE GELS
-C
-C PURPOSE
-C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
-C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
-C IS ASSUMED TO BE STORED COLUMNWISE.
-C
-C USAGE
-C CALL GELS(R,A,M,N,EPS,IER,AUX)
-C
-C DESCRIPTION OF PARAMETERS
-C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
-C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
-C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
-C M BY M COEFFICIENT MATRIX. (DESTROYED)
-C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
-C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
-C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
-C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
-C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
-C IER=0 - NO ERROR,
-C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
-C PIVOT ELEMENT AT ANY ELIMINATION STEP
-C EQUAL TO 0,
-C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
-C CANCE INDICATED AT ELIMINATION STEP K+1,
-C WHERE PIVOT ELEMENT WAS LESS THAN OR
-C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
-C ABSOLUTELY GREATEST MAIN DIAGONAL
-C ELEMENT OF MATRIX A.
-C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
-C
-C REMARKS
-C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
-C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
-C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
-C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
-C TOO.
-C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
-C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
-C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
-C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
-C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
-C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
-C GIVEN IN CASE M=1.
-C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
-C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
-C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
-C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
-C
-C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
-C NONE
-C
-C METHOD
-C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
-C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
-C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
-C
-C ..................................................................
-C
-*/
-\f
-/* igamil()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igamil();
- *
- * x = igamil( a, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * igamc( a, x ) = y.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(y) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Tested for a ranging from 0.5 to 30 and x from 0 to 0.5.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,0.5 3400 8.8e-16 1.3e-16
- * IEEE 0,0.5 10000 1.1e-14 1.0e-15
- *
- */
-\f
-/* igaml.c
- *
- * Incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igaml();
- *
- * y = igaml( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 4000 4.4e-15 6.3e-16
- * IEEE 0,30 10000 3.6e-14 5.1e-15
- *
- */
-\f/* igamcl()
- *
- * Complemented incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igamcl();
- *
- * y = igamcl( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 2000 2.7e-15 4.0e-16
- * IEEE 0,30 60000 1.4e-12 6.3e-15
- *
- */
-\f
-/* incbetl.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, incbetl();
- *
- * y = incbetl( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion
- * or, when b*x is small, by a power series.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) with x between 0 and 1.
- * arithmetic domain # trials peak rms
- * IEEE 0,5 20000 4.5e-18 2.4e-19
- * IEEE 0,100 100000 3.9e-17 1.0e-17
- * Half-integer a, b:
- * IEEE .5,10000 100000 3.9e-14 4.4e-15
- * Outputs smaller than the IEEE gradual underflow threshold
- * were excluded from these statistics.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * incbetl domain x<0, x>1 0.0
- */
-\f
-/* incbil()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, incbil();
- *
- * x = incbil( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y.
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 .5,10000 10000 1.1e-14 1.4e-16
- */
-\f
-/* j0l.c
- *
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, j0l();
- *
- * y = j0l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of first kind, order zero of the argument.
- *
- * The domain is divided into the intervals [0, 9] and
- * (9, infinity). In the first interval the rational approximation
- * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) P7(x^2) / Q8(x^2),
- * where r, s, t are the first three zeros of the function.
- * In the second interval the expansion is in terms of the
- * modulus M0(x) = sqrt(J0(x)^2 + Y0(x)^2) and phase P0(x)
- * = atan(Y0(x)/J0(x)). M0 is approximated by sqrt(1/x)P7(1/x)/Q7(1/x).
- * The approximation to J0 is M0 * cos(x - pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 100000 2.8e-19 7.4e-20
- *
- *
- */
-\f/* y0l.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y0l();
- *
- * y = y0l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 5>, [5,9> and
- * [9, infinity). In the first interval a rational approximation
- * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
- *
- * In the second interval, the approximation is
- * (x - p)(x - q)(x - r)(x - s)P7(x)/Q7(x)
- * where p, q, r, s are zeros of y0(x).
- *
- * The third interval uses the same approximations to modulus
- * and phase as j0(x), whence y0(x) = modulus * sin(phase).
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 100000 3.4e-19 7.6e-20
- *
- */
-\f
-/* j1l.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, j1l();
- *
- * y = j1l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 9] and
- * (9, infinity). In the first interval the rational approximation
- * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) x P8(x^2) / Q8(x^2),
- * where r, s, t are the first three zeros of the function.
- * In the second interval the expansion is in terms of the
- * modulus M1(x) = sqrt(J1(x)^2 + Y1(x)^2) and phase P1(x)
- * = atan(Y1(x)/J1(x)). M1 is approximated by sqrt(1/x)P7(1/x)/Q8(1/x).
- * The approximation to j1 is M1 * cos(x - 3 pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 40000 1.8e-19 5.0e-20
- *
- *
- */
-\f/* y1l.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1l();
- *
- * y = y1l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 4.5>, [4.5,9> and
- * [9, infinity). In the first interval a rational approximation
- * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
- *
- * In the second interval, the approximation is
- * (x - p)(x - q)(x - r)(x - s)P9(x)/Q10(x)
- * where p, q, r, s are zeros of y1(x).
- *
- * The third interval uses the same approximations to modulus
- * and phase as j1(x), whence y1(x) = modulus * sin(phase).
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 36000 2.7e-19 5.3e-20
- *
- */
-\f
-/* jnl.c
- *
- * Bessel function of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * long double x, y, jnl();
- *
- * y = jnl( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The ratio of jn(x) to j0(x) is computed by backward
- * recurrence. First the ratio jn/jn-1 is found by a
- * continued fraction expansion. Then the recurrence
- * relating successive orders is applied until j0 or j1 is
- * reached.
- *
- * If n = 0 or 1 the routine for j0 or j1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE -30, 30 5000 3.3e-19 4.7e-20
- *
- *
- * Not suitable for large n or x.
- *
- */
-\f
-/* ldrand.c
- *
- * Pseudorandom number generator
- *
- *
- *
- * SYNOPSIS:
- *
- * double y;
- * int ldrand();
- *
- * ldrand( &y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Yields a random number 1.0 <= y < 2.0.
- *
- * The three-generator congruential algorithm by Brian
- * Wichmann and David Hill (BYTE magazine, March, 1987,
- * pp 127-8) is used.
- *
- * Versions invoked by the different arithmetic compile
- * time options IBMPC, and MIEEE, produce the same sequences.
- *
- */
-\f
-/* log10l.c
- *
- * Common logarithm, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, log10l();
- *
- * y = log10l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 10 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20
- * IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns MINLOG
- * log domain: x < 0; returns MINLOG
- */
-\f
-/* log2l.c
- *
- * Base 2 logarithm, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, log2l();
- *
- * y = log2l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 2 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the (natural)
- * logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20
- * IEEE exp(+-10000) 70000 5.4e-20 2.3e-20
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns MINLOG
- * log domain: x < 0; returns MINLOG
- */
-\f
-/* logl.c
- *
- * Natural logarithm, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, logl();
- *
- * y = logl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20
- * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns MINLOG
- * log domain: x < 0; returns MINLOG
- */
-\f
-/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * int mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file mconf.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * mconf.h
- *
- */
-\f
-/* nbdtrl.c
- *
- * Negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, nbdtrl();
- *
- * y = nbdtrl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the negative
- * binomial distribution:
- *
- * k
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * In a sequence of Bernoulli trials, this is the probability
- * that k or fewer failures precede the nth success.
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (k,n,p) with k and n between 1 and 10,000
- * and p between 0 and 1.
- *
- * arithmetic domain # trials peak rms
- * Absolute error:
- * IEEE 0,10000 10000 9.8e-15 2.1e-16
- *
- */
-\f/* nbdtrcl.c
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, nbdtrcl();
- *
- * y = nbdtrcl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * See incbetl.c.
- *
- */
-\f/* nbdtril
- *
- * Functional inverse of negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, nbdtril();
- *
- * p = nbdtril( k, n, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the argument p such that nbdtr(k,n,p) is equal to y.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,y), with y between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100
- * See also incbil.c.
- */
-\f
-/* ndtril.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, ndtril();
- *
- * x = ndtril( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2 log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z) .
- * For larger arguments, x/sqrt(2 pi) = w + w^3 R(w^2)/S(w^2)) ,
- * where w = y - 0.5 .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * Arguments uniformly distributed:
- * IEEE 0, 1 5000 7.8e-19 9.9e-20
- * Arguments exponentially distributed:
- * IEEE exp(-11355),-1 30000 1.7e-19 4.3e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtril domain x <= 0 -MAXNUML
- * ndtril domain x >= 1 MAXNUML
- *
- */
-\f
-/* ndtril.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, ndtril();
- *
- * x = ndtril( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2 log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z) .
- * For larger arguments, x/sqrt(2 pi) = w + w^3 R(w^2)/S(w^2)) ,
- * where w = y - 0.5 .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * Arguments uniformly distributed:
- * IEEE 0, 1 5000 7.8e-19 9.9e-20
- * Arguments exponentially distributed:
- * IEEE exp(-11355),-1 30000 1.7e-19 4.3e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtril domain x <= 0 -MAXNUML
- * ndtril domain x >= 1 MAXNUML
- *
- */
-\f
-/* pdtrl.c
- *
- * Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * long double m, y, pdtrl();
- *
- * y = pdtrl( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the first k terms of the Poisson
- * distribution:
- *
- * k j
- * -- -m m
- * > e --
- * -- j!
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the relation
- *
- * y = pdtr( k, m ) = igamc( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- */
-\f/* pdtrcl()
- *
- * Complemented poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * long double m, y, pdtrcl();
- *
- * y = pdtrcl( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the Poisson
- * distribution:
- *
- * inf. j
- * -- -m m
- * > e --
- * -- j!
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the formula
- *
- * y = pdtrc( k, m ) = igam( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam.c.
- *
- */
-\f/* pdtril()
- *
- * Inverse Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * long double m, y, pdtrl();
- *
- * m = pdtril( k, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Poisson variable x such that the integral
- * from 0 to x of the Poisson density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * m = igami( k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pdtri domain y < 0 or y >= 1 0.0
- * k < 0
- *
- */
-\f
-/* polevll.c
- * p1evll.c
- *
- * Evaluate polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * long double x, y, coef[N+1], polevl[];
- *
- * y = polevll( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates polynomial of degree N:
- *
- * 2 N
- * y = C + C x + C x +...+ C x
- * 0 1 2 N
- *
- * Coefficients are stored in reverse order:
- *
- * coef[0] = C , ..., coef[N] = C .
- * N 0
- *
- * The function p1evll() assumes that coef[N] = 1.0 and is
- * omitted from the array. Its calling arguments are
- * otherwise the same as polevll().
- *
- * This module also contains the following globally declared constants:
- * MAXNUML = 1.189731495357231765021263853E4932L;
- * MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
- * MAXLOGL = 1.1356523406294143949492E4L;
- * MINLOGL = -1.1355137111933024058873E4L;
- * LOGE2L = 6.9314718055994530941723E-1L;
- * LOG2EL = 1.4426950408889634073599E0L;
- * PIL = 3.1415926535897932384626L;
- * PIO2L = 1.5707963267948966192313L;
- * PIO4L = 7.8539816339744830961566E-1L;
- *
- * SPEED:
- *
- * In the interest of speed, there are no checks for out
- * of bounds arithmetic. This routine is used by most of
- * the functions in the library. Depending on available
- * equipment features, the user may wish to rewrite the
- * program in microcode or assembly language.
- *
- */
-\f
-/* powil.c
- *
- * Real raised to integer power, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, powil();
- * int n;
- *
- * y = powil( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns argument x raised to the nth power.
- * The routine efficiently decomposes n as a sum of powers of
- * two. The desired power is a product of two-to-the-kth
- * powers of x. Thus to compute the 32767 power of x requires
- * 28 multiplications instead of 32767 multiplications.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic x domain n domain # trials peak rms
- * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18
- * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
- * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
- *
- * Returns MAXNUM on overflow, zero on underflow.
- *
- */
-\f
-/* powl.c
- *
- * Power function, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, z, powl();
- *
- * z = powl( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/32 and pseudo extended precision arithmetic to
- * obtain several extra bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * The relative error of pow(x,y) can be estimated
- * by y dl ln(2), where dl is the absolute error of
- * the internally computed base 2 logarithm. At the ends
- * of the approximation interval the logarithm equal 1/32
- * and its relative error is about 1 lsb = 1.1e-19. Hence
- * the predicted relative error in the result is 2.3e-21 y .
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- *
- * IEEE +-1000 40000 2.8e-18 3.7e-19
- * .001 < x < 1000, with log(x) uniformly distributed.
- * -1000 < y < 1000, y uniformly distributed.
- *
- * IEEE 0,8700 60000 6.5e-18 1.0e-18
- * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pow overflow x**y > MAXNUM MAXNUM
- * pow underflow x**y < 1/MAXNUM 0.0
- * pow domain x<0 and y noninteger 0.0
- *
- */
-\f
-/* sinhl.c
- *
- * Hyperbolic sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, sinhl();
- *
- * y = sinhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic sine of argument in the range MINLOGL to
- * MAXLOGL.
- *
- * The range is partitioned into two segments. If |x| <= 1, a
- * rational function of the form x + x**3 P(x)/Q(x) is employed.
- * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -2,2 10000 1.5e-19 3.9e-20
- * IEEE +-10000 30000 1.1e-19 2.8e-20
- *
- */
-\f
-/* sinl.c
- *
- * Circular sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, sinl();
- *
- * y = sinl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by the Cody
- * and Waite polynomial form
- * x + x**3 P(x**2) .
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - .5 x**2 + x**4 Q(x**2) .
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-5.5e11 200,000 1.2e-19 2.9e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 2**39 0.0
- *
- * Loss of precision occurs for x > 2**39 = 5.49755813888e11.
- * The routine as implemented flags a TLOSS error for
- * x > 2**39 and returns 0.0.
- */
-\f/* cosl.c
- *
- * Circular cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, cosl();
- *
- * y = cosl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - .5 x**2 + x**4 Q(x**2) .
- * Between pi/4 and pi/2 the sine is represented by the Cody
- * and Waite polynomial form
- * x + x**3 P(x**2) .
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-5.5e11 50000 1.2e-19 2.9e-20
- */
-\f
-/* sqrtl.c
- *
- * Square root, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, sqrtl();
- *
- * y = sqrtl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the square root of x.
- *
- * Range reduction involves isolating the power of two of the
- * argument and using a polynomial approximation to obtain
- * a rough value for the square root. Then Heron's iteration
- * is used three times to converge to an accurate value.
- *
- * Note, some arithmetic coprocessors such as the 8087 and
- * 68881 produce correctly rounded square roots, which this
- * routine will not.
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10 30000 8.1e-20 3.1e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sqrt domain x < 0 0.0
- *
- */
-\f
-/* stdtrl.c
- *
- * Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double p, t, stdtrl();
- * int k;
- *
- * p = stdtrl( k, t );
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral from minus infinity to t of the Student
- * t distribution with integer k > 0 degrees of freedom:
- *
- * t
- * -
- * | |
- * - | 2 -(k+1)/2
- * | ( (k+1)/2 ) | ( x )
- * ---------------------- | ( 1 + --- ) dx
- * - | ( k )
- * sqrt( k pi ) | ( k/2 ) |
- * | |
- * -
- * -inf.
- *
- * Relation to incomplete beta integral:
- *
- * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
- * where
- * z = k/(k + t**2).
- *
- * For t < -1.6, this is the method of computation. For higher t,
- * a direct method is derived from integration by parts.
- * Since the function is symmetric about t=0, the area under the
- * right tail of the density is found by calling the function
- * with -t instead of t.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 100. The "domain" refers to t.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -100,-1.6 10000 5.7e-18 9.8e-19
- * IEEE -1.6,100 10000 3.8e-18 1.0e-19
- */
-\f
-/* stdtril.c
- *
- * Functional inverse of Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double p, t, stdtril();
- * int k;
- *
- * t = stdtril( k, p );
- *
- *
- * DESCRIPTION:
- *
- * Given probability p, finds the argument t such that stdtrl(k,t)
- * is equal to p.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 100. The "domain" refers to p:
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 3500 4.2e-17 4.1e-18
- */
-\f
-/* tanhl.c
- *
- * Hyperbolic tangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, tanhl();
- *
- * y = tanhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic tangent of argument in the range MINLOGL to
- * MAXLOGL.
- *
- * A rational function is used for |x| < 0.625. The form
- * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
- * Otherwise,
- * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -2,2 30000 1.3e-19 2.4e-20
- *
- */
-\f
-/* tanl.c
- *
- * Circular tangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, tanl();
- *
- * y = tanl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-1.07e9 30000 1.9e-19 4.8e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tan total loss x > 2^39 0.0
- *
- */
-\f/* cotl.c
- *
- * Circular cotangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, cotl();
- *
- * y = cotl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-1.07e9 30000 1.9e-19 5.1e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 2^39 0.0
- * cot singularity x = 0 MAXNUM
- *
- */
-\f
-/* unityl.c
- *
- * Relative error approximations for function arguments near
- * unity.
- *
- * log1p(x) = log(1+x)
- * expm1(x) = exp(x) - 1
- * cos1m(x) = cos(x) - 1
- *
- */
-\f
-/* ynl.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, ynl();
- * int n;
- *
- * y = ynl( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0l() and y1l().
- *
- * If n = 0 or 1 the routine for y0l or y1l is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative error when y > 1.
- * x >= 0, -30 <= n <= +30.
- * arithmetic domain # trials peak rms
- * IEEE -30, 30 10000 1.3e-18 1.8e-19
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ynl singularity x = 0 MAXNUML
- * ynl overflow MAXNUML
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
+++ /dev/null
-/* acoshl.c
- *
- * Inverse hyperbolic cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, acoshl();
- *
- * y = acoshl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a rational approximation
- *
- * sqrt(2z) * P(z)/Q(z)
- *
- * where z = x-1, is used. Otherwise,
- *
- * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 1,3 30000 2.0e-19 3.9e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acoshl domain |x| < 1 0.0
- *
- */
-\f
-/* acosh.c */
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1991, 1998 by Stephen L. Moshier
-*/
-
-
-/* acosh(1+x) = sqrt(2x) * R(x), interval 0 < x < 0.5 */
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
- 2.9071989653343333587238E-5L,
- 3.2906030801088967279449E-3L,
- 6.3034445964862182128388E-2L,
- 4.1587081802731351459504E-1L,
- 1.0989714347599256302467E0L,
- 9.9999999999999999999715E-1L,
-};
-static long double Q[] = {
- 1.0443462486787584738322E-4L,
- 6.0085845375571145826908E-3L,
- 8.7750439986662958343370E-2L,
- 4.9564621536841869854584E-1L,
- 1.1823047680932589605190E0L,
- 1.0000000000000000000028E0L,
-};
-#endif
-
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x4536,0x4dba,0x9f55,0xf3df,0x3fef, XPD
-0x23a5,0xf9aa,0x289c,0xd7a7,0x3ff6, XPD
-0x7e8b,0x8645,0x341f,0x8118,0x3ffb, XPD
-0x0fd5,0x937f,0x0515,0xd4ed,0x3ffd, XPD
-0x2364,0xc41b,0x1891,0x8cab,0x3fff, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-static short Q[] = {
-0x1e7c,0x4f16,0xe98c,0xdb03,0x3ff1, XPD
-0xc319,0xc272,0xa90a,0xc4e3,0x3ff7, XPD
-0x2f83,0x9e5e,0x80af,0xb3b6,0x3ffb, XPD
-0xe1e0,0xc97c,0x573a,0xfdc5,0x3ffd, XPD
-0xcdf2,0x6ec5,0xc33c,0x9755,0x3fff, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3fef0000,0xf3df9f55,0x4dba4536,
-0x3ff60000,0xd7a7289c,0xf9aa23a5,
-0x3ffb0000,0x8118341f,0x86457e8b,
-0x3ffd0000,0xd4ed0515,0x937f0fd5,
-0x3fff0000,0x8cab1891,0xc41b2364,
-0x3fff0000,0x80000000,0x00000000,
-};
-static long Q[] = {
-0x3ff10000,0xdb03e98c,0x4f161e7c,
-0x3ff70000,0xc4e3a90a,0xc272c319,
-0x3ffb0000,0xb3b680af,0x9e5e2f83,
-0x3ffd0000,0xfdc5573a,0xc97ce1e0,
-0x3fff0000,0x9755c33c,0x6ec5cdf2,
-0x3fff0000,0x80000000,0x00000000,
-};
-#endif
-
-extern long double LOGE2L;
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-#ifdef ANSIPROT
-extern long double logl ( long double );
-extern long double sqrtl ( long double );
-extern long double polevll ( long double, void *, int );
-extern int isnanl ( long double );
-#else
-long double logl(), sqrtl(), polevll(), isnanl();
-#endif
-
-long double acoshl(x)
-long double x;
-{
-long double a, z;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-if( x < 1.0L )
- {
- mtherr( "acoshl", DOMAIN );
-#ifdef NANS
- return(NANL);
-#else
- return(0.0L);
-#endif
- }
-
-if( x > 1.0e10 )
- {
-#ifdef INFINITIES
- if( x == INFINITYL )
- return( INFINITYL );
-#endif
- return( logl(x) + LOGE2L );
- }
-
-z = x - 1.0L;
-
-if( z < 0.5L )
- {
- a = sqrtl(2.0L*z) * (polevll(z, P, 5) / polevll(z, Q, 5) );
- return( a );
- }
-
-a = sqrtl( z*(x+1.0L) );
-return( logl(x + a) );
-}
+++ /dev/null
-/* arcdot.c
- *
- * Angle between two vectors
- *
- *
- *
- *
- * SYNOPSIS:
- *
- * long double p[3], q[3], arcdotl();
- *
- * y = arcdotl( p, q );
- *
- *
- *
- * DESCRIPTION:
- *
- * For two vectors p, q, the angle A between them is given by
- *
- * p.q / (|p| |q|) = cos A .
- *
- * where "." represents inner product, "|x|" the length of vector x.
- * If the angle is small, an expression in sin A is preferred.
- * Set r = q - p. Then
- *
- * p.q = p.p + p.r ,
- *
- * |p|^2 = p.p ,
- *
- * |q|^2 = p.p + 2 p.r + r.r ,
- *
- * p.p^2 + 2 p.p p.r + p.r^2
- * cos^2 A = ----------------------------
- * p.p (p.p + 2 p.r + r.r)
- *
- * p.p + 2 p.r + p.r^2 / p.p
- * = --------------------------- ,
- * p.p + 2 p.r + r.r
- *
- * sin^2 A = 1 - cos^2 A
- *
- * r.r - p.r^2 / p.p
- * = --------------------
- * p.p + 2 p.r + r.r
- *
- * = (r.r - p.r^2 / p.p) / q.q .
- *
- * ACCURACY:
- *
- * About 1 ULP. See arcdot.c.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double acosl ( long double );
-extern long double asinl ( long double );
-extern long double atanl ( long double );
-#else
-long double sqrtl(), acosl(), asinl(), atanl();
-#endif
-extern long double PIL;
-
-long double arcdotl(p,q)
-long double p[], q[];
-{
-long double pp, pr, qq, rr, rt, pt, qt, pq;
-int i;
-
-pq = 0.0L;
-qq = 0.0L;
-pp = 0.0L;
-pr = 0.0L;
-rr = 0.0L;
-for (i=0; i<3; i++)
- {
- pt = p[i];
- qt = q[i];
- pq += pt * qt;
- qq += qt * qt;
- pp += pt * pt;
- rt = qt - pt;
- pr += pt * rt;
- rr += rt * rt;
- }
-if (rr == 0.0L || pp == 0.0L || qq == 0.0L)
- return 0.0L;
-rt = (rr - (pr * pr) / pp) / qq;
-if (rt <= 0.75L)
- {
- rt = sqrtl(rt);
- qt = asinl(rt);
- if (pq < 0.0L)
- qt = PIL - qt;
- }
-else
- {
- pt = pq / sqrtl(pp*qq);
- qt = acosl(pt);
- }
-return qt;
-}
+++ /dev/null
-/* asinhl.c
- *
- * Inverse hyperbolic sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, asinhl();
- *
- * y = asinhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic sine of argument.
- *
- * If |x| < 0.5, the function is approximated by a rational
- * form x + x**3 P(x)/Q(x). Otherwise,
- *
- * asinh(x) = log( x + sqrt(1 + x*x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -3,3 30000 1.7e-19 3.5e-20
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1991, 1998 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
--7.2157234864927687427374E-1L,
--1.3005588097490352458918E1L,
--5.9112383795679709212744E1L,
--9.5372702442289028811361E1L,
--4.9802880260861844539014E1L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
- 2.8754968540389640419671E1L,
- 2.0990255691901160529390E2L,
- 5.9265075560893800052658E2L,
- 7.0670399135805956780660E2L,
- 2.9881728156517107462943E2L,
-};
-#endif
-
-
-#ifdef IBMPC
-static short P[] = {
-0x8f42,0x2584,0xf727,0xb8b8,0xbffe, XPD
-0x9d56,0x7f7c,0xe38b,0xd016,0xc002, XPD
-0xc518,0xdc2d,0x14bc,0xec73,0xc004, XPD
-0x99fe,0xc18a,0xd2da,0xbebe,0xc005, XPD
-0xb46c,0x3c05,0x263e,0xc736,0xc004, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0xdfed,0x33db,0x2cf2,0xe60a,0x4003, XPD
-0xf109,0x61ee,0x0df8,0xd1e7,0x4006, XPD
-0xf21e,0xda84,0xa5fa,0x9429,0x4008, XPD
-0x13fc,0xc4e2,0x0e31,0xb0ad,0x4008, XPD
-0x485c,0xad04,0x9cae,0x9568,0x4007, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0xbffe0000,0xb8b8f727,0x25848f42,
-0xc0020000,0xd016e38b,0x7f7c9d56,
-0xc0040000,0xec7314bc,0xdc2dc518,
-0xc0050000,0xbebed2da,0xc18a99fe,
-0xc0040000,0xc736263e,0x3c05b46c,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40030000,0xe60a2cf2,0x33dbdfed,
-0x40060000,0xd1e70df8,0x61eef109,
-0x40080000,0x9429a5fa,0xda84f21e,
-0x40080000,0xb0ad0e31,0xc4e213fc,
-0x40070000,0x95689cae,0xad04485c,
-};
-#endif
-
-extern long double LOGE2L;
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef ANSIPROT
-extern long double logl ( long double );
-extern long double sqrtl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-extern int isfinitel ( long double );
-#else
-long double logl(), sqrtl(), polevll(), p1evll(), isnanl(), isfinitel();
-#endif
-
-long double asinhl(x)
-long double x;
-{
-long double a, z;
-int sign;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-#ifdef MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-#ifdef INFINITIES
- if( !isfinitel(x) )
- return(x);
-#endif
-if( x < 0.0L )
- {
- sign = -1;
- x = -x;
- }
-else
- sign = 1;
-
-if( x > 1.0e10L )
- {
- return( sign * (logl(x) + LOGE2L) );
- }
-
-z = x * x;
-if( x < 0.5L )
- {
- a = ( polevll(z, P, 4)/p1evll(z, Q, 5) ) * z;
- a = a * x + x;
- if( sign < 0 )
- a = -a;
- return(a);
- }
-
-a = sqrtl( z + 1.0L );
-return( sign * logl(x + a) );
-}
+++ /dev/null
-/* asinl.c
- *
- * Inverse circular sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, asinl();
- *
- * y = asinl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
- *
- * A rational function of the form x + x**3 P(x**2)/Q(x**2)
- * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
- * transformed by the identity
- *
- * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 30000 2.7e-19 4.8e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * asinl domain |x| > 1 NANL
- *
- */
-\f/* acosl()
- *
- * Inverse circular cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acosl();
- *
- * y = acosl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose cosine
- * is x.
- *
- * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
- * near 1, there is cancellation error in subtracting asin(x)
- * from pi/2. Hence if x < -0.5,
- *
- * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
- *
- * or if x > +0.5,
- *
- * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 30000 1.4e-19 3.5e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acosl domain |x| > 1 NANL
- */
-\f
-/* asin.c */
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1990, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
- 3.7769340062433674871612E-3L,
--6.1212919176969202969441E-1L,
- 5.9303993515791417710775E0L,
--1.8631697621590161441592E1L,
- 2.3314603132141795720634E1L,
--1.0087146579384916260197E1L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
--1.5684335624873146511217E1L,
- 7.8702951549021104258866E1L,
--1.7078401170625864261444E2L,
- 1.6712291455718995937376E2L,
--6.0522879476309497128868E1L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0x59d1,0x3509,0x7009,0xf786,0x3ff6, XPD
-0xbe97,0x93e6,0x7fab,0x9cb4,0xbffe, XPD
-0x8bf5,0x6810,0xd4dc,0xbdc5,0x4001, XPD
-0x9bd4,0x8d86,0xb77b,0x950d,0xc003, XPD
-0x3b0f,0x9e25,0x4ea5,0xba84,0x4003, XPD
-0xea38,0xc6a9,0xf3cf,0xa164,0xc002, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x1229,0x8516,0x09e9,0xfaf3,0xc002, XPD
-0xb5c3,0xf36f,0xe943,0x9d67,0x4005, XPD
-0xe11a,0xbe0f,0xb4fd,0xaac8,0xc006, XPD
-0x4c69,0x1355,0x7754,0xa71f,0x4006, XPD
-0xded7,0xa9fe,0x6db7,0xf217,0xc004, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3ff60000,0xf7867009,0x350959d1,
-0xbffe0000,0x9cb47fab,0x93e6be97,
-0x40010000,0xbdc5d4dc,0x68108bf5,
-0xc0030000,0x950db77b,0x8d869bd4,
-0x40030000,0xba844ea5,0x9e253b0f,
-0xc0020000,0xa164f3cf,0xc6a9ea38,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0020000,0xfaf309e9,0x85161229,
-0x40050000,0x9d67e943,0xf36fb5c3,
-0xc0060000,0xaac8b4fd,0xbe0fe11a,
-0x40060000,0xa71f7754,0x13554c69,
-0xc0040000,0xf2176db7,0xa9feded7,
-};
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-#ifdef ANSIPROT
-extern long double ldexpl ( long double, int );
-extern long double sqrtl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-long double asinl ( long double );
-#else
-long double ldexpl(), sqrtl(), polevll(), p1evll();
-long double asinl();
-#endif
-
-long double asinl(x)
-long double x;
-{
-long double a, p, z, zz;
-short sign, flag;
-extern long double PIO2L;
-
-if( x > 0 )
- {
- sign = 1;
- a = x;
- }
-else
- {
- sign = -1;
- a = -x;
- }
-
-if( a > 1.0L )
- {
- mtherr( "asinl", DOMAIN );
-#ifdef NANS
- return( NANL );
-#else
- return( 0.0L );
-#endif
- }
-
-if( a < 1.0e-8L )
- {
- z = a;
- goto done;
- }
-
-if( a > 0.5L )
- {
- zz = 0.5L -a;
- zz = ldexpl( zz + 0.5L, -1 );
- z = sqrtl( zz );
- flag = 1;
- }
-else
- {
- z = a;
- zz = z * z;
- flag = 0;
- }
-
-p = zz * polevll( zz, P, 5)/p1evll( zz, Q, 5);
-z = z * p + z;
-if( flag != 0 )
- {
- z = z + z;
- z = PIO2L - z;
- }
-done:
-if( sign < 0 )
- z = -z;
-return(z);
-}
-
-
-extern long double PIO2L, PIL;
-
-long double acosl(x)
-long double x;
-{
-
-if( x < -1.0L )
- goto domerr;
-
-if( x < -0.5L)
- return( PIL - 2.0L * asinl( sqrtl(0.5L*(1.0L+x)) ) );
-
-if( x > 1.0L )
- {
-domerr: mtherr( "acosl", DOMAIN );
-#ifdef NANS
- return( NANL );
-#else
- return( 0.0L );
-#endif
- }
-
-if( x > 0.5L )
- return( 2.0L * asinl( sqrtl(0.5L*(1.0L-x) ) ) );
-
-return( PIO2L - asinl(x) );
-}
+++ /dev/null
-/* atanhl.c
- *
- * Inverse hyperbolic tangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, atanhl();
- *
- * y = atanhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic tangent of argument in the range
- * MINLOGL to MAXLOGL.
- *
- * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
- * employed. Otherwise,
- * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1,1 30000 1.1e-19 3.3e-20
- *
- */
-\f
-
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright (C) 1987, 1991, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
- 2.9647757819596835680719E-3L,
--8.0026596513099094380633E-1L,
- 7.7920941408493040219831E0L,
--2.4330686602187898836837E1L,
- 3.0204265014595622991082E1L,
--1.2961142942114056581210E1L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
--1.3729634163247557081869E1L,
- 6.2320841104088512332185E1L,
--1.2469344457045341444078E2L,
- 1.1394285233959210574352E2L,
--3.8883428826342169425890E1L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0x3aa2,0x036b,0xaf06,0xc24c,0x3ff6, XPD
-0x528e,0x56e8,0x3af4,0xccde,0xbffe, XPD
-0x9d89,0xc9a1,0xd5cf,0xf958,0x4001, XPD
-0xa653,0x6cfa,0x3f04,0xc2a5,0xc003, XPD
-0xc651,0x2b3d,0x55b2,0xf1a2,0x4003, XPD
-0xd76d,0xf293,0xd76b,0xcf60,0xc002, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0xd1b9,0x5314,0x94df,0xdbac,0xc002, XPD
-0x3caa,0x0517,0x8a92,0xf948,0x4004, XPD
-0x535e,0xaf5f,0x0b2a,0xf963,0xc005, XPD
-0xa6f9,0xb702,0xbd8a,0xe3e2,0x4005, XPD
-0xe136,0xf5ee,0xa190,0x9b88,0xc004, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3ff60000,0xc24caf06,0x036b3aa2,
-0xbffe0000,0xccde3af4,0x56e8528e,
-0x40010000,0xf958d5cf,0xc9a19d89,
-0xc0030000,0xc2a53f04,0x6cfaa653,
-0x40030000,0xf1a255b2,0x2b3dc651,
-0xc0020000,0xcf60d76b,0xf293d76d,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0020000,0xdbac94df,0x5314d1b9,
-0x40040000,0xf9488a92,0x05173caa,
-0xc0050000,0xf9630b2a,0xaf5f535e,
-0x40050000,0xe3e2bd8a,0xb702a6f9,
-0xc0040000,0x9b88a190,0xf5eee136,
-};
-#endif
-
-extern long double MAXNUML;
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double logl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-#else
-long double fabsl(), logl(), polevll(), p1evll();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double atanhl(x)
-long double x;
-{
-long double s, z;
-
-#ifdef MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-z = fabsl(x);
-if( z >= 1.0L )
- {
- if( x == 1.0L )
- {
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- return( MAXNUML );
-#endif
- }
- if( x == -1.0L )
- {
-#ifdef INFINITIES
- return( -INFINITYL );
-#else
- return( -MAXNUML );
-#endif
- }
- mtherr( "atanhl", DOMAIN );
-#ifdef NANS
- return( NANL );
-#else
- return( MAXNUML );
-#endif
- }
-
-if( z < 1.0e-8L )
- return(x);
-
-if( z < 0.5L )
- {
- z = x * x;
- s = x + x * z * (polevll(z, P, 5) / p1evll(z, Q, 5));
- return(s);
- }
-
-return( 0.5L * logl((1.0L+x)/(1.0L-x)) );
-}
+++ /dev/null
-/* atanl.c
- *
- * Inverse circular tangent, long double precision
- * (arctangent)
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, atanl();
- *
- * y = atanl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle between -pi/2 and +pi/2 whose tangent
- * is x.
- *
- * Range reduction is from four intervals into the interval
- * from zero to tan( pi/8 ). The approximant uses a rational
- * function of degree 3/4 of the form x + x**3 P(x)/Q(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 150000 1.3e-19 3.0e-20
- *
- */
-\f/* atan2l()
- *
- * Quadrant correct inverse circular tangent,
- * long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, z, atan2l();
- *
- * z = atan2l( y, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns radian angle whose tangent is y/x.
- * Define compile time symbol ANSIC = 1 for ANSI standard,
- * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
- * 0 to 2PI, args (x,y).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10, 10 60000 1.7e-19 3.2e-20
- * See atan.c.
- *
- */
-\f
-/* atan.c */
-
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1990, 1998 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
--8.6863818178092187535440E-1L,
--1.4683508633175792446076E1L,
--6.3976888655834347413154E1L,
--9.9988763777265819915721E1L,
--5.0894116899623603312185E1L,
-};
-static long double Q[] = {
-/* 1.00000000000000000000E0L,*/
- 2.2981886733594175366172E1L,
- 1.4399096122250781605352E2L,
- 3.6144079386152023162701E2L,
- 3.9157570175111990631099E2L,
- 1.5268235069887081006606E2L,
-};
-
-/* tan( 3*pi/8 ) */
-static long double T3P8 = 2.41421356237309504880169L;
-
-/* tan( pi/8 ) */
-static long double TP8 = 4.1421356237309504880169e-1L;
-#endif
-
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x8ece,0xce53,0x1266,0xde5f,0xbffe, XPD
-0x07e6,0xa061,0xa6bf,0xeaef,0xc002, XPD
-0x53ee,0xf291,0x557f,0xffe8,0xc004, XPD
-0xf9d6,0xeda6,0x3f3e,0xc7fa,0xc005, XPD
-0xb6c3,0x6abc,0x9361,0xcb93,0xc004, XPD
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x54d4,0x894e,0xe76e,0xb7da,0x4003, XPD
-0x76b9,0x7a46,0xafa2,0x8ffd,0x4006, XPD
-0xe3a9,0xe9c0,0x6bee,0xb4b8,0x4007, XPD
-0xabc1,0x50a7,0xb098,0xc3c9,0x4007, XPD
-0x891c,0x100d,0xae89,0x98ae,0x4006, XPD
-};
-
-/* tan( 3*pi/8 ) = 2.41421356237309504880 */
-static unsigned short T3P8A[] = {0x3242,0xfcef,0x7999,0x9a82,0x4000, XPD};
-#define T3P8 *(long double *)T3P8A
-
-/* tan( pi/8 ) = 0.41421356237309504880 */
-static unsigned short TP8A[] = {0x9211,0xe779,0xcccf,0xd413,0x3ffd, XPD};
-#define TP8 *(long double *)TP8A
-#endif
-
-#ifdef MIEEE
-static unsigned long P[] = {
-0xbffe0000,0xde5f1266,0xce538ece,
-0xc0020000,0xeaefa6bf,0xa06107e6,
-0xc0040000,0xffe8557f,0xf29153ee,
-0xc0050000,0xc7fa3f3e,0xeda6f9d6,
-0xc0040000,0xcb939361,0x6abcb6c3,
-};
-static unsigned long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40030000,0xb7dae76e,0x894e54d4,
-0x40060000,0x8ffdafa2,0x7a4676b9,
-0x40070000,0xb4b86bee,0xe9c0e3a9,
-0x40070000,0xc3c9b098,0x50a7abc1,
-0x40060000,0x98aeae89,0x100d891c,
-};
-
-/* tan( 3*pi/8 ) = 2.41421356237309504880 */
-static long T3P8A[] = {0x40000000,0x9a827999,0xfcef3242};
-#define T3P8 *(long double *)T3P8A
-
-/* tan( pi/8 ) = 0.41421356237309504880 */
-static long TP8A[] = {0x3ffd0000,0xd413cccf,0xe7799211};
-#define TP8 *(long double *)TP8A
-#endif
-
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double fabsl ( long double );
-extern int signbitl ( long double );
-extern int isnanl ( long double );
-long double atanl ( long double );
-#else
-long double polevll(), p1evll(), fabsl(), signbitl(), isnanl();
-long double atanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-#ifdef MINUSZERO
-extern long double NEGZEROL;
-#endif
-
-long double atanl(x)
-long double x;
-{
-extern long double PIO2L, PIO4L;
-long double y, z;
-short sign;
-
-#ifdef MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITYL )
- return( PIO2L );
-if( x == -INFINITYL )
- return( -PIO2L );
-#endif
-/* make argument positive and save the sign */
-sign = 1;
-if( x < 0.0L )
- {
- sign = -1;
- x = -x;
- }
-
-/* range reduction */
-if( x > T3P8 )
- {
- y = PIO2L;
- x = -( 1.0L/x );
- }
-
-else if( x > TP8 )
- {
- y = PIO4L;
- x = (x-1.0L)/(x+1.0L);
- }
-else
- y = 0.0L;
-
-/* rational form in x**2 */
-z = x * x;
-y = y + ( polevll( z, P, 4 ) / p1evll( z, Q, 5 ) ) * z * x + x;
-
-if( sign < 0 )
- y = -y;
-
-return(y);
-}
-\f
-/* atan2 */
-
-
-extern long double PIL, PIO2L, MAXNUML;
-
-#if ANSIC
-long double atan2l( y, x )
-#else
-long double atan2l( x, y )
-#endif
-long double x, y;
-{
-long double z, w;
-short code;
-
-code = 0;
-
-if( x < 0.0L )
- code = 2;
-if( y < 0.0L )
- code |= 1;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-if( isnanl(y) )
- return(y);
-#endif
-#ifdef MINUSZERO
-if( y == 0.0L )
- {
- if( signbitl(y) )
- {
- if( x > 0.0L )
- z = y;
- else if( x < 0.0L )
- z = -PIL;
- else
- {
- if( signbitl(x) )
- z = -PIL;
- else
- z = y;
- }
- }
- else /* y is +0 */
- {
- if( x == 0.0L )
- {
- if( signbitl(x) )
- z = PIL;
- else
- z = 0.0L;
- }
- else if( x > 0.0L )
- z = 0.0L;
- else
- z = PIL;
- }
- return z;
- }
-if( x == 0.0L )
- {
- if( y > 0.0L )
- z = PIO2L;
- else
- z = -PIO2L;
- return z;
- }
-#endif /* MINUSZERO */
-#ifdef INFINITIES
-if( x == INFINITYL )
- {
- if( y == INFINITYL )
- z = 0.25L * PIL;
- else if( y == -INFINITYL )
- z = -0.25L * PIL;
- else if( y < 0.0L )
- z = NEGZEROL;
- else
- z = 0.0L;
- return z;
- }
-if( x == -INFINITYL )
- {
- if( y == INFINITYL )
- z = 0.75L * PIL;
- else if( y == -INFINITYL )
- z = -0.75L * PIL;
- else if( y >= 0.0L )
- z = PIL;
- else
- z = -PIL;
- return z;
- }
-if( y == INFINITYL )
- return( PIO2L );
-if( y == -INFINITYL )
- return( -PIO2L );
-#endif /* INFINITIES */
-
-#ifdef INFINITIES
-if( x == 0.0L )
-#else
-if( fabsl(x) <= (fabsl(y) / MAXNUML) )
-#endif
- {
- if( code & 1 )
- {
-#if ANSIC
- return( -PIO2L );
-#else
- return( 3.0L*PIO2L );
-#endif
- }
- if( y == 0.0L )
- return( 0.0L );
- return( PIO2L );
- }
-
-if( y == 0.0L )
- {
- if( code & 2 )
- return( PIL );
- return( 0.0L );
- }
-
-
-switch( code )
- {
- default:
-#if ANSIC
- case 0:
- case 1: w = 0.0L; break;
- case 2: w = PIL; break;
- case 3: w = -PIL; break;
-#else
- case 0: w = 0.0L; break;
- case 1: w = 2.0L * PIL; break;
- case 2:
- case 3: w = PIL; break;
-#endif
- }
-
-z = w + atanl( y/x );
-#ifdef MINUSZERO
-if( z == 0.0L && y < 0.0L )
- z = NEGZEROL;
-#endif
-return( z );
-}
+++ /dev/null
-/* bdtrl.c
- *
- * Binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, bdtrl();
- *
- * y = bdtrl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the Binomial
- * probability density:
- *
- * k
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (k,n,p) with a and b between 0
- * and 10000 and p between 0 and 1.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10000 3000 1.6e-14 2.2e-15
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrl domain k < 0 0.0
- * n < k
- * x < 0, x > 1
- *
- */
-\f/* bdtrcl()
- *
- * Complemented binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, bdtrcl();
- *
- * y = bdtrcl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 through n of the Binomial
- * probability density:
- *
- * n
- * -- ( n ) j n-j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * See incbet.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtrcl domain x<0, x>1, n<k 0.0
- */
-\f/* bdtril()
- *
- * Inverse binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, bdtril();
- *
- * p = bdtril( k, n, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the event probability p such that the sum of the
- * terms 0 through k of the Binomial probability density
- * is equal to the given cumulative probability y.
- *
- * This is accomplished using the inverse beta integral
- * function and the relation
- *
- * 1 - p = incbi( n-k, k+1, y ).
- *
- * ACCURACY:
- *
- * See incbi.c.
- * Tested at random k, n between 1 and 10000. The "domain" refers to p:
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 3500 2.0e-15 8.2e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * bdtril domain k < 0, n <= k 0.0
- * x < 0, x > 1
- */
-\f
-/* bdtr() */
-
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double incbetl ( long double, long double, long double );
-extern long double incbil ( long double, long double, long double );
-extern long double powl ( long double, long double );
-extern long double expm1l ( long double );
-extern long double log1pl ( long double );
-#else
-long double incbetl(), incbil(), powl(), expm1l(), log1pl();
-#endif
-
-long double bdtrcl( k, n, p )
-int k, n;
-long double p;
-{
-long double dk, dn;
-
-if( (p < 0.0L) || (p > 1.0L) )
- goto domerr;
-if( k < 0 )
- return( 1.0L );
-
-if( n < k )
- {
-domerr:
- mtherr( "bdtrcl", DOMAIN );
- return( 0.0L );
- }
-
-if( k == n )
- return( 0.0L );
-dn = n - k;
-if( k == 0 )
- {
- if( p < .01L )
- dk = -expm1l( dn * log1pl(-p) );
- else
- dk = 1.0L - powl( 1.0L-p, dn );
- }
-else
- {
- dk = k + 1;
- dk = incbetl( dk, dn, p );
- }
-return( dk );
-}
-
-
-
-long double bdtrl( k, n, p )
-int k, n;
-long double p;
-{
-long double dk, dn, q;
-
-if( (p < 0.0L) || (p > 1.0L) )
- goto domerr;
-if( (k < 0) || (n < k) )
- {
-domerr:
- mtherr( "bdtrl", DOMAIN );
- return( 0.0L );
- }
-
-if( k == n )
- return( 1.0L );
-
-q = 1.0L - p;
-dn = n - k;
-if( k == 0 )
- {
- dk = powl( q, dn );
- }
-else
- {
- dk = k + 1;
- dk = incbetl( dn, dk, q );
- }
-return( dk );
-}
-
-
-long double bdtril( k, n, y )
-int k, n;
-long double y;
-{
-long double dk, dn, p;
-
-if( (y < 0.0L) || (y > 1.0L) )
- goto domerr;
-if( (k < 0) || (n <= k) )
- {
-domerr:
- mtherr( "bdtril", DOMAIN );
- return( 0.0L );
- }
-
-dn = n - k;
-if( k == 0 )
- {
- if( y > 0.8L )
- p = -expm1l( log1pl(y-1.0L) / dn );
- else
- p = 1.0L - powl( y, 1.0L/dn );
- }
-else
- {
- dk = k + 1;
- p = incbetl( dn, dk, y );
- if( p > 0.5 )
- p = incbil( dk, dn, 1.0L-y );
- else
- p = 1.0 - incbil( dn, dk, y );
- }
-return( p );
-}
+++ /dev/null
-
-/* btdtrl.c
- *
- * Beta distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, btdtrl();
- *
- * y = btdtrl( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the beta density
- * function:
- *
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * P(x) = ---------- | t (1-t) dt
- * - - | |
- * | (a) | (b) -
- * 0
- *
- *
- * The mean value of this distribution is a/(a+b). The variance
- * is ab/[(a+b)^2 (a+b+1)].
- *
- * This function is identical to the incomplete beta integral
- * function, incbetl(a, b, x).
- *
- * The complemented function is
- *
- * 1 - P(1-x) = incbetl( b, a, x );
- *
- *
- * ACCURACY:
- *
- * See incbetl.c.
- *
- */
-\f
-/* btdtrl() */
-
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1995 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-#include <math.h>
-#ifdef ANSIPROT
-extern long double incbetl ( long double, long double, long double );
-#else
-long double incbetl();
-#endif
-
-long double btdtrl( a, b, x )
-long double a, b, x;
-{
-
-return( incbetl( a, b, x ) );
-}
+++ /dev/null
-/* cbrtl.c
- *
- * Cube root, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, cbrtl();
- *
- * y = cbrtl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the cube root of the argument, which may be negative.
- *
- * Range reduction involves determining the power of 2 of
- * the argument. A polynomial of degree 2 applied to the
- * mantissa, and multiplication by the cube root of 1, 2, or 4
- * approximates the root to within about 0.1%. Then Newton's
- * iteration is used three times to converge to an accurate
- * result.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE .125,8 80000 7.0e-20 2.2e-20
- * IEEE exp(+-707) 100000 7.0e-20 2.4e-20
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: January, 1991
-Copyright 1984, 1991 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-static long double CBRT2 = 1.2599210498948731647672L;
-static long double CBRT4 = 1.5874010519681994747517L;
-static long double CBRT2I = 0.79370052598409973737585L;
-static long double CBRT4I = 0.62996052494743658238361L;
-
-#ifdef ANSIPROT
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-#else
-long double frexpl(), ldexpl();
-extern int isnanl();
-#endif
-
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-
-long double cbrtl(x)
-long double x;
-{
-int e, rem, sign;
-long double z;
-
-
-#ifdef NANS
-if(isnanl(x))
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITYL)
- return(x);
-if( x == -INFINITYL)
- return(x);
-#endif
-if( x == 0 )
- return( x );
-if( x > 0 )
- sign = 1;
-else
- {
- sign = -1;
- x = -x;
- }
-
-z = x;
-/* extract power of 2, leaving
- * mantissa between 0.5 and 1
- */
-x = frexpl( x, &e );
-
-/* Approximate cube root of number between .5 and 1,
- * peak relative error = 1.2e-6
- */
-x = (((( 1.3584464340920900529734e-1L * x
- - 6.3986917220457538402318e-1L) * x
- + 1.2875551670318751538055e0L) * x
- - 1.4897083391357284957891e0L) * x
- + 1.3304961236013647092521e0L) * x
- + 3.7568280825958912391243e-1L;
-
-/* exponent divided by 3 */
-if( e >= 0 )
- {
- rem = e;
- e /= 3;
- rem -= 3*e;
- if( rem == 1 )
- x *= CBRT2;
- else if( rem == 2 )
- x *= CBRT4;
- }
-else
- { /* argument less than 1 */
- e = -e;
- rem = e;
- e /= 3;
- rem -= 3*e;
- if( rem == 1 )
- x *= CBRT2I;
- else if( rem == 2 )
- x *= CBRT4I;
- e = -e;
- }
-
-/* multiply by power of 2 */
-x = ldexpl( x, e );
-
-/* Newton iteration */
-
-x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
-x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
-
-if( sign < 0 )
- x = -x;
-return(x);
-}
+++ /dev/null
-/* chdtrl.c
- *
- * Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double df, x, y, chdtrl();
- *
- * y = chdtrl( df, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the left hand tail (from 0 to x)
- * of the Chi square probability density function with
- * v degrees of freedom.
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtr domain x < 0 or v < 1 0.0
- */
-\f/* chdtrcl()
- *
- * Complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double v, x, y, chdtrcl();
- *
- * y = chdtrcl( v, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the right hand tail (from x to
- * infinity) of the Chi square probability density function
- * with v degrees of freedom:
- *
- *
- * inf.
- * -
- * 1 | | v/2-1 -t/2
- * P( x | v ) = ----------- | t e dt
- * v/2 - | |
- * 2 | (v/2) -
- * x
- *
- * where x is the Chi-square variable.
- *
- * The incomplete gamma integral is used, according to the
- * formula
- *
- * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
- *
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtrc domain x < 0 or v < 1 0.0
- */
-\f/* chdtril()
- *
- * Inverse of complemented Chi-square distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double df, x, y, chdtril();
- *
- * x = chdtril( df, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Chi-square argument x such that the integral
- * from x to infinity of the Chi-square density is equal
- * to the given cumulative probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * x/2 = igami( df/2, y );
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * chdtri domain y < 0 or y > 1 0.0
- * v < 1
- *
- */
-\f
-/* chdtr() */
-
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double igamcl ( long double, long double );
-extern long double igaml ( long double, long double );
-extern long double igamil ( long double, long double );
-#else
-long double igamcl(), igaml(), igamil();
-#endif
-
-long double chdtrcl(df,x)
-long double df, x;
-{
-
-if( (x < 0.0L) || (df < 1.0L) )
- {
- mtherr( "chdtrcl", DOMAIN );
- return(0.0L);
- }
-return( igamcl( 0.5L*df, 0.5L*x ) );
-}
-
-
-
-long double chdtrl(df,x)
-long double df, x;
-{
-
-if( (x < 0.0L) || (df < 1.0L) )
- {
- mtherr( "chdtrl", DOMAIN );
- return(0.0L);
- }
-return( igaml( 0.5L*df, 0.5L*x ) );
-}
-
-
-
-long double chdtril( df, y )
-long double df, y;
-{
-long double x;
-
-if( (y < 0.0L) || (y > 1.0L) || (df < 1.0L) )
- {
- mtherr( "chdtril", DOMAIN );
- return(0.0L);
- }
-
-x = igamil( 0.5L * df, y );
-return( 2.0L * x );
-}
+++ /dev/null
-/* clogl.c
- *
- * Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clogl();
- * cmplxl z, w;
- *
- * clogl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns complex logarithm to the base e (2.718...) of
- * the complex argument x.
- *
- * If z = x + iy, r = sqrt( x**2 + y**2 ),
- * then
- * w = log(r) + i arctan(y/x).
- *
- * The arctangent ranges from -PI to +PI.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 7000 8.5e-17 1.9e-17
- * IEEE -10,+10 30000 5.0e-15 1.1e-16
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
- * absolute error 1.0e-16.
- */
-\f
-#include <math.h>
-#ifdef ANSIPROT
-static void cchshl ( long double x, long double *c, long double *s );
-static long double redupil ( long double x );
-static long double ctansl ( cmplxl *z );
-long double cabsl ( cmplxl *x );
-void csqrtl ( cmplxl *x, cmplxl *y );
-void caddl ( cmplxl *x, cmplxl *y, cmplxl *z );
-extern long double fabsl ( long double );
-extern long double sqrtl ( long double );
-extern long double logl ( long double );
-extern long double expl ( long double );
-extern long double atan2l ( long double, long double );
-extern long double coshl ( long double );
-extern long double sinhl ( long double );
-extern long double asinl ( long double );
-extern long double sinl ( long double );
-extern long double cosl ( long double );
-void clogl ( cmplxl *, cmplxl *);
-void casinl ( cmplxl *, cmplxl *);
-#else
-static void cchshl();
-static long double redupil();
-static long double ctansl();
-long double cabsl(), fabsl(), sqrtl();
-lnog double logl(), expl(), atan2l(), coshl(), sinhl();
-long double asinl(), sinl(), cosl();
-void caddl(), csqrtl(), clogl(), casinl();
-#endif
-
-extern long double MAXNUML, MACHEPL, PIL, PIO2L;
-
-void clogl( z, w )
-register cmplxl *z, *w;
-{
-long double p, rr;
-
-/*rr = sqrt( z->r * z->r + z->i * z->i );*/
-rr = cabsl(z);
-p = logl(rr);
-#if ANSIC
-rr = atan2l( z->i, z->r );
-#else
-rr = atan2l( z->r, z->i );
-if( rr > PIL )
- rr -= PIL + PIL;
-#endif
-w->i = rr;
-w->r = p;
-}
-\f/* cexpl()
- *
- * Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexpl();
- * cmplxl z, w;
- *
- * cexpl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the exponential of the complex argument z
- * into the complex result w.
- *
- * If
- * z = x + iy,
- * r = exp(x),
- *
- * then
- *
- * w = r cos y + i r sin y.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8700 3.7e-17 1.1e-17
- * IEEE -10,+10 30000 3.0e-16 8.7e-17
- *
- */
-\f
-void cexpl( z, w )
-register cmplxl *z, *w;
-{
-long double r;
-
-r = expl( z->r );
-w->r = r * cosl( z->i );
-w->i = r * sinl( z->i );
-}
-\f/* csinl()
- *
- * Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csinl();
- * cmplxl z, w;
- *
- * csinl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = sin x cosh y + i cos x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 5.3e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- * Also tested by csin(casin(z)) = z.
- *
- */
-\f
-void csinl( z, w )
-register cmplxl *z, *w;
-{
-long double ch, sh;
-
-cchshl( z->i, &ch, &sh );
-w->r = sinl( z->r ) * ch;
-w->i = cosl( z->r ) * sh;
-}
-
-
-
-/* calculate cosh and sinh */
-
-static void cchshl( x, c, s )
-long double x, *c, *s;
-{
-long double e, ei;
-
-if( fabsl(x) <= 0.5L )
- {
- *c = coshl(x);
- *s = sinhl(x);
- }
-else
- {
- e = expl(x);
- ei = 0.5L/e;
- e = 0.5L * e;
- *s = e - ei;
- *c = e + ei;
- }
-}
-
-\f/* ccosl()
- *
- * Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccosl();
- * cmplxl z, w;
- *
- * ccosl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * w = cos x cosh y - i sin x sinh y.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 8400 4.5e-17 1.3e-17
- * IEEE -10,+10 30000 3.8e-16 1.0e-16
- */
-\f
-void ccosl( z, w )
-register cmplxl *z, *w;
-{
-long double ch, sh;
-
-cchshl( z->i, &ch, &sh );
-w->r = cosl( z->r ) * ch;
-w->i = -sinl( z->r ) * sh;
-}
-\f/* ctanl()
- *
- * Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctanl();
- * cmplxl z, w;
- *
- * ctanl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x + i sinh 2y
- * w = --------------------.
- * cos 2x + cosh 2y
- *
- * On the real axis the denominator is zero at odd multiples
- * of PI/2. The denominator is evaluated by its Taylor
- * series near these points.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 7.1e-17 1.6e-17
- * IEEE -10,+10 30000 7.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
- */
-\f
-void ctanl( z, w )
-register cmplxl *z, *w;
-{
-long double d;
-
-d = cosl( 2.0L * z->r ) + coshl( 2.0L * z->i );
-
-if( fabsl(d) < 0.25L )
- d = ctansl(z);
-
-if( d == 0.0L )
- {
- mtherr( "ctan", OVERFLOW );
- w->r = MAXNUML;
- w->i = MAXNUML;
- return;
- }
-
-w->r = sinl( 2.0L * z->r ) / d;
-w->i = sinhl( 2.0L * z->i ) / d;
-}
-\f/* ccotl()
- *
- * Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccotl();
- * cmplxl z, w;
- *
- * ccotl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- *
- * sin 2x - i sinh 2y
- * w = --------------------.
- * cosh 2y - cos 2x
- *
- * On the real axis, the denominator has zeros at even
- * multiples of PI/2. Near these points it is evaluated
- * by a Taylor series.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 3000 6.5e-17 1.6e-17
- * IEEE -10,+10 30000 9.2e-16 1.2e-16
- * Also tested by ctan * ccot = 1 + i0.
- */
-\f
-void ccotl( z, w )
-register cmplxl *z, *w;
-{
-long double d;
-
-d = coshl(2.0L * z->i) - cosl(2.0L * z->r);
-
-if( fabsl(d) < 0.25L )
- d = ctansl(z);
-
-if( d == 0.0L )
- {
- mtherr( "ccot", OVERFLOW );
- w->r = MAXNUML;
- w->i = MAXNUML;
- return;
- }
-
-w->r = sinl( 2.0L * z->r ) / d;
-w->i = -sinhl( 2.0L * z->i ) / d;
-}
-\f
-/* Program to subtract nearest integer multiple of PI */
-/* extended precision value of PI: */
-#ifdef UNK
-static double DP1 = 3.14159265160560607910E0;
-static double DP2 = 1.98418714791870343106E-9;
-static double DP3 = 1.14423774522196636802E-17;
-#endif
-
-#ifdef DEC
-static unsigned short P1[] = {0040511,0007732,0120000,0000000,};
-static unsigned short P2[] = {0031010,0055060,0100000,0000000,};
-static unsigned short P3[] = {0022123,0011431,0105056,0001560,};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef IBMPC
-static unsigned short P1[] = {0x0000,0x5400,0x21fb,0x4009};
-static unsigned short P2[] = {0x0000,0x1000,0x0b46,0x3e21};
-static unsigned short P3[] = {0xc06e,0x3145,0x6263,0x3c6a};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-#ifdef MIEEE
-static unsigned short P1[] = {
-0x4009,0x21fb,0x5400,0x0000
-};
-static unsigned short P2[] = {
-0x3e21,0x0b46,0x1000,0x0000
-};
-static unsigned short P3[] = {
-0x3c6a,0x6263,0x3145,0xc06e
-};
-#define DP1 *(double *)P1
-#define DP2 *(double *)P2
-#define DP3 *(double *)P3
-#endif
-
-static long double redupil(x)
-long double x;
-{
-long double t;
-long i;
-
-t = x/PIL;
-if( t >= 0.0L )
- t += 0.5L;
-else
- t -= 0.5L;
-
-i = t; /* the multiple */
-t = i;
-t = ((x - t * DP1) - t * DP2) - t * DP3;
-return(t);
-}
-\f
-/* Taylor series expansion for cosh(2y) - cos(2x) */
-
-static long double ctansl(z)
-cmplxl *z;
-{
-long double f, x, x2, y, y2, rn, t;
-long double d;
-
-x = fabsl( 2.0L * z->r );
-y = fabsl( 2.0L * z->i );
-
-x = redupil(x);
-
-x = x * x;
-y = y * y;
-x2 = 1.0L;
-y2 = 1.0L;
-f = 1.0L;
-rn = 0.0;
-d = 0.0;
-do
- {
- rn += 1.0L;
- f *= rn;
- rn += 1.0L;
- f *= rn;
- x2 *= x;
- y2 *= y;
- t = y2 + x2;
- t /= f;
- d += t;
-
- rn += 1.0L;
- f *= rn;
- rn += 1.0L;
- f *= rn;
- x2 *= x;
- y2 *= y;
- t = y2 - x2;
- t /= f;
- d += t;
- }
-while( fabsl(t/d) > MACHEPL );
-return(d);
-}
-\f/* casinl()
- *
- * Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casinl();
- * cmplxl z, w;
- *
- * casinl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- * 2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 10100 2.1e-15 3.4e-16
- * IEEE -10,+10 30000 2.2e-14 2.7e-15
- * Larger relative error can be observed for z near zero.
- * Also tested by csin(casin(z)) = z.
- */
-\f
-void casinl( z, w )
-cmplxl *z, *w;
-{
-static cmplxl ca, ct, zz, z2;
-long double x, y;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0L )
- {
- if( fabsl(x) > 1.0L )
- {
- w->r = PIO2L;
- w->i = 0.0L;
- mtherr( "casinl", DOMAIN );
- }
- else
- {
- w->r = asinl(x);
- w->i = 0.0L;
- }
- return;
- }
-
-/* Power series expansion */
-/*
-b = cabsl(z);
-if( b < 0.125L )
-{
-z2.r = (x - y) * (x + y);
-z2.i = 2.0L * x * y;
-
-cn = 1.0L;
-n = 1.0L;
-ca.r = x;
-ca.i = y;
-sum.r = x;
-sum.i = y;
-do
- {
- ct.r = z2.r * ca.r - z2.i * ca.i;
- ct.i = z2.r * ca.i + z2.i * ca.r;
- ca.r = ct.r;
- ca.i = ct.i;
-
- cn *= n;
- n += 1.0L;
- cn /= n;
- n += 1.0L;
- b = cn/n;
-
- ct.r *= b;
- ct.i *= b;
- sum.r += ct.r;
- sum.i += ct.i;
- b = fabsl(ct.r) + fabs(ct.i);
- }
-while( b > MACHEPL );
-w->r = sum.r;
-w->i = sum.i;
-return;
-}
-*/
-
-
-ca.r = x;
-ca.i = y;
-
-ct.r = -ca.i; /* iz */
-ct.i = ca.r;
-
- /* sqrt( 1 - z*z) */
-/* cmul( &ca, &ca, &zz ) */
-zz.r = (ca.r - ca.i) * (ca.r + ca.i); /*x * x - y * y */
-zz.i = 2.0L * ca.r * ca.i;
-
-zz.r = 1.0L - zz.r;
-zz.i = -zz.i;
-csqrtl( &zz, &z2 );
-
-caddl( &z2, &ct, &zz );
-clogl( &zz, &zz );
-w->r = zz.i; /* mult by 1/i = -i */
-w->i = -zz.r;
-return;
-}
-\f/* cacosl()
- *
- * Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacosl();
- * cmplxl z, w;
- *
- * cacosl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z = PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5200 1.6e-15 2.8e-16
- * IEEE -10,+10 30000 1.8e-14 2.2e-15
- */
-\f
-void cacosl( z, w )
-cmplxl *z, *w;
-{
-
-casinl( z, w );
-w->r = PIO2L - w->r;
-w->i = -w->i;
-}
-\f/* catanl()
- *
- * Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catanl();
- * cmplxl z, w;
- *
- * catanl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * If
- * z = x + iy,
- *
- * then
- * 1 ( 2x )
- * Re w = - arctan(-----------) + k PI
- * 2 ( 2 2)
- * (1 - x - y )
- *
- * ( 2 2)
- * 1 (x + (y+1) )
- * Im w = - log(------------)
- * 4 ( 2 2)
- * (x + (y-1) )
- *
- * Where k is an arbitrary integer.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 5900 1.3e-16 7.8e-18
- * IEEE -10,+10 30000 2.3e-15 8.5e-17
- * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
- * had peak relative error 1.5e-16, rms relative error
- * 2.9e-17. See also clog().
- */
-\f
-void catanl( z, w )
-cmplxl *z, *w;
-{
-long double a, t, x, x2, y;
-
-x = z->r;
-y = z->i;
-
-if( (x == 0.0L) && (y > 1.0L) )
- goto ovrf;
-
-x2 = x * x;
-a = 1.0L - x2 - (y * y);
-if( a == 0.0L )
- goto ovrf;
-
-#if ANSIC
-t = atan2l( 2.0L * x, a ) * 0.5L;
-#else
-t = atan2l( a, 2.0 * x ) * 0.5L;
-#endif
-w->r = redupil( t );
-
-t = y - 1.0L;
-a = x2 + (t * t);
-if( a == 0.0L )
- goto ovrf;
-
-t = y + 1.0L;
-a = (x2 + (t * t))/a;
-w->i = logl(a)/4.0;
-return;
-
-ovrf:
-mtherr( "catanl", OVERFLOW );
-w->r = MAXNUML;
-w->i = MAXNUML;
-}
+++ /dev/null
-/* cmplxl.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * long double r; real part
- * long double i; imaginary part
- * }cmplxl;
- *
- * cmplxl *a, *b, *c;
- *
- * caddl( a, b, c ); c = b + a
- * csubl( a, b, c ); c = b - a
- * cmull( a, b, c ); c = b * a
- * cdivl( a, b, c ); c = b / a
- * cnegl( c ); c = -c
- * cmovl( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
-\f * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * DEC cadd 10000 1.4e-17 3.4e-18
- * IEEE cadd 100000 1.1e-16 2.7e-17
- * DEC csub 10000 1.4e-17 4.5e-18
- * IEEE csub 100000 1.1e-16 3.4e-17
- * DEC cmul 3000 2.3e-17 8.7e-18
- * IEEE cmul 100000 2.1e-16 6.9e-17
- * DEC cdiv 18000 4.9e-17 1.3e-17
- * IEEE cdiv 100000 3.7e-16 1.1e-16
- */
-\f/* cmplx.c
- * complex number arithmetic
- */
-
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-/*
-typedef struct
- {
- long double r;
- long double i;
- }cmplxl;
-*/
-
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double cabsl ( cmplxl * );
-extern long double sqrtl ( long double );
-extern long double atan2l ( long double, long double );
-extern long double cosl ( long double );
-extern long double sinl ( long double );
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-void cdivl ( cmplxl *, cmplxl *, cmplxl * );
-void caddl ( cmplxl *, cmplxl *, cmplxl * );
-#else
-long double fabsl(), cabsl(), sqrtl(), atan2l(), cosl(), sinl();
-long double frexpl(), ldexpl();
-int isnanl();
-void cdivl(), caddl();
-#endif
-
-
-extern double MAXNUML, MACHEPL, PIL, PIO2L, INFINITYL, NANL;
-cmplx czerol = {0.0L, 0.0L};
-cmplx conel = {1.0L, 0.0L};
-
-
-/* c = b + a */
-
-void caddl( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-
-c->r = b->r + a->r;
-c->i = b->i + a->i;
-}
-
-
-/* c = b - a */
-
-void csubl( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-
-c->r = b->r - a->r;
-c->i = b->i - a->i;
-}
-
-/* c = b * a */
-
-void cmull( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-long double y;
-
-y = b->r * a->r - b->i * a->i;
-c->i = b->r * a->i + b->i * a->r;
-c->r = y;
-}
-
-
-
-/* c = b / a */
-
-void cdivl( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-long double y, p, q, w;
-
-
-y = a->r * a->r + a->i * a->i;
-p = b->r * a->r + b->i * a->i;
-q = b->i * a->r - b->r * a->i;
-
-if( y < 1.0L )
- {
- w = MAXNUML * y;
- if( (fabsl(p) > w) || (fabsl(q) > w) || (y == 0.0L) )
- {
- c->r = INFINITYL;
- c->i = INFINITYL;
- mtherr( "cdivl", OVERFLOW );
- return;
- }
- }
-c->r = p/y;
-c->i = q/y;
-}
-
-
-/* b = a
- Caution, a `short' is assumed to be 16 bits wide. */
-
-void cmovl( a, b )
-void *a, *b;
-{
-register short *pa, *pb;
-int i;
-
-pa = (short *) a;
-pb = (short *) b;
-i = 16;
-do
- *pb++ = *pa++;
-while( --i );
-}
-
-
-void cnegl( a )
-register cmplxl *a;
-{
-
-a->r = -a->r;
-a->i = -a->i;
-}
-
-/* cabsl()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * long double cabsl();
- * cmplxl z;
- * long double a;
- *
- * a = cabs( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -30,+30 30000 3.2e-17 9.2e-18
- * IEEE -10,+10 100000 2.7e-16 6.9e-17
- */
-\f
-
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/*
-typedef struct
- {
- long double r;
- long double i;
- }cmplxl;
-*/
-
-#ifdef UNK
-#define PRECL 32
-#define MAXEXPL 16384
-#define MINEXPL -16384
-#endif
-#ifdef IBMPC
-#define PRECL 32
-#define MAXEXPL 16384
-#define MINEXPL -16384
-#endif
-#ifdef MIEEE
-#define PRECL 32
-#define MAXEXPL 16384
-#define MINEXPL -16384
-#endif
-
-
-long double cabsl( z )
-register cmplxl *z;
-{
-long double x, y, b, re, im;
-int ex, ey, e;
-
-#ifdef INFINITIES
-/* Note, cabs(INFINITY,NAN) = INFINITY. */
-if( z->r == INFINITYL || z->i == INFINITYL
- || z->r == -INFINITYL || z->i == -INFINITYL )
- return( INFINITYL );
-#endif
-
-#ifdef NANS
-if( isnanl(z->r) )
- return(z->r);
-if( isnanl(z->i) )
- return(z->i);
-#endif
-
-re = fabsl( z->r );
-im = fabsl( z->i );
-
-if( re == 0.0 )
- return( im );
-if( im == 0.0 )
- return( re );
-
-/* Get the exponents of the numbers */
-x = frexpl( re, &ex );
-y = frexpl( im, &ey );
-
-/* Check if one number is tiny compared to the other */
-e = ex - ey;
-if( e > PRECL )
- return( re );
-if( e < -PRECL )
- return( im );
-
-/* Find approximate exponent e of the geometric mean. */
-e = (ex + ey) >> 1;
-
-/* Rescale so mean is about 1 */
-x = ldexpl( re, -e );
-y = ldexpl( im, -e );
-
-/* Hypotenuse of the right triangle */
-b = sqrtl( x * x + y * y );
-
-/* Compute the exponent of the answer. */
-y = frexpl( b, &ey );
-ey = e + ey;
-
-/* Check it for overflow and underflow. */
-if( ey > MAXEXPL )
- {
- mtherr( "cabsl", OVERFLOW );
- return( INFINITYL );
- }
-if( ey < MINEXPL )
- return(0.0L);
-
-/* Undo the scaling */
-b = ldexpl( b, e );
-return( b );
-}
-\f/* csqrtl()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrtl();
- * cmplxl z, w;
- *
- * csqrtl( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The root chosen
- * is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC -10,+10 25000 3.2e-17 9.6e-18
- * IEEE -10,+10 100000 3.2e-16 7.7e-17
- *
- * 2
- * Also tested by csqrt( z ) = z, and tested by arguments
- * close to the real axis.
- */
-\f
-
-void csqrtl( z, w )
-cmplxl *z, *w;
-{
-cmplxl q, s;
-long double x, y, r, t;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0L )
- {
- if( x < 0.0L )
- {
- w->r = 0.0L;
- w->i = sqrtl(-x);
- return;
- }
- else
- {
- w->r = sqrtl(x);
- w->i = 0.0L;
- return;
- }
- }
-
-
-if( x == 0.0L )
- {
- r = fabsl(y);
- r = sqrtl(0.5L*r);
- if( y > 0.0L )
- w->r = r;
- else
- w->r = -r;
- w->i = r;
- return;
- }
-
-/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
- * The relative error in the first term is approximately y^2/12x^2 .
- */
-if( (fabsl(y) < 2.e-4L * fabsl(x))
- && (x > 0) )
- {
- t = 0.25L*y*(y/x);
- }
-else
- {
- r = cabsl(z);
- t = 0.5L*(r - x);
- }
-
-r = sqrtl(t);
-q.i = r;
-q.r = y/(2.0L*r);
-/* Heron iteration in complex arithmetic */
-cdivl( &q, z, &s );
-caddl( &q, &s, w );
-w->r *= 0.5L;
-w->i *= 0.5L;
-
-cdivl( &q, z, &s );
-caddl( &q, &s, w );
-w->r *= 0.5L;
-w->i *= 0.5L;
-}
-
-
-long double hypotl( x, y )
-long double x, y;
-{
-cmplxl z;
-
-z.r = x;
-z.i = y;
-return( cabsl(&z) );
-}
+++ /dev/null
-/* coshl.c
- *
- * Hyperbolic cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, coshl();
- *
- * y = coshl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic cosine of argument in the range MINLOGL to
- * MAXLOGL.
- *
- * cosh(x) = ( exp(x) + exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-10000 30000 1.1e-19 2.8e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cosh overflow |x| > MAXLOGL+LOGE2L INFINITYL
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1985, 1991, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-extern long double MAXLOGL, MAXNUML, LOGE2L;
-#ifdef ANSIPROT
-extern long double expl ( long double );
-extern int isnanl ( long double );
-#else
-long double expl(), isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double coshl(x)
-long double x;
-{
-long double y;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-if( x < 0 )
- x = -x;
-if( x > (MAXLOGL + LOGE2L) )
- {
- mtherr( "coshl", OVERFLOW );
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- return( MAXNUML );
-#endif
- }
-if( x >= (MAXLOGL - LOGE2L) )
- {
- y = expl(0.5L * x);
- y = (0.5L * y) * y;
- return(y);
- }
-y = expl(x);
-y = 0.5L * (y + 1.0L / y);
-return( y );
-}
+++ /dev/null
-/* econst.c */
-/* e type constants used by high precision check routines */
-
-#include "ehead.h"
-
-
-#if NE == 10
-/* 0.0 */
-unsigned short ezero[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};
-
-/* 5.0E-1 */
-unsigned short ehalf[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,};
-
-/* 1.0E0 */
-unsigned short eone[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
-
-/* 2.0E0 */
-unsigned short etwo[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,};
-
-/* 3.2E1 */
-unsigned short e32[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,};
-
-/* 6.93147180559945309417232121458176568075500134360255E-1 */
-unsigned short elog2[NE] =
- {0x40f3, 0xf6af, 0x03f2, 0xb398,
- 0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};
-
-/* 1.41421356237309504880168872420969807856967187537695E0 */
-unsigned short esqrt2[NE] =
- {0x1d6f, 0xbe9f, 0x754a, 0x89b3,
- 0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};
-
-/* 3.14159265358979323846264338327950288419716939937511E0 */
-unsigned short epi[NE] =
- {0x2902, 0x1cd1, 0x80dc, 0x628b,
- 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
-
-/* 5.7721566490153286060651209008240243104215933593992E-1 */
-unsigned short eeul[NE] = {
-0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
-
-#else
-
-/* 0.0 */
-unsigned short ezero[NE] = {
-0, 0000000,0000000,0000000,0000000,0000000,};
-/* 5.0E-1 */
-unsigned short ehalf[NE] = {
-0, 0000000,0000000,0000000,0100000,0x3ffe,};
-/* 1.0E0 */
-unsigned short eone[NE] = {
-0, 0000000,0000000,0000000,0100000,0x3fff,};
-/* 2.0E0 */
-unsigned short etwo[NE] = {
-0, 0000000,0000000,0000000,0100000,0040000,};
-/* 3.2E1 */
-unsigned short e32[NE] = {
-0, 0000000,0000000,0000000,0100000,0040004,};
-/* 6.93147180559945309417232121458176568075500134360255E-1 */
-unsigned short elog2[NE] = {
-0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,};
-/* 1.41421356237309504880168872420969807856967187537695E0 */
-unsigned short esqrt2[NE] = {
-0x597e,0x6484,0174736,0171463,0132404,0x3fff,};
-/* 2/sqrt(PI) =
- * 1.12837916709551257389615890312154517168810125865800E0 */
-unsigned short eoneopi[NE] = {
-0x71d5,0x688d,0012333,0135202,0110156,0x3fff,};
-/* 3.14159265358979323846264338327950288419716939937511E0 */
-unsigned short epi[NE] = {
-0xc4c6,0xc234,0020550,0155242,0144417,0040000,};
-/* 5.7721566490153286060651209008240243104215933593992E-1 */
-unsigned short eeul[NE] = {
-0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
-#endif
-extern unsigned short ezero[];
-extern unsigned short ehalf[];
-extern unsigned short eone[];
-extern unsigned short etwo[];
-extern unsigned short e32[];
-extern unsigned short elog2[];
-extern unsigned short esqrt2[];
-extern unsigned short eoneopi[];
-extern unsigned short epi[];
-extern unsigned short eeul[];
-
+++ /dev/null
-
-/* Include file for extended precision arithmetic programs.
- */
-
-/* Number of 16 bit words in external x type format */
-#define NE 6
-/* #define NE 10 */
-
-/* Number of 16 bit words in internal format */
-#define NI (NE+3)
-
-/* Array offset to exponent */
-#define E 1
-
-/* Array offset to high guard word */
-#define M 2
-
-/* Number of bits of precision */
-#define NBITS ((NI-4)*16)
-
-/* Maximum number of decimal digits in ASCII conversion
- * = NBITS*log10(2)
- */
-#define NDEC (NBITS*8/27)
-
-/* The exponent of 1.0 */
-#define EXONE (0x3fff)
-
-
-void eadd(), esub(), emul(), ediv();
-int ecmp(), enormlz(), eshift();
-void eshup1(), eshup8(), eshup6(), eshdn1(), eshdn8(), eshdn6();
-void eabs(), eneg(), emov(), eclear(), einfin(), efloor();
-void eldexp(), efrexp(), eifrac(), ltoe();
-void esqrt(), elog(), eexp(), etanh(), epow();
-void asctoe(), asctoe24(), asctoe53(), asctoe64();
-void etoasc(), e24toasc(), e53toasc(), e64toasc();
-void etoe64(), etoe53(), etoe24(), e64toe(), e53toe(), e24toe();
-int mtherr();
-
-extern unsigned short ezero[], ehalf[], eone[], etwo[];
-extern unsigned short elog2[], esqrt2[];
-
-
-/* by Stephen L. Moshier. */
+++ /dev/null
-/* elliel.c
- *
- * Incomplete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double phi, m, y, elliel();
- *
- * y = elliel( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * phi
- * -
- * | |
- * | 2
- * E(phi_\m) = | sqrt( 1 - m sin t ) dt
- * |
- * | |
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random arguments with phi in [-10, 10] and m in
- * [0, 1].
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 50000 2.7e-18 2.3e-19
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1984, 1987, 1993, 1995 by Stephen L. Moshier
-*/
-
-/* Incomplete elliptic integral of second kind */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double fabsl ( long double );
-extern long double logl ( long double );
-extern long double sinl ( long double );
-extern long double tanl ( long double );
-extern long double atanl ( long double );
-extern long double floorl ( long double );
-extern long double ellpel ( long double );
-extern long double ellpkl ( long double );
-long double elliel ( long double, long double );
-#else
-long double sqrtl(), fabsl(), logl(), sinl(), tanl(), atanl(), floorl();
-long double ellpel(), ellpkl(), elliel();
-#endif
-extern long double PIL, PIO2L, MACHEPL;
-
-
-long double elliel( phi, m )
-long double phi, m;
-{
-long double a, b, c, e, temp, lphi, t, E;
-int d, mod, npio2, sign;
-
-if( m == 0.0L )
- return( phi );
-lphi = phi;
-npio2 = floorl( lphi/PIO2L );
-if( npio2 & 1 )
- npio2 += 1;
-lphi = lphi - npio2 * PIO2L;
-if( lphi < 0.0L )
- {
- lphi = -lphi;
- sign = -1;
- }
-else
- {
- sign = 1;
- }
-a = 1.0L - m;
-E = ellpel( a );
-if( a == 0.0L )
- {
- temp = sinl( lphi );
- goto done;
- }
-t = tanl( lphi );
-b = sqrtl(a);
-if( fabsl(t) > 10.0L )
- {
- /* Transform the amplitude */
- e = 1.0L/(b*t);
- /* ... but avoid multiple recursions. */
- if( fabsl(e) < 10.0L )
- {
- e = atanl(e);
- temp = E + m * sinl( lphi ) * sinl( e ) - elliel( e, m );
- goto done;
- }
- }
-c = sqrtl(m);
-a = 1.0L;
-d = 1;
-e = 0.0L;
-mod = 0;
-
-while( fabsl(c/a) > MACHEPL )
- {
- temp = b/a;
- lphi = lphi + atanl(t*temp) + mod * PIL;
- mod = (lphi + PIO2L)/PIL;
- t = t * ( 1.0L + temp )/( 1.0L - temp * t * t );
- c = 0.5L*( a - b );
- temp = sqrtl( a * b );
- a = 0.5L*( a + b );
- b = temp;
- d += d;
- e += c * sinl(lphi);
- }
-
-temp = E / ellpkl( 1.0L - m );
-temp *= (atanl(t) + mod * PIL)/(d * a);
-temp += e;
-
-done:
-
-if( sign < 0 )
- temp = -temp;
-temp += npio2 * E;
-return( temp );
-}
+++ /dev/null
-/* ellikl.c
- *
- * Incomplete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double phi, m, y, ellikl();
- *
- * y = ellikl( phi, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * phi
- * -
- * | |
- * | dt
- * F(phi_\m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * of amplitude phi and modulus m, using the arithmetic -
- * geometric mean algorithm.
- *
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points with m in [0, 1] and phi as indicated.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 30000 3.6e-18 4.1e-19
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1984, 1987, 1995 by Stephen L. Moshier
-*/
-
-/* Incomplete elliptic integral of first kind */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double fabsl ( long double );
-extern long double logl ( long double );
-extern long double tanl ( long double );
-extern long double atanl ( long double );
-extern long double floorl ( long double );
-extern long double ellpkl ( long double );
-long double ellikl ( long double, long double );
-#else
-long double sqrtl(), fabsl(), logl(), tanl(), atanl(), floorl(), ellpkl();
-long double ellikl();
-#endif
-extern long double PIL, PIO2L, MACHEPL, MAXNUML;
-
-long double ellikl( phi, m )
-long double phi, m;
-{
-long double a, b, c, e, temp, t, K;
-int d, mod, sign, npio2;
-
-if( m == 0.0L )
- return( phi );
-a = 1.0L - m;
-if( a == 0.0L )
- {
- if( fabsl(phi) >= PIO2L )
- {
- mtherr( "ellikl", SING );
- return( MAXNUML );
- }
- return( logl( tanl( 0.5L*(PIO2L + phi) ) ) );
- }
-npio2 = floorl( phi/PIO2L );
-if( npio2 & 1 )
- npio2 += 1;
-if( npio2 )
- {
- K = ellpkl( a );
- phi = phi - npio2 * PIO2L;
- }
-else
- K = 0.0L;
-if( phi < 0.0L )
- {
- phi = -phi;
- sign = -1;
- }
-else
- sign = 0;
-b = sqrtl(a);
-t = tanl( phi );
-if( fabsl(t) > 10.0L )
- {
- /* Transform the amplitude */
- e = 1.0L/(b*t);
- /* ... but avoid multiple recursions. */
- if( fabsl(e) < 10.0L )
- {
- e = atanl(e);
- if( npio2 == 0 )
- K = ellpkl( a );
- temp = K - ellikl( e, m );
- goto done;
- }
- }
-a = 1.0L;
-c = sqrtl(m);
-d = 1;
-mod = 0;
-
-while( fabsl(c/a) > MACHEPL )
- {
- temp = b/a;
- phi = phi + atanl(t*temp) + mod * PIL;
- mod = (phi + PIO2L)/PIL;
- t = t * ( 1.0L + temp )/( 1.0L - temp * t * t );
- c = 0.5L * ( a - b );
- temp = sqrtl( a * b );
- a = 0.5L * ( a + b );
- b = temp;
- d += d;
- }
-
-temp = (atanl(t) + mod * PIL)/(d * a);
-
-done:
-if( sign < 0 )
- temp = -temp;
-temp += npio2 * K;
-return( temp );
-}
+++ /dev/null
-/* ellpel.c
- *
- * Complete elliptic integral of the second kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double m1, y, ellpel();
- *
- * y = ellpel( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- * pi/2
- * -
- * | | 2
- * E(m) = | sqrt( 1 - m sin t ) dt
- * | |
- * -
- * 0
- *
- * Where m = 1 - m1, using the approximation
- *
- * P(x) - x log x Q(x).
- *
- * Though there are no singularities, the argument m1 is used
- * rather than m for compatibility with ellpk().
- *
- * E(1) = 1; E(0) = pi/2.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 1 10000 1.1e-19 3.5e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpel domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpe.c */
-
-/* Elliptic integral of second kind */
-
-/*
-Cephes Math Library, Release 2.3: October, 1995
-Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#if UNK
-static long double P[12] = {
- 3.198937812032341294902E-5L,
- 7.742523238588775116241E-4L,
- 4.140384701571542000550E-3L,
- 7.963509564694454269086E-3L,
- 7.280911706839967541799E-3L,
- 5.044067167184043853799E-3L,
- 5.076832243257395296304E-3L,
- 7.155775630578315248130E-3L,
- 1.154485760526450950611E-2L,
- 2.183137319801117971860E-2L,
- 5.680519271556930583433E-2L,
- 4.431471805599467050354E-1L,
-};
-static long double Q[12] = {
- 6.393938134301205485085E-6L,
- 2.741404591220851603273E-4L,
- 2.480876752984331133799E-3L,
- 8.770638497964078750003E-3L,
- 1.676835725889463343319E-2L,
- 2.281970801531577700830E-2L,
- 2.767367465121309044166E-2L,
- 3.364167778770018154356E-2L,
- 4.272453406734691973083E-2L,
- 5.859374951483909267451E-2L,
- 9.374999999923942267270E-2L,
- 2.499999999999998643587E-1L,
-};
-#endif
-#if IBMPC
-static short P[] = {
-0x7a78,0x5a02,0x554d,0x862c,0x3ff0, XPD
-0x34db,0xa965,0x31a3,0xcaf7,0x3ff4, XPD
-0xca6c,0x6c00,0x1071,0x87ac,0x3ff7, XPD
-0x4cdb,0x125d,0x6149,0x8279,0x3ff8, XPD
-0xadbd,0x3d8f,0xb6d5,0xee94,0x3ff7, XPD
-0x8189,0xcd0e,0xb3c2,0xa548,0x3ff7, XPD
-0x32b5,0xdd64,0x8e39,0xa65b,0x3ff7, XPD
-0x0344,0xc9db,0xff27,0xea7a,0x3ff7, XPD
-0xba2d,0x806a,0xa476,0xbd26,0x3ff8, XPD
-0xc3e0,0x30fa,0xb53d,0xb2d7,0x3ff9, XPD
-0x23b8,0x4d33,0x8fcf,0xe8ac,0x3ffa, XPD
-0xbc79,0xa39f,0x2fef,0xe2e4,0x3ffd, XPD
-};
-static short Q[] = {
-0x89f1,0xe234,0x82a6,0xd68b,0x3fed, XPD
-0x202a,0x96b3,0x8273,0x8fba,0x3ff3, XPD
-0xc183,0xfc45,0x3484,0xa296,0x3ff6, XPD
-0x683e,0xe201,0xb960,0x8fb2,0x3ff8, XPD
-0x721a,0x1b6a,0xcb41,0x895d,0x3ff9, XPD
-0x4eee,0x295f,0x6574,0xbaf0,0x3ff9, XPD
-0x3ade,0xc98f,0xe6f2,0xe2b3,0x3ff9, XPD
-0xd470,0x1784,0xdb1e,0x89cb,0x3ffa, XPD
-0xa649,0xe5c1,0xebc8,0xaeff,0x3ffa, XPD
-0x84c0,0xa8f5,0xffde,0xefff,0x3ffa, XPD
-0x5506,0xf94f,0xffff,0xbfff,0x3ffb, XPD
-0xd8e7,0xffff,0xffff,0xffff,0x3ffc, XPD
-};
-#endif
-#if MIEEE
-static long P[36] = {
-0x3ff00000,0x862c554d,0x5a027a78,
-0x3ff40000,0xcaf731a3,0xa96534db,
-0x3ff70000,0x87ac1071,0x6c00ca6c,
-0x3ff80000,0x82796149,0x125d4cdb,
-0x3ff70000,0xee94b6d5,0x3d8fadbd,
-0x3ff70000,0xa548b3c2,0xcd0e8189,
-0x3ff70000,0xa65b8e39,0xdd6432b5,
-0x3ff70000,0xea7aff27,0xc9db0344,
-0x3ff80000,0xbd26a476,0x806aba2d,
-0x3ff90000,0xb2d7b53d,0x30fac3e0,
-0x3ffa0000,0xe8ac8fcf,0x4d3323b8,
-0x3ffd0000,0xe2e42fef,0xa39fbc79,
-};
-static long Q[36] = {
-0x3fed0000,0xd68b82a6,0xe23489f1,
-0x3ff30000,0x8fba8273,0x96b3202a,
-0x3ff60000,0xa2963484,0xfc45c183,
-0x3ff80000,0x8fb2b960,0xe201683e,
-0x3ff90000,0x895dcb41,0x1b6a721a,
-0x3ff90000,0xbaf06574,0x295f4eee,
-0x3ff90000,0xe2b3e6f2,0xc98f3ade,
-0x3ffa0000,0x89cbdb1e,0x1784d470,
-0x3ffa0000,0xaeffebc8,0xe5c1a649,
-0x3ffa0000,0xefffffde,0xa8f584c0,
-0x3ffb0000,0xbfffffff,0xf94f5506,
-0x3ffc0000,0xffffffff,0xffffd8e7,
-};
-#endif
-
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double logl ( long double );
-#else
-long double polevll(), logl();
-#endif
-
-long double ellpel(x)
-long double x;
-{
-
-if( (x <= 0.0L) || (x > 1.0L) )
- {
- if( x == 0.0L )
- return( 1.0L );
- mtherr( "ellpel", DOMAIN );
- return( 0.0L );
- }
-return( 1.0L + x * polevll(x,P,11) - logl(x) * (x * polevll(x,Q,11)) );
-}
+++ /dev/null
-/* ellpjl.c
- *
- * Jacobian Elliptic Functions
- *
- *
- *
- * SYNOPSIS:
- *
- * long double u, m, sn, cn, dn, phi;
- * int ellpjl();
- *
- * ellpjl( u, m, _&sn, _&cn, _&dn, _&phi );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
- * and dn(u|m) of parameter m between 0 and 1, and real
- * argument u.
- *
- * These functions are periodic, with quarter-period on the
- * real axis equal to the complete elliptic integral
- * ellpk(1.0-m).
- *
- * Relation to incomplete elliptic integral:
- * If u = ellik(phi,m), then sn(u|m) = sin(phi),
- * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
- *
- * Computation is by means of the arithmetic-geometric mean
- * algorithm, except when m is within 1e-12 of 0 or 1. In the
- * latter case with m close to 1, the approximation applies
- * only for phi < pi/2.
- *
- * ACCURACY:
- *
- * Tested at random points with u between 0 and 10, m between
- * 0 and 1.
- *
- * Absolute error (* = relative error):
- * arithmetic function # trials peak rms
- * IEEE sn 10000 1.7e-18 2.3e-19
- * IEEE cn 20000 1.6e-18 2.2e-19
- * IEEE dn 10000 4.7e-15 2.7e-17
- * IEEE phi 10000 4.0e-19* 6.6e-20*
- *
- * Accuracy deteriorates when u is large.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1984, 1987, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double fabsl ( long double );
-extern long double sinl ( long double );
-extern long double cosl ( long double );
-extern long double asinl ( long double );
-extern long double tanhl ( long double );
-extern long double sinhl ( long double );
-extern long double coshl ( long double );
-extern long double atanl ( long double );
-extern long double expl ( long double );
-#else
-long double sqrtl(), fabsl(), sinl(), cosl(), asinl(), tanhl();
-long double sinhl(), coshl(), atanl(), expl();
-#endif
-extern long double PIO2L, MACHEPL;
-
-int ellpjl( u, m, sn, cn, dn, ph )
-long double u, m;
-long double *sn, *cn, *dn, *ph;
-{
-long double ai, b, phi, t, twon;
-long double a[9], c[9];
-int i;
-
-
-/* Check for special cases */
-
-if( m < 0.0L || m > 1.0L )
- {
- mtherr( "ellpjl", DOMAIN );
- *sn = 0.0L;
- *cn = 0.0L;
- *ph = 0.0L;
- *dn = 0.0L;
- return(-1);
- }
-if( m < 1.0e-12L )
- {
- t = sinl(u);
- b = cosl(u);
- ai = 0.25L * m * (u - t*b);
- *sn = t - ai*b;
- *cn = b + ai*t;
- *ph = u - ai;
- *dn = 1.0L - 0.5L*m*t*t;
- return(0);
- }
-
-if( m >= 0.999999999999L )
- {
- ai = 0.25L * (1.0L-m);
- b = coshl(u);
- t = tanhl(u);
- phi = 1.0L/b;
- twon = b * sinhl(u);
- *sn = t + ai * (twon - u)/(b*b);
- *ph = 2.0L*atanl(expl(u)) - PIO2L + ai*(twon - u)/b;
- ai *= t * phi;
- *cn = phi - ai * (twon - u);
- *dn = phi + ai * (twon + u);
- return(0);
- }
-
-
-/* A. G. M. scale */
-a[0] = 1.0L;
-b = sqrtl(1.0L - m);
-c[0] = sqrtl(m);
-twon = 1.0L;
-i = 0;
-
-while( fabsl(c[i]/a[i]) > MACHEPL )
- {
- if( i > 7 )
- {
- mtherr( "ellpjl", OVERFLOW );
- goto done;
- }
- ai = a[i];
- ++i;
- c[i] = 0.5L * ( ai - b );
- t = sqrtl( ai * b );
- a[i] = 0.5L * ( ai + b );
- b = t;
- twon *= 2.0L;
- }
-
-done:
-
-/* backward recurrence */
-phi = twon * a[i] * u;
-do
- {
- t = c[i] * sinl(phi) / a[i];
- b = phi;
- phi = 0.5L * (asinl(t) + phi);
- }
-while( --i );
-
-*sn = sinl(phi);
-t = cosl(phi);
-*cn = t;
-*dn = t/cosl(phi-b);
-*ph = phi;
-return(0);
-}
+++ /dev/null
-/* ellpkl.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * long double m1, y, ellpkl();
- *
- * y = ellpkl( m1 );
- *
- *
- *
- * DESCRIPTION:
- *
- * Approximates the integral
- *
- *
- *
- * pi/2
- * -
- * | |
- * | dt
- * K(m) = | ------------------
- * | 2
- * | | sqrt( 1 - m sin t )
- * -
- * 0
- *
- * where m = 1 - m1, using the approximation
- *
- * P(x) - log x Q(x).
- *
- * The argument m1 is used rather than m so that the logarithmic
- * singularity at m = 1 will be shifted to the origin; this
- * preserves maximum accuracy.
- *
- * K(0) = pi/2.
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 10000 1.1e-19 3.3e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpkl domain x<0, x>1 0.0
- *
- */
-\f
-/* ellpkl.c */
-
-
-/*
-Cephes Math Library, Release 2.3: October, 1995
-Copyright 1984, 1987, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#if UNK
-static long double P[13] = {
- 1.247539729154838838628E-6L,
- 2.149421654232011240659E-4L,
- 2.265267575136470585139E-3L,
- 6.723088676584254248821E-3L,
- 8.092066790639263075808E-3L,
- 5.664069509748147028621E-3L,
- 4.579865994050801042865E-3L,
- 5.797368411662027645234E-3L,
- 8.767698209432225911803E-3L,
- 1.493761594388688915057E-2L,
- 3.088514457872042326871E-2L,
- 9.657359027999314232753E-2L,
- 1.386294361119890618992E0L,
-};
-static long double Q[12] = {
- 5.568631677757315398993E-5L,
- 1.036110372590318802997E-3L,
- 5.500459122138244213579E-3L,
- 1.337330436245904844528E-2L,
- 2.033103735656990487115E-2L,
- 2.522868345512332304268E-2L,
- 3.026786461242788135379E-2L,
- 3.738370118296930305919E-2L,
- 4.882812208418620146046E-2L,
- 7.031249999330222751046E-2L,
- 1.249999999999978263154E-1L,
- 4.999999999999999999924E-1L,
-};
-static long double C1 = 1.386294361119890618834L; /* log(4) */
-#endif
-#if IBMPC
-static short P[] = {
-0xf098,0xad01,0x2381,0xa771,0x3feb, XPD
-0xd6ed,0xea22,0x1922,0xe162,0x3ff2, XPD
-0x3733,0xe2f1,0xe226,0x9474,0x3ff6, XPD
-0x3031,0x3c9d,0x5aff,0xdc4d,0x3ff7, XPD
-0x9a46,0x4310,0x968e,0x8494,0x3ff8, XPD
-0xbe4c,0x3ff2,0xa8a7,0xb999,0x3ff7, XPD
-0xf35c,0x0eaf,0xb355,0x9612,0x3ff7, XPD
-0xbc56,0x8fd4,0xd9dd,0xbdf7,0x3ff7, XPD
-0xc01e,0x867f,0x6444,0x8fa6,0x3ff8, XPD
-0x4ba3,0x6392,0xe6fd,0xf4bc,0x3ff8, XPD
-0x62c3,0xbb12,0xd7bc,0xfd02,0x3ff9, XPD
-0x08fe,0x476c,0x5fdf,0xc5c8,0x3ffb, XPD
-0x79ad,0xd1cf,0x17f7,0xb172,0x3fff, XPD
-};
-static short Q[] = {
-0x96a4,0x8474,0xba33,0xe990,0x3ff0, XPD
-0xe5a7,0xa50e,0x1854,0x87ce,0x3ff5, XPD
-0x8999,0x72e3,0x3205,0xb43d,0x3ff7, XPD
-0x3255,0x13eb,0xb438,0xdb1b,0x3ff8, XPD
-0xb717,0x497f,0x4691,0xa68d,0x3ff9, XPD
-0x30be,0x8c6b,0x624b,0xceac,0x3ff9, XPD
-0xa858,0x2a0d,0x5014,0xf7f4,0x3ff9, XPD
-0x8615,0xbfa6,0xa6df,0x991f,0x3ffa, XPD
-0x103c,0xa076,0xff37,0xc7ff,0x3ffa, XPD
-0xf508,0xc515,0xffff,0x8fff,0x3ffb, XPD
-0x1af5,0xfffb,0xffff,0xffff,0x3ffb, XPD
-0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD
-};
-static unsigned short ac1[] = {
-0x79ac,0xd1cf,0x17f7,0xb172,0x3fff, XPD
-};
-#define C1 (*(long double *)ac1)
-#endif
-
-#ifdef MIEEE
-static long P[39] = {
-0x3feb0000,0xa7712381,0xad01f098,
-0x3ff20000,0xe1621922,0xea22d6ed,
-0x3ff60000,0x9474e226,0xe2f13733,
-0x3ff70000,0xdc4d5aff,0x3c9d3031,
-0x3ff80000,0x8494968e,0x43109a46,
-0x3ff70000,0xb999a8a7,0x3ff2be4c,
-0x3ff70000,0x9612b355,0x0eaff35c,
-0x3ff70000,0xbdf7d9dd,0x8fd4bc56,
-0x3ff80000,0x8fa66444,0x867fc01e,
-0x3ff80000,0xf4bce6fd,0x63924ba3,
-0x3ff90000,0xfd02d7bc,0xbb1262c3,
-0x3ffb0000,0xc5c85fdf,0x476c08fe,
-0x3fff0000,0xb17217f7,0xd1cf79ad,
-};
-static long Q[36] = {
-0x3ff00000,0xe990ba33,0x847496a4,
-0x3ff50000,0x87ce1854,0xa50ee5a7,
-0x3ff70000,0xb43d3205,0x72e38999,
-0x3ff80000,0xdb1bb438,0x13eb3255,
-0x3ff90000,0xa68d4691,0x497fb717,
-0x3ff90000,0xceac624b,0x8c6b30be,
-0x3ff90000,0xf7f45014,0x2a0da858,
-0x3ffa0000,0x991fa6df,0xbfa68615,
-0x3ffa0000,0xc7ffff37,0xa076103c,
-0x3ffb0000,0x8fffffff,0xc515f508,
-0x3ffb0000,0xffffffff,0xfffb1af5,
-0x3ffe0000,0x80000000,0x00000000,
-};
-static unsigned long ac1[] = {
-0x3fff0000,0xb17217f7,0xd1cf79ac
-};
-#define C1 (*(long double *)ac1)
-#endif
-
-
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double logl ( long double );
-#else
-long double polevll(), logl();
-#endif
-extern long double MACHEPL, MAXNUML;
-
-long double ellpkl(x)
-long double x;
-{
-
-if( (x < 0.0L) || (x > 1.0L) )
- {
- mtherr( "ellpkl", DOMAIN );
- return( 0.0L );
- }
-
-if( x > MACHEPL )
- {
- return( polevll(x,P,12) - logl(x) * polevll(x,Q,11) );
- }
-else
- {
- if( x == 0.0L )
- {
- mtherr( "ellpkl", SING );
- return( MAXNUML );
- }
- else
- {
- return( C1 - 0.5L * logl(x) );
- }
- }
-}
+++ /dev/null
-/* exp10l.c
- *
- * Base 10 exponential function, long double precision
- * (Common antilogarithm)
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, exp10l()
- *
- * y = exp10l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 10 raised to the x power.
- *
- * Range reduction is accomplished by expressing the argument
- * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
- * The Pade' form
- *
- * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- *
- * is used to approximate 10**f.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-4900 30000 1.0e-19 2.7e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp10l underflow x < -MAXL10 0.0
- * exp10l overflow x > MAXL10 MAXNUM
- *
- * IEEE arithmetic: MAXL10 = 4932.0754489586679023819
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: January, 1991
-Copyright 1984, 1991 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
- 3.1341179396892496811523E1L,
- 4.5618283154904699073999E3L,
- 1.3433113468542797218610E5L,
- 7.6025447914440301593592E5L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0,*/
- 4.7705440288425157637739E2L,
- 2.9732606548049614870598E4L,
- 4.0843697951001026189583E5L,
- 6.6034865026929015925608E5L,
-};
-/*static long double LOG102 = 3.0102999566398119521373889e-1L;*/
-static long double LOG210 = 3.3219280948873623478703L;
-static long double LG102A = 3.01025390625e-1L;
-static long double LG102B = 4.6050389811952137388947e-6L;
-#endif
-
-
-#ifdef IBMPC
-static short P[] = {
-0x399a,0x7dc7,0xbc43,0xfaba,0x4003, XPD
-0xb526,0xdf32,0xa063,0x8e8e,0x400b, XPD
-0x18da,0xafa1,0xc89e,0x832e,0x4010, XPD
-0x503d,0x9352,0xe7aa,0xb99b,0x4012, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x947d,0x7855,0xf6ac,0xee86,0x4007, XPD
-0x18cf,0x7749,0x368d,0xe849,0x400d, XPD
-0x85be,0x2560,0x9f58,0xc76e,0x4011, XPD
-0x6d3c,0x80c5,0xca67,0xa137,0x4012, XPD
-};
-/*
-static short L102[] = {0xf799,0xfbcf,0x9a84,0x9a20,0x3ffd, XPD};
-#define LOG102 *(long double *)L102
-*/
-static short L210[] = {0x8afe,0xcd1b,0x784b,0xd49a,0x4000, XPD};
-#define LOG210 *(long double *)L210
-static short L102A[] = {0x0000,0x0000,0x0000,0x9a20,0x3ffd, XPD};
-#define LG102A *(long double *)L102A
-static short L102B[] = {0x8f89,0xf798,0xfbcf,0x9a84,0x3fed, XPD};
-#define LG102B *(long double *)L102B
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x40030000,0xfababc43,0x7dc7399a,
-0x400b0000,0x8e8ea063,0xdf32b526,
-0x40100000,0x832ec89e,0xafa118da,
-0x40120000,0xb99be7aa,0x9352503d,
-};
-static long Q[] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40070000,0xee86f6ac,0x7855947d,
-0x400d0000,0xe849368d,0x774918cf,
-0x40110000,0xc76e9f58,0x256085be,
-0x40120000,0xa137ca67,0x80c56d3c,
-};
-/*
-static long L102[] = {0x3ffd0000,0x9a209a84,0xfbcff799};
-#define LOG102 *(long double *)L102
-*/
-static long L210[] = {0x40000000,0xd49a784b,0xcd1b8afe};
-#define LOG210 *(long double *)L210
-static long L102A[] = {0x3ffd0000,0x9a200000,0x00000000};
-#define LG102A *(long double *)L102A
-static long L102B[] = {0x3fed0000,0x9a84fbcf,0xf7988f89};
-#define LG102B *(long double *)L102B
-#endif
-
-static long double MAXL10 = 4.9320754489586679023819e3L;
-extern long double MAXNUML;
-#ifdef ANSIPROT
-extern long double floorl ( long double );
-extern long double ldexpl ( long double, int );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-#else
-long double floorl(), ldexpl(), polevll(), p1evll(), isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-
-long double exp10l(x)
-long double x;
-{
-long double px, xx;
-short n;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-if( x > MAXL10 )
- {
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- mtherr( "exp10l", OVERFLOW );
- return( MAXNUML );
-#endif
- }
-
-if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
- {
-#ifndef INFINITIES
- mtherr( "exp10l", UNDERFLOW );
-#endif
- return(0.0L);
- }
-
-/* Express 10**x = 10**g 2**n
- * = 10**g 10**( n log10(2) )
- * = 10**( g + n log10(2) )
- */
-px = floorl( LOG210 * x + 0.5L );
-n = px;
-x -= px * LG102A;
-x -= px * LG102B;
-
-/* rational approximation for exponential
- * of the fractional part:
- * 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
-xx = x * x;
-px = x * polevll( xx, P, 3 );
-x = px/( p1evll( xx, Q, 4 ) - px );
-x = 1.0L + ldexpl( x, 1 );
-
-/* multiply by power of 2 */
-x = ldexpl( x, n );
-return(x);
-}
+++ /dev/null
-/* exp2l.c
- *
- * Base 2 exponential function, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, exp2l();
- *
- * y = exp2l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns 2 raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- * x k f
- * 2 = 2 2.
- *
- * A Pade' form
- *
- * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
- *
- * approximates 2**x in the basic range [-0.5, 0.5].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-16300 300000 9.1e-20 2.6e-20
- *
- *
- * See exp.c for comments on error amplification.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp2l underflow x < -16382 0.0
- * exp2l overflow x >= 16384 MAXNUM
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1991, 1998 by Stephen L. Moshier
-*/
-
-
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
- 6.0614853552242266094567E1L,
- 3.0286971917562792508623E4L,
- 2.0803843631901852422887E6L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0,*/
- 1.7492876999891839021063E3L,
- 3.2772515434906797273099E5L,
- 6.0027204078348487957118E6L,
-};
-#endif
-
-
-#ifdef IBMPC
-static short P[] = {
-0xffd8,0x6ad6,0x9c2b,0xf275,0x4004, XPD
-0x3426,0x2dc5,0xf19f,0xec9d,0x400d, XPD
-0x7ec0,0xd041,0x02e7,0xfdf4,0x4013, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x575b,0x9b93,0x34d6,0xdaa9,0x4009, XPD
-0xe38d,0x6d74,0xa4f0,0xa005,0x4011, XPD
-0xb37e,0xcfba,0x40d0,0xb730,0x4015, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x40040000,0xf2759c2b,0x6ad6ffd8,
-0x400d0000,0xec9df19f,0x2dc53426,
-0x40130000,0xfdf402e7,0xd0417ec0,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40090000,0xdaa934d6,0x9b93575b,
-0x40110000,0xa005a4f0,0x6d74e38d,
-0x40150000,0xb73040d0,0xcfbab37e,
-};
-#endif
-
-#define MAXL2L 16384.0L
-#define MINL2L -16382.0L
-
-
-extern long double MAXNUML;
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double floorl ( long double );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-#else
-long double polevll(), p1evll(), floorl(), ldexpl(), isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-
-long double exp2l(x)
-long double x;
-{
-long double px, xx;
-int n;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-if( x > MAXL2L)
- {
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- mtherr( "exp2l", OVERFLOW );
- return( MAXNUML );
-#endif
- }
-
-if( x < MINL2L )
- {
-#ifndef INFINITIES
- mtherr( "exp2l", UNDERFLOW );
-#endif
- return(0.0L);
- }
-
-xx = x; /* save x */
-/* separate into integer and fractional parts */
-px = floorl(x+0.5L);
-n = px;
-x = x - px;
-
-/* rational approximation
- * exp2(x) = 1.0 + 2xP(xx)/(Q(xx) - P(xx))
- * where xx = x**2
- */
-xx = x * x;
-px = x * polevll( xx, P, 2 );
-x = px / ( p1evll( xx, Q, 3 ) - px );
-x = 1.0L + ldexpl( x, 1 );
-
-/* scale by power of 2 */
-x = ldexpl( x, n );
-return(x);
-}
+++ /dev/null
-/* expl.c
- *
- * Exponential function, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, expl();
- *
- * y = expl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns e (2.71828...) raised to the x power.
- *
- * Range reduction is accomplished by separating the argument
- * into an integer k and fraction f such that
- *
- * x k f
- * e = 2 e.
- *
- * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
- * in the basic range [-0.5 ln 2, 0.5 ln 2].
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-10000 50000 1.12e-19 2.81e-20
- *
- *
- * Error amplification in the exponential function can be
- * a serious matter. The error propagation involves
- * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
- * which shows that a 1 lsb error in representing X produces
- * a relative error of X times 1 lsb in the function.
- * While the routine gives an accurate result for arguments
- * that are exactly represented by a long double precision
- * computer number, the result contains amplified roundoff
- * error for large arguments not exactly represented.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * exp underflow x < MINLOG 0.0
- * exp overflow x > MAXLOG MAXNUM
- *
- */
-\f
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1990, 1998 by Stephen L. Moshier
-*/
-
-
-/* Exponential function */
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[3] = {
- 1.2617719307481059087798E-4L,
- 3.0299440770744196129956E-2L,
- 9.9999999999999999991025E-1L,
-};
-static long double Q[4] = {
- 3.0019850513866445504159E-6L,
- 2.5244834034968410419224E-3L,
- 2.2726554820815502876593E-1L,
- 2.0000000000000000000897E0L,
-};
-static long double C1 = 6.9314575195312500000000E-1L;
-static long double C2 = 1.4286068203094172321215E-6L;
-#endif
-
-#ifdef DEC
-not supported in long double precision
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0x424e,0x225f,0x6eaf,0x844e,0x3ff2, XPD
-0xf39e,0x5163,0x8866,0xf836,0x3ff9, XPD
-0xfffe,0xffff,0xffff,0xffff,0x3ffe, XPD
-};
-static short Q[] = {
-0xff1e,0xb2fc,0xb5e1,0xc975,0x3fec, XPD
-0xff3e,0x45b5,0xcda8,0xa571,0x3ff6, XPD
-0x9ee1,0x3f03,0x4cc4,0xe8b8,0x3ffc, XPD
-0x0000,0x0000,0x0000,0x8000,0x4000, XPD
-};
-static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD};
-#define C1 (*(long double *)sc1)
-static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD};
-#define C2 (*(long double *)sc2)
-#endif
-
-#ifdef MIEEE
-static long P[9] = {
-0x3ff20000,0x844e6eaf,0x225f424e,
-0x3ff90000,0xf8368866,0x5163f39e,
-0x3ffe0000,0xffffffff,0xfffffffe,
-};
-static long Q[12] = {
-0x3fec0000,0xc975b5e1,0xb2fcff1e,
-0x3ff60000,0xa571cda8,0x45b5ff3e,
-0x3ffc0000,0xe8b84cc4,0x3f039ee1,
-0x40000000,0x80000000,0x00000000,
-};
-static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
-#define C1 (*(long double *)sc1)
-static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
-#define C2 (*(long double *)sc2)
-#endif
-
-extern long double LOG2EL, MAXLOGL, MINLOGL, MAXNUML;
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double floorl ( long double );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-#else
-long double polevll(), floorl(), ldexpl(), isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-
-long double expl(x)
-long double x;
-{
-long double px, xx;
-int n;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-if( x > MAXLOGL)
- {
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- mtherr( "expl", OVERFLOW );
- return( MAXNUML );
-#endif
- }
-
-if( x < MINLOGL )
- {
-#ifndef INFINITIES
- mtherr( "expl", UNDERFLOW );
-#endif
- return(0.0L);
- }
-
-/* Express e**x = e**g 2**n
- * = e**g e**( n loge(2) )
- * = e**( g + n loge(2) )
- */
-px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */
-n = px;
-x -= px * C1;
-x -= px * C2;
-
-
-/* rational approximation for exponential
- * of the fractional part:
- * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
-xx = x * x;
-px = x * polevll( xx, P, 2 );
-x = px/( polevll( xx, Q, 3 ) - px );
-x = 1.0L + ldexpl( x, 1 );
-
-x = ldexpl( x, n );
-return(x);
-}
+++ /dev/null
-/* fdtrl.c
- *
- * F distribution, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * long double x, y, fdtrl();
- *
- * y = fdtrl( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from zero to x under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density). This is the density
- * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
- * variables having Chi square distributions with df1
- * and df2 degrees of freedom, respectively.
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbetl( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
- *
- *
- * The arguments a and b are greater than zero, and x
- * x is nonnegative.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) in the indicated intervals.
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 1,100 10000 9.3e-18 2.9e-19
- * IEEE 0,1 1,10000 10000 1.9e-14 2.9e-15
- * IEEE 1,5 1,10000 10000 5.8e-15 1.4e-16
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrl domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtrcl()
- *
- * Complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * long double x, y, fdtrcl();
- *
- * y = fdtrcl( df1, df2, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area from x to infinity under the F density
- * function (also known as Snedcor's density or the
- * variance ratio density).
- *
- *
- * inf.
- * -
- * 1 | | a-1 b-1
- * 1-P(x) = ------ | t (1-t) dt
- * B(a,b) | |
- * -
- * x
- *
- * (See fdtr.c.)
- *
- * The incomplete beta integral is used, according to the
- * formula
- *
- * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
- *
- *
- * ACCURACY:
- *
- * See incbet.c.
- * Tested at random points (a,b,x).
- *
- * x a,b Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 0,100 10000 4.2e-18 3.3e-19
- * IEEE 0,1 1,10000 10000 7.2e-15 2.6e-16
- * IEEE 1,5 1,10000 10000 1.7e-14 3.0e-15
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtrcl domain a<0, b<0, x<0 0.0
- *
- */
-\f/* fdtril()
- *
- * Inverse of complemented F distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int df1, df2;
- * long double x, p, fdtril();
- *
- * x = fdtril( df1, df2, p );
- *
- * DESCRIPTION:
- *
- * Finds the F density argument x such that the integral
- * from x to infinity of the F density is equal to the
- * given probability p.
- *
- * This is accomplished using the inverse beta integral
- * function and the relations
- *
- * z = incbi( df2/2, df1/2, p )
- * x = df2 (1-z) / (df1 z).
- *
- * Note: the following relations hold for the inverse of
- * the uncomplemented F distribution:
- *
- * z = incbi( df1/2, df2/2, p )
- * x = df2 z / (df1 (1-z)).
- *
- * ACCURACY:
- *
- * See incbi.c.
- * Tested at random points (a,b,p).
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * For p between .001 and 1:
- * IEEE 1,100 40000 4.6e-18 2.7e-19
- * IEEE 1,10000 30000 1.7e-14 1.4e-16
- * For p between 10^-6 and .001:
- * IEEE 1,100 20000 1.9e-15 3.9e-17
- * IEEE 1,10000 30000 2.7e-15 4.0e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * fdtril domain p <= 0 or p > 1 0.0
- * v < 1
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double incbetl ( long double, long double, long double );
-extern long double incbil ( long double, long double, long double );
-#else
-long double incbetl(), incbil();
-#endif
-
-long double fdtrcl( ia, ib, x )
-int ia, ib;
-long double x;
-{
-long double a, b, w;
-
-if( (ia < 1) || (ib < 1) || (x < 0.0L) )
- {
- mtherr( "fdtrcl", DOMAIN );
- return( 0.0L );
- }
-a = ia;
-b = ib;
-w = b / (b + a * x);
-return( incbetl( 0.5L*b, 0.5L*a, w ) );
-}
-
-
-
-long double fdtrl( ia, ib, x )
-int ia, ib;
-long double x;
-{
-long double a, b, w;
-
-if( (ia < 1) || (ib < 1) || (x < 0.0L) )
- {
- mtherr( "fdtrl", DOMAIN );
- return( 0.0L );
- }
-a = ia;
-b = ib;
-w = a * x;
-w = w / (b + w);
-return( incbetl(0.5L*a, 0.5L*b, w) );
-}
-
-
-long double fdtril( ia, ib, y )
-int ia, ib;
-long double y;
-{
-long double a, b, w, x;
-
-if( (ia < 1) || (ib < 1) || (y <= 0.0L) || (y > 1.0L) )
- {
- mtherr( "fdtril", DOMAIN );
- return( 0.0L );
- }
-a = ia;
-b = ib;
-/* Compute probability for x = 0.5. */
-w = incbetl( 0.5L*b, 0.5L*a, 0.5L );
-/* If that is greater than y, then the solution w < .5.
- Otherwise, solve at 1-y to remove cancellation in (b - b*w). */
-if( w > y || y < 0.001L)
- {
- w = incbil( 0.5L*b, 0.5L*a, y );
- x = (b - b*w)/(a*w);
- }
-else
- {
- w = incbil( 0.5L*a, 0.5L*b, 1.0L - y );
- x = b*w/(a*(1.0L-w));
- }
-return(x);
-}
+++ /dev/null
-/* ceill()
- * floorl()
- * frexpl()
- * ldexpl()
- * fabsl()
- * signbitl()
- * isnanl()
- * isfinitel()
- *
- * Floating point numeric utilities
- *
- *
- *
- * SYNOPSIS:
- *
- * long double ceill(), floorl(), frexpl(), ldexpl(), fabsl();
- * int signbitl(), isnanl(), isfinitel();
- * long double x, y;
- * int expnt, n;
- *
- * y = floorl(x);
- * y = ceill(x);
- * y = frexpl( x, &expnt );
- * y = ldexpl( x, n );
- * y = fabsl( x );
- * n = signbitl(x);
- * n = isnanl(x);
- * n = isfinitel(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * The following routines return a long double precision floating point
- * result:
- *
- * floorl() returns the largest integer less than or equal to x.
- * It truncates toward minus infinity.
- *
- * ceill() returns the smallest integer greater than or equal
- * to x. It truncates toward plus infinity.
- *
- * frexpl() extracts the exponent from x. It returns an integer
- * power of two to expnt and the significand between 0.5 and 1
- * to y. Thus x = y * 2**expn.
- *
- * ldexpl() multiplies x by 2**n.
- *
- * fabsl() returns the absolute value of its argument.
- *
- * These functions are part of the standard C run time library
- * for some but not all C compilers. The ones supplied are
- * written in C for IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- * The IEEE versions assume that denormal numbers are implemented
- * in the arithmetic. Some modifications will be required if
- * the arithmetic has abrupt rather than gradual underflow.
- */
-\f
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1987, 1988, 1992, 1998 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-/* This is defined in mconf.h. */
-/* #define DENORMAL 1 */
-
-#ifdef UNK
-/* Change UNK into something else. */
-#undef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-#endif
-
-#ifdef IBMPC
-#define EXPMSK 0x800f
-#define MEXP 0x7ff
-#define NBITS 64
-#endif
-
-#ifdef MIEEE
-#define EXPMSK 0x800f
-#define MEXP 0x7ff
-#define NBITS 64
-#endif
-
-extern double MAXNUML;
-
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double floorl ( long double );
-extern int isnanl ( long double );
-#else
-long double fabsl(), floorl();
-int isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double fabsl(x)
-long double x;
-{
-union
- {
- long double d;
- short i[6];
- } u;
-
-u.d = x;
-#ifdef IBMPC
- u.i[4] &= 0x7fff;
-#endif
-#ifdef MIEEE
- u.i[0] &= 0x7fff;
-#endif
-return( u.d );
-}
-
-
-
-long double ceill(x)
-long double x;
-{
-long double y;
-
-#ifdef UNK
-mtherr( "ceill", DOMAIN );
-return(0.0L);
-#endif
-#ifdef INFINITIES
-if(x == -INFINITYL)
- return(x);
-#endif
-#ifdef MINUSZERO
-if(x == 0.0L)
- return(x);
-#endif
-y = floorl(x);
-if( y < x )
- y += 1.0L;
-return(y);
-}
-
-
-
-
-/* Bit clearing masks: */
-
-static unsigned short bmask[] = {
-0xffff,
-0xfffe,
-0xfffc,
-0xfff8,
-0xfff0,
-0xffe0,
-0xffc0,
-0xff80,
-0xff00,
-0xfe00,
-0xfc00,
-0xf800,
-0xf000,
-0xe000,
-0xc000,
-0x8000,
-0x0000,
-};
-
-
-
-
-long double floorl(x)
-long double x;
-{
-unsigned short *p;
-union
- {
- long double y;
- unsigned short sh[6];
- } u;
-int e;
-
-#ifdef UNK
-mtherr( "floor", DOMAIN );
-return(0.0L);
-#endif
-#ifdef INFINITIES
-if( x == INFINITYL )
- return(x);
-#endif
-#ifdef MINUSZERO
-if(x == 0.0L)
- return(x);
-#endif
-u.y = x;
-/* find the exponent (power of 2) */
-#ifdef IBMPC
-p = (unsigned short *)&u.sh[4];
-e = (*p & 0x7fff) - 0x3fff;
-p -= 4;
-#endif
-
-#ifdef MIEEE
-p = (unsigned short *)&u.sh[0];
-e = (*p & 0x7fff) - 0x3fff;
-p += 5;
-#endif
-
-if( e < 0 )
- {
- if( u.y < 0.0L )
- return( -1.0L );
- else
- return( 0.0L );
- }
-
-e = (NBITS -1) - e;
-/* clean out 16 bits at a time */
-while( e >= 16 )
- {
-#ifdef IBMPC
- *p++ = 0;
-#endif
-
-#ifdef MIEEE
- *p-- = 0;
-#endif
- e -= 16;
- }
-
-/* clear the remaining bits */
-if( e > 0 )
- *p &= bmask[e];
-
-if( (x < 0) && (u.y != x) )
- u.y -= 1.0L;
-
-return(u.y);
-}
-
-
-
-long double frexpl( x, pw2 )
-long double x;
-int *pw2;
-{
-union
- {
- long double y;
- unsigned short sh[6];
- } u;
-int i, k;
-short *q;
-
-u.y = x;
-
-#ifdef NANS
-if(isnanl(x))
- {
- *pw2 = 0;
- return(x);
- }
-#endif
-#ifdef INFINITIES
-if(x == -INFINITYL)
- {
- *pw2 = 0;
- return(x);
- }
-#endif
-#ifdef MINUSZERO
-if(x == 0.0L)
- {
- *pw2 = 0;
- return(x);
- }
-#endif
-
-#ifdef UNK
-mtherr( "frexpl", DOMAIN );
-return(0.0L);
-#endif
-
-/* find the exponent (power of 2) */
-#ifdef IBMPC
-q = (short *)&u.sh[4];
-i = *q & 0x7fff;
-#endif
-
-#ifdef MIEEE
-q = (short *)&u.sh[0];
-i = *q & 0x7fff;
-#endif
-
-if( i == 0 )
- {
- if( u.y == 0.0L )
- {
- *pw2 = 0;
- return(0.0L);
- }
-/* Number is denormal or zero */
-#ifdef DENORMAL
-/* Handle denormal number. */
-do
- {
- u.y *= 2.0L;
- i -= 1;
- k = *q & 0x7fff;
- }
-while( (k == 0) && (i > -66) );
-i = i + k;
-#else
- *pw2 = 0;
- return(0.0L);
-#endif /* DENORMAL */
- }
-
-*pw2 = i - 0x3ffe;
-/* *q = 0x3ffe; */
-/* Preserve sign of argument. */
-*q &= 0x8000;
-*q |= 0x3ffe;
-return( u.y );
-}
-
-
-
-
-
-
-long double ldexpl( x, pw2 )
-long double x;
-int pw2;
-{
-union
- {
- long double y;
- unsigned short sh[6];
- } u;
-unsigned short *q;
-long e;
-
-#ifdef UNK
-mtherr( "ldexp", DOMAIN );
-return(0.0L);
-#endif
-
-u.y = x;
-#ifdef IBMPC
-q = (unsigned short *)&u.sh[4];
-#endif
-#ifdef MIEEE
-q = (unsigned short *)&u.sh[0];
-#endif
-while( (e = (*q & 0x7fffL)) == 0 )
- {
-#ifdef DENORMAL
- if( u.y == 0.0L )
- {
- return( 0.0L );
- }
-/* Input is denormal. */
- if( pw2 > 0 )
- {
- u.y *= 2.0L;
- pw2 -= 1;
- }
- if( pw2 < 0 )
- {
- if( pw2 < -64 )
- return(0.0L);
- u.y *= 0.5L;
- pw2 += 1;
- }
- if( pw2 == 0 )
- return(u.y);
-#else
- return( 0.0L );
-#endif
- }
-
-e = e + pw2;
-
-/* Handle overflow */
-if( e > 0x7fffL )
- {
- return( MAXNUML );
- }
-*q &= 0x8000;
-/* Handle denormalized results */
-if( e < 1 )
- {
-#ifdef DENORMAL
- if( e < -64 )
- return(0.0L);
-
-#ifdef IBMPC
- *(q-1) |= 0x8000;
-#endif
-#ifdef MIEEE
- *(q+2) |= 0x8000;
-#endif
-
- while( e < 1 )
- {
- u.y *= 0.5L;
- e += 1;
- }
- e = 0;
-#else
- return(0.0L);
-#endif
- }
-
-*q |= (unsigned short) e & 0x7fff;
-return(u.y);
-}
-
+++ /dev/null
-long double floorl(), ldexpl(), frexpl();
-
-#define N 16382
-void prnum();
-int printf();
-void exit();
-
-void main()
-{
-long double x, f, y, last, z, z0, y1;
-int i, k, e, e0, errs;
-
-errs = 0;
-f = 0.1L;
-x = f;
-last = x;
-z0 = frexpl( x, &e0 );
-printf( "frexpl(%.2Le) = %.5Le, %d\n", x, z0, e0 );
-k = 0;
-for( i=0; i<N+5; i++ )
- {
- y = ldexpl( f, k );
- if( y != x )
- {
- printf( "ldexpl(%.1Le, %d) = %.5Le, s.b. %.5Le\n",
- f, k, y, x );
- ++errs;
- }
- z = frexpl( y, &e );
- if( (e != k+e0) || (z != z0) )
- {
- printf( "frexpl(%.1Le) = %.5Le, %d; s.b. %.5Le, %d\n",
- y, z, e, z0, k+e0 );
- ++errs;
- }
- x += x;
- if( x == last )
- break;
- last = x;
- k += 1;
- }
-printf( "i = %d\n", k );
-prnum( "last y =", &y );
-printf("\n");
-
-f = 0.1L;
-x = f;
-last = x;
-k = 0;
-for( i=0; i<N+64; i++ )
- {
- y = ldexpl( f, k );
- if( y != x )
- {
- printf( "ldexpl(%.1Le, %d) = %.5Le, s.b. %.5Le\n",
- f, k, y, x );
- ++errs;
- }
- z = frexpl( y, &e );
- if(
-#if 1
- (e > -N+1) &&
-#endif
- ((e != k+e0) || (z != z0)) )
- {
- printf( "frexpl(%.1Le) = %.5Le, %d; s.b. %.5Le, %d\n",
- y, z, e, z0, k+e0 );
- ++errs;
- }
- y1 = ldexpl( z, e );
- if( y1 != y )
- {
- printf( "ldexpl(%.1Le, %d) = %.5Le, s.b. %.5Le\n",
- z, e, y1, y );
- ++errs;
- }
-
- x *= 0.5L;
- if( x == 0.0L )
- break;
- if( x == last )
- break;
- last = x;
- k -= 1;
- }
-printf( "i = %d\n", k );
-prnum( "last y =", &y );
-
-printf( "\n%d errors\n", errs );
-exit(0);
-}
-
-
-void prnum(str, x)
-char *str;
-unsigned short *x;
-{
-int i;
-
-printf( "%s ", str );
-printf( "%.5Le = ", *(long double *)x );
-for( i=0; i<5; i++ )
- printf( "%04x ", *x++ );
-}
+++ /dev/null
-/* fltest.c
- * Test program for floor(), frexp(), ldexp()
- */
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier (moshier@world.std.com)
-*/
-
-
-
-/*#include <math.h>*/
-#define MACHEPL 5.42101086242752217003726400434970855712890625E-20L
-#define N 16300
-
-void flierr();
-int printf();
-void exit();
-
-int
-main()
-{
-long double x, y, y0, z, f, x00, y00;
-int i, j, e, e0;
-int errfr, errld, errfl, underexp, err, errth, e00;
-long double frexpl(), ldexpl(), floorl();
-
-
-/*
-if( 1 )
- goto flrtst;
-*/
-
-printf( "Testing frexpl() and ldexpl().\n" );
-errth = 0.0L;
-errfr = 0;
-errld = 0;
-underexp = 0;
-f = 1.0L;
-x00 = 2.0L;
-y00 = 0.5L;
-e00 = 2;
-
-for( j=0; j<20; j++ )
-{
-if( j == 10 )
- {
- f = 1.0L;
- x00 = 2.0L;
- e00 = 1;
-/* Find 2**(2**14) / 2 */
- for( i=0; i<13; i++ )
- {
- x00 *= x00;
- e00 += e00;
- }
- y00 = x00/2.0L;
- x00 = x00 * y00;
- e00 += e00;
- y00 = 0.5L;
- }
-x = x00 * f;
-y0 = y00 * f;
-e0 = e00;
-
-#if 1
-/* If ldexp, frexp support denormal numbers, this should work. */
-for( i=0; i<16448; i++ )
-#else
-for( i=0; i<16383; i++ )
-#endif
- {
- x /= 2.0L;
- e0 -= 1;
- if( x == 0.0L )
- {
- if( f == 1.0L )
- underexp = e0;
- y0 = 0.0L;
- e0 = 0;
- }
- y = frexpl( x, &e );
- if( (e0 < -16383) && (e != e0) )
- {
- if( e == (e0 - 1) )
- {
- e += 1;
- y /= 2.0L;
- }
- if( e == (e0 + 1) )
- {
- e -= 1;
- y *= 2.0L;
- }
- }
- err = y - y0;
- if( y0 != 0.0L )
- err /= y0;
- if( err < 0.0L )
- err = -err;
- if( e0 > -1023 )
- errth = 0.0L;
- else
- {/* Denormal numbers may have rounding errors */
- if( e0 == -16383 )
- {
- errth = 2.0L * MACHEPL;
- }
- else
- {
- errth *= 2.0L;
- }
- }
-
- if( (x != 0.0L) && ((err > errth) || (e != e0)) )
- {
- printf( "Test %d: ", j+1 );
- printf( " frexpl( %.20Le) =?= %.20Le * 2**%d;", x, y, e );
- printf( " should be %.20Le * 2**%d\n", y0, e0 );
- errfr += 1;
- }
- y = ldexpl( x, 1-e0 );
- err = y - 1.0L;
- if( err < 0.0L )
- err = -err;
- if( (err > errth) && ((x == 0.0L) && (y != 0.0L)) )
- {
- printf( "Test %d: ", j+1 );
- printf( "ldexpl( %.15Le, %d ) =?= %.15Le;", x, 1-e0, y );
- if( x != 0.0L )
- printf( " should be %.15Le\n", f );
- else
- printf( " should be %.15Le\n", 0.0L );
- errld += 1;
- }
- if( x == 0.0L )
- {
- break;
- }
- }
-f = f * 1.08005973889L;
-}
-
-if( (errld == 0) && (errfr == 0) )
- {
- printf( "No errors found.\n" );
- }
-
-/*flrtst:*/
-
-printf( "Testing floorl().\n" );
-errfl = 0;
-
-f = 1.0L/MACHEPL;
-x00 = 1.0L;
-for( j=0; j<57; j++ )
-{
-x = x00 - 1.0L;
-for( i=0; i<128; i++ )
- {
- y = floorl(x);
- if( y != x )
- {
- flierr( x, y, j );
- errfl += 1;
- }
-/* Warning! the if() statement is compiler dependent,
- * since x-0.49 may be held in extra precision accumulator
- * so would never compare equal to x! The subroutine call
- * y = floor() forces z to be stored as a double and reloaded
- * for the if() statement.
- */
- z = x - 0.49L;
- y = floorl(z);
- if( z == x )
- break;
- if( y != (x - 1.0L) )
- {
- flierr( z, y, j );
- errfl += 1;
- }
-
- z = x + 0.49L;
- y = floorl(z);
- if( z != x )
- {
- if( y != x )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- x = -x;
- y = floorl(x);
- if( z != x )
- {
- if( y != x )
- {
- flierr( x, y, j );
- errfl += 1;
- }
- }
- z = x + 0.49L;
- y = floorl(z);
- if( z != x )
- {
- if( y != x )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- z = x - 0.49L;
- y = floorl(z);
- if( z != x )
- {
- if( y != (x - 1.0L) )
- {
- flierr( z, y, j );
- errfl += 1;
- }
- }
- x = -x;
- x += 1.0L;
- }
-x00 = x00 + x00;
-}
-y = floorl(0.0L);
-if( y != 0.0L )
- {
- flierr( 0.0L, y, 57 );
- errfl += 1;
- }
-y = floorl(-0.0L);
-if( y != 0.0L )
- {
- flierr( -0.0L, y, 58 );
- errfl += 1;
- }
-y = floorl(-1.0L);
-if( y != -1.0L )
- {
- flierr( -1.0L, y, 59 );
- errfl += 1;
- }
-y = floorl(-0.1L);
-if( y != -1.0l )
- {
- flierr( -0.1L, y, 60 );
- errfl += 1;
- }
-
-if( errfl == 0 )
- printf( "No errors found in floorl().\n" );
-exit(0);
-return 0;
-}
-
-void flierr( x, y, k )
-long double x, y;
-int k;
-{
-printf( "Test %d: ", k+1 );
-printf( "floorl(%.15Le) =?= %.15Le\n", x, y );
-}
+++ /dev/null
-/* gammal.c
- *
- * Gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, gammal();
- * extern int sgngam;
- *
- * y = gammal( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
- *
- * Arguments |x| <= 13 are reduced by recurrence and the function
- * approximated by a rational function of degree 7/8 in the
- * interval (2,3). Large arguments are handled by Stirling's
- * formula. Large negative arguments are made positive using
- * a reflection formula.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -40,+40 10000 3.6e-19 7.9e-20
- * IEEE -1755,+1755 10000 4.8e-18 6.5e-19
- *
- * Accuracy for large arguments is dominated by error in powl().
- *
- */\f
-/* lgaml()
- *
- * Natural logarithm of gamma function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, lgaml();
- * extern int sgngam;
- *
- * y = lgaml( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of the absolute
- * value of the gamma function of the argument.
- * The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
- *
- * For arguments greater than 33, the logarithm of the gamma
- * function is approximated by the logarithmic version of
- * Stirling's formula using a polynomial approximation of
- * degree 4. Arguments between -33 and +33 are reduced by
- * recurrence to the interval [2,3] of a rational approximation.
- * The cosecant reflection formula is employed for arguments
- * less than -33.
- *
- * Arguments greater than MAXLGML (10^4928) return MAXNUML.
- *
- *
- *
- * ACCURACY:
- *
- *
- * arithmetic domain # trials peak rms
- * IEEE -40, 40 100000 2.2e-19 4.6e-20
- * IEEE 10^-2000,10^+2000 20000 1.6e-19 3.3e-20
- * The error criterion was relative when the function magnitude
- * was greater than one but absolute when it was less than one.
- *
- */
-\f
-/* gamma.c */
-/* gamma function */
-
-/*
-Copyright 1994 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-/*
-gamma(x+2) = gamma(x+2) P(x)/Q(x)
-0 <= x <= 1
-Relative error
-n=7, d=8
-Peak error = 1.83e-20
-Relative error spread = 8.4e-23
-*/
-#if UNK
-static long double P[8] = {
- 4.212760487471622013093E-5L,
- 4.542931960608009155600E-4L,
- 4.092666828394035500949E-3L,
- 2.385363243461108252554E-2L,
- 1.113062816019361559013E-1L,
- 3.629515436640239168939E-1L,
- 8.378004301573126728826E-1L,
- 1.000000000000000000009E0L,
-};
-static long double Q[9] = {
--1.397148517476170440917E-5L,
- 2.346584059160635244282E-4L,
--1.237799246653152231188E-3L,
--7.955933682494738320586E-4L,
- 2.773706565840072979165E-2L,
--4.633887671244534213831E-2L,
--2.243510905670329164562E-1L,
- 4.150160950588455434583E-1L,
- 9.999999999999999999908E-1L,
-};
-#endif
-#if IBMPC
-static short P[] = {
-0x434a,0x3f22,0x2bda,0xb0b2,0x3ff0, XPD
-0xf5aa,0xe82f,0x335b,0xee2e,0x3ff3, XPD
-0xbe6c,0x3757,0xc717,0x861b,0x3ff7, XPD
-0x7f43,0x5196,0xb166,0xc368,0x3ff9, XPD
-0x9549,0x8eb5,0x8c3a,0xe3f4,0x3ffb, XPD
-0x8d75,0x23af,0xc8e4,0xb9d4,0x3ffd, XPD
-0x29cf,0x19b3,0x16c8,0xd67a,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-static short Q[] = {
-0x5473,0x2de8,0x1268,0xea67,0xbfee, XPD
-0x334b,0xc2f0,0xa2dd,0xf60e,0x3ff2, XPD
-0xbeed,0x1853,0xa691,0xa23d,0xbff5, XPD
-0x296e,0x7cb1,0x5dfd,0xd08f,0xbff4, XPD
-0x0417,0x7989,0xd7bc,0xe338,0x3ff9, XPD
-0x3295,0x3698,0xd580,0xbdcd,0xbffa, XPD
-0x75ef,0x3ab7,0x4ad3,0xe5bc,0xbffc, XPD
-0xe458,0x2ec7,0xfd57,0xd47c,0x3ffd, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-#endif
-#if MIEEE
-static long P[24] = {
-0x3ff00000,0xb0b22bda,0x3f22434a,
-0x3ff30000,0xee2e335b,0xe82ff5aa,
-0x3ff70000,0x861bc717,0x3757be6c,
-0x3ff90000,0xc368b166,0x51967f43,
-0x3ffb0000,0xe3f48c3a,0x8eb59549,
-0x3ffd0000,0xb9d4c8e4,0x23af8d75,
-0x3ffe0000,0xd67a16c8,0x19b329cf,
-0x3fff0000,0x80000000,0x00000000,
-};
-static long Q[27] = {
-0xbfee0000,0xea671268,0x2de85473,
-0x3ff20000,0xf60ea2dd,0xc2f0334b,
-0xbff50000,0xa23da691,0x1853beed,
-0xbff40000,0xd08f5dfd,0x7cb1296e,
-0x3ff90000,0xe338d7bc,0x79890417,
-0xbffa0000,0xbdcdd580,0x36983295,
-0xbffc0000,0xe5bc4ad3,0x3ab775ef,
-0x3ffd0000,0xd47cfd57,0x2ec7e458,
-0x3fff0000,0x80000000,0x00000000,
-};
-#endif
-/*
-static long double P[] = {
--3.01525602666895735709e0L,
--3.25157411956062339893e1L,
--2.92929976820724030353e2L,
--1.70730828800510297666e3L,
--7.96667499622741999770e3L,
--2.59780216007146401957e4L,
--5.99650230220855581642e4L,
--7.15743521530849602425e4L
-};
-static long double Q[] = {
- 1.00000000000000000000e0L,
--1.67955233807178858919e1L,
- 8.85946791747759881659e1L,
- 5.69440799097468430177e1L,
--1.98526250512761318471e3L,
- 3.31667508019495079814e3L,
- 1.60577839621734713377e4L,
--2.97045081369399940529e4L,
--7.15743521530849602412e4L
-};
-*/
-#define MAXGAML 1755.455L
-/*static long double LOGPI = 1.14472988584940017414L;*/
-
-/* Stirling's formula for the gamma function
-gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
-z(x) = x
-13 <= x <= 1024
-Relative error
-n=8, d=0
-Peak error = 9.44e-21
-Relative error spread = 8.8e-4
-*/
-#if UNK
-static long double STIR[9] = {
- 7.147391378143610789273E-4L,
--2.363848809501759061727E-5L,
--5.950237554056330156018E-4L,
- 6.989332260623193171870E-5L,
- 7.840334842744753003862E-4L,
--2.294719747873185405699E-4L,
--2.681327161876304418288E-3L,
- 3.472222222230075327854E-3L,
- 8.333333333333331800504E-2L,
-};
-#endif
-#if IBMPC
-static short STIR[] = {
-0x6ede,0x69f7,0x54e3,0xbb5d,0x3ff4, XPD
-0xc395,0x0295,0x4443,0xc64b,0xbfef, XPD
-0xba6f,0x7c59,0x5e47,0x9bfb,0xbff4, XPD
-0x5704,0x1a39,0xb11d,0x9293,0x3ff1, XPD
-0x30b7,0x1a21,0x98b2,0xcd87,0x3ff4, XPD
-0xbef3,0x7023,0x6a08,0xf09e,0xbff2, XPD
-0x3a1c,0x5ac8,0x3478,0xafb9,0xbff6, XPD
-0xc3c9,0x906e,0x38e3,0xe38e,0x3ff6, XPD
-0xa1d5,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
-};
-#endif
-#if MIEEE
-static long STIR[27] = {
-0x3ff40000,0xbb5d54e3,0x69f76ede,
-0xbfef0000,0xc64b4443,0x0295c395,
-0xbff40000,0x9bfb5e47,0x7c59ba6f,
-0x3ff10000,0x9293b11d,0x1a395704,
-0x3ff40000,0xcd8798b2,0x1a2130b7,
-0xbff20000,0xf09e6a08,0x7023bef3,
-0xbff60000,0xafb93478,0x5ac83a1c,
-0x3ff60000,0xe38e38e3,0x906ec3c9,
-0x3ffb0000,0xaaaaaaaa,0xaaaaa1d5,
-};
-#endif
-#define MAXSTIR 1024.0L
-static long double SQTPI = 2.50662827463100050242E0L;
-
-/* 1/gamma(x) = z P(z)
- * z(x) = 1/x
- * 0 < x < 0.03125
- * Peak relative error 4.2e-23
- */
-#if UNK
-static long double S[9] = {
--1.193945051381510095614E-3L,
- 7.220599478036909672331E-3L,
--9.622023360406271645744E-3L,
--4.219773360705915470089E-2L,
- 1.665386113720805206758E-1L,
--4.200263503403344054473E-2L,
--6.558780715202540684668E-1L,
- 5.772156649015328608253E-1L,
- 1.000000000000000000000E0L,
-};
-#endif
-#if IBMPC
-static short S[] = {
-0xbaeb,0xd6d3,0x25e5,0x9c7e,0xbff5, XPD
-0xfe9a,0xceb4,0xc74e,0xec9a,0x3ff7, XPD
-0x9225,0xdfef,0xb0e9,0x9da5,0xbff8, XPD
-0x10b0,0xec17,0x87dc,0xacd7,0xbffa, XPD
-0x6b8d,0x7515,0x1905,0xaa89,0x3ffc, XPD
-0xf183,0x126b,0xf47d,0xac0a,0xbffa, XPD
-0x7bf6,0x57d1,0xa013,0xa7e7,0xbffe, XPD
-0xc7a9,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-#endif
-#if MIEEE
-static long S[27] = {
-0xbff50000,0x9c7e25e5,0xd6d3baeb,
-0x3ff70000,0xec9ac74e,0xceb4fe9a,
-0xbff80000,0x9da5b0e9,0xdfef9225,
-0xbffa0000,0xacd787dc,0xec1710b0,
-0x3ffc0000,0xaa891905,0x75156b8d,
-0xbffa0000,0xac0af47d,0x126bf183,
-0xbffe0000,0xa7e7a013,0x57d17bf6,
-0x3ffe0000,0x93c467e3,0x7db0c7a9,
-0x3fff0000,0x80000000,0x00000000,
-};
-#endif
-/* 1/gamma(-x) = z P(z)
- * z(x) = 1/x
- * 0 < x < 0.03125
- * Peak relative error 5.16e-23
- * Relative error spread = 2.5e-24
- */
-#if UNK
-static long double SN[9] = {
- 1.133374167243894382010E-3L,
- 7.220837261893170325704E-3L,
- 9.621911155035976733706E-3L,
--4.219773343731191721664E-2L,
--1.665386113944413519335E-1L,
--4.200263503402112910504E-2L,
- 6.558780715202536547116E-1L,
- 5.772156649015328608727E-1L,
--1.000000000000000000000E0L,
-};
-#endif
-#if IBMPC
-static short SN[] = {
-0x5dd1,0x02de,0xb9f7,0x948d,0x3ff5, XPD
-0x989b,0xdd68,0xc5f1,0xec9c,0x3ff7, XPD
-0x2ca1,0x18f0,0x386f,0x9da5,0x3ff8, XPD
-0x783f,0x41dd,0x87d1,0xacd7,0xbffa, XPD
-0x7a5b,0xd76d,0x1905,0xaa89,0xbffc, XPD
-0x7f64,0x1234,0xf47d,0xac0a,0xbffa, XPD
-0x5e26,0x57d1,0xa013,0xa7e7,0x3ffe, XPD
-0xc7aa,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0xbfff, XPD
-};
-#endif
-#if MIEEE
-static long SN[27] = {
-0x3ff50000,0x948db9f7,0x02de5dd1,
-0x3ff70000,0xec9cc5f1,0xdd68989b,
-0x3ff80000,0x9da5386f,0x18f02ca1,
-0xbffa0000,0xacd787d1,0x41dd783f,
-0xbffc0000,0xaa891905,0xd76d7a5b,
-0xbffa0000,0xac0af47d,0x12347f64,
-0x3ffe0000,0xa7e7a013,0x57d15e26,
-0x3ffe0000,0x93c467e3,0x7db0c7aa,
-0xbfff0000,0x80000000,0x00000000,
-};
-#endif
-
-int sgngaml = 0;
-extern int sgngaml;
-extern long double MAXLOGL, MAXNUML, PIL;
-/* #define PIL 3.14159265358979323846L */
-/* #define MAXNUML 1.189731495357231765021263853E4932L */
-
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double lgaml ( long double );
-extern long double logl ( long double );
-extern long double expl ( long double );
-extern long double gammal ( long double );
-extern long double sinl ( long double );
-extern long double floorl ( long double );
-extern long double powl ( long double, long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-extern int isfinitel ( long double );
-static long double stirf ( long double );
-#else
-long double fabsl(), lgaml(), logl(), expl(), gammal(), sinl();
-long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel();
-static long double stirf();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-/* Gamma function computed by Stirling's formula.
- */
-static long double stirf(x)
-long double x;
-{
-long double y, w, v;
-
-w = 1.0L/x;
-/* For large x, use rational coefficients from the analytical expansion. */
-if( x > 1024.0L )
- w = (((((6.97281375836585777429E-5L * w
- + 7.84039221720066627474E-4L) * w
- - 2.29472093621399176955E-4L) * w
- - 2.68132716049382716049E-3L) * w
- + 3.47222222222222222222E-3L) * w
- + 8.33333333333333333333E-2L) * w
- + 1.0L;
-else
- w = 1.0L + w * polevll( w, STIR, 8 );
-y = expl(x);
-if( x > MAXSTIR )
- { /* Avoid overflow in pow() */
- v = powl( x, 0.5L * x - 0.25L );
- y = v * (v / y);
- }
-else
- {
- y = powl( x, x - 0.5L ) / y;
- }
-y = SQTPI * y * w;
-return( y );
-}
-
-
-
-long double gammal(x)
-long double x;
-{
-long double p, q, z;
-int i;
-
-sgngaml = 1;
-#ifdef NANS
-if( isnanl(x) )
- return(NANL);
-#endif
-#ifdef INFINITIES
-if(x == INFINITYL)
- return(INFINITYL);
-#ifdef NANS
-if(x == -INFINITYL)
- goto gamnan;
-#endif
-#endif
-q = fabsl(x);
-
-if( q > 13.0L )
- {
- if( q > MAXGAML )
- goto goverf;
- if( x < 0.0L )
- {
- p = floorl(q);
- if( p == q )
- {
-gamnan:
-#ifdef NANS
- mtherr( "gammal", DOMAIN );
- return (NANL);
-#else
- goto goverf;
-#endif
- }
- i = p;
- if( (i & 1) == 0 )
- sgngaml = -1;
- z = q - p;
- if( z > 0.5L )
- {
- p += 1.0L;
- z = q - p;
- }
- z = q * sinl( PIL * z );
- z = fabsl(z) * stirf(q);
- if( z <= PIL/MAXNUML )
- {
-goverf:
-#ifdef INFINITIES
- return( sgngaml * INFINITYL);
-#else
- mtherr( "gammal", OVERFLOW );
- return( sgngaml * MAXNUML);
-#endif
- }
- z = PIL/z;
- }
- else
- {
- z = stirf(x);
- }
- return( sgngaml * z );
- }
-
-z = 1.0L;
-while( x >= 3.0L )
- {
- x -= 1.0L;
- z *= x;
- }
-
-while( x < -0.03125L )
- {
- z /= x;
- x += 1.0L;
- }
-
-if( x <= 0.03125L )
- goto small;
-
-while( x < 2.0L )
- {
- z /= x;
- x += 1.0L;
- }
-
-if( x == 2.0L )
- return(z);
-
-x -= 2.0L;
-p = polevll( x, P, 7 );
-q = polevll( x, Q, 8 );
-return( z * p / q );
-
-small:
-if( x == 0.0L )
- {
- goto gamnan;
- }
-else
- {
- if( x < 0.0L )
- {
- x = -x;
- q = z / (x * polevll( x, SN, 8 ));
- }
- else
- q = z / (x * polevll( x, S, 8 ));
- }
-return q;
-}
-
-
-
-/* A[]: Stirling's formula expansion of log gamma
- * B[], C[]: log gamma function between 2 and 3
- */
-
-
-/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x A(1/x^2)
- * x >= 8
- * Peak relative error 1.51e-21
- * Relative spread of error peaks 5.67e-21
- */
-#if UNK
-static long double A[7] = {
- 4.885026142432270781165E-3L,
--1.880801938119376907179E-3L,
- 8.412723297322498080632E-4L,
--5.952345851765688514613E-4L,
- 7.936507795855070755671E-4L,
--2.777777777750349603440E-3L,
- 8.333333333333331447505E-2L,
-};
-#endif
-#if IBMPC
-static short A[] = {
-0xd984,0xcc08,0x91c2,0xa012,0x3ff7, XPD
-0x3d91,0x0304,0x3da1,0xf685,0xbff5, XPD
-0x3bdc,0xaad1,0xd492,0xdc88,0x3ff4, XPD
-0x8b20,0x9fce,0x844e,0x9c09,0xbff4, XPD
-0xf8f2,0x30e5,0x0092,0xd00d,0x3ff4, XPD
-0x4d88,0x03a8,0x60b6,0xb60b,0xbff6, XPD
-0x9fcc,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
-};
-#endif
-#if MIEEE
-static long A[21] = {
-0x3ff70000,0xa01291c2,0xcc08d984,
-0xbff50000,0xf6853da1,0x03043d91,
-0x3ff40000,0xdc88d492,0xaad13bdc,
-0xbff40000,0x9c09844e,0x9fce8b20,
-0x3ff40000,0xd00d0092,0x30e5f8f2,
-0xbff60000,0xb60b60b6,0x03a84d88,
-0x3ffb0000,0xaaaaaaaa,0xaaaa9fcc,
-};
-#endif
-
-/* log gamma(x+2) = x B(x)/C(x)
- * 0 <= x <= 1
- * Peak relative error 7.16e-22
- * Relative spread of error peaks 4.78e-20
- */
-#if UNK
-static long double B[7] = {
--2.163690827643812857640E3L,
--8.723871522843511459790E4L,
--1.104326814691464261197E6L,
--6.111225012005214299996E6L,
--1.625568062543700591014E7L,
--2.003937418103815175475E7L,
--8.875666783650703802159E6L,
-};
-static long double C[7] = {
-/* 1.000000000000000000000E0L,*/
--5.139481484435370143617E2L,
--3.403570840534304670537E4L,
--6.227441164066219501697E5L,
--4.814940379411882186630E6L,
--1.785433287045078156959E7L,
--3.138646407656182662088E7L,
--2.099336717757895876142E7L,
-};
-#endif
-#if IBMPC
-static short B[] = {
-0x9557,0x4995,0x0da1,0x873b,0xc00a, XPD
-0xfe44,0x9af8,0x5b8c,0xaa63,0xc00f, XPD
-0x5aa8,0x7cf5,0x3684,0x86ce,0xc013, XPD
-0x259a,0x258c,0xf206,0xba7f,0xc015, XPD
-0xbe18,0x1ca3,0xc0a0,0xf80a,0xc016, XPD
-0x168f,0x2c42,0x6717,0x98e3,0xc017, XPD
-0x2051,0x9d55,0x92c8,0x876e,0xc016, XPD
-};
-static short C[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xaa77,0xcf2f,0xae76,0x807c,0xc008, XPD
-0xb280,0x0d74,0xb55a,0x84f3,0xc00e, XPD
-0xa505,0xcd30,0x81dc,0x9809,0xc012, XPD
-0x3369,0x4246,0xb8c2,0x92f0,0xc015, XPD
-0x63cf,0x6aee,0xbe6f,0x8837,0xc017, XPD
-0x26bb,0xccc7,0xb009,0xef75,0xc017, XPD
-0x462b,0xbae8,0xab96,0xa02a,0xc017, XPD
-};
-#endif
-#if MIEEE
-static long B[21] = {
-0xc00a0000,0x873b0da1,0x49959557,
-0xc00f0000,0xaa635b8c,0x9af8fe44,
-0xc0130000,0x86ce3684,0x7cf55aa8,
-0xc0150000,0xba7ff206,0x258c259a,
-0xc0160000,0xf80ac0a0,0x1ca3be18,
-0xc0170000,0x98e36717,0x2c42168f,
-0xc0160000,0x876e92c8,0x9d552051,
-};
-static long C[21] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0080000,0x807cae76,0xcf2faa77,
-0xc00e0000,0x84f3b55a,0x0d74b280,
-0xc0120000,0x980981dc,0xcd30a505,
-0xc0150000,0x92f0b8c2,0x42463369,
-0xc0170000,0x8837be6f,0x6aee63cf,
-0xc0170000,0xef75b009,0xccc726bb,
-0xc0170000,0xa02aab96,0xbae8462b,
-};
-#endif
-
-/* log( sqrt( 2*pi ) ) */
-static long double LS2PI = 0.91893853320467274178L;
-#define MAXLGM 1.04848146839019521116e+4928L
-
-
-/* Logarithm of gamma function */
-
-
-long double lgaml(x)
-long double x;
-{
-long double p, q, w, z, f, nx;
-int i;
-
-sgngaml = 1;
-#ifdef NANS
-if( isnanl(x) )
- return(NANL);
-#endif
-#ifdef INFINITIES
-if( !isfinitel(x) )
- return(INFINITYL);
-#endif
-if( x < -34.0L )
- {
- q = -x;
- w = lgaml(q); /* note this modifies sgngam! */
- p = floorl(q);
- if( p == q )
- {
-#ifdef INFINITIES
- mtherr( "lgaml", SING );
- return (INFINITYL);
-#else
- goto loverf;
-#endif
- }
- i = p;
- if( (i & 1) == 0 )
- sgngaml = -1;
- else
- sgngaml = 1;
- z = q - p;
- if( z > 0.5L )
- {
- p += 1.0L;
- z = p - q;
- }
- z = q * sinl( PIL * z );
- if( z == 0.0L )
- goto loverf;
-/* z = LOGPI - logl( z ) - w; */
- z = logl( PIL/z ) - w;
- return( z );
- }
-
-if( x < 13.0L )
- {
- z = 1.0L;
- nx = floorl( x + 0.5L );
- f = x - nx;
- while( x >= 3.0L )
- {
- nx -= 1.0L;
- x = nx + f;
- z *= x;
- }
- while( x < 2.0L )
- {
- if( fabsl(x) <= 0.03125 )
- goto lsmall;
- z /= nx + f;
- nx += 1.0L;
- x = nx + f;
- }
- if( z < 0.0L )
- {
- sgngaml = -1;
- z = -z;
- }
- else
- sgngaml = 1;
- if( x == 2.0L )
- return( logl(z) );
- x = (nx - 2.0L) + f;
- p = x * polevll( x, B, 6 ) / p1evll( x, C, 7);
- return( logl(z) + p );
- }
-
-if( x > MAXLGM )
- {
-loverf:
-#ifdef INFINITIES
- return( sgngaml * INFINITYL );
-#else
- mtherr( "lgaml", OVERFLOW );
- return( sgngaml * MAXNUML );
-#endif
- }
-
-q = ( x - 0.5L ) * logl(x) - x + LS2PI;
-if( x > 1.0e10L )
- return(q);
-p = 1.0L/(x*x);
-q += polevll( p, A, 6 ) / x;
-return( q );
-
-
-lsmall:
-if( x == 0.0L )
- goto loverf;
-if( x < 0.0L )
- {
- x = -x;
- q = z / (x * polevll( x, SN, 8 ));
- }
-else
- q = z / (x * polevll( x, S, 8 ));
-if( q < 0.0L )
- {
- sgngaml = -1;
- q = -q;
- }
-else
- sgngaml = 1;
-q = logl( q );
-return(q);
-}
+++ /dev/null
-/* gdtrl.c
- *
- * Gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, gdtrl();
- *
- * y = gdtrl( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from zero to x of the gamma probability
- * density function:
- *
- *
- * x
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * 0
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igam( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igam().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrl domain x < 0 0.0
- *
- */
-\f/* gdtrcl.c
- *
- * Complemented gamma distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, gdtrcl();
- *
- * y = gdtrcl( a, b, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the integral from x to infinity of the gamma
- * probability density function:
- *
- *
- * inf.
- * b -
- * a | | b-1 -at
- * y = ----- | t e dt
- * - | |
- * | (b) -
- * x
- *
- * The incomplete gamma integral is used, according to the
- * relation
- *
- * y = igamc( b, ax ).
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * gdtrcl domain x < 0 0.0
- *
- */
-\f
-/* gdtrl() */
-
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double igaml ( long double, long double );
-extern long double igamcl ( long double, long double );
-#else
-long double igaml(), igamcl();
-#endif
-
-long double gdtrl( a, b, x )
-long double a, b, x;
-{
-
-if( x < 0.0L )
- {
- mtherr( "gdtrl", DOMAIN );
- return( 0.0L );
- }
-return( igaml( b, a * x ) );
-}
-
-
-
-long double gdtrcl( a, b, x )
-long double a, b, x;
-{
-
-if( x < 0.0L )
- {
- mtherr( "gdtrcl", DOMAIN );
- return( 0.0L );
- }
-return( igamcl( b, a * x ) );
-}
+++ /dev/null
-/*
-C
-C ..................................................................
-C
-C SUBROUTINE GELS
-C
-C PURPOSE
-C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
-C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
-C IS ASSUMED TO BE STORED COLUMNWISE.
-C
-C USAGE
-C CALL GELS(R,A,M,N,EPS,IER,AUX)
-C
-C DESCRIPTION OF PARAMETERS
-C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
-C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
-C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
-C M BY M COEFFICIENT MATRIX. (DESTROYED)
-C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
-C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
-C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
-C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
-C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
-C IER=0 - NO ERROR,
-C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
-C PIVOT ELEMENT AT ANY ELIMINATION STEP
-C EQUAL TO 0,
-C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
-C CANCE INDICATED AT ELIMINATION STEP K+1,
-C WHERE PIVOT ELEMENT WAS LESS THAN OR
-C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
-C ABSOLUTELY GREATEST MAIN DIAGONAL
-C ELEMENT OF MATRIX A.
-C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
-C
-C REMARKS
-C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
-C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
-C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
-C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
-C TOO.
-C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
-C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
-C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
-C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
-C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
-C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
-C GIVEN IN CASE M=1.
-C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
-C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
-C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
-C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
-C
-C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
-C NONE
-C
-C METHOD
-C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
-C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
-C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
-C
-C ..................................................................
-C
-*/
-
-#include <stdio.h>
-#define fabsl(x) ( (x) < 0.0L ? -(x) : (x) )
-
-int gels( A, R, M, EPS, AUX )
-long double A[],R[];
-int M;
-long double EPS;
-long double AUX[];
-{
-int I, J, K, L, IER;
-int II, LL, LLD, LR, LT, LST, LLST, LEND;
-long double tb, piv, tol, pivi;
-
-IER = 0;
-if( M <= 0 )
- {
-fatal:
- IER = -1;
- goto done;
- }
-/* SEARCH FOR GREATEST MAIN DIAGONAL ELEMENT */
-
-/* Diagonal elements are at A(i,i) = 0, 2, 5, 9, 14, ...
- * A(i,j) = A( i(i-1)/2 + j - 1 )
- */
-piv = 0.0L;
-I = 0;
-J = 0;
-L = 0;
-for( K=1; K<=M; K++ )
- {
- L += K;
- tb = fabsl( A[L-1] );
- if( tb > piv )
- {
- piv = tb;
- I = L;
- J = K;
- }
- }
-tol = EPS * piv;
-
-/*
-C MAIN DIAGONAL ELEMENT A(I)=A(J,J) IS FIRST PIVOT ELEMENT.
-C PIV CONTAINS THE ABSOLUTE VALUE OF A(I).
-*/
-
-/* START ELIMINATION LOOP */
-LST = 0;
-LEND = M - 1;
-for( K=1; K<=M; K++ )
- {
-/* TEST ON USEFULNESS OF SYMMETRIC ALGORITHM */
- if( piv <= 0.0L )
- {
- printf( "gels: piv <= 0 at K = %d\n", K );
- goto fatal;
- }
- if( IER == 0 )
- {
- if( piv <= tol )
- {
- IER = K;
-/*
- goto done;
-*/
- }
- }
- LT = J - K;
- LST += K;
-
-/* PIVOT ROW REDUCTION AND ROW INTERCHANGE IN RIGHT HAND SIDE R */
- pivi = 1.0L / A[I-1];
- L = K;
- LL = L + LT;
- tb = pivi * R[LL-1];
- R[LL-1] = R[L-1];
- R[L-1] = tb;
-/* IS ELIMINATION TERMINATED */
- if( K >= M )
- break;
-/*
-C ROW AND COLUMN INTERCHANGE AND PIVOT ROW REDUCTION IN MATRIX A.
-C ELEMENTS OF PIVOT COLUMN ARE SAVED IN AUXILIARY VECTOR AUX.
-*/
- LR = LST + (LT*(K+J-1))/2;
- LL = LR;
- L=LST;
- for( II=K; II<=LEND; II++ )
- {
- L += II;
- LL += 1;
- if( L == LR )
- {
- A[LL-1] = A[LST-1];
- tb = A[L-1];
- goto lab13;
- }
- if( L > LR )
- LL = L + LT;
-
- tb = A[LL-1];
- A[LL-1] = A[L-1];
-lab13:
- AUX[II-1] = tb;
- A[L-1] = pivi * tb;
- }
-/* SAVE COLUMN INTERCHANGE INFORMATION */
- A[LST-1] = LT;
-/* ELEMENT REDUCTION AND SEARCH FOR NEXT PIVOT */
- piv = 0.0L;
- LLST = LST;
- LT = 0;
- for( II=K; II<=LEND; II++ )
- {
- pivi = -AUX[II-1];
- LL = LLST;
- LT += 1;
- for( LLD=II; LLD<=LEND; LLD++ )
- {
- LL += LLD;
- L = LL + LT;
- A[L-1] += pivi * A[LL-1];
- }
- LLST += II;
- LR = LLST + LT;
- tb =fabsl( A[LR-1] );
- if( tb > piv )
- {
- piv = tb;
- I = LR;
- J = II + 1;
- }
- LR = K;
- LL = LR + LT;
- R[LL-1] += pivi * R[LR-1];
- }
- }
-/* END OF ELIMINATION LOOP */
-
-/* BACK SUBSTITUTION AND BACK INTERCHANGE */
-
-if( LEND <= 0 )
- {
- printf( "gels: LEND = %d\n", LEND );
- if( LEND < 0 )
- goto fatal;
- goto done;
- }
-II = M;
-for( I=2; I<=M; I++ )
- {
- LST -= II;
- II -= 1;
- L = A[LST-1] + 0.5L;
- J = II;
- tb = R[J-1];
- LL = J;
- K = LST;
- for( LT=II; LT<=LEND; LT++ )
- {
- LL += 1;
- K += LT;
- tb -= A[K-1] * R[LL-1];
- }
- K = J + L;
- R[J-1] = R[K-1];
- R[K-1] = tb;
- }
-done:
-if( IER )
- printf( "gels error %d!\n", IER );
-return( IER );
-}
+++ /dev/null
-/* ieee.c
- *
- * Extended precision IEEE binary floating point arithmetic routines
- *
- * Numbers are stored in C language as arrays of 16-bit unsigned
- * short integers. The arguments of the routines are pointers to
- * the arrays.
- *
- *
- * External e type data structure, simulates Intel 8087 chip
- * temporary real format but possibly with a larger significand:
- *
- * NE-1 significand words (least significant word first,
- * most significant bit is normally set)
- * exponent (value = EXONE for 1.0,
- * top bit is the sign)
- *
- *
- * Internal data structure of a number (a "word" is 16 bits):
- *
- * ei[0] sign word (0 for positive, 0xffff for negative)
- * ei[1] biased exponent (value = EXONE for the number 1.0)
- * ei[2] high guard word (always zero after normalization)
- * ei[3]
- * to ei[NI-2] significand (NI-4 significand words,
- * most significant word first,
- * most significant bit is set)
- * ei[NI-1] low guard word (0x8000 bit is rounding place)
- *
- *
- *
- * Routines for external format numbers
- *
- * asctoe( string, e ) ASCII string to extended double e type
- * asctoe64( string, &d ) ASCII string to long double
- * asctoe53( string, &d ) ASCII string to double
- * asctoe24( string, &f ) ASCII string to single
- * asctoeg( string, e, prec ) ASCII string to specified precision
- * e24toe( &f, e ) IEEE single precision to e type
- * e53toe( &d, e ) IEEE double precision to e type
- * e64toe( &d, e ) IEEE long double precision to e type
- * eabs(e) absolute value
- * eadd( a, b, c ) c = b + a
- * eclear(e) e = 0
- * ecmp (a, b) Returns 1 if a > b, 0 if a == b,
- * -1 if a < b, -2 if either a or b is a NaN.
- * ediv( a, b, c ) c = b / a
- * efloor( a, b ) truncate to integer, toward -infinity
- * efrexp( a, exp, s ) extract exponent and significand
- * eifrac( e, &l, frac ) e to long integer and e type fraction
- * euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
- * einfin( e ) set e to infinity, leaving its sign alone
- * eldexp( a, n, b ) multiply by 2**n
- * emov( a, b ) b = a
- * emul( a, b, c ) c = b * a
- * eneg(e) e = -e
- * eround( a, b ) b = nearest integer value to a
- * esub( a, b, c ) c = b - a
- * e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
- * e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
- * e64toasc( &d, str, n ) long double to ASCII string
- * etoasc( e, str, n ) e to ASCII string, n digits after decimal
- * etoe24( e, &f ) convert e type to IEEE single precision
- * etoe53( e, &d ) convert e type to IEEE double precision
- * etoe64( e, &d ) convert e type to IEEE long double precision
- * ltoe( &l, e ) long (32 bit) integer to e type
- * ultoe( &l, e ) unsigned long (32 bit) integer to e type
- * eisneg( e ) 1 if sign bit of e != 0, else 0
- * eisinf( e ) 1 if e has maximum exponent (non-IEEE)
- * or is infinite (IEEE)
- * eisnan( e ) 1 if e is a NaN
- * esqrt( a, b ) b = square root of a
- *
- *
- * Routines for internal format numbers
- *
- * eaddm( ai, bi ) add significands, bi = bi + ai
- * ecleaz(ei) ei = 0
- * ecleazs(ei) set ei = 0 but leave its sign alone
- * ecmpm( ai, bi ) compare significands, return 1, 0, or -1
- * edivm( ai, bi ) divide significands, bi = bi / ai
- * emdnorm(ai,l,s,exp) normalize and round off
- * emovi( a, ai ) convert external a to internal ai
- * emovo( ai, a ) convert internal ai to external a
- * emovz( ai, bi ) bi = ai, low guard word of bi = 0
- * emulm( ai, bi ) multiply significands, bi = bi * ai
- * enormlz(ei) left-justify the significand
- * eshdn1( ai ) shift significand and guards down 1 bit
- * eshdn8( ai ) shift down 8 bits
- * eshdn6( ai ) shift down 16 bits
- * eshift( ai, n ) shift ai n bits up (or down if n < 0)
- * eshup1( ai ) shift significand and guards up 1 bit
- * eshup8( ai ) shift up 8 bits
- * eshup6( ai ) shift up 16 bits
- * esubm( ai, bi ) subtract significands, bi = bi - ai
- *
- *
- * The result is always normalized and rounded to NI-4 word precision
- * after each arithmetic operation.
- *
- * Exception flags are NOT fully supported.
- *
- * Define INFINITY in mconf.h for support of infinity; otherwise a
- * saturation arithmetic is implemented.
- *
- * Define NANS for support of Not-a-Number items; otherwise the
- * arithmetic will never produce a NaN output, and might be confused
- * by a NaN input.
- * If NaN's are supported, the output of ecmp(a,b) is -2 if
- * either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
- * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
- * if in doubt.
- * Signaling NaN's are NOT supported; they are treated the same
- * as quiet NaN's.
- *
- * Denormals are always supported here where appropriate (e.g., not
- * for conversion to DEC numbers).
- */
-
-/*
- * Revision history:
- *
- * 5 Jan 84 PDP-11 assembly language version
- * 2 Mar 86 fixed bug in asctoq()
- * 6 Dec 86 C language version
- * 30 Aug 88 100 digit version, improved rounding
- * 15 May 92 80-bit long double support
- *
- * Author: S. L. Moshier.
- */
-
-#include <stdio.h>
-#include <math.h>
-#include "ehead.h"
-
-/* Change UNK into something else. */
-#ifdef UNK
-#undef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-#endif
-
-/* NaN's require infinity support. */
-#ifdef NANS
-#ifndef INFINITY
-#define INFINITY
-#endif
-#endif
-
-/* This handles 64-bit long ints. */
-#define LONGBITS (8 * sizeof(long))
-
-/* Control register for rounding precision.
- * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
- */
-int rndprc = NBITS;
-extern int rndprc;
-
-#ifdef ANSIPROT
-extern void eaddm ( unsigned short *, unsigned short * );
-extern void esubm ( unsigned short *, unsigned short * );
-extern void emdnorm ( unsigned short *, int, int, long, int );
-extern void asctoeg ( char *, unsigned short *, int );
-extern void enan ( unsigned short *, int );
-extern void asctoe24 ( char *, unsigned short * );
-extern void asctoe53 ( char *, unsigned short * );
-extern void asctoe64 ( char *, unsigned short * );
-extern void asctoe113 ( char *, unsigned short * );
-extern void eremain ( unsigned short *, unsigned short *, unsigned short * );
-extern void einit ( void );
-extern void eiremain ( unsigned short *, unsigned short * );
-extern int ecmp ( unsigned short *, unsigned short * );
-extern int edivm ( unsigned short *, unsigned short * );
-extern int emulm ( unsigned short *, unsigned short * );
-extern int eisneg ( unsigned short * );
-extern int eisinf ( unsigned short * );
-extern void emovi ( unsigned short *, unsigned short * );
-extern void emovo ( unsigned short *, unsigned short * );
-extern void emovz ( unsigned short *, unsigned short * );
-extern void ecleaz ( unsigned short * );
-extern void eadd1 ( unsigned short *, unsigned short *, unsigned short * );
-extern int eisnan ( unsigned short * );
-extern int eiisnan ( unsigned short * );
-static void toe24( unsigned short *, unsigned short * );
-static void toe53( unsigned short *, unsigned short * );
-static void toe64( unsigned short *, unsigned short * );
-static void toe113( unsigned short *, unsigned short * );
-void einfin ( unsigned short * );
-void eshdn1 ( unsigned short * );
-void eshup1 ( unsigned short * );
-void eshup6 ( unsigned short * );
-void eshdn6 ( unsigned short * );
-void eshup8 ( unsigned short * );
-void eshdn8 ( unsigned short * );
-void m16m ( unsigned short, unsigned short *, unsigned short * );
-int ecmpm ( unsigned short *, unsigned short * );
-int enormlz ( unsigned short * );
-void ecleazs ( unsigned short * );
-int eshift ( unsigned short *, int );
-void emov ( unsigned short *, unsigned short * );
-void eneg ( unsigned short * );
-void eclear ( unsigned short * );
-void efloor ( unsigned short *, unsigned short * );
-void eadd ( unsigned short *, unsigned short *, unsigned short * );
-void esub ( unsigned short *, unsigned short *, unsigned short * );
-void ediv ( unsigned short *, unsigned short *, unsigned short * );
-void emul ( unsigned short *, unsigned short *, unsigned short * );
-void e24toe ( unsigned short *, unsigned short * );
-void e53toe ( unsigned short *, unsigned short * );
-void e64toe ( unsigned short *, unsigned short * );
-void e113toe ( unsigned short *, unsigned short * );
-void etoasc ( unsigned short *, char *, int );
-static int eiisinf ( unsigned short * );
-#else
-void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
-static void toe24(), toe53(), toe64(), toe113();
-void eremain(), einit(), eiremain();
-int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
-void emovi(), emovo(), emovz(), ecleaz(), eadd1();
-/* void etodec(), todec(), dectoe(); */
-int eisnan(), eiisnan(), ecmpm(), enormlz(), eshift();
-void einfin(), eshdn1(), eshup1(), eshup6(), eshdn6();
-void eshup8(), eshdn8(), m16m();
-void eadd(), esub(), ediv(), emul();
-void ecleazs(), emov(), eneg(), eclear(), efloor();
-void e24toe(), e53toe(), e64toe(), e113toe(), etoasc();
-static int eiisinf();
-#endif
-
-
-void einit()
-{
-}
-
-/*
-; Clear out entire external format number.
-;
-; unsigned short x[];
-; eclear( x );
-*/
-
-void eclear( x )
-register unsigned short *x;
-{
-register int i;
-
-for( i=0; i<NE; i++ )
- *x++ = 0;
-}
-
-
-
-/* Move external format number from a to b.
- *
- * emov( a, b );
- */
-
-void emov( a, b )
-register unsigned short *a, *b;
-{
-register int i;
-
-for( i=0; i<NE; i++ )
- *b++ = *a++;
-}
-
-
-/*
-; Absolute value of external format number
-;
-; short x[NE];
-; eabs( x );
-*/
-
-void eabs(x)
-unsigned short x[]; /* x is the memory address of a short */
-{
-
-x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */
-}
-
-
-
-
-/*
-; Negate external format number
-;
-; unsigned short x[NE];
-; eneg( x );
-*/
-
-void eneg(x)
-unsigned short x[];
-{
-
-#ifdef NANS
-if( eisnan(x) )
- return;
-#endif
-x[NE-1] ^= 0x8000; /* Toggle the sign bit */
-}
-
-
-
-/* Return 1 if external format number is negative,
- * else return zero.
- */
-int eisneg(x)
-unsigned short x[];
-{
-
-#ifdef NANS
-if( eisnan(x) )
- return( 0 );
-#endif
-if( x[NE-1] & 0x8000 )
- return( 1 );
-else
- return( 0 );
-}
-
-
-/* Return 1 if external format number has maximum possible exponent,
- * else return zero.
- */
-int eisinf(x)
-unsigned short x[];
-{
-
-if( (x[NE-1] & 0x7fff) == 0x7fff )
- {
-#ifdef NANS
- if( eisnan(x) )
- return( 0 );
-#endif
- return( 1 );
- }
-else
- return( 0 );
-}
-
-/* Check if e-type number is not a number.
- */
-int eisnan(x)
-unsigned short x[];
-{
-
-#ifdef NANS
-int i;
-/* NaN has maximum exponent */
-if( (x[NE-1] & 0x7fff) != 0x7fff )
- return (0);
-/* ... and non-zero significand field. */
-for( i=0; i<NE-1; i++ )
- {
- if( *x++ != 0 )
- return (1);
- }
-#endif
-return (0);
-}
-
-/*
-; Fill entire number, including exponent and significand, with
-; largest possible number. These programs implement a saturation
-; value that is an ordinary, legal number. A special value
-; "infinity" may also be implemented; this would require tests
-; for that value and implementation of special rules for arithmetic
-; operations involving inifinity.
-*/
-
-void einfin(x)
-register unsigned short *x;
-{
-register int i;
-
-#ifdef INFINITY
-for( i=0; i<NE-1; i++ )
- *x++ = 0;
-*x |= 32767;
-#else
-for( i=0; i<NE-1; i++ )
- *x++ = 0xffff;
-*x |= 32766;
-if( rndprc < NBITS )
- {
- if (rndprc == 113)
- {
- *(x - 9) = 0;
- *(x - 8) = 0;
- }
- if( rndprc == 64 )
- {
- *(x-5) = 0;
- }
- if( rndprc == 53 )
- {
- *(x-4) = 0xf800;
- }
- else
- {
- *(x-4) = 0;
- *(x-3) = 0;
- *(x-2) = 0xff00;
- }
- }
-#endif
-}
-
-
-
-/* Move in external format number,
- * converting it to internal format.
- */
-void emovi( a, b )
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-int i;
-
-q = b;
-p = a + (NE-1); /* point to last word of external number */
-/* get the sign bit */
-if( *p & 0x8000 )
- *q++ = 0xffff;
-else
- *q++ = 0;
-/* get the exponent */
-*q = *p--;
-*q++ &= 0x7fff; /* delete the sign bit */
-#ifdef INFINITY
-if( (*(q-1) & 0x7fff) == 0x7fff )
- {
-#ifdef NANS
- if( eisnan(a) )
- {
- *q++ = 0;
- for( i=3; i<NI; i++ )
- *q++ = *p--;
- return;
- }
-#endif
- for( i=2; i<NI; i++ )
- *q++ = 0;
- return;
- }
-#endif
-/* clear high guard word */
-*q++ = 0;
-/* move in the significand */
-for( i=0; i<NE-1; i++ )
- *q++ = *p--;
-/* clear low guard word */
-*q = 0;
-}
-
-
-/* Move internal format number out,
- * converting it to external format.
- */
-void emovo( a, b )
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-unsigned short i;
-
-p = a;
-q = b + (NE-1); /* point to output exponent */
-/* combine sign and exponent */
-i = *p++;
-if( i )
- *q-- = *p++ | 0x8000;
-else
- *q-- = *p++;
-#ifdef INFINITY
-if( *(p-1) == 0x7fff )
- {
-#ifdef NANS
- if( eiisnan(a) )
- {
- enan( b, NBITS );
- return;
- }
-#endif
- einfin(b);
- return;
- }
-#endif
-/* skip over guard word */
-++p;
-/* move the significand */
-for( i=0; i<NE-1; i++ )
- *q-- = *p++;
-}
-
-
-
-
-/* Clear out internal format number.
- */
-
-void ecleaz( xi )
-register unsigned short *xi;
-{
-register int i;
-
-for( i=0; i<NI; i++ )
- *xi++ = 0;
-}
-
-/* same, but don't touch the sign. */
-
-void ecleazs( xi )
-register unsigned short *xi;
-{
-register int i;
-
-++xi;
-for(i=0; i<NI-1; i++)
- *xi++ = 0;
-}
-
-
-
-
-/* Move internal format number from a to b.
- */
-void emovz( a, b )
-register unsigned short *a, *b;
-{
-register int i;
-
-for( i=0; i<NI-1; i++ )
- *b++ = *a++;
-/* clear low guard word */
-*b = 0;
-}
-
-/* Return nonzero if internal format number is a NaN.
- */
-
-int eiisnan (x)
-unsigned short x[];
-{
-int i;
-
-if( (x[E] & 0x7fff) == 0x7fff )
- {
- for( i=M+1; i<NI; i++ )
- {
- if( x[i] != 0 )
- return(1);
- }
- }
-return(0);
-}
-
-#ifdef INFINITY
-/* Return nonzero if internal format number is infinite. */
-
-static int
-eiisinf (x)
- unsigned short x[];
-{
-
-#ifdef NANS
- if (eiisnan (x))
- return (0);
-#endif
- if ((x[E] & 0x7fff) == 0x7fff)
- return (1);
- return (0);
-}
-#endif
-
-/*
-; Compare significands of numbers in internal format.
-; Guard words are included in the comparison.
-;
-; unsigned short a[NI], b[NI];
-; cmpm( a, b );
-;
-; for the significands:
-; returns +1 if a > b
-; 0 if a == b
-; -1 if a < b
-*/
-int ecmpm( a, b )
-register unsigned short *a, *b;
-{
-int i;
-
-a += M; /* skip up to significand area */
-b += M;
-for( i=M; i<NI; i++ )
- {
- if( *a++ != *b++ )
- goto difrnt;
- }
-return(0);
-
-difrnt:
-if( *(--a) > *(--b) )
- return(1);
-else
- return(-1);
-}
-
-
-/*
-; Shift significand down by 1 bit
-*/
-
-void eshdn1(x)
-register unsigned short *x;
-{
-register unsigned short bits;
-int i;
-
-x += M; /* point to significand area */
-
-bits = 0;
-for( i=M; i<NI; i++ )
- {
- if( *x & 1 )
- bits |= 1;
- *x >>= 1;
- if( bits & 2 )
- *x |= 0x8000;
- bits <<= 1;
- ++x;
- }
-}
-
-
-
-/*
-; Shift significand up by 1 bit
-*/
-
-void eshup1(x)
-register unsigned short *x;
-{
-register unsigned short bits;
-int i;
-
-x += NI-1;
-bits = 0;
-
-for( i=M; i<NI; i++ )
- {
- if( *x & 0x8000 )
- bits |= 1;
- *x <<= 1;
- if( bits & 2 )
- *x |= 1;
- bits <<= 1;
- --x;
- }
-}
-
-
-
-/*
-; Shift significand down by 8 bits
-*/
-
-void eshdn8(x)
-register unsigned short *x;
-{
-register unsigned short newbyt, oldbyt;
-int i;
-
-x += M;
-oldbyt = 0;
-for( i=M; i<NI; i++ )
- {
- newbyt = *x << 8;
- *x >>= 8;
- *x |= oldbyt;
- oldbyt = newbyt;
- ++x;
- }
-}
-
-/*
-; Shift significand up by 8 bits
-*/
-
-void eshup8(x)
-register unsigned short *x;
-{
-int i;
-register unsigned short newbyt, oldbyt;
-
-x += NI-1;
-oldbyt = 0;
-
-for( i=M; i<NI; i++ )
- {
- newbyt = *x >> 8;
- *x <<= 8;
- *x |= oldbyt;
- oldbyt = newbyt;
- --x;
- }
-}
-
-/*
-; Shift significand up by 16 bits
-*/
-
-void eshup6(x)
-register unsigned short *x;
-{
-int i;
-register unsigned short *p;
-
-p = x + M;
-x += M + 1;
-
-for( i=M; i<NI-1; i++ )
- *p++ = *x++;
-
-*p = 0;
-}
-
-/*
-; Shift significand down by 16 bits
-*/
-
-void eshdn6(x)
-register unsigned short *x;
-{
-int i;
-register unsigned short *p;
-
-x += NI-1;
-p = x + 1;
-
-for( i=M; i<NI-1; i++ )
- *(--p) = *(--x);
-
-*(--p) = 0;
-}
-\f
-/*
-; Add significands
-; x + y replaces y
-*/
-
-void eaddm( x, y )
-unsigned short *x, *y;
-{
-register unsigned long a;
-int i;
-unsigned int carry;
-
-x += NI-1;
-y += NI-1;
-carry = 0;
-for( i=M; i<NI; i++ )
- {
- a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
- if( a & 0x10000 )
- carry = 1;
- else
- carry = 0;
- *y = (unsigned short )a;
- --x;
- --y;
- }
-}
-
-/*
-; Subtract significands
-; y - x replaces y
-*/
-
-void esubm( x, y )
-unsigned short *x, *y;
-{
-unsigned long a;
-int i;
-unsigned int carry;
-
-x += NI-1;
-y += NI-1;
-carry = 0;
-for( i=M; i<NI; i++ )
- {
- a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
- if( a & 0x10000 )
- carry = 1;
- else
- carry = 0;
- *y = (unsigned short )a;
- --x;
- --y;
- }
-}
-
-
-/* Divide significands */
-
-static unsigned short equot[NI] = {0}; /* was static */
-
-#if 0
-int edivm( den, num )
-unsigned short den[], num[];
-{
-int i;
-register unsigned short *p, *q;
-unsigned short j;
-
-p = &equot[0];
-*p++ = num[0];
-*p++ = num[1];
-
-for( i=M; i<NI; i++ )
- {
- *p++ = 0;
- }
-
-/* Use faster compare and subtraction if denominator
- * has only 15 bits of significane.
- */
-p = &den[M+2];
-if( *p++ == 0 )
- {
- for( i=M+3; i<NI; i++ )
- {
- if( *p++ != 0 )
- goto fulldiv;
- }
- if( (den[M+1] & 1) != 0 )
- goto fulldiv;
- eshdn1(num);
- eshdn1(den);
-
- p = &den[M+1];
- q = &num[M+1];
-
- for( i=0; i<NBITS+2; i++ )
- {
- if( *p <= *q )
- {
- *q -= *p;
- j = 1;
- }
- else
- {
- j = 0;
- }
- eshup1(equot);
- equot[NI-2] |= j;
- eshup1(num);
- }
- goto divdon;
- }
-
-/* The number of quotient bits to calculate is
- * NBITS + 1 scaling guard bit + 1 roundoff bit.
- */
-fulldiv:
-
-p = &equot[NI-2];
-for( i=0; i<NBITS+2; i++ )
- {
- if( ecmpm(den,num) <= 0 )
- {
- esubm(den, num);
- j = 1; /* quotient bit = 1 */
- }
- else
- j = 0;
- eshup1(equot);
- *p |= j;
- eshup1(num);
- }
-
-divdon:
-
-eshdn1( equot );
-eshdn1( equot );
-
-/* test for nonzero remainder after roundoff bit */
-p = &num[M];
-j = 0;
-for( i=M; i<NI; i++ )
- {
- j |= *p++;
- }
-if( j )
- j = 1;
-
-
-for( i=0; i<NI; i++ )
- num[i] = equot[i];
-return( (int )j );
-}
-
-/* Multiply significands */
-int emulm( a, b )
-unsigned short a[], b[];
-{
-unsigned short *p, *q;
-int i, j, k;
-
-equot[0] = b[0];
-equot[1] = b[1];
-for( i=M; i<NI; i++ )
- equot[i] = 0;
-
-p = &a[NI-2];
-k = NBITS;
-while( *p == 0 ) /* significand is not supposed to be all zero */
- {
- eshdn6(a);
- k -= 16;
- }
-if( (*p & 0xff) == 0 )
- {
- eshdn8(a);
- k -= 8;
- }
-
-q = &equot[NI-1];
-j = 0;
-for( i=0; i<k; i++ )
- {
- if( *p & 1 )
- eaddm(b, equot);
-/* remember if there were any nonzero bits shifted out */
- if( *q & 1 )
- j |= 1;
- eshdn1(a);
- eshdn1(equot);
- }
-
-for( i=0; i<NI; i++ )
- b[i] = equot[i];
-
-/* return flag for lost nonzero bits */
-return(j);
-}
-
-#else
-
-/* Multiply significand of e-type number b
-by 16-bit quantity a, e-type result to c. */
-
-void m16m( a, b, c )
-unsigned short a;
-unsigned short b[], c[];
-{
-register unsigned short *pp;
-register unsigned long carry;
-unsigned short *ps;
-unsigned short p[NI];
-unsigned long aa, m;
-int i;
-
-aa = a;
-pp = &p[NI-2];
-*pp++ = 0;
-*pp = 0;
-ps = &b[NI-1];
-
-for( i=M+1; i<NI; i++ )
- {
- if( *ps == 0 )
- {
- --ps;
- --pp;
- *(pp-1) = 0;
- }
- else
- {
- m = (unsigned long) aa * *ps--;
- carry = (m & 0xffff) + *pp;
- *pp-- = (unsigned short )carry;
- carry = (carry >> 16) + (m >> 16) + *pp;
- *pp = (unsigned short )carry;
- *(pp-1) = carry >> 16;
- }
- }
-for( i=M; i<NI; i++ )
- c[i] = p[i];
-}
-
-
-/* Divide significands. Neither the numerator nor the denominator
-is permitted to have its high guard word nonzero. */
-
-
-int edivm( den, num )
-unsigned short den[], num[];
-{
-int i;
-register unsigned short *p;
-unsigned long tnum;
-unsigned short j, tdenm, tquot;
-unsigned short tprod[NI+1];
-
-p = &equot[0];
-*p++ = num[0];
-*p++ = num[1];
-
-for( i=M; i<NI; i++ )
- {
- *p++ = 0;
- }
-eshdn1( num );
-tdenm = den[M+1];
-for( i=M; i<NI; i++ )
- {
- /* Find trial quotient digit (the radix is 65536). */
- tnum = (((unsigned long) num[M]) << 16) + num[M+1];
-
- /* Do not execute the divide instruction if it will overflow. */
- if( (tdenm * ((unsigned long)0xffffL)) < tnum )
- tquot = 0xffff;
- else
- tquot = tnum / tdenm;
-
- /* Prove that the divide worked. */
-/*
- tcheck = (unsigned long )tquot * tdenm;
- if( tnum - tcheck > tdenm )
- tquot = 0xffff;
-*/
- /* Multiply denominator by trial quotient digit. */
- m16m( tquot, den, tprod );
- /* The quotient digit may have been overestimated. */
- if( ecmpm( tprod, num ) > 0 )
- {
- tquot -= 1;
- esubm( den, tprod );
- if( ecmpm( tprod, num ) > 0 )
- {
- tquot -= 1;
- esubm( den, tprod );
- }
- }
-/*
- if( ecmpm( tprod, num ) > 0 )
- {
- eshow( "tprod", tprod );
- eshow( "num ", num );
- printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
- tnum, den[M+1], tquot );
- }
-*/
- esubm( tprod, num );
-/*
- if( ecmpm( num, den ) >= 0 )
- {
- eshow( "num ", num );
- eshow( "den ", den );
- printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
- tnum, den[M+1], tquot );
- }
-*/
- equot[i] = tquot;
- eshup6(num);
- }
-/* test for nonzero remainder after roundoff bit */
-p = &num[M];
-j = 0;
-for( i=M; i<NI; i++ )
- {
- j |= *p++;
- }
-if( j )
- j = 1;
-
-for( i=0; i<NI; i++ )
- num[i] = equot[i];
-
-return( (int )j );
-}
-
-
-
-/* Multiply significands */
-int emulm( a, b )
-unsigned short a[], b[];
-{
-unsigned short *p, *q;
-unsigned short pprod[NI];
-unsigned short j;
-int i;
-
-equot[0] = b[0];
-equot[1] = b[1];
-for( i=M; i<NI; i++ )
- equot[i] = 0;
-
-j = 0;
-p = &a[NI-1];
-q = &equot[NI-1];
-for( i=M+1; i<NI; i++ )
- {
- if( *p == 0 )
- {
- --p;
- }
- else
- {
- m16m( *p--, b, pprod );
- eaddm(pprod, equot);
- }
- j |= *q;
- eshdn6(equot);
- }
-
-for( i=0; i<NI; i++ )
- b[i] = equot[i];
-
-/* return flag for lost nonzero bits */
-return( (int)j );
-}
-
-
-/*
-eshow(str, x)
-char *str;
-unsigned short *x;
-{
-int i;
-
-printf( "%s ", str );
-for( i=0; i<NI; i++ )
- printf( "%04x ", *x++ );
-printf( "\n" );
-}
-*/
-#endif
-
-
-
-/*
- * Normalize and round off.
- *
- * The internal format number to be rounded is "s".
- * Input "lost" indicates whether the number is exact.
- * This is the so-called sticky bit.
- *
- * Input "subflg" indicates whether the number was obtained
- * by a subtraction operation. In that case if lost is nonzero
- * then the number is slightly smaller than indicated.
- *
- * Input "exp" is the biased exponent, which may be negative.
- * the exponent field of "s" is ignored but is replaced by
- * "exp" as adjusted by normalization and rounding.
- *
- * Input "rcntrl" is the rounding control.
- */
-
-static int rlast = -1;
-static int rw = 0;
-static unsigned short rmsk = 0;
-static unsigned short rmbit = 0;
-static unsigned short rebit = 0;
-static int re = 0;
-static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0};
-
-void emdnorm( s, lost, subflg, exp, rcntrl )
-unsigned short s[];
-int lost;
-int subflg;
-long exp;
-int rcntrl;
-{
-int i, j;
-unsigned short r;
-
-/* Normalize */
-j = enormlz( s );
-
-/* a blank significand could mean either zero or infinity. */
-#ifndef INFINITY
-if( j > NBITS )
- {
- ecleazs( s );
- return;
- }
-#endif
-exp -= j;
-#ifndef INFINITY
-if( exp >= 32767L )
- goto overf;
-#else
-if( (j > NBITS) && (exp < 32767L) )
- {
- ecleazs( s );
- return;
- }
-#endif
-if( exp < 0L )
- {
- if( exp > (long )(-NBITS-1) )
- {
- j = (int )exp;
- i = eshift( s, j );
- if( i )
- lost = 1;
- }
- else
- {
- ecleazs( s );
- return;
- }
- }
-/* Round off, unless told not to by rcntrl. */
-if( rcntrl == 0 )
- goto mdfin;
-/* Set up rounding parameters if the control register changed. */
-if( rndprc != rlast )
- {
- ecleaz( rbit );
- switch( rndprc )
- {
- default:
- case NBITS:
- rw = NI-1; /* low guard word */
- rmsk = 0xffff;
- rmbit = 0x8000;
- rebit = 1;
- re = rw - 1;
- break;
- case 113:
- rw = 10;
- rmsk = 0x7fff;
- rmbit = 0x4000;
- rebit = 0x8000;
- re = rw;
- break;
- case 64:
- rw = 7;
- rmsk = 0xffff;
- rmbit = 0x8000;
- rebit = 1;
- re = rw-1;
- break;
-/* For DEC arithmetic */
- case 56:
- rw = 6;
- rmsk = 0xff;
- rmbit = 0x80;
- rebit = 0x100;
- re = rw;
- break;
- case 53:
- rw = 6;
- rmsk = 0x7ff;
- rmbit = 0x0400;
- rebit = 0x800;
- re = rw;
- break;
- case 24:
- rw = 4;
- rmsk = 0xff;
- rmbit = 0x80;
- rebit = 0x100;
- re = rw;
- break;
- }
- rbit[re] = rebit;
- rlast = rndprc;
- }
-
-/* Shift down 1 temporarily if the data structure has an implied
- * most significant bit and the number is denormal.
- * For rndprc = 64 or NBITS, there is no implied bit.
- * But Intel long double denormals lose one bit of significance even so.
- */
-#ifdef IBMPC
-if( (exp <= 0) && (rndprc != NBITS) )
-#else
-if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
-#endif
- {
- lost |= s[NI-1] & 1;
- eshdn1(s);
- }
-/* Clear out all bits below the rounding bit,
- * remembering in r if any were nonzero.
- */
-r = s[rw] & rmsk;
-if( rndprc < NBITS )
- {
- i = rw + 1;
- while( i < NI )
- {
- if( s[i] )
- r |= 1;
- s[i] = 0;
- ++i;
- }
- }
-s[rw] &= ~rmsk;
-if( (r & rmbit) != 0 )
- {
- if( r == rmbit )
- {
- if( lost == 0 )
- { /* round to even */
- if( (s[re] & rebit) == 0 )
- goto mddone;
- }
- else
- {
- if( subflg != 0 )
- goto mddone;
- }
- }
- eaddm( rbit, s );
- }
-mddone:
-#ifdef IBMPC
-if( (exp <= 0) && (rndprc != NBITS) )
-#else
-if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
-#endif
- {
- eshup1(s);
- }
-if( s[2] != 0 )
- { /* overflow on roundoff */
- eshdn1(s);
- exp += 1;
- }
-mdfin:
-s[NI-1] = 0;
-if( exp >= 32767L )
- {
-#ifndef INFINITY
-overf:
-#endif
-#ifdef INFINITY
- s[1] = 32767;
- for( i=2; i<NI-1; i++ )
- s[i] = 0;
-#else
- s[1] = 32766;
- s[2] = 0;
- for( i=M+1; i<NI-1; i++ )
- s[i] = 0xffff;
- s[NI-1] = 0;
- if( (rndprc < 64) || (rndprc == 113) )
- {
- s[rw] &= ~rmsk;
- if( rndprc == 24 )
- {
- s[5] = 0;
- s[6] = 0;
- }
- }
-#endif
- return;
- }
-if( exp < 0 )
- s[1] = 0;
-else
- s[1] = (unsigned short )exp;
-}
-
-
-
-/*
-; Subtract external format numbers.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; esub( a, b, c ); c = b - a
-*/
-
-static int subflg = 0;
-
-void esub( a, b, c )
-unsigned short *a, *b, *c;
-{
-
-#ifdef NANS
-if( eisnan(a) )
- {
- emov (a, c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Infinity minus infinity is a NaN.
- * Test for subtracting infinities of the same sign.
- */
-if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0))
- {
- mtherr( "esub", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-subflg = 1;
-eadd1( a, b, c );
-}
-
-
-/*
-; Add.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; eadd( a, b, c ); c = b + a
-*/
-void eadd( a, b, c )
-unsigned short *a, *b, *c;
-{
-
-#ifdef NANS
-/* NaN plus anything is a NaN. */
-if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Infinity minus infinity is a NaN.
- * Test for adding infinities of opposite signs.
- */
-if( eisinf(a) && eisinf(b)
- && ((eisneg(a) ^ eisneg(b)) != 0) )
- {
- mtherr( "eadd", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-subflg = 0;
-eadd1( a, b, c );
-}
-
-void eadd1( a, b, c )
-unsigned short *a, *b, *c;
-{
-unsigned short ai[NI], bi[NI], ci[NI];
-int i, lost, j, k;
-long lt, lta, ltb;
-
-#ifdef INFINITY
-if( eisinf(a) )
- {
- emov(a,c);
- if( subflg )
- eneg(c);
- return;
- }
-if( eisinf(b) )
- {
- emov(b,c);
- return;
- }
-#endif
-emovi( a, ai );
-emovi( b, bi );
-if( subflg )
- ai[0] = ~ai[0];
-
-/* compare exponents */
-lta = ai[E];
-ltb = bi[E];
-lt = lta - ltb;
-if( lt > 0L )
- { /* put the larger number in bi */
- emovz( bi, ci );
- emovz( ai, bi );
- emovz( ci, ai );
- ltb = bi[E];
- lt = -lt;
- }
-lost = 0;
-if( lt != 0L )
- {
- if( lt < (long )(-NBITS-1) )
- goto done; /* answer same as larger addend */
- k = (int )lt;
- lost = eshift( ai, k ); /* shift the smaller number down */
- }
-else
- {
-/* exponents were the same, so must compare significands */
- i = ecmpm( ai, bi );
- if( i == 0 )
- { /* the numbers are identical in magnitude */
- /* if different signs, result is zero */
- if( ai[0] != bi[0] )
- {
- eclear(c);
- return;
- }
- /* if same sign, result is double */
- /* double denomalized tiny number */
- if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) )
- {
- eshup1( bi );
- goto done;
- }
- /* add 1 to exponent unless both are zero! */
- for( j=1; j<NI-1; j++ )
- {
- if( bi[j] != 0 )
- {
-/* This could overflow, but let emovo take care of that. */
- ltb += 1;
- break;
- }
- }
- bi[E] = (unsigned short )ltb;
- goto done;
- }
- if( i > 0 )
- { /* put the larger number in bi */
- emovz( bi, ci );
- emovz( ai, bi );
- emovz( ci, ai );
- }
- }
-if( ai[0] == bi[0] )
- {
- eaddm( ai, bi );
- subflg = 0;
- }
-else
- {
- esubm( ai, bi );
- subflg = 1;
- }
-emdnorm( bi, lost, subflg, ltb, 64 );
-
-done:
-emovo( bi, c );
-}
-
-
-
-/*
-; Divide.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; ediv( a, b, c ); c = b / a
-*/
-void ediv( a, b, c )
-unsigned short *a, *b, *c;
-{
-unsigned short ai[NI], bi[NI];
-int i, sign;
-long lt, lta, ltb;
-
-/* IEEE says if result is not a NaN, the sign is "-" if and only if
- operands have opposite signs -- but flush -0 to 0 later if not IEEE. */
-sign = eisneg(a) ^ eisneg(b);
-
-#ifdef NANS
-/* Return any NaN input. */
-if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Zero over zero, or infinity over infinity, is a NaN. */
-if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0))
- || (eisinf (a) && eisinf (b)) )
- {
- mtherr( "ediv", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-/* Infinity over anything else is infinity. */
-#ifdef INFINITY
-if( eisinf(b) )
- {
- einfin(c);
- goto divsign;
- }
-if( eisinf(a) )
- {
- eclear(c);
- goto divsign;
- }
-#endif
-emovi( a, ai );
-emovi( b, bi );
-lta = ai[E];
-ltb = bi[E];
-if( bi[E] == 0 )
- { /* See if numerator is zero. */
- for( i=1; i<NI-1; i++ )
- {
- if( bi[i] != 0 )
- {
- ltb -= enormlz( bi );
- goto dnzro1;
- }
- }
- eclear(c);
- goto divsign;
- }
-dnzro1:
-
-if( ai[E] == 0 )
- { /* possible divide by zero */
- for( i=1; i<NI-1; i++ )
- {
- if( ai[i] != 0 )
- {
- lta -= enormlz( ai );
- goto dnzro2;
- }
- }
- einfin(c);
- mtherr( "ediv", SING );
- goto divsign;
- }
-dnzro2:
-
-i = edivm( ai, bi );
-/* calculate exponent */
-lt = ltb - lta + EXONE;
-emdnorm( bi, i, 0, lt, 64 );
-emovo( bi, c );
-
-divsign:
-
-if( sign )
- *(c+(NE-1)) |= 0x8000;
-else
- *(c+(NE-1)) &= ~0x8000;
-}
-
-
-
-/*
-; Multiply.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; emul( a, b, c ); c = b * a
-*/
-void emul( a, b, c )
-unsigned short *a, *b, *c;
-{
-unsigned short ai[NI], bi[NI];
-int i, j, sign;
-long lt, lta, ltb;
-
-/* IEEE says if result is not a NaN, the sign is "-" if and only if
- operands have opposite signs -- but flush -0 to 0 later if not IEEE. */
-sign = eisneg(a) ^ eisneg(b);
-
-#ifdef NANS
-/* NaN times anything is the same NaN. */
-if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Zero times infinity is a NaN. */
-if( (eisinf(a) && (ecmp(b,ezero) == 0))
- || (eisinf(b) && (ecmp(a,ezero) == 0)) )
- {
- mtherr( "emul", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-/* Infinity times anything else is infinity. */
-#ifdef INFINITY
-if( eisinf(a) || eisinf(b) )
- {
- einfin(c);
- goto mulsign;
- }
-#endif
-emovi( a, ai );
-emovi( b, bi );
-lta = ai[E];
-ltb = bi[E];
-if( ai[E] == 0 )
- {
- for( i=1; i<NI-1; i++ )
- {
- if( ai[i] != 0 )
- {
- lta -= enormlz( ai );
- goto mnzer1;
- }
- }
- eclear(c);
- goto mulsign;
- }
-mnzer1:
-
-if( bi[E] == 0 )
- {
- for( i=1; i<NI-1; i++ )
- {
- if( bi[i] != 0 )
- {
- ltb -= enormlz( bi );
- goto mnzer2;
- }
- }
- eclear(c);
- goto mulsign;
- }
-mnzer2:
-
-/* Multiply significands */
-j = emulm( ai, bi );
-/* calculate exponent */
-lt = lta + ltb - (EXONE - 1);
-emdnorm( bi, j, 0, lt, 64 );
-emovo( bi, c );
-/* IEEE says sign is "-" if and only if operands have opposite signs. */
-mulsign:
-if( sign )
- *(c+(NE-1)) |= 0x8000;
-else
- *(c+(NE-1)) &= ~0x8000;
-}
-
-
-
-
-/*
-; Convert IEEE double precision to e type
-; double d;
-; unsigned short x[N+2];
-; e53toe( &d, x );
-*/
-void e53toe( pe, y )
-unsigned short *pe, *y;
-{
-#ifdef DEC
-
-dectoe( pe, y ); /* see etodec.c */
-
-#else
-
-register unsigned short r;
-register unsigned short *p, *e;
-unsigned short yy[NI];
-int denorm, k;
-
-e = pe;
-denorm = 0; /* flag if denormalized number */
-ecleaz(yy);
-#ifdef IBMPC
-e += 3;
-#endif
-r = *e;
-yy[0] = 0;
-if( r & 0x8000 )
- yy[0] = 0xffff;
-yy[M] = (r & 0x0f) | 0x10;
-r &= ~0x800f; /* strip sign and 4 significand bits */
-#ifdef INFINITY
-if( r == 0x7ff0 )
- {
-#ifdef NANS
-#ifdef IBMPC
- if( ((pe[3] & 0xf) != 0) || (pe[2] != 0)
- || (pe[1] != 0) || (pe[0] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#else
- if( ((pe[0] & 0xf) != 0) || (pe[1] != 0)
- || (pe[2] != 0) || (pe[3] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( yy[0] )
- eneg(y);
- return;
- }
-#endif
-r >>= 4;
-/* If zero exponent, then the significand is denormalized.
- * So, take back the understood high significand bit. */
-if( r == 0 )
- {
- denorm = 1;
- yy[M] &= ~0x10;
- }
-r += EXONE - 01777;
-yy[E] = r;
-p = &yy[M+1];
-#ifdef IBMPC
-*p++ = *(--e);
-*p++ = *(--e);
-*p++ = *(--e);
-#endif
-#ifdef MIEEE
-++e;
-*p++ = *e++;
-*p++ = *e++;
-*p++ = *e++;
-#endif
-(void )eshift( yy, -5 );
-if( denorm )
- { /* if zero exponent, then normalize the significand */
- if( (k = enormlz(yy)) > NBITS )
- ecleazs(yy);
- else
- yy[E] -= (unsigned short )(k-1);
- }
-emovo( yy, y );
-#endif /* not DEC */
-}
-
-void e64toe( pe, y )
-unsigned short *pe, *y;
-{
-unsigned short yy[NI];
-unsigned short *p, *q, *e;
-int i;
-
-e = pe;
-p = yy;
-for( i=0; i<NE-5; i++ )
- *p++ = 0;
-#ifdef IBMPC
-for( i=0; i<5; i++ )
- *p++ = *e++;
-#endif
-#ifdef DEC
-for( i=0; i<5; i++ )
- *p++ = *e++;
-#endif
-#ifdef MIEEE
-p = &yy[0] + (NE-1);
-*p-- = *e++;
-++e;
-for( i=0; i<4; i++ )
- *p-- = *e++;
-#endif
-
-#ifdef IBMPC
-/* For Intel long double, shift denormal significand up 1
- -- but only if the top significand bit is zero. */
-if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
- {
- unsigned short temp[NI+1];
- emovi(yy, temp);
- eshup1(temp);
- emovo(temp,y);
- return;
- }
-#endif
-#ifdef INFINITY
-/* Point to the exponent field. */
-p = &yy[NE-1];
-if( *p == 0x7fff )
- {
-#ifdef NANS
-#ifdef IBMPC
- for( i=0; i<4; i++ )
- {
- if((i != 3 && pe[i] != 0)
- /* Check for Intel long double infinity pattern. */
- || (i == 3 && pe[i] != 0x8000))
- {
- enan( y, NBITS );
- return;
- }
- }
-#else
- for( i=1; i<=4; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( *p & 0x8000 )
- eneg(y);
- return;
- }
-#endif
-p = yy;
-q = y;
-for( i=0; i<NE; i++ )
- *q++ = *p++;
-}
-
-void e113toe(pe,y)
-unsigned short *pe, *y;
-{
-register unsigned short r;
-unsigned short *e, *p;
-unsigned short yy[NI];
-int i;
-
-e = pe;
-ecleaz(yy);
-#ifdef IBMPC
-e += 7;
-#endif
-r = *e;
-yy[0] = 0;
-if( r & 0x8000 )
- yy[0] = 0xffff;
-r &= 0x7fff;
-#ifdef INFINITY
-if( r == 0x7fff )
- {
-#ifdef NANS
-#ifdef IBMPC
- for( i=0; i<7; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
-#else
- for( i=1; i<8; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( *e & 0x8000 )
- eneg(y);
- return;
- }
-#endif /* INFINITY */
-yy[E] = r;
-p = &yy[M + 1];
-#ifdef IBMPC
-for( i=0; i<7; i++ )
- *p++ = *(--e);
-#endif
-#ifdef MIEEE
-++e;
-for( i=0; i<7; i++ )
- *p++ = *e++;
-#endif
-/* If denormal, remove the implied bit; else shift down 1. */
-if( r == 0 )
- {
- yy[M] = 0;
- }
-else
- {
- yy[M] = 1;
- eshift( yy, -1 );
- }
-emovo(yy,y);
-}
-
-
-/*
-; Convert IEEE single precision to e type
-; float d;
-; unsigned short x[N+2];
-; dtox( &d, x );
-*/
-void e24toe( pe, y )
-unsigned short *pe, *y;
-{
-register unsigned short r;
-register unsigned short *p, *e;
-unsigned short yy[NI];
-int denorm, k;
-
-e = pe;
-denorm = 0; /* flag if denormalized number */
-ecleaz(yy);
-#ifdef IBMPC
-e += 1;
-#endif
-#ifdef DEC
-e += 1;
-#endif
-r = *e;
-yy[0] = 0;
-if( r & 0x8000 )
- yy[0] = 0xffff;
-yy[M] = (r & 0x7f) | 0200;
-r &= ~0x807f; /* strip sign and 7 significand bits */
-#ifdef INFINITY
-if( r == 0x7f80 )
- {
-#ifdef NANS
-#ifdef MIEEE
- if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#else
- if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( yy[0] )
- eneg(y);
- return;
- }
-#endif
-r >>= 7;
-/* If zero exponent, then the significand is denormalized.
- * So, take back the understood high significand bit. */
-if( r == 0 )
- {
- denorm = 1;
- yy[M] &= ~0200;
- }
-r += EXONE - 0177;
-yy[E] = r;
-p = &yy[M+1];
-#ifdef IBMPC
-*p++ = *(--e);
-#endif
-#ifdef DEC
-*p++ = *(--e);
-#endif
-#ifdef MIEEE
-++e;
-*p++ = *e++;
-#endif
-(void )eshift( yy, -8 );
-if( denorm )
- { /* if zero exponent, then normalize the significand */
- if( (k = enormlz(yy)) > NBITS )
- ecleazs(yy);
- else
- yy[E] -= (unsigned short )(k-1);
- }
-emovo( yy, y );
-}
-
-void etoe113(x,e)
-unsigned short *x, *e;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 113 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E];
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 113;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe113 (xi, e);
-}
-
-/* move out internal format to ieee long double */
-static void toe113(a,b)
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-unsigned short i;
-
-#ifdef NANS
-if( eiisnan(a) )
- {
- enan( b, 113 );
- return;
- }
-#endif
-p = a;
-#ifdef MIEEE
-q = b;
-#else
-q = b + 7; /* point to output exponent */
-#endif
-
-/* If not denormal, delete the implied bit. */
-if( a[E] != 0 )
- {
- eshup1 (a);
- }
-/* combine sign and exponent */
-i = *p++;
-#ifdef MIEEE
-if( i )
- *q++ = *p++ | 0x8000;
-else
- *q++ = *p++;
-#else
-if( i )
- *q-- = *p++ | 0x8000;
-else
- *q-- = *p++;
-#endif
-/* skip over guard word */
-++p;
-/* move the significand */
-#ifdef MIEEE
-for (i = 0; i < 7; i++)
- *q++ = *p++;
-#else
-for (i = 0; i < 7; i++)
- *q-- = *p++;
-#endif
-}
-
-
-void etoe64( x, e )
-unsigned short *x, *e;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 64 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E]; /* adjust exponent for offset */
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 64;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe64( xi, e );
-}
-
-/* move out internal format to ieee long double */
-static void toe64( a, b )
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-unsigned short i;
-
-#ifdef NANS
-if( eiisnan(a) )
- {
- enan( b, 64 );
- return;
- }
-#endif
-#ifdef IBMPC
-/* Shift Intel denormal significand down 1. */
-if( a[E] == 0 )
- eshdn1(a);
-#endif
-p = a;
-#ifdef MIEEE
-q = b;
-#else
-q = b + 4; /* point to output exponent */
-#if 1
-/* NOTE: if data type is 96 bits wide, clear the last word here. */
-*(q+1)= 0;
-#endif
-#endif
-
-/* combine sign and exponent */
-i = *p++;
-#ifdef MIEEE
-if( i )
- *q++ = *p++ | 0x8000;
-else
- *q++ = *p++;
-*q++ = 0;
-#else
-if( i )
- *q-- = *p++ | 0x8000;
-else
- *q-- = *p++;
-#endif
-/* skip over guard word */
-++p;
-/* move the significand */
-#ifdef MIEEE
-for( i=0; i<4; i++ )
- *q++ = *p++;
-#else
-#ifdef INFINITY
-if (eiisinf (a))
- {
- /* Intel long double infinity. */
- *q-- = 0x8000;
- *q-- = 0;
- *q-- = 0;
- *q = 0;
- return;
- }
-#endif
-for( i=0; i<4; i++ )
- *q-- = *p++;
-#endif
-}
-
-
-/*
-; e type to IEEE double precision
-; double d;
-; unsigned short x[NE];
-; etoe53( x, &d );
-*/
-
-#ifdef DEC
-
-void etoe53( x, e )
-unsigned short *x, *e;
-{
-etodec( x, e ); /* see etodec.c */
-}
-
-static void toe53( x, y )
-unsigned short *x, *y;
-{
-todec( x, y );
-}
-
-#else
-
-void etoe53( x, e )
-unsigned short *x, *e;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 53 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 53;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe53( xi, e );
-}
-
-
-static void toe53( x, y )
-unsigned short *x, *y;
-{
-unsigned short i;
-unsigned short *p;
-
-
-#ifdef NANS
-if( eiisnan(x) )
- {
- enan( y, 53 );
- return;
- }
-#endif
-p = &x[0];
-#ifdef IBMPC
-y += 3;
-#endif
-*y = 0; /* output high order */
-if( *p++ )
- *y = 0x8000; /* output sign bit */
-
-i = *p++;
-if( i >= (unsigned int )2047 )
- { /* Saturate at largest number less than infinity. */
-#ifdef INFINITY
- *y |= 0x7ff0;
-#ifdef IBMPC
- *(--y) = 0;
- *(--y) = 0;
- *(--y) = 0;
-#endif
-#ifdef MIEEE
- ++y;
- *y++ = 0;
- *y++ = 0;
- *y++ = 0;
-#endif
-#else
- *y |= (unsigned short )0x7fef;
-#ifdef IBMPC
- *(--y) = 0xffff;
- *(--y) = 0xffff;
- *(--y) = 0xffff;
-#endif
-#ifdef MIEEE
- ++y;
- *y++ = 0xffff;
- *y++ = 0xffff;
- *y++ = 0xffff;
-#endif
-#endif
- return;
- }
-if( i == 0 )
- {
- (void )eshift( x, 4 );
- }
-else
- {
- i <<= 4;
- (void )eshift( x, 5 );
- }
-i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */
-*y |= (unsigned short )i; /* high order output already has sign bit set */
-#ifdef IBMPC
-*(--y) = *p++;
-*(--y) = *p++;
-*(--y) = *p;
-#endif
-#ifdef MIEEE
-++y;
-*y++ = *p++;
-*y++ = *p++;
-*y++ = *p++;
-#endif
-}
-
-#endif /* not DEC */
-
-
-
-/*
-; e type to IEEE single precision
-; float d;
-; unsigned short x[N+2];
-; xtod( x, &d );
-*/
-void etoe24( x, e )
-unsigned short *x, *e;
-{
-long exp;
-unsigned short xi[NI];
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 24 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 24;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe24( xi, e );
-}
-
-static void toe24( x, y )
-unsigned short *x, *y;
-{
-unsigned short i;
-unsigned short *p;
-
-#ifdef NANS
-if( eiisnan(x) )
- {
- enan( y, 24 );
- return;
- }
-#endif
-p = &x[0];
-#ifdef IBMPC
-y += 1;
-#endif
-#ifdef DEC
-y += 1;
-#endif
-*y = 0; /* output high order */
-if( *p++ )
- *y = 0x8000; /* output sign bit */
-
-i = *p++;
-if( i >= 255 )
- { /* Saturate at largest number less than infinity. */
-#ifdef INFINITY
- *y |= (unsigned short )0x7f80;
-#ifdef IBMPC
- *(--y) = 0;
-#endif
-#ifdef DEC
- *(--y) = 0;
-#endif
-#ifdef MIEEE
- ++y;
- *y = 0;
-#endif
-#else
- *y |= (unsigned short )0x7f7f;
-#ifdef IBMPC
- *(--y) = 0xffff;
-#endif
-#ifdef DEC
- *(--y) = 0xffff;
-#endif
-#ifdef MIEEE
- ++y;
- *y = 0xffff;
-#endif
-#endif
- return;
- }
-if( i == 0 )
- {
- (void )eshift( x, 7 );
- }
-else
- {
- i <<= 7;
- (void )eshift( x, 8 );
- }
-i |= *p++ & (unsigned short )0x7f; /* *p = xi[M] */
-*y |= i; /* high order output already has sign bit set */
-#ifdef IBMPC
-*(--y) = *p;
-#endif
-#ifdef DEC
-*(--y) = *p;
-#endif
-#ifdef MIEEE
-++y;
-*y = *p;
-#endif
-}
-
-
-/* Compare two e type numbers.
- *
- * unsigned short a[NE], b[NE];
- * ecmp( a, b );
- *
- * returns +1 if a > b
- * 0 if a == b
- * -1 if a < b
- * -2 if either a or b is a NaN.
- */
-int ecmp( a, b )
-unsigned short *a, *b;
-{
-unsigned short ai[NI], bi[NI];
-register unsigned short *p, *q;
-register int i;
-int msign;
-
-#ifdef NANS
-if (eisnan (a) || eisnan (b))
- return( -2 );
-#endif
-emovi( a, ai );
-p = ai;
-emovi( b, bi );
-q = bi;
-
-if( *p != *q )
- { /* the signs are different */
-/* -0 equals + 0 */
- for( i=1; i<NI-1; i++ )
- {
- if( ai[i] != 0 )
- goto nzro;
- if( bi[i] != 0 )
- goto nzro;
- }
- return(0);
-nzro:
- if( *p == 0 )
- return( 1 );
- else
- return( -1 );
- }
-/* both are the same sign */
-if( *p == 0 )
- msign = 1;
-else
- msign = -1;
-i = NI-1;
-do
- {
- if( *p++ != *q++ )
- {
- goto diff;
- }
- }
-while( --i > 0 );
-
-return(0); /* equality */
-
-
-
-diff:
-
-if( *(--p) > *(--q) )
- return( msign ); /* p is bigger */
-else
- return( -msign ); /* p is littler */
-}
-
-
-
-
-/* Find nearest integer to x = floor( x + 0.5 )
- *
- * unsigned short x[NE], y[NE]
- * eround( x, y );
- */
-void eround( x, y )
-unsigned short *x, *y;
-{
-
-eadd( ehalf, x, y );
-efloor( y, y );
-}
-
-
-
-
-/*
-; convert long (32-bit) integer to e type
-;
-; long l;
-; unsigned short x[NE];
-; ltoe( &l, x );
-; note &l is the memory address of l
-*/
-void ltoe( lp, y )
-long *lp; /* lp is the memory address of a long integer */
-unsigned short *y; /* y is the address of a short */
-{
-unsigned short yi[NI];
-unsigned long ll;
-int k;
-
-ecleaz( yi );
-if( *lp < 0 )
- {
- ll = (unsigned long )( -(*lp) ); /* make it positive */
- yi[0] = 0xffff; /* put correct sign in the e type number */
- }
-else
- {
- ll = (unsigned long )( *lp );
- }
-/* move the long integer to yi significand area */
-if( sizeof(long) == 8 )
- {
- yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
- yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
- yi[M + 2] = (unsigned short) (ll >> 16);
- yi[M + 3] = (unsigned short) ll;
- yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
- }
-else
- {
- yi[M] = (unsigned short )(ll >> 16);
- yi[M+1] = (unsigned short )ll;
- yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
- }
-if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
- ecleaz( yi ); /* it was zero */
-else
- yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
-emovo( yi, y ); /* output the answer */
-}
-
-/*
-; convert unsigned long (32-bit) integer to e type
-;
-; unsigned long l;
-; unsigned short x[NE];
-; ltox( &l, x );
-; note &l is the memory address of l
-*/
-void ultoe( lp, y )
-unsigned long *lp; /* lp is the memory address of a long integer */
-unsigned short *y; /* y is the address of a short */
-{
-unsigned short yi[NI];
-unsigned long ll;
-int k;
-
-ecleaz( yi );
-ll = *lp;
-
-/* move the long integer to ayi significand area */
-if( sizeof(long) == 8 )
- {
- yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
- yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
- yi[M + 2] = (unsigned short) (ll >> 16);
- yi[M + 3] = (unsigned short) ll;
- yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
- }
-else
- {
- yi[M] = (unsigned short )(ll >> 16);
- yi[M+1] = (unsigned short )ll;
- yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
- }
-if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
- ecleaz( yi ); /* it was zero */
-else
- yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
-emovo( yi, y ); /* output the answer */
-}
-
-
-/*
-; Find long integer and fractional parts
-
-; long i;
-; unsigned short x[NE], frac[NE];
-; xifrac( x, &i, frac );
-
- The integer output has the sign of the input. The fraction is
- the positive fractional part of abs(x).
-*/
-void eifrac( x, i, frac )
-unsigned short *x;
-long *i;
-unsigned short *frac;
-{
-unsigned short xi[NI];
-int j, k;
-unsigned long ll;
-
-emovi( x, xi );
-k = (int )xi[E] - (EXONE - 1);
-if( k <= 0 )
- {
-/* if exponent <= 0, integer = 0 and real output is fraction */
- *i = 0L;
- emovo( xi, frac );
- return;
- }
-if( k > (8 * sizeof(long) - 1) )
- {
-/*
-; long integer overflow: output large integer
-; and correct fraction
-*/
- j = 8 * sizeof(long) - 1;
- if( xi[0] )
- *i = (long) ((unsigned long) 1) << j;
- else
- *i = (long) (((unsigned long) (~(0L))) >> 1);
- (void )eshift( xi, k );
- }
-if( k > 16 )
- {
-/*
- Shift more than 16 bits: shift up k-16 mod 16
- then shift by 16's.
-*/
- j = k - ((k >> 4) << 4);
- eshift (xi, j);
- ll = xi[M];
- k -= j;
- do
- {
- eshup6 (xi);
- ll = (ll << 16) | xi[M];
- }
- while ((k -= 16) > 0);
- *i = ll;
- if (xi[0])
- *i = -(*i);
- }
-else
- {
-/* shift not more than 16 bits */
- eshift( xi, k );
- *i = (long )xi[M] & 0xffff;
- if( xi[0] )
- *i = -(*i);
- }
-xi[0] = 0;
-xi[E] = EXONE - 1;
-xi[M] = 0;
-if( (k = enormlz( xi )) > NBITS )
- ecleaz( xi );
-else
- xi[E] -= (unsigned short )k;
-
-emovo( xi, frac );
-}
-
-
-/*
-; Find unsigned long integer and fractional parts
-
-; unsigned long i;
-; unsigned short x[NE], frac[NE];
-; xifrac( x, &i, frac );
-
- A negative e type input yields integer output = 0
- but correct fraction.
-*/
-void euifrac( x, i, frac )
-unsigned short *x;
-unsigned long *i;
-unsigned short *frac;
-{
-unsigned short xi[NI];
-int j, k;
-unsigned long ll;
-
-emovi( x, xi );
-k = (int )xi[E] - (EXONE - 1);
-if( k <= 0 )
- {
-/* if exponent <= 0, integer = 0 and argument is fraction */
- *i = 0L;
- emovo( xi, frac );
- return;
- }
-if( k > (8 * sizeof(long)) )
- {
-/*
-; long integer overflow: output large integer
-; and correct fraction
-*/
- *i = ~(0L);
- (void )eshift( xi, k );
- }
-else if( k > 16 )
- {
-/*
- Shift more than 16 bits: shift up k-16 mod 16
- then shift up by 16's.
-*/
- j = k - ((k >> 4) << 4);
- eshift (xi, j);
- ll = xi[M];
- k -= j;
- do
- {
- eshup6 (xi);
- ll = (ll << 16) | xi[M];
- }
- while ((k -= 16) > 0);
- *i = ll;
- }
-else
- {
-/* shift not more than 16 bits */
- eshift( xi, k );
- *i = (long )xi[M] & 0xffff;
- }
-
-if( xi[0] ) /* A negative value yields unsigned integer 0. */
- *i = 0L;
-
-xi[0] = 0;
-xi[E] = EXONE - 1;
-xi[M] = 0;
-if( (k = enormlz( xi )) > NBITS )
- ecleaz( xi );
-else
- xi[E] -= (unsigned short )k;
-
-emovo( xi, frac );
-}
-
-
-
-/*
-; Shift significand
-;
-; Shifts significand area up or down by the number of bits
-; given by the variable sc.
-*/
-int eshift( x, sc )
-unsigned short *x;
-int sc;
-{
-unsigned short lost;
-unsigned short *p;
-
-if( sc == 0 )
- return( 0 );
-
-lost = 0;
-p = x + NI-1;
-
-if( sc < 0 )
- {
- sc = -sc;
- while( sc >= 16 )
- {
- lost |= *p; /* remember lost bits */
- eshdn6(x);
- sc -= 16;
- }
-
- while( sc >= 8 )
- {
- lost |= *p & 0xff;
- eshdn8(x);
- sc -= 8;
- }
-
- while( sc > 0 )
- {
- lost |= *p & 1;
- eshdn1(x);
- sc -= 1;
- }
- }
-else
- {
- while( sc >= 16 )
- {
- eshup6(x);
- sc -= 16;
- }
-
- while( sc >= 8 )
- {
- eshup8(x);
- sc -= 8;
- }
-
- while( sc > 0 )
- {
- eshup1(x);
- sc -= 1;
- }
- }
-if( lost )
- lost = 1;
-return( (int )lost );
-}
-
-
-
-/*
-; normalize
-;
-; Shift normalizes the significand area pointed to by argument
-; shift count (up = positive) is returned.
-*/
-int enormlz(x)
-unsigned short x[];
-{
-register unsigned short *p;
-int sc;
-
-sc = 0;
-p = &x[M];
-if( *p != 0 )
- goto normdn;
-++p;
-if( *p & 0x8000 )
- return( 0 ); /* already normalized */
-while( *p == 0 )
- {
- eshup6(x);
- sc += 16;
-/* With guard word, there are NBITS+16 bits available.
- * return true if all are zero.
- */
- if( sc > NBITS )
- return( sc );
- }
-/* see if high byte is zero */
-while( (*p & 0xff00) == 0 )
- {
- eshup8(x);
- sc += 8;
- }
-/* now shift 1 bit at a time */
-while( (*p & 0x8000) == 0)
- {
- eshup1(x);
- sc += 1;
- if( sc > (NBITS+16) )
- {
- mtherr( "enormlz", UNDERFLOW );
- return( sc );
- }
- }
-return( sc );
-
-/* Normalize by shifting down out of the high guard word
- of the significand */
-normdn:
-
-if( *p & 0xff00 )
- {
- eshdn8(x);
- sc -= 8;
- }
-while( *p != 0 )
- {
- eshdn1(x);
- sc -= 1;
-
- if( sc < -NBITS )
- {
- mtherr( "enormlz", OVERFLOW );
- return( sc );
- }
- }
-return( sc );
-}
-
-
-
-
-/* Convert e type number to decimal format ASCII string.
- * The constants are for 64 bit precision.
- */
-
-#define NTEN 12
-#define MAXP 4096
-
-#if NE == 10
-static unsigned short etens[NTEN + 1][NE] =
-{
- {0x6576, 0x4a92, 0x804a, 0x153f,
- 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
- {0x6a32, 0xce52, 0x329a, 0x28ce,
- 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
- {0x526c, 0x50ce, 0xf18b, 0x3d28,
- 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
- {0x9c66, 0x58f8, 0xbc50, 0x5c54,
- 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
- {0x851e, 0xeab7, 0x98fe, 0x901b,
- 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
- {0x0235, 0x0137, 0x36b1, 0x336c,
- 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
- {0x50f8, 0x25fb, 0xc76b, 0x6b71,
- 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
-};
-
-static unsigned short emtens[NTEN + 1][NE] =
-{
- {0x2030, 0xcffc, 0xa1c3, 0x8123,
- 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */
- {0x8264, 0xd2cb, 0xf2ea, 0x12d4,
- 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */
- {0xf53f, 0xf698, 0x6bd3, 0x0158,
- 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
- {0xe731, 0x04d4, 0xe3f2, 0xd332,
- 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
- {0xa23e, 0x5308, 0xfefb, 0x1155,
- 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
- {0xe26d, 0xdbde, 0xd05d, 0xb3f6,
- 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
- {0x2a20, 0x6224, 0x47b3, 0x98d7,
- 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
- {0x0b5b, 0x4af2, 0xa581, 0x18ed,
- 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
- {0xbf71, 0xa9b3, 0x7989, 0xbe68,
- 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
- {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
- 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
- {0xc155, 0xa4a8, 0x404e, 0x6113,
- 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
- {0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
- 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
- {0xcccd, 0xcccc, 0xcccc, 0xcccc,
- 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */
-};
-#else
-static unsigned short etens[NTEN+1][NE] = {
-{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
-{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
-{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
-{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
-{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
-{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
-{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
-{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
-{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
-{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
-{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
-{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
-{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
-};
-
-static unsigned short emtens[NTEN+1][NE] = {
-{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */
-{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */
-{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,},
-{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,},
-{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,},
-{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,},
-{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,},
-{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,},
-{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,},
-{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,},
-{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,},
-{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,},
-{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */
-};
-#endif
-
-void e24toasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e24toe( x, w );
-etoasc( w, string, ndigs );
-}
-
-
-void e53toasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e53toe( x, w );
-etoasc( w, string, ndigs );
-}
-
-
-void e64toasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e64toe( x, w );
-etoasc( w, string, ndigs );
-}
-
-void e113toasc (x, string, ndigs)
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e113toe (x, w);
-etoasc (w, string, ndigs);
-}
-
-
-void etoasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-long digit;
-unsigned short y[NI], t[NI], u[NI], w[NI];
-unsigned short *p, *r, *ten;
-unsigned short sign;
-int i, j, k, expon, rndsav;
-char *s, *ss;
-unsigned short m;
-
-rndsav = rndprc;
-#ifdef NANS
-if( eisnan(x) )
- {
- sprintf( string, " NaN " );
- goto bxit;
- }
-#endif
-rndprc = NBITS; /* set to full precision */
-emov( x, y ); /* retain external format */
-if( y[NE-1] & 0x8000 )
- {
- sign = 0xffff;
- y[NE-1] &= 0x7fff;
- }
-else
- {
- sign = 0;
- }
-expon = 0;
-ten = &etens[NTEN][0];
-emov( eone, t );
-/* Test for zero exponent */
-if( y[NE-1] == 0 )
- {
- for( k=0; k<NE-1; k++ )
- {
- if( y[k] != 0 )
- goto tnzro; /* denormalized number */
- }
- goto isone; /* legal all zeros */
- }
-tnzro:
-
-/* Test for infinity.
- */
-if( y[NE-1] == 0x7fff )
- {
- if( sign )
- sprintf( string, " -Infinity " );
- else
- sprintf( string, " Infinity " );
- goto bxit;
- }
-
-/* Test for exponent nonzero but significand denormalized.
- * This is an error condition.
- */
-if( (y[NE-1] != 0) && ((y[NE-2] & 0x8000) == 0) )
- {
- mtherr( "etoasc", DOMAIN );
- sprintf( string, "NaN" );
- goto bxit;
- }
-
-/* Compare to 1.0 */
-i = ecmp( eone, y );
-if( i == 0 )
- goto isone;
-
-if( i < 0 )
- { /* Number is greater than 1 */
-/* Convert significand to an integer and strip trailing decimal zeros. */
- emov( y, u );
- u[NE-1] = EXONE + NBITS - 1;
-
- p = &etens[NTEN-4][0];
- m = 16;
-do
- {
- ediv( p, u, t );
- efloor( t, w );
- for( j=0; j<NE-1; j++ )
- {
- if( t[j] != w[j] )
- goto noint;
- }
- emov( t, u );
- expon += (int )m;
-noint:
- p += NE;
- m >>= 1;
- }
-while( m != 0 );
-
-/* Rescale from integer significand */
- u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1);
- emov( u, y );
-/* Find power of 10 */
- emov( eone, t );
- m = MAXP;
- p = &etens[0][0];
- while( ecmp( ten, u ) <= 0 )
- {
- if( ecmp( p, u ) <= 0 )
- {
- ediv( p, u, u );
- emul( p, t, t );
- expon += (int )m;
- }
- m >>= 1;
- if( m == 0 )
- break;
- p += NE;
- }
- }
-else
- { /* Number is less than 1.0 */
-/* Pad significand with trailing decimal zeros. */
- if( y[NE-1] == 0 )
- {
- while( (y[NE-2] & 0x8000) == 0 )
- {
- emul( ten, y, y );
- expon -= 1;
- }
- }
- else
- {
- emovi( y, w );
- for( i=0; i<NDEC+1; i++ )
- {
- if( (w[NI-1] & 0x7) != 0 )
- break;
-/* multiply by 10 */
- emovz( w, u );
- eshdn1( u );
- eshdn1( u );
- eaddm( w, u );
- u[1] += 3;
- while( u[2] != 0 )
- {
- eshdn1(u);
- u[1] += 1;
- }
- if( u[NI-1] != 0 )
- break;
- if( eone[NE-1] <= u[1] )
- break;
- emovz( u, w );
- expon -= 1;
- }
- emovo( w, y );
- }
- k = -MAXP;
- p = &emtens[0][0];
- r = &etens[0][0];
- emov( y, w );
- emov( eone, t );
- while( ecmp( eone, w ) > 0 )
- {
- if( ecmp( p, w ) >= 0 )
- {
- emul( r, w, w );
- emul( r, t, t );
- expon += k;
- }
- k /= 2;
- if( k == 0 )
- break;
- p += NE;
- r += NE;
- }
- ediv( t, eone, t );
- }
-isone:
-/* Find the first (leading) digit. */
-emovi( t, w );
-emovz( w, t );
-emovi( y, w );
-emovz( w, y );
-eiremain( t, y );
-digit = equot[NI-1];
-while( (digit == 0) && (ecmp(y,ezero) != 0) )
- {
- eshup1( y );
- emovz( y, u );
- eshup1( u );
- eshup1( u );
- eaddm( u, y );
- eiremain( t, y );
- digit = equot[NI-1];
- expon -= 1;
- }
-s = string;
-if( sign )
- *s++ = '-';
-else
- *s++ = ' ';
-/* Examine number of digits requested by caller. */
-if( ndigs < 0 )
- ndigs = 0;
-if( ndigs > NDEC )
- ndigs = NDEC;
-if( digit == 10 )
- {
- *s++ = '1';
- *s++ = '.';
- if( ndigs > 0 )
- {
- *s++ = '0';
- ndigs -= 1;
- }
- expon += 1;
- }
-else
- {
- *s++ = (char )digit + '0';
- *s++ = '.';
- }
-/* Generate digits after the decimal point. */
-for( k=0; k<=ndigs; k++ )
- {
-/* multiply current number by 10, without normalizing */
- eshup1( y );
- emovz( y, u );
- eshup1( u );
- eshup1( u );
- eaddm( u, y );
- eiremain( t, y );
- *s++ = (char )equot[NI-1] + '0';
- }
-digit = equot[NI-1];
---s;
-ss = s;
-/* round off the ASCII string */
-if( digit > 4 )
- {
-/* Test for critical rounding case in ASCII output. */
- if( digit == 5 )
- {
- emovo( y, t );
- if( ecmp(t,ezero) != 0 )
- goto roun; /* round to nearest */
- if( (*(s-1) & 1) == 0 )
- goto doexp; /* round to even */
- }
-/* Round up and propagate carry-outs */
-roun:
- --s;
- k = *s & 0x7f;
-/* Carry out to most significant digit? */
- if( k == '.' )
- {
- --s;
- k = *s;
- k += 1;
- *s = (char )k;
-/* Most significant digit carries to 10? */
- if( k > '9' )
- {
- expon += 1;
- *s = '1';
- }
- goto doexp;
- }
-/* Round up and carry out from less significant digits */
- k += 1;
- *s = (char )k;
- if( k > '9' )
- {
- *s = '0';
- goto roun;
- }
- }
-doexp:
-/*
-if( expon >= 0 )
- sprintf( ss, "e+%d", expon );
-else
- sprintf( ss, "e%d", expon );
-*/
- sprintf( ss, "E%d", expon );
-bxit:
-rndprc = rndsav;
-}
-
-
-
-
-/*
-; ASCTOQ
-; ASCTOQ.MAC LATEST REV: 11 JAN 84
-; SLM, 3 JAN 78
-;
-; Convert ASCII string to quadruple precision floating point
-;
-; Numeric input is free field decimal number
-; with max of 15 digits with or without
-; decimal point entered as ASCII from teletype.
-; Entering E after the number followed by a second
-; number causes the second number to be interpreted
-; as a power of 10 to be multiplied by the first number
-; (i.e., "scientific" notation).
-;
-; Usage:
-; asctoq( string, q );
-*/
-
-/* ASCII to single */
-void asctoe24( s, y )
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, 24 );
-}
-
-
-/* ASCII to double */
-void asctoe53( s, y )
-char *s;
-unsigned short *y;
-{
-#ifdef DEC
-asctoeg( s, y, 56 );
-#else
-asctoeg( s, y, 53 );
-#endif
-}
-
-
-/* ASCII to long double */
-void asctoe64( s, y )
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, 64 );
-}
-
-/* ASCII to 128-bit long double */
-void asctoe113 (s, y)
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, 113 );
-}
-
-/* ASCII to super double */
-void asctoe( s, y )
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, NBITS );
-}
-
-/* Space to make a copy of the input string: */
-static char lstr[82] = {0};
-
-void asctoeg( ss, y, oprec )
-char *ss;
-unsigned short *y;
-int oprec;
-{
-unsigned short yy[NI], xt[NI], tt[NI];
-int esign, decflg, sgnflg, nexp, exp, prec, lost;
-int k, trail, c, rndsav;
-long lexp;
-unsigned short nsign, *p;
-char *sp, *s;
-
-/* Copy the input string. */
-s = ss;
-while( *s == ' ' ) /* skip leading spaces */
- ++s;
-sp = lstr;
-for( k=0; k<79; k++ )
- {
- if( (*sp++ = *s++) == '\0' )
- break;
- }
-*sp = '\0';
-s = lstr;
-
-rndsav = rndprc;
-rndprc = NBITS; /* Set to full precision */
-lost = 0;
-nsign = 0;
-decflg = 0;
-sgnflg = 0;
-nexp = 0;
-exp = 0;
-prec = 0;
-ecleaz( yy );
-trail = 0;
-
-nxtcom:
-k = *s - '0';
-if( (k >= 0) && (k <= 9) )
- {
-/* Ignore leading zeros */
- if( (prec == 0) && (decflg == 0) && (k == 0) )
- goto donchr;
-/* Identify and strip trailing zeros after the decimal point. */
- if( (trail == 0) && (decflg != 0) )
- {
- sp = s;
- while( (*sp >= '0') && (*sp <= '9') )
- ++sp;
-/* Check for syntax error */
- c = *sp & 0x7f;
- if( (c != 'e') && (c != 'E') && (c != '\0')
- && (c != '\n') && (c != '\r') && (c != ' ')
- && (c != ',') )
- goto error;
- --sp;
- while( *sp == '0' )
- *sp-- = 'z';
- trail = 1;
- if( *s == 'z' )
- goto donchr;
- }
-/* If enough digits were given to more than fill up the yy register,
- * continuing until overflow into the high guard word yy[2]
- * guarantees that there will be a roundoff bit at the top
- * of the low guard word after normalization.
- */
- if( yy[2] == 0 )
- {
- if( decflg )
- nexp += 1; /* count digits after decimal point */
- eshup1( yy ); /* multiply current number by 10 */
- emovz( yy, xt );
- eshup1( xt );
- eshup1( xt );
- eaddm( xt, yy );
- ecleaz( xt );
- xt[NI-2] = (unsigned short )k;
- eaddm( xt, yy );
- }
- else
- {
- /* Mark any lost non-zero digit. */
- lost |= k;
- /* Count lost digits before the decimal point. */
- if (decflg == 0)
- nexp -= 1;
- }
- prec += 1;
- goto donchr;
- }
-
-switch( *s )
- {
- case 'z':
- break;
- case 'E':
- case 'e':
- goto expnt;
- case '.': /* decimal point */
- if( decflg )
- goto error;
- ++decflg;
- break;
- case '-':
- nsign = 0xffff;
- if( sgnflg )
- goto error;
- ++sgnflg;
- break;
- case '+':
- if( sgnflg )
- goto error;
- ++sgnflg;
- break;
- case ',':
- case ' ':
- case '\0':
- case '\n':
- case '\r':
- goto daldone;
- case 'i':
- case 'I':
- goto infinite;
- default:
- error:
-#ifdef NANS
- enan( yy, NI*16 );
-#else
- mtherr( "asctoe", DOMAIN );
- ecleaz(yy);
-#endif
- goto aexit;
- }
-donchr:
-++s;
-goto nxtcom;
-
-/* Exponent interpretation */
-expnt:
-
-esign = 1;
-exp = 0;
-++s;
-/* check for + or - */
-if( *s == '-' )
- {
- esign = -1;
- ++s;
- }
-if( *s == '+' )
- ++s;
-while( (*s >= '0') && (*s <= '9') )
- {
- exp *= 10;
- exp += *s++ - '0';
- if (exp > 4977)
- {
- if (esign < 0)
- goto zero;
- else
- goto infinite;
- }
- }
-if( esign < 0 )
- exp = -exp;
-if( exp > 4932 )
- {
-infinite:
- ecleaz(yy);
- yy[E] = 0x7fff; /* infinity */
- goto aexit;
- }
-if( exp < -4977 )
- {
-zero:
- ecleaz(yy);
- goto aexit;
- }
-
-daldone:
-nexp = exp - nexp;
-/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
-while( (nexp > 0) && (yy[2] == 0) )
- {
- emovz( yy, xt );
- eshup1( xt );
- eshup1( xt );
- eaddm( yy, xt );
- eshup1( xt );
- if( xt[2] != 0 )
- break;
- nexp -= 1;
- emovz( xt, yy );
- }
-if( (k = enormlz(yy)) > NBITS )
- {
- ecleaz(yy);
- goto aexit;
- }
-lexp = (EXONE - 1 + NBITS) - k;
-emdnorm( yy, lost, 0, lexp, 64 );
-/* convert to external format */
-
-
-/* Multiply by 10**nexp. If precision is 64 bits,
- * the maximum relative error incurred in forming 10**n
- * for 0 <= n <= 324 is 8.2e-20, at 10**180.
- * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
- * For 0 >= n >= -999, it is -1.55e-19 at 10**-435.
- */
-lexp = yy[E];
-if( nexp == 0 )
- {
- k = 0;
- goto expdon;
- }
-esign = 1;
-if( nexp < 0 )
- {
- nexp = -nexp;
- esign = -1;
- if( nexp > 4096 )
- { /* Punt. Can't handle this without 2 divides. */
- emovi( etens[0], tt );
- lexp -= tt[E];
- k = edivm( tt, yy );
- lexp += EXONE;
- nexp -= 4096;
- }
- }
-p = &etens[NTEN][0];
-emov( eone, xt );
-exp = 1;
-do
- {
- if( exp & nexp )
- emul( p, xt, xt );
- p -= NE;
- exp = exp + exp;
- }
-while( exp <= MAXP );
-
-emovi( xt, tt );
-if( esign < 0 )
- {
- lexp -= tt[E];
- k = edivm( tt, yy );
- lexp += EXONE;
- }
-else
- {
- lexp += tt[E];
- k = emulm( tt, yy );
- lexp -= EXONE - 1;
- }
-
-expdon:
-
-/* Round and convert directly to the destination type */
-if( oprec == 53 )
- lexp -= EXONE - 0x3ff;
-else if( oprec == 24 )
- lexp -= EXONE - 0177;
-#ifdef DEC
-else if( oprec == 56 )
- lexp -= EXONE - 0201;
-#endif
-rndprc = oprec;
-emdnorm( yy, k, 0, lexp, 64 );
-
-aexit:
-
-rndprc = rndsav;
-yy[0] = nsign;
-switch( oprec )
- {
-#ifdef DEC
- case 56:
- todec( yy, y ); /* see etodec.c */
- break;
-#endif
- case 53:
- toe53( yy, y );
- break;
- case 24:
- toe24( yy, y );
- break;
- case 64:
- toe64( yy, y );
- break;
- case 113:
- toe113( yy, y );
- break;
- case NBITS:
- emovo( yy, y );
- break;
- }
-}
-
-
-
-/* y = largest integer not greater than x
- * (truncated toward minus infinity)
- *
- * unsigned short x[NE], y[NE]
- *
- * efloor( x, y );
- */
-static unsigned short bmask[] = {
-0xffff,
-0xfffe,
-0xfffc,
-0xfff8,
-0xfff0,
-0xffe0,
-0xffc0,
-0xff80,
-0xff00,
-0xfe00,
-0xfc00,
-0xf800,
-0xf000,
-0xe000,
-0xc000,
-0x8000,
-0x0000,
-};
-
-void efloor( x, y )
-unsigned short x[], y[];
-{
-register unsigned short *p;
-int e, expon, i;
-unsigned short f[NE];
-
-emov( x, f ); /* leave in external format */
-expon = (int )f[NE-1];
-e = (expon & 0x7fff) - (EXONE - 1);
-if( e <= 0 )
- {
- eclear(y);
- goto isitneg;
- }
-/* number of bits to clear out */
-e = NBITS - e;
-emov( f, y );
-if( e <= 0 )
- return;
-
-p = &y[0];
-while( e >= 16 )
- {
- *p++ = 0;
- e -= 16;
- }
-/* clear the remaining bits */
-*p &= bmask[e];
-/* truncate negatives toward minus infinity */
-isitneg:
-
-if( (unsigned short )expon & (unsigned short )0x8000 )
- {
- for( i=0; i<NE-1; i++ )
- {
- if( f[i] != y[i] )
- {
- esub( eone, y, y );
- break;
- }
- }
- }
-}
-
-
-/* unsigned short x[], s[];
- * long *exp;
- *
- * efrexp( x, exp, s );
- *
- * Returns s and exp such that s * 2**exp = x and .5 <= s < 1.
- * For example, 1.1 = 0.55 * 2**1
- * Handles denormalized numbers properly using long integer exp.
- */
-void efrexp( x, exp, s )
-unsigned short x[];
-long *exp;
-unsigned short s[];
-{
-unsigned short xi[NI];
-long li;
-
-emovi( x, xi );
-li = (long )((short )xi[1]);
-
-if( li == 0 )
- {
- li -= enormlz( xi );
- }
-xi[1] = 0x3ffe;
-emovo( xi, s );
-*exp = li - 0x3ffe;
-}
-
-
-
-/* unsigned short x[], y[];
- * long pwr2;
- *
- * eldexp( x, pwr2, y );
- *
- * Returns y = x * 2**pwr2.
- */
-void eldexp( x, pwr2, y )
-unsigned short x[];
-long pwr2;
-unsigned short y[];
-{
-unsigned short xi[NI];
-long li;
-int i;
-
-emovi( x, xi );
-li = xi[1];
-li += pwr2;
-i = 0;
-emdnorm( xi, i, i, li, 64 );
-emovo( xi, y );
-}
-
-
-/* c = remainder after dividing b by a
- * Least significant integer quotient bits left in equot[].
- */
-void eremain( a, b, c )
-unsigned short a[], b[], c[];
-{
-unsigned short den[NI], num[NI];
-
-#ifdef NANS
-if( eisinf(b) || (ecmp(a,ezero) == 0) || eisnan(a) || eisnan(b))
- {
- enan( c, NBITS );
- return;
- }
-#endif
-if( ecmp(a,ezero) == 0 )
- {
- mtherr( "eremain", SING );
- eclear( c );
- return;
- }
-emovi( a, den );
-emovi( b, num );
-eiremain( den, num );
-/* Sign of remainder = sign of quotient */
-if( a[0] == b[0] )
- num[0] = 0;
-else
- num[0] = 0xffff;
-emovo( num, c );
-}
-
-
-void eiremain( den, num )
-unsigned short den[], num[];
-{
-long ld, ln;
-unsigned short j;
-
-ld = den[E];
-ld -= enormlz( den );
-ln = num[E];
-ln -= enormlz( num );
-ecleaz( equot );
-while( ln >= ld )
- {
- if( ecmpm(den,num) <= 0 )
- {
- esubm(den, num);
- j = 1;
- }
- else
- {
- j = 0;
- }
- eshup1(equot);
- equot[NI-1] |= j;
- eshup1(num);
- ln -= 1;
- }
-emdnorm( num, 0, 0, ln, 0 );
-}
-
-/* NaN bit patterns
- */
-#ifdef MIEEE
-unsigned short nan113[8] = {
- 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
-unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
-unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff};
-unsigned short nan24[2] = {0x7fff, 0xffff};
-#endif
-
-#ifdef IBMPC
-unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff};
-unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0};
-unsigned short nan53[4] = {0, 0, 0, 0xfff8};
-unsigned short nan24[2] = {0, 0xffc0};
-#endif
-
-
-void enan (nan, size)
-unsigned short *nan;
-int size;
-{
-int i, n;
-unsigned short *p;
-
-switch( size )
- {
-#ifndef DEC
- case 113:
- n = 8;
- p = nan113;
- break;
-
- case 64:
- n = 6;
- p = nan64;
- break;
-
- case 53:
- n = 4;
- p = nan53;
- break;
-
- case 24:
- n = 2;
- p = nan24;
- break;
-
- case NBITS:
- for( i=0; i<NE-2; i++ )
- *nan++ = 0;
- *nan++ = 0xc000;
- *nan++ = 0x7fff;
- return;
-
- case NI*16:
- *nan++ = 0;
- *nan++ = 0x7fff;
- *nan++ = 0;
- *nan++ = 0xc000;
- for( i=4; i<NI; i++ )
- *nan++ = 0;
- return;
-#endif
- default:
- mtherr( "enan", DOMAIN );
- return;
- }
-for (i=0; i < n; i++)
- *nan++ = *p++;
-}
-
-
-
-/* Longhand square root. */
-
-static int esqinited = 0;
-static unsigned short sqrndbit[NI];
-
-void esqrt( x, y )
-unsigned short *x, *y;
-{
-unsigned short temp[NI], num[NI], sq[NI], xx[NI];
-int i, j, k, n, nlups;
-long m, exp;
-
-if( esqinited == 0 )
- {
- ecleaz( sqrndbit );
- sqrndbit[NI-2] = 1;
- esqinited = 1;
- }
-/* Check for arg <= 0 */
-i = ecmp( x, ezero );
-if( i <= 0 )
- {
-#ifdef NANS
- if (i == -2)
- {
- enan (y, NBITS);
- return;
- }
-#endif
- eclear(y);
- if( i < 0 )
- mtherr( "esqrt", DOMAIN );
- return;
- }
-
-#ifdef INFINITY
-if( eisinf(x) )
- {
- eclear(y);
- einfin(y);
- return;
- }
-#endif
-/* Bring in the arg and renormalize if it is denormal. */
-emovi( x, xx );
-m = (long )xx[1]; /* local long word exponent */
-if( m == 0 )
- m -= enormlz( xx );
-
-/* Divide exponent by 2 */
-m -= 0x3ffe;
-exp = (unsigned short )( (m / 2) + 0x3ffe );
-
-/* Adjust if exponent odd */
-if( (m & 1) != 0 )
- {
- if( m > 0 )
- exp += 1;
- eshdn1( xx );
- }
-
-ecleaz( sq );
-ecleaz( num );
-n = 8; /* get 8 bits of result per inner loop */
-nlups = rndprc;
-j = 0;
-
-while( nlups > 0 )
- {
-/* bring in next word of arg */
- if( j < NE )
- num[NI-1] = xx[j+3];
-/* Do additional bit on last outer loop, for roundoff. */
- if( nlups <= 8 )
- n = nlups + 1;
- for( i=0; i<n; i++ )
- {
-/* Next 2 bits of arg */
- eshup1( num );
- eshup1( num );
-/* Shift up answer */
- eshup1( sq );
-/* Make trial divisor */
- for( k=0; k<NI; k++ )
- temp[k] = sq[k];
- eshup1( temp );
- eaddm( sqrndbit, temp );
-/* Subtract and insert answer bit if it goes in */
- if( ecmpm( temp, num ) <= 0 )
- {
- esubm( temp, num );
- sq[NI-2] |= 1;
- }
- }
- nlups -= n;
- j += 1;
- }
-
-/* Adjust for extra, roundoff loop done. */
-exp += (NBITS - 1) - rndprc;
-
-/* Sticky bit = 1 if the remainder is nonzero. */
-k = 0;
-for( i=3; i<NI; i++ )
- k |= (int )num[i];
-
-/* Renormalize and round off. */
-emdnorm( sq, k, 0, exp, 64 );
-emovo( sq, y );
-}
+++ /dev/null
-/* igamil()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igamil();
- *
- * x = igamil( a, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * igamc( a, x ) = y.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(y) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Tested for a ranging from 0.5 to 30 and x from 0 to 0.5.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,0.5 3400 8.8e-16 1.3e-16
- * IEEE 0,0.5 10000 1.1e-14 1.0e-15
- *
- */
-\f
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern long double MACHEPL, MAXNUML, MAXLOGL, MINLOGL;
-#ifdef ANSIPROT
-extern long double ndtril ( long double );
-extern long double expl ( long double );
-extern long double fabsl ( long double );
-extern long double logl ( long double );
-extern long double sqrtl ( long double );
-extern long double lgaml ( long double );
-extern long double igamcl ( long double, long double );
-#else
-long double ndtril(), expl(), fabsl(), logl(), sqrtl(), lgaml();
-long double igamcl();
-#endif
-
-long double igamil( a, y0 )
-long double a, y0;
-{
-long double x0, x1, x, yl, yh, y, d, lgm, dithresh;
-int i, dir;
-
-/* bound the solution */
-x0 = MAXNUML;
-yl = 0.0L;
-x1 = 0.0L;
-yh = 1.0L;
-dithresh = 4.0 * MACHEPL;
-
-/* approximation to inverse function */
-d = 1.0L/(9.0L*a);
-y = ( 1.0L - d - ndtril(y0) * sqrtl(d) );
-x = a * y * y * y;
-
-lgm = lgaml(a);
-
-for( i=0; i<10; i++ )
- {
- if( x > x0 || x < x1 )
- goto ihalve;
- y = igamcl(a,x);
- if( y < yl || y > yh )
- goto ihalve;
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- }
- else
- {
- x1 = x;
- yh = y;
- }
-/* compute the derivative of the function at this point */
- d = (a - 1.0L) * logl(x0) - x0 - lgm;
- if( d < -MAXLOGL )
- goto ihalve;
- d = -expl(d);
-/* compute the step to the next approximation of x */
- d = (y - y0)/d;
- x = x - d;
- if( i < 3 )
- continue;
- if( fabsl(d/x) < dithresh )
- goto done;
- }
-
-/* Resort to interval halving if Newton iteration did not converge. */
-ihalve:
-
-d = 0.0625L;
-if( x0 == MAXNUML )
- {
- if( x <= 0.0L )
- x = 1.0L;
- while( x0 == MAXNUML )
- {
- x = (1.0L + d) * x;
- y = igamcl( a, x );
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- break;
- }
- d = d + d;
- }
- }
-d = 0.5L;
-dir = 0;
-
-for( i=0; i<400; i++ )
- {
- x = x1 + d * (x0 - x1);
- y = igamcl( a, x );
- lgm = (x0 - x1)/(x1 + x0);
- if( fabsl(lgm) < dithresh )
- break;
- lgm = (y - y0)/y0;
- if( fabsl(lgm) < dithresh )
- break;
- if( x <= 0.0L )
- break;
- if( y > y0 )
- {
- x1 = x;
- yh = y;
- if( dir < 0 )
- {
- dir = 0;
- d = 0.5L;
- }
- else if( dir > 1 )
- d = 0.5L * d + 0.5L;
- else
- d = (y0 - yl)/(yh - yl);
- dir += 1;
- }
- else
- {
- x0 = x;
- yl = y;
- if( dir > 0 )
- {
- dir = 0;
- d = 0.5L;
- }
- else if( dir < -1 )
- d = 0.5L * d;
- else
- d = (y0 - yl)/(yh - yl);
- dir -= 1;
- }
- }
-if( x == 0.0L )
- mtherr( "igamil", UNDERFLOW );
-
-done:
-return( x );
-}
+++ /dev/null
-/* igaml.c
- *
- * Incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igaml();
- *
- * y = igaml( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 4000 4.4e-15 6.3e-16
- * IEEE 0,30 10000 3.6e-14 5.1e-15
- *
- */
-\f/* igamcl()
- *
- * Complemented incomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igamcl();
- *
- * y = igamcl( a, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,30 2000 2.7e-15 4.0e-16
- * IEEE 0,30 60000 1.4e-12 6.3e-15
- *
- */
-\f
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1985, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double lgaml ( long double );
-extern long double expl ( long double );
-extern long double logl ( long double );
-extern long double fabsl ( long double );
-extern long double gammal ( long double );
-long double igaml ( long double, long double );
-long double igamcl ( long double, long double );
-#else
-long double lgaml(), expl(), logl(), fabsl(), igaml(), gammal();
-long double igamcl();
-#endif
-
-#define BIG 9.223372036854775808e18L
-#define MAXGAML 1755.455L
-extern long double MACHEPL, MINLOGL;
-
-long double igamcl( a, x )
-long double a, x;
-{
-long double ans, c, yc, ax, y, z, r, t;
-long double pk, pkm1, pkm2, qk, qkm1, qkm2;
-
-if( (x <= 0.0L) || ( a <= 0.0L) )
- return( 1.0L );
-
-if( (x < 1.0L) || (x < a) )
- return( 1.0L - igaml(a,x) );
-
-ax = a * logl(x) - x - lgaml(a);
-if( ax < MINLOGL )
- {
- mtherr( "igamcl", UNDERFLOW );
- return( 0.0L );
- }
-ax = expl(ax);
-
-/* continued fraction */
-y = 1.0L - a;
-z = x + y + 1.0L;
-c = 0.0L;
-pkm2 = 1.0L;
-qkm2 = x;
-pkm1 = x + 1.0L;
-qkm1 = z * x;
-ans = pkm1/qkm1;
-
-do
- {
- c += 1.0L;
- y += 1.0L;
- z += 2.0L;
- yc = y * c;
- pk = pkm1 * z - pkm2 * yc;
- qk = qkm1 * z - qkm2 * yc;
- if( qk != 0.0L )
- {
- r = pk/qk;
- t = fabsl( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0L;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
- if( fabsl(pk) > BIG )
- {
- pkm2 /= BIG;
- pkm1 /= BIG;
- qkm2 /= BIG;
- qkm1 /= BIG;
- }
- }
-while( t > MACHEPL );
-
-return( ans * ax );
-}
-
-
-
-/* left tail of incomplete gamma function:
- *
- * inf. k
- * a -x - x
- * x e > ----------
- * - -
- * k=0 | (a+k+1)
- *
- */
-
-long double igaml( a, x )
-long double a, x;
-{
-long double ans, ax, c, r;
-
-if( (x <= 0.0L) || ( a <= 0.0L) )
- return( 0.0L );
-
-if( (x > 1.0L) && (x > a ) )
- return( 1.0L - igamcl(a,x) );
-
-ax = a * logl(x) - x - lgaml(a);
-if( ax < MINLOGL )
- {
- mtherr( "igaml", UNDERFLOW );
- return( 0.0L );
- }
-ax = expl(ax);
-
-/* power series */
-r = a;
-c = 1.0L;
-ans = 1.0L;
-
-do
- {
- r += 1.0L;
- c *= x/r;
- ans += c;
- }
-while( c/ans > MACHEPL );
-
-return( ans * ax/a );
-}
+++ /dev/null
-/* incbetl.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, incbetl();
- *
- * y = incbetl( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion
- * or, when b*x is small, by a power series.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,x) with x between 0 and 1.
- * arithmetic domain # trials peak rms
- * IEEE 0,5 20000 4.5e-18 2.4e-19
- * IEEE 0,100 100000 3.9e-17 1.0e-17
- * Half-integer a, b:
- * IEEE .5,10000 100000 3.9e-14 4.4e-15
- * Outputs smaller than the IEEE gradual underflow threshold
- * were excluded from these statistics.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * incbetl domain x<0, x>1 0.0
- */
-\f
-
-/*
-Cephes Math Library, Release 2.3: January, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#define MAXGAML 1755.455L
-static long double big = 9.223372036854775808e18L;
-static long double biginv = 1.084202172485504434007e-19L;
-extern long double MACHEPL, MINLOGL, MAXLOGL;
-
-#ifdef ANSIPROT
-extern long double gammal ( long double );
-extern long double lgaml ( long double );
-extern long double expl ( long double );
-extern long double logl ( long double );
-extern long double fabsl ( long double );
-extern long double powl ( long double, long double );
-static long double incbcfl( long double, long double, long double );
-static long double incbdl( long double, long double, long double );
-static long double pseriesl( long double, long double, long double );
-#else
-long double gammal(), lgaml(), expl(), logl(), fabsl(), powl();
-static long double incbcfl(), incbdl(), pseriesl();
-#endif
-
-long double incbetl( aa, bb, xx )
-long double aa, bb, xx;
-{
-long double a, b, t, x, w, xc, y;
-int flag;
-
-if( aa <= 0.0L || bb <= 0.0L )
- goto domerr;
-
-if( (xx <= 0.0L) || ( xx >= 1.0L) )
- {
- if( xx == 0.0L )
- return( 0.0L );
- if( xx == 1.0L )
- return( 1.0L );
-domerr:
- mtherr( "incbetl", DOMAIN );
- return( 0.0L );
- }
-
-flag = 0;
-if( (bb * xx) <= 1.0L && xx <= 0.95L)
- {
- t = pseriesl(aa, bb, xx);
- goto done;
- }
-
-w = 1.0L - xx;
-
-/* Reverse a and b if x is greater than the mean. */
-if( xx > (aa/(aa+bb)) )
- {
- flag = 1;
- a = bb;
- b = aa;
- xc = xx;
- x = w;
- }
-else
- {
- a = aa;
- b = bb;
- xc = w;
- x = xx;
- }
-
-if( flag == 1 && (b * x) <= 1.0L && x <= 0.95L)
- {
- t = pseriesl(a, b, x);
- goto done;
- }
-
-/* Choose expansion for optimal convergence */
-y = x * (a+b-2.0L) - (a-1.0L);
-if( y < 0.0L )
- w = incbcfl( a, b, x );
-else
- w = incbdl( a, b, x ) / xc;
-
-/* Multiply w by the factor
- a b _ _ _
- x (1-x) | (a+b) / ( a | (a) | (b) ) . */
-
-y = a * logl(x);
-t = b * logl(xc);
-if( (a+b) < MAXGAML && fabsl(y) < MAXLOGL && fabsl(t) < MAXLOGL )
- {
- t = powl(xc,b);
- t *= powl(x,a);
- t /= a;
- t *= w;
- t *= gammal(a+b) / (gammal(a) * gammal(b));
- goto done;
- }
-else
- {
- /* Resort to logarithms. */
- y += t + lgaml(a+b) - lgaml(a) - lgaml(b);
- y += logl(w/a);
- if( y < MINLOGL )
- t = 0.0L;
- else
- t = expl(y);
- }
-
-done:
-
-if( flag == 1 )
- {
- if( t <= MACHEPL )
- t = 1.0L - MACHEPL;
- else
- t = 1.0L - t;
- }
-return( t );
-}
-\f
-/* Continued fraction expansion #1
- * for incomplete beta integral
- */
-
-static long double incbcfl( a, b, x )
-long double a, b, x;
-{
-long double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
-long double k1, k2, k3, k4, k5, k6, k7, k8;
-long double r, t, ans, thresh;
-int n;
-
-k1 = a;
-k2 = a + b;
-k3 = a;
-k4 = a + 1.0L;
-k5 = 1.0L;
-k6 = b - 1.0L;
-k7 = k4;
-k8 = a + 2.0L;
-
-pkm2 = 0.0L;
-qkm2 = 1.0L;
-pkm1 = 1.0L;
-qkm1 = 1.0L;
-ans = 1.0L;
-r = 1.0L;
-n = 0;
-thresh = 3.0L * MACHEPL;
-do
- {
-
- xk = -( x * k1 * k2 )/( k3 * k4 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = ( x * k5 * k6 )/( k7 * k8 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if( qk != 0.0L )
- r = pk/qk;
- if( r != 0.0L )
- {
- t = fabsl( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0L;
-
- if( t < thresh )
- goto cdone;
-
- k1 += 1.0L;
- k2 += 1.0L;
- k3 += 2.0L;
- k4 += 2.0L;
- k5 += 1.0L;
- k6 -= 1.0L;
- k7 += 2.0L;
- k8 += 2.0L;
-
- if( (fabsl(qk) + fabsl(pk)) > big )
- {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
- }
- if( (fabsl(qk) < biginv) || (fabsl(pk) < biginv) )
- {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- }
-while( ++n < 400 );
-mtherr( "incbetl", PLOSS );
-
-cdone:
-return(ans);
-}
-
-\f
-/* Continued fraction expansion #2
- * for incomplete beta integral
- */
-
-static long double incbdl( a, b, x )
-long double a, b, x;
-{
-long double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
-long double k1, k2, k3, k4, k5, k6, k7, k8;
-long double r, t, ans, z, thresh;
-int n;
-
-k1 = a;
-k2 = b - 1.0L;
-k3 = a;
-k4 = a + 1.0L;
-k5 = 1.0L;
-k6 = a + b;
-k7 = a + 1.0L;
-k8 = a + 2.0L;
-
-pkm2 = 0.0L;
-qkm2 = 1.0L;
-pkm1 = 1.0L;
-qkm1 = 1.0L;
-z = x / (1.0L-x);
-ans = 1.0L;
-r = 1.0L;
-n = 0;
-thresh = 3.0L * MACHEPL;
-do
- {
-
- xk = -( z * k1 * k2 )/( k3 * k4 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = ( z * k5 * k6 )/( k7 * k8 );
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if( qk != 0.0L )
- r = pk/qk;
- if( r != 0.0L )
- {
- t = fabsl( (ans - r)/r );
- ans = r;
- }
- else
- t = 1.0L;
-
- if( t < thresh )
- goto cdone;
-
- k1 += 1.0L;
- k2 -= 1.0L;
- k3 += 2.0L;
- k4 += 2.0L;
- k5 += 1.0L;
- k6 += 1.0L;
- k7 += 2.0L;
- k8 += 2.0L;
-
- if( (fabsl(qk) + fabsl(pk)) > big )
- {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
- }
- if( (fabsl(qk) < biginv) || (fabsl(pk) < biginv) )
- {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- }
-while( ++n < 400 );
-mtherr( "incbetl", PLOSS );
-
-cdone:
-return(ans);
-}
-
-/* Power series for incomplete gamma integral.
- Use when b*x is small. */
-
-static long double pseriesl( a, b, x )
-long double a, b, x;
-{
-long double s, t, u, v, n, t1, z, ai;
-
-ai = 1.0L / a;
-u = (1.0L - b) * x;
-v = u / (a + 1.0L);
-t1 = v;
-t = u;
-n = 2.0L;
-s = 0.0L;
-z = MACHEPL * ai;
-while( fabsl(v) > z )
- {
- u = (n - b) * x / n;
- t *= u;
- v = t / (a + n);
- s += v;
- n += 1.0L;
- }
-s += t1;
-s += ai;
-
-u = a * logl(x);
-if( (a+b) < MAXGAML && fabsl(u) < MAXLOGL )
- {
- t = gammal(a+b)/(gammal(a)*gammal(b));
- s = s * t * powl(x,a);
- }
-else
- {
- t = lgaml(a+b) - lgaml(a) - lgaml(b) + u + logl(s);
- if( t < MINLOGL )
- s = 0.0L;
- else
- s = expl(t);
- }
-return(s);
-}
+++ /dev/null
-/* incbil()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, b, x, y, incbil();
- *
- * x = incbil( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y.
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 .5,10000 10000 1.1e-14 1.4e-16
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern long double MACHEPL, MAXNUML, MAXLOGL, MINLOGL;
-#ifdef ANSIPROT
-extern long double incbetl ( long double, long double, long double );
-extern long double expl ( long double );
-extern long double fabsl ( long double );
-extern long double logl ( long double );
-extern long double sqrtl ( long double );
-extern long double lgaml ( long double );
-extern long double ndtril ( long double );
-#else
-long double incbetl(), expl(), fabsl(), logl(), sqrtl(), lgaml();
-long double ndtril();
-#endif
-
-long double incbil( aa, bb, yy0 )
-long double aa, bb, yy0;
-{
-long double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
-int i, rflg, dir, nflg;
-
-
-if( yy0 <= 0.0L )
- return(0.0L);
-if( yy0 >= 1.0L )
- return(1.0L);
-x0 = 0.0L;
-yl = 0.0L;
-x1 = 1.0L;
-yh = 1.0L;
-if( aa <= 1.0L || bb <= 1.0L )
- {
- dithresh = 1.0e-7L;
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- x = a/(a+b);
- y = incbetl( a, b, x );
- nflg = 0;
- goto ihalve;
- }
-else
- {
- nflg = 0;
- dithresh = 1.0e-4L;
- }
-
-/* approximation to inverse function */
-
-yp = -ndtril( yy0 );
-
-if( yy0 > 0.5L )
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0L - yy0;
- yp = -yp;
- }
-else
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
-
-lgm = (yp * yp - 3.0L)/6.0L;
-x = 2.0L/( 1.0L/(2.0L * a-1.0L) + 1.0L/(2.0L * b - 1.0L) );
-d = yp * sqrtl( x + lgm ) / x
- - ( 1.0L/(2.0L * b - 1.0L) - 1.0L/(2.0L * a - 1.0L) )
- * (lgm + (5.0L/6.0L) - 2.0L/(3.0L * x));
-d = 2.0L * d;
-if( d < MINLOGL )
- {
- x = 1.0L;
- goto under;
- }
-x = a/( a + b * expl(d) );
-y = incbetl( a, b, x );
-yp = (y - y0)/y0;
-if( fabsl(yp) < 0.2 )
- goto newt;
-
-/* Resort to interval halving if not close enough. */
-ihalve:
-
-dir = 0;
-di = 0.5L;
-for( i=0; i<400; i++ )
- {
- if( i != 0 )
- {
- x = x0 + di * (x1 - x0);
- if( x == 1.0L )
- x = 1.0L - MACHEPL;
- if( x == 0.0L )
- {
- di = 0.5;
- x = x0 + di * (x1 - x0);
- if( x == 0.0 )
- goto under;
- }
- y = incbetl( a, b, x );
- yp = (x1 - x0)/(x1 + x0);
- if( fabsl(yp) < dithresh )
- goto newt;
- yp = (y-y0)/y0;
- if( fabsl(yp) < dithresh )
- goto newt;
- }
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- if( dir < 0 )
- {
- dir = 0;
- di = 0.5L;
- }
- else if( dir > 3 )
- di = 1.0L - (1.0L - di) * (1.0L - di);
- else if( dir > 1 )
- di = 0.5L * di + 0.5L;
- else
- di = (y0 - y)/(yh - yl);
- dir += 1;
- if( x0 > 0.95L )
- {
- if( rflg == 1 )
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
- else
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0 - yy0;
- }
- x = 1.0L - x;
- y = incbetl( a, b, x );
- x0 = 0.0;
- yl = 0.0;
- x1 = 1.0;
- yh = 1.0;
- goto ihalve;
- }
- }
- else
- {
- x1 = x;
- if( rflg == 1 && x1 < MACHEPL )
- {
- x = 0.0L;
- goto done;
- }
- yh = y;
- if( dir > 0 )
- {
- dir = 0;
- di = 0.5L;
- }
- else if( dir < -3 )
- di = di * di;
- else if( dir < -1 )
- di = 0.5L * di;
- else
- di = (y - y0)/(yh - yl);
- dir -= 1;
- }
- }
-mtherr( "incbil", PLOSS );
-if( x0 >= 1.0L )
- {
- x = 1.0L - MACHEPL;
- goto done;
- }
-if( x <= 0.0L )
- {
-under:
- mtherr( "incbil", UNDERFLOW );
- x = 0.0L;
- goto done;
- }
-
-newt:
-
-if( nflg )
- goto done;
-nflg = 1;
-lgm = lgaml(a+b) - lgaml(a) - lgaml(b);
-
-for( i=0; i<15; i++ )
- {
- /* Compute the function at this point. */
- if( i != 0 )
- y = incbetl(a,b,x);
- if( y < yl )
- {
- x = x0;
- y = yl;
- }
- else if( y > yh )
- {
- x = x1;
- y = yh;
- }
- else if( y < y0 )
- {
- x0 = x;
- yl = y;
- }
- else
- {
- x1 = x;
- yh = y;
- }
- if( x == 1.0L || x == 0.0L )
- break;
- /* Compute the derivative of the function at this point. */
- d = (a - 1.0L) * logl(x) + (b - 1.0L) * logl(1.0L - x) + lgm;
- if( d < MINLOGL )
- goto done;
- if( d > MAXLOGL )
- break;
- d = expl(d);
- /* Compute the step to the next approximation of x. */
- d = (y - y0)/d;
- xt = x - d;
- if( xt <= x0 )
- {
- y = (x - x0) / (x1 - x0);
- xt = x0 + 0.5L * y * (x - x0);
- if( xt <= 0.0L )
- break;
- }
- if( xt >= x1 )
- {
- y = (x1 - x) / (x1 - x0);
- xt = x1 - 0.5L * y * (x1 - x);
- if( xt >= 1.0L )
- break;
- }
- x = xt;
- if( fabsl(d/x) < (128.0L * MACHEPL) )
- goto done;
- }
-/* Did not converge. */
-dithresh = 256.0L * MACHEPL;
-goto ihalve;
-
-done:
-if( rflg )
- {
- if( x <= MACHEPL )
- x = 1.0L - MACHEPL;
- else
- x = 1.0L - x;
- }
-return( x );
-}
+++ /dev/null
-/* isnanl()
- * isfinitel()
- * signbitl()
- *
- * Floating point IEEE special number tests
- *
- *
- *
- * SYNOPSIS:
- *
- * int signbitl(), isnanl(), isfinitel();
- * long double x, y;
- *
- * n = signbitl(x);
- * n = isnanl(x);
- * n = isfinitel(x);
- *
- *
- *
- * DESCRIPTION:
- *
- * These functions are part of the standard C run time library
- * for some but not all C compilers. The ones supplied are
- * written in C for IEEE arithmetic. They should
- * be used only if your compiler library does not already have
- * them.
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.7: June, 1998
-Copyright 1992, 1998 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-/* This is defined in mconf.h. */
-/* #define DENORMAL 1 */
-
-#ifdef UNK
-/* Change UNK into something else. */
-#undef UNK
-#if BIGENDIAN
-#define MIEEE 1
-#else
-#define IBMPC 1
-#endif
-#endif
-
-
-/* Return 1 if the sign bit of x is 1, else 0. */
-
-int signbitl(x)
-long double x;
-{
-union
- {
- long double d;
- short s[6];
- int i[3];
- } u;
-
-u.d = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- return( u.s[4] < 0 );
-#endif
-#ifdef MIEEE
- return( u.i[0] < 0 );
-#endif
- }
-else
- {
-#ifdef IBMPC
- return( u.s[4] < 0 );
-#endif
-#ifdef MIEEE
- return( u.s[0] < 0 );
-#endif
- }
-}
-
-
-/* Return 1 if x is a number that is Not a Number, else return 0. */
-
-int isnanl(x)
-long double x;
-{
-#ifdef NANS
-union
- {
- long double d;
- unsigned short s[6];
- unsigned int i[3];
- } u;
-
-u.d = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- if( ((u.s[4] & 0x7fff) == 0x7fff)
- && (((u.i[1] & 0x7fffffff)!= 0) || (u.i[0] != 0)))
- return 1;
-#endif
-#ifdef MIEEE
- if( ((u.i[0] & 0x7fff0000) == 0x7fff0000)
- && (((u.i[1] & 0x7fffffff) != 0) || (u.i[2] != 0)))
- return 1;
-#endif
- return(0);
- }
-else
- { /* size int not 4 */
-#ifdef IBMPC
- if( (u.s[4] & 0x7fff) == 0x7fff)
- {
- if((u.s[3] & 0x7fff) | u.s[2] | u.s[1] | u.s[0])
- return(1);
- }
-#endif
-#ifdef MIEEE
- if( (u.s[0] & 0x7fff) == 0x7fff)
- {
- if((u.s[2] & 0x7fff) | u.s[3] | u.s[4] | u.s[5])
- return(1);
- }
-#endif
- return(0);
- } /* size int not 4 */
-
-#else
-/* No NANS. */
-return(0);
-#endif
-}
-
-
-/* Return 1 if x is not infinite and is not a NaN. */
-
-int isfinitel(x)
-long double x;
-{
-#ifdef INFINITIES
-union
- {
- long double d;
- unsigned short s[6];
- unsigned int i[3];
- } u;
-
-u.d = x;
-
-if( sizeof(int) == 4 )
- {
-#ifdef IBMPC
- if( (u.s[4] & 0x7fff) != 0x7fff)
- return 1;
-#endif
-#ifdef MIEEE
- if( (u.i[0] & 0x7fff0000) != 0x7fff0000)
- return 1;
-#endif
- return(0);
- }
-else
- {
-#ifdef IBMPC
- if( (u.s[4] & 0x7fff) != 0x7fff)
- return 1;
-#endif
-#ifdef MIEEE
- if( (u.s[0] & 0x7fff) != 0x7fff)
- return 1;
-#endif
- return(0);
- }
-#else
-/* No INFINITY. */
-return(1);
-#endif
-}
+++ /dev/null
-/* j0l.c
- *
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, j0l();
- *
- * y = j0l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of first kind, order zero of the argument.
- *
- * The domain is divided into the intervals [0, 9] and
- * (9, infinity). In the first interval the rational approximation
- * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) P7(x^2) / Q8(x^2),
- * where r, s, t are the first three zeros of the function.
- * In the second interval the expansion is in terms of the
- * modulus M0(x) = sqrt(J0(x)^2 + Y0(x)^2) and phase P0(x)
- * = atan(Y0(x)/J0(x)). M0 is approximated by sqrt(1/x)P7(1/x)/Q7(1/x).
- * The approximation to J0 is M0 * cos(x - pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 100000 2.8e-19 7.4e-20
- *
- *
- */
-\f/* y0l.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y0l();
- *
- * y = y0l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 5>, [5,9> and
- * [9, infinity). In the first interval a rational approximation
- * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
- *
- * In the second interval, the approximation is
- * (x - p)(x - q)(x - r)(x - s)P7(x)/Q7(x)
- * where p, q, r, s are zeros of y0(x).
- *
- * The third interval uses the same approximations to modulus
- * and phase as j0(x), whence y0(x) = modulus * sin(phase).
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 100000 3.4e-19 7.6e-20
- *
- */
-
-/* Copyright 1994 by Stephen L. Moshier (moshier@world.std.com). */
-
-#include <math.h>
-
-/*
-j0(x) = (x^2-JZ1)(x^2-JZ2)(x^2-JZ3)P(x**2)/Q(x**2)
-0 <= x <= 9
-Relative error
-n=7, d=8
-Peak error = 8.49e-22
-Relative error spread = 2.2e-3
-*/
-#if UNK
-static long double j0n[8] = {
- 1.296848754518641770562E0L,
--3.239201943301299801018E3L,
- 3.490002040733471400107E6L,
--2.076797068740966813173E9L,
- 7.283696461857171054941E11L,
--1.487926133645291056388E14L,
- 1.620335009643150402368E16L,
--7.173386747526788067407E17L,
-};
-static long double j0d[8] = {
-/* 1.000000000000000000000E0L,*/
- 2.281959869176887763845E3L,
- 2.910386840401647706984E6L,
- 2.608400226578100610991E9L,
- 1.752689035792859338860E12L,
- 8.879132373286001289461E14L,
- 3.265560832845194013669E17L,
- 7.881340554308432241892E19L,
- 9.466475654163919450528E21L,
-};
-#endif
-#if IBMPC
-static short j0n[] = {
-0xf759,0x4208,0x23d6,0xa5ff,0x3fff, XPD
-0xa9a8,0xe62b,0x3b28,0xca73,0xc00a, XPD
-0xfe10,0xb608,0x4829,0xd503,0x4014, XPD
-0x008c,0x7b60,0xd119,0xf792,0xc01d, XPD
-0x943a,0x69b7,0x36ca,0xa996,0x4026, XPD
-0x1b0b,0x6331,0x7add,0x8753,0xc02e, XPD
-0x4018,0xad26,0x71ba,0xe643,0x4034, XPD
-0xb96c,0xc486,0xfb95,0x9f47,0xc03a, XPD
-};
-static short j0d[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xbdfe,0xc832,0x5b9f,0x8e9f,0x400a, XPD
-0xe1a0,0x923f,0xcb5c,0xb1a2,0x4014, XPD
-0x66d2,0x93fe,0x0762,0x9b79,0x401e, XPD
-0xfed1,0x086d,0x3425,0xcc0a,0x4027, XPD
-0x0841,0x8cb6,0x5a46,0xc9e3,0x4030, XPD
-0x3d2c,0xed55,0x20e1,0x9105,0x4039, XPD
-0xfdce,0xa4ca,0x2ed8,0x88b8,0x4041, XPD
-0x00ac,0xfb2b,0x6f62,0x804b,0x4048, XPD
-};
-#endif
-#if MIEEE
-static long j0n[24] = {
-0x3fff0000,0xa5ff23d6,0x4208f759,
-0xc00a0000,0xca733b28,0xe62ba9a8,
-0x40140000,0xd5034829,0xb608fe10,
-0xc01d0000,0xf792d119,0x7b60008c,
-0x40260000,0xa99636ca,0x69b7943a,
-0xc02e0000,0x87537add,0x63311b0b,
-0x40340000,0xe64371ba,0xad264018,
-0xc03a0000,0x9f47fb95,0xc486b96c,
-};
-static long j0d[24] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x400a0000,0x8e9f5b9f,0xc832bdfe,
-0x40140000,0xb1a2cb5c,0x923fe1a0,
-0x401e0000,0x9b790762,0x93fe66d2,
-0x40270000,0xcc0a3425,0x086dfed1,
-0x40300000,0xc9e35a46,0x8cb60841,
-0x40390000,0x910520e1,0xed553d2c,
-0x40410000,0x88b82ed8,0xa4cafdce,
-0x40480000,0x804b6f62,0xfb2b00ac,
-};
-#endif
-/*
-sqrt(j0^2(1/x^2) + y0^2(1/x^2)) = z P(z**2)/Q(z**2)
-z(x) = 1/sqrt(x)
-Relative error
-n=7, d=7
-Peak error = 1.80e-20
-Relative error spread = 5.1e-2
-*/
-#if UNK
-static long double modulusn[8] = {
- 3.947542376069224461532E-1L,
- 6.864682945702134624126E0L,
- 1.021369773577974343844E1L,
- 7.626141421290849630523E0L,
- 2.842537511425216145635E0L,
- 7.162842530423205720962E-1L,
- 9.036664453160200052296E-2L,
- 8.461833426898867839659E-3L,
-};
-static long double modulusd[7] = {
-/* 1.000000000000000000000E0L,*/
- 9.117176038171821115904E0L,
- 1.301235226061478261481E1L,
- 9.613002539386213788182E0L,
- 3.569671060989910901903E0L,
- 8.983920141407590632423E-1L,
- 1.132577931332212304986E-1L,
- 1.060533546154121770442E-2L,
-};
-#endif
-#if IBMPC
-static short modulusn[] = {
-0x8559,0xf552,0x3a38,0xca1d,0x3ffd, XPD
-0x38a3,0xa663,0x7b91,0xdbab,0x4001, XPD
-0xb343,0x2673,0x4e51,0xa36b,0x4002, XPD
-0x5e4b,0xe3af,0x59bb,0xf409,0x4001, XPD
-0xb1cd,0x4e5e,0x2274,0xb5ec,0x4000, XPD
-0xcfe9,0x74e0,0x67a1,0xb75e,0x3ffe, XPD
-0x6b78,0x4cc6,0x25b7,0xb912,0x3ffb, XPD
-0xcb2b,0x4b73,0x8075,0x8aa3,0x3ff8, XPD
-};
-static short modulusd[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0x4498,0x3d2a,0xf3fb,0x91df,0x4002, XPD
-0x5e3d,0xb5f4,0x9848,0xd032,0x4002, XPD
-0xb837,0x3075,0xdbc0,0x99ce,0x4002, XPD
-0x775a,0x1b79,0x7d9c,0xe475,0x4000, XPD
-0x7e3f,0xb8dd,0x04df,0xe5fd,0x3ffe, XPD
-0xed5a,0x31cd,0xb3ac,0xe7f3,0x3ffb, XPD
-0x8a83,0x1b80,0x003e,0xadc2,0x3ff8, XPD
-};
-#endif
-#if MIEEE
-static long modulusn[24] = {
-0x3ffd0000,0xca1d3a38,0xf5528559,
-0x40010000,0xdbab7b91,0xa66338a3,
-0x40020000,0xa36b4e51,0x2673b343,
-0x40010000,0xf40959bb,0xe3af5e4b,
-0x40000000,0xb5ec2274,0x4e5eb1cd,
-0x3ffe0000,0xb75e67a1,0x74e0cfe9,
-0x3ffb0000,0xb91225b7,0x4cc66b78,
-0x3ff80000,0x8aa38075,0x4b73cb2b,
-};
-static long modulusd[21] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40020000,0x91dff3fb,0x3d2a4498,
-0x40020000,0xd0329848,0xb5f45e3d,
-0x40020000,0x99cedbc0,0x3075b837,
-0x40000000,0xe4757d9c,0x1b79775a,
-0x3ffe0000,0xe5fd04df,0xb8dd7e3f,
-0x3ffb0000,0xe7f3b3ac,0x31cded5a,
-0x3ff80000,0xadc2003e,0x1b808a83,
-};
-#endif
-/*
-atan(y0(x)/j0(x)) = x - pi/4 + x P(x**2)/Q(x**2)
-Absolute error
-n=5, d=6
-Peak error = 2.80e-21
-Relative error spread = 5.5e-1
-*/
-#if UNK
-static long double phasen[6] = {
--7.356766355393571519038E-1L,
--5.001635199922493694706E-1L,
--7.737323518141516881715E-2L,
--3.998893155826990642730E-3L,
--7.496317036829964150970E-5L,
--4.290885090773112963542E-7L,
-};
-static long double phased[6] = {
-/* 1.000000000000000000000E0L,*/
- 7.377856408614376072745E0L,
- 4.285043297797736118069E0L,
- 6.348446472935245102890E-1L,
- 3.229866782185025048457E-2L,
- 6.014932317342190404134E-4L,
- 3.432708072618490390095E-6L,
-};
-#endif
-#if IBMPC
-static short phasen[] = {
-0x5106,0x12a6,0x4dd2,0xbc55,0xbffe, XPD
-0x1e30,0x04da,0xb769,0x800a,0xbffe, XPD
-0x8d8a,0x84e7,0xdbd5,0x9e75,0xbffb, XPD
-0xe514,0x8866,0x25a9,0x8309,0xbff7, XPD
-0xdc17,0x325e,0x8baf,0x9d35,0xbff1, XPD
-0x4c2f,0x2dd8,0x79c3,0xe65d,0xbfe9, XPD
-};
-static short phased[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xf3e9,0xb2a5,0x6652,0xec17,0x4001, XPD
-0x4b69,0x3f87,0x131f,0x891f,0x4001, XPD
-0x6f25,0x2a95,0x2dc6,0xa285,0x3ffe, XPD
-0x37bf,0xfcc8,0x9b9f,0x844b,0x3ffa, XPD
-0xac5c,0x4806,0x8709,0x9dad,0x3ff4, XPD
-0x4c8c,0x2dd8,0x79c3,0xe65d,0x3fec, XPD
-};
-#endif
-#if MIEEE
-static long phasen[18] = {
-0xbffe0000,0xbc554dd2,0x12a65106,
-0xbffe0000,0x800ab769,0x04da1e30,
-0xbffb0000,0x9e75dbd5,0x84e78d8a,
-0xbff70000,0x830925a9,0x8866e514,
-0xbff10000,0x9d358baf,0x325edc17,
-0xbfe90000,0xe65d79c3,0x2dd84c2f,
-};
-static long phased[18] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40010000,0xec176652,0xb2a5f3e9,
-0x40010000,0x891f131f,0x3f874b69,
-0x3ffe0000,0xa2852dc6,0x2a956f25,
-0x3ffa0000,0x844b9b9f,0xfcc837bf,
-0x3ff40000,0x9dad8709,0x4806ac5c,
-0x3fec0000,0xe65d79c3,0x2dd84c8c,
-};
-#endif
-#define JZ1 5.783185962946784521176L
-#define JZ2 30.47126234366208639908L
-#define JZ3 7.488700679069518344489e1L
-
-#define PIO4L 0.78539816339744830961566L
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double fabsl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double cosl ( long double );
-extern long double sinl ( long double );
-extern long double logl ( long double );
-long double j0l ( long double );
-#else
-long double sqrtl(), fabsl(), polevll(), p1evll(), cosl(), sinl(), logl();
-long double j0l();
-#endif
-
-long double j0l(x)
-long double x;
-{
-long double xx, y, z, modulus, phase;
-
-xx = x * x;
-if( xx < 81.0L )
- {
- y = (xx - JZ1) * (xx - JZ2) * (xx -JZ3);
- y *= polevll( xx, j0n, 7 ) / p1evll( xx, j0d, 8 );
- return y;
- }
-
-y = fabsl(x);
-xx = 1.0/xx;
-phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
-
-z = 1.0/y;
-modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 7 );
-
-y = modulus * cosl( y - PIO4L + z*phase) / sqrtl(y);
-return y;
-}
-
-
-/*
-y0(x) = 2/pi * log(x) * j0(x) + P(z**2)/Q(z**2)
-0 <= x <= 5
-Absolute error
-n=7, d=7
-Peak error = 8.55e-22
-Relative error spread = 2.7e-1
-*/
-#if UNK
-static long double y0n[8] = {
- 1.556909814120445353691E4L,
--1.464324149797947303151E7L,
- 5.427926320587133391307E9L,
--9.808510181632626683952E11L,
- 8.747842804834934784972E13L,
--3.461898868011666236539E15L,
- 4.421767595991969611983E16L,
--1.847183690384811186958E16L,
-};
-static long double y0d[7] = {
-/* 1.000000000000000000000E0L,*/
- 1.040792201755841697889E3L,
- 6.256391154086099882302E5L,
- 2.686702051957904669677E8L,
- 8.630939306572281881328E10L,
- 2.027480766502742538763E13L,
- 3.167750475899536301562E15L,
- 2.502813268068711844040E17L,
-};
-#endif
-#if IBMPC
-static short y0n[] = {
-0x126c,0x20be,0x647f,0xf344,0x400c, XPD
-0x2ec0,0x7b95,0x297f,0xdf70,0xc016, XPD
-0x2fdd,0x4b27,0xca98,0xa1c3,0x401f, XPD
-0x3e3c,0xb343,0x46c9,0xe45f,0xc026, XPD
-0xb219,0x37ba,0x5142,0x9f1f,0x402d, XPD
-0x23c9,0x6b29,0x4244,0xc4c9,0xc032, XPD
-0x501f,0x6264,0xbdf4,0x9d17,0x4036, XPD
-0x5fbd,0x0171,0x135a,0x8340,0xc035, XPD
-};
-static short y0d[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0x9057,0x7f25,0x59b7,0x8219,0x4009, XPD
-0xd938,0xb6b2,0x71d8,0x98be,0x4012, XPD
-0x97a4,0x90fa,0xa7e9,0x801c,0x401b, XPD
-0x553b,0x4dc8,0x8695,0xa0c3,0x4023, XPD
-0x6732,0x8c1b,0xc5ab,0x9384,0x402b, XPD
-0x04d3,0xa629,0xd61d,0xb410,0x4032, XPD
-0x241a,0x8f2b,0x629a,0xde4b,0x4038, XPD
-};
-#endif
-#if MIEEE
-static long y0n[24] = {
-0x400c0000,0xf344647f,0x20be126c,
-0xc0160000,0xdf70297f,0x7b952ec0,
-0x401f0000,0xa1c3ca98,0x4b272fdd,
-0xc0260000,0xe45f46c9,0xb3433e3c,
-0x402d0000,0x9f1f5142,0x37bab219,
-0xc0320000,0xc4c94244,0x6b2923c9,
-0x40360000,0x9d17bdf4,0x6264501f,
-0xc0350000,0x8340135a,0x01715fbd,
-};
-static long y0d[21] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40090000,0x821959b7,0x7f259057,
-0x40120000,0x98be71d8,0xb6b2d938,
-0x401b0000,0x801ca7e9,0x90fa97a4,
-0x40230000,0xa0c38695,0x4dc8553b,
-0x402b0000,0x9384c5ab,0x8c1b6732,
-0x40320000,0xb410d61d,0xa62904d3,
-0x40380000,0xde4b629a,0x8f2b241a,
-};
-#endif
-/*
-y0(x) = (x-Y0Z1)(x-Y0Z2)(x-Y0Z3)(x-Y0Z4)P(x)/Q(x)
-4.5 <= x <= 9
-Absolute error
-n=9, d=9
-Peak error = 2.35e-20
-Relative error spread = 7.8e-13
-*/
-#if UNK
-static long double y059n[10] = {
- 2.368715538373384869796E-2L,
--1.472923738545276751402E0L,
- 2.525993724177105060507E1L,
- 7.727403527387097461580E1L,
--4.578271827238477598563E3L,
- 7.051411242092171161986E3L,
- 1.951120419910720443331E5L,
- 6.515211089266670755622E5L,
--1.164760792144532266855E5L,
--5.566567444353735925323E5L,
-};
-static long double y059d[9] = {
-/* 1.000000000000000000000E0L,*/
--6.235501989189125881723E1L,
- 2.224790285641017194158E3L,
--5.103881883748705381186E4L,
- 8.772616606054526158657E5L,
--1.096162986826467060921E7L,
- 1.083335477747278958468E8L,
--7.045635226159434678833E8L,
- 3.518324187204647941098E9L,
- 1.173085288957116938494E9L,
-};
-#endif
-#if IBMPC
-static short y059n[] = {
-0x992f,0xab45,0x90b6,0xc20b,0x3ff9, XPD
-0x1207,0x46ea,0xc3db,0xbc88,0xbfff, XPD
-0x5504,0x035a,0x59fa,0xca14,0x4003, XPD
-0xd5a3,0xf673,0x4e59,0x9a8c,0x4005, XPD
-0x62e0,0xc25b,0x2cb3,0x8f12,0xc00b, XPD
-0xe8fa,0x4b44,0x4a39,0xdc5b,0x400b, XPD
-0x49e2,0xfb52,0x02af,0xbe8a,0x4010, XPD
-0x8c07,0x29e3,0x11be,0x9f10,0x4012, XPD
-0xfd54,0xb2fe,0x0a23,0xe37e,0xc00f, XPD
-0xf90c,0x3510,0x0be9,0x87e7,0xc012, XPD
-};
-static short y059d[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xdebf,0xa468,0x8a55,0xf96b,0xc004, XPD
-0xad09,0x8e6a,0xa502,0x8b0c,0x400a, XPD
-0xa28c,0x5563,0xd19f,0xc75e,0xc00e, XPD
-0xe8b6,0xd705,0xda91,0xd62c,0x4012, XPD
-0xec8a,0x4697,0xddde,0xa742,0xc016, XPD
-0x27ff,0xca92,0x3d78,0xcea1,0x4019, XPD
-0xe26b,0x76b9,0x250a,0xa7fb,0xc01c, XPD
-0xceb6,0x3463,0x5ddb,0xd1b5,0x401e, XPD
-0x3b3b,0xea0b,0xb8d1,0x8bd7,0x401d, XPD
-};
-#endif
-#if MIEEE
-static long y059n[30] = {
-0x3ff90000,0xc20b90b6,0xab45992f,
-0xbfff0000,0xbc88c3db,0x46ea1207,
-0x40030000,0xca1459fa,0x035a5504,
-0x40050000,0x9a8c4e59,0xf673d5a3,
-0xc00b0000,0x8f122cb3,0xc25b62e0,
-0x400b0000,0xdc5b4a39,0x4b44e8fa,
-0x40100000,0xbe8a02af,0xfb5249e2,
-0x40120000,0x9f1011be,0x29e38c07,
-0xc00f0000,0xe37e0a23,0xb2fefd54,
-0xc0120000,0x87e70be9,0x3510f90c,
-};
-static long y059d[27] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0040000,0xf96b8a55,0xa468debf,
-0x400a0000,0x8b0ca502,0x8e6aad09,
-0xc00e0000,0xc75ed19f,0x5563a28c,
-0x40120000,0xd62cda91,0xd705e8b6,
-0xc0160000,0xa742ddde,0x4697ec8a,
-0x40190000,0xcea13d78,0xca9227ff,
-0xc01c0000,0xa7fb250a,0x76b9e26b,
-0x401e0000,0xd1b55ddb,0x3463ceb6,
-0x401d0000,0x8bd7b8d1,0xea0b3b3b,
-};
-#endif
-#define TWOOPI 6.36619772367581343075535E-1L
-#define Y0Z1 3.957678419314857868376e0L
-#define Y0Z2 7.086051060301772697624e0L
-#define Y0Z3 1.022234504349641701900e1L
-#define Y0Z4 1.336109747387276347827e1L
-/* #define MAXNUML 1.189731495357231765021e4932L */
-extern long double MAXNUML;
-
-long double y0l(x)
-long double x;
-{
-long double xx, y, z, modulus, phase;
-
-if( x < 0.0 )
- {
- return (-MAXNUML);
- }
-xx = x * x;
-if( xx < 81.0L )
- {
- if( xx < 20.25L )
- {
- y = TWOOPI * logl(x) * j0l(x);
- y += polevll( xx, y0n, 7 ) / p1evll( xx, y0d, 7 );
- }
- else
- {
- y = (x - Y0Z1)*(x - Y0Z2)*(x - Y0Z3)*(x - Y0Z4);
- y *= polevll( x, y059n, 9 ) / p1evll( x, y059d, 9 );
- }
- return y;
- }
-
-y = fabsl(x);
-xx = 1.0/xx;
-phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
-
-z = 1.0/y;
-modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 7 );
-
-y = modulus * sinl( y - PIO4L + z*phase) / sqrtl(y);
-return y;
-}
+++ /dev/null
-/* j1l.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, j1l();
- *
- * y = j1l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 9] and
- * (9, infinity). In the first interval the rational approximation
- * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) x P8(x^2) / Q8(x^2),
- * where r, s, t are the first three zeros of the function.
- * In the second interval the expansion is in terms of the
- * modulus M1(x) = sqrt(J1(x)^2 + Y1(x)^2) and phase P1(x)
- * = atan(Y1(x)/J1(x)). M1 is approximated by sqrt(1/x)P7(1/x)/Q8(1/x).
- * The approximation to j1 is M1 * cos(x - 3 pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 40000 1.8e-19 5.0e-20
- *
- *
- */
-\f/* y1l.c
- *
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1l();
- *
- * y = y1l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 4.5>, [4.5,9> and
- * [9, infinity). In the first interval a rational approximation
- * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
- *
- * In the second interval, the approximation is
- * (x - p)(x - q)(x - r)(x - s)P9(x)/Q10(x)
- * where p, q, r, s are zeros of y1(x).
- *
- * The third interval uses the same approximations to modulus
- * and phase as j1(x), whence y1(x) = modulus * sin(phase).
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 36000 2.7e-19 5.3e-20
- *
- */
-
-/* Copyright 1994 by Stephen L. Moshier (moshier@world.std.com). */
-
-#include <math.h>
-
-/*
-j1(x) = (x^2-r0^2)(x^2-r1^2)(x^2-r2^2) x P(x**2)/Q(x**2)
-0 <= x <= 9
-Relative error
-n=8, d=8
-Peak error = 2e-21
-*/
-#if UNK
-static long double j1n[9] = {
--2.63469779622127762897E-4L,
- 9.31329762279632791262E-1L,
--1.46280142797793933909E3L,
- 1.32000129539331214495E6L,
--7.41183271195454042842E8L,
- 2.626500686552841932403E11L,
--5.68263073022183470933E13L,
- 6.80006297997263446982E15L,
--3.41470097444474566748E17L,
-};
-static long double j1d[8] = {
-/* 1.00000000000000000000E0L,*/
- 2.95267951972943745733E3L,
- 4.78723926343829674773E6L,
- 5.37544732957807543920E9L,
- 4.46866213886267829490E12L,
- 2.76959756375961607085E15L,
- 1.23367806884831151194E18L,
- 3.57325874689695599524E20L,
- 5.10779045516141578461E22L,
-};
-#endif
-#if IBMPC
-static short j1n[] = {
-0xf72f,0x18cc,0x50b2,0x8a22,0xbff3, XPD
-0x6dc3,0xc850,0xa096,0xee6b,0x3ffe, XPD
-0x29f3,0x496b,0xa54c,0xb6d9,0xc009, XPD
-0x38f5,0xf72b,0x0a5c,0xa122,0x4013, XPD
-0x1ac8,0xc825,0x3c9c,0xb0b6,0xc01c, XPD
-0x038e,0xbd23,0xa7fa,0xf49c,0x4024, XPD
-0x636c,0x4d29,0x9f71,0xcebb,0xc02c, XPD
-0xd3c2,0xf8f0,0xf852,0xc144,0x4033, XPD
-0xd8d8,0x7311,0xa7d2,0x97a4,0xc039, XPD
-};
-static short j1d[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xbaf9,0x146e,0xdf50,0xb88a,0x400a, XPD
-0x6a17,0xe162,0x4e86,0x9218,0x4015, XPD
-0x6041,0xc9fe,0x6890,0xa033,0x401f, XPD
-0xb498,0xfdd5,0x209e,0x820e,0x4029, XPD
-0x0122,0x56c0,0xf2ef,0x9d6e,0x4032, XPD
-0xe6c0,0xa725,0x3d56,0x88f7,0x403b, XPD
-0x665d,0xb178,0x242e,0x9af7,0x4043, XPD
-0xdd67,0xf5b3,0x0522,0xad0f,0x404a, XPD
-};
-#endif
-#if MIEEE
-static long j1n[27] = {
-0xbff30000,0x8a2250b2,0x18ccf72f,
-0x3ffe0000,0xee6ba096,0xc8506dc3,
-0xc0090000,0xb6d9a54c,0x496b29f3,
-0x40130000,0xa1220a5c,0xf72b38f5,
-0xc01c0000,0xb0b63c9c,0xc8251ac8,
-0x40240000,0xf49ca7fa,0xbd23038e,
-0xc02c0000,0xcebb9f71,0x4d29636c,
-0x40330000,0xc144f852,0xf8f0d3c2,
-0xc0390000,0x97a4a7d2,0x7311d8d8,
-};
-static long j1d[24] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x400a0000,0xb88adf50,0x146ebaf9,
-0x40150000,0x92184e86,0xe1626a17,
-0x401f0000,0xa0336890,0xc9fe6041,
-0x40290000,0x820e209e,0xfdd5b498,
-0x40320000,0x9d6ef2ef,0x56c00122,
-0x403b0000,0x88f73d56,0xa725e6c0,
-0x40430000,0x9af7242e,0xb178665d,
-0x404a0000,0xad0f0522,0xf5b3dd67,
-};
-#endif
-/*
-sqrt(j0^2(1/x^2) + y0^2(1/x^2)) = z P(z**2)/Q(z**2)
-z(x) = 1/sqrt(x)
-Relative error
-n=7, d=8
-Peak error = 1.35e=20
-Relative error spread = 9.9e0
-*/
-#if UNK
-static long double modulusn[8] = {
--5.041742205078442098874E0L,
- 3.918474430130242177355E-1L,
- 2.527521168680500659056E0L,
- 7.172146812845906480743E0L,
- 2.859499532295180940060E0L,
- 1.014671139779858141347E0L,
- 1.255798064266130869132E-1L,
- 1.596507617085714650238E-2L,
-};
-static long double modulusd[8] = {
-/* 1.000000000000000000000E0L,*/
--6.233092094568239317498E0L,
--9.214128701852838347002E-1L,
- 2.531772200570435289832E0L,
- 8.755081357265851765640E0L,
- 3.554340386955608261463E0L,
- 1.267949948774331531237E0L,
- 1.573909467558180942219E-1L,
- 2.000925566825407466160E-2L,
-};
-#endif
-#if IBMPC
-static short modulusn[] = {
-0x3d53,0xb598,0xf3bf,0xa155,0xc001, XPD
-0x3111,0x863a,0x3a61,0xc8a0,0x3ffd, XPD
-0x7d55,0xdb8c,0xe825,0xa1c2,0x4000, XPD
-0xe5e2,0x6914,0x3a08,0xe582,0x4001, XPD
-0x71e6,0x88a5,0x0a53,0xb702,0x4000, XPD
-0x2cb0,0xc657,0xbe70,0x81e0,0x3fff, XPD
-0x6de4,0x8fae,0xfe26,0x8097,0x3ffc, XPD
-0xa905,0x05fb,0x3101,0x82c9,0x3ff9, XPD
-};
-static short modulusd[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0x2603,0x640e,0x7d8d,0xc775,0xc001, XPD
-0x77b5,0x8f2d,0xb6bf,0xebe1,0xbffe, XPD
-0x6420,0x97ce,0x8e44,0xa208,0x4000, XPD
-0x0260,0x746b,0xd030,0x8c14,0x4002, XPD
-0x77b6,0x34e2,0x501a,0xe37a,0x4000, XPD
-0x37ce,0x79ae,0x2f15,0xa24c,0x3fff, XPD
-0xfc82,0x02c7,0x17a4,0xa12b,0x3ffc, XPD
-0x1237,0xcc6c,0x7356,0xa3ea,0x3ff9, XPD
-};
-#endif
-#if MIEEE
-static long modulusn[24] = {
-0xc0010000,0xa155f3bf,0xb5983d53,
-0x3ffd0000,0xc8a03a61,0x863a3111,
-0x40000000,0xa1c2e825,0xdb8c7d55,
-0x40010000,0xe5823a08,0x6914e5e2,
-0x40000000,0xb7020a53,0x88a571e6,
-0x3fff0000,0x81e0be70,0xc6572cb0,
-0x3ffc0000,0x8097fe26,0x8fae6de4,
-0x3ff90000,0x82c93101,0x05fba905,
-};
-static long modulusd[24] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0010000,0xc7757d8d,0x640e2603,
-0xbffe0000,0xebe1b6bf,0x8f2d77b5,
-0x40000000,0xa2088e44,0x97ce6420,
-0x40020000,0x8c14d030,0x746b0260,
-0x40000000,0xe37a501a,0x34e277b6,
-0x3fff0000,0xa24c2f15,0x79ae37ce,
-0x3ffc0000,0xa12b17a4,0x02c7fc82,
-0x3ff90000,0xa3ea7356,0xcc6c1237,
-};
-#endif
-/*
-atan(y1(x)/j1(x)) = x - 3pi/4 + z P(z**2)/Q(z**2)
-z(x) = 1/x
-Absolute error
-n=5, d=6
-Peak error = 4.83e-21
-Relative error spread = 1.9e0
-*/
-#if UNK
-static long double phasen[6] = {
- 2.010456367705144783933E0L,
- 1.587378144541918176658E0L,
- 2.682837461073751055565E-1L,
- 1.472572645054468815027E-2L,
- 2.884976126715926258586E-4L,
- 1.708502235134706284899E-6L,
-};
-static long double phased[6] = {
-/* 1.000000000000000000000E0L,*/
- 6.809332495854873089362E0L,
- 4.518597941618813112665E0L,
- 7.320149039410806471101E-1L,
- 3.960155028960712309814E-2L,
- 7.713202197319040439861E-4L,
- 4.556005960359216767984E-6L,
-};
-#endif
-#if IBMPC
-static short phasen[] = {
-0xebc0,0x5506,0x512f,0x80ab,0x4000, XPD
-0x6050,0x98aa,0x3500,0xcb2f,0x3fff, XPD
-0xe907,0x28b9,0x7cb7,0x895c,0x3ffd, XPD
-0xa830,0xf4a3,0x2c60,0xf144,0x3ff8, XPD
-0xf74f,0xbe87,0x7e7d,0x9741,0x3ff3, XPD
-0x540c,0xc1d5,0xb096,0xe54f,0x3feb, XPD
-};
-static short phased[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xefe3,0x292c,0x0d43,0xd9e6,0x4001, XPD
-0xb1f2,0xe0d2,0x5ab5,0x9098,0x4001, XPD
-0xc39e,0x9c8c,0x5428,0xbb65,0x3ffe, XPD
-0x98f8,0xd610,0x3c35,0xa235,0x3ffa, XPD
-0xa853,0x55fb,0x6c79,0xca32,0x3ff4, XPD
-0x8d72,0x2be3,0xcb0f,0x98df,0x3fed, XPD
-};
-#endif
-#if MIEEE
-static long phasen[18] = {
-0x40000000,0x80ab512f,0x5506ebc0,
-0x3fff0000,0xcb2f3500,0x98aa6050,
-0x3ffd0000,0x895c7cb7,0x28b9e907,
-0x3ff80000,0xf1442c60,0xf4a3a830,
-0x3ff30000,0x97417e7d,0xbe87f74f,
-0x3feb0000,0xe54fb096,0xc1d5540c,
-};
-static long phased[18] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40010000,0xd9e60d43,0x292cefe3,
-0x40010000,0x90985ab5,0xe0d2b1f2,
-0x3ffe0000,0xbb655428,0x9c8cc39e,
-0x3ffa0000,0xa2353c35,0xd61098f8,
-0x3ff40000,0xca326c79,0x55fba853,
-0x3fed0000,0x98dfcb0f,0x2be38d72,
-};
-#endif
-#define JZ1 1.46819706421238932572e1L
-#define JZ2 4.92184563216946036703e1L
-#define JZ3 1.03499453895136580332e2L
-
-#define THPIO4L 2.35619449019234492885L
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double fabsl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double cosl ( long double );
-extern long double sinl ( long double );
-extern long double logl ( long double );
-long double j1l (long double );
-#else
-long double sqrtl(), fabsl(), polevll(), p1evll(), cosl(), sinl(), logl();
-long double j1l();
-#endif
-
-long double j1l(x)
-long double x;
-{
-long double xx, y, z, modulus, phase;
-
-xx = x * x;
-if( xx < 81.0L )
- {
- y = (xx - JZ1) * (xx - JZ2) * (xx - JZ3);
- y *= x * polevll( xx, j1n, 8 ) / p1evll( xx, j1d, 8 );
- return y;
- }
-
-y = fabsl(x);
-xx = 1.0/xx;
-phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
-
-z = 1.0/y;
-modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 8 );
-
-y = modulus * cosl( y - THPIO4L + z*phase) / sqrtl(y);
-if( x < 0 )
- y = -y;
-return y;
-}
-
-/*
-y1(x) = 2/pi * (log(x) * j1(x) - 1/x) + R(x^2) z P(z**2)/Q(z**2)
-0 <= x <= 4.5
-z(x) = x
-Absolute error
-n=6, d=7
-Peak error = 7.25e-22
-Relative error spread = 4.5e-2
-*/
-#if UNK
-static long double y1n[7] = {
--1.288901054372751879531E5L,
- 9.914315981558815369372E7L,
--2.906793378120403577274E10L,
- 3.954354656937677136266E12L,
--2.445982226888344140154E14L,
- 5.685362960165615942886E15L,
--2.158855258453711703120E16L,
-};
-static long double y1d[7] = {
-/* 1.000000000000000000000E0L,*/
- 8.926354644853231136073E2L,
- 4.679841933793707979659E5L,
- 1.775133253792677466651E8L,
- 5.089532584184822833416E10L,
- 1.076474894829072923244E13L,
- 1.525917240904692387994E15L,
- 1.101136026928555260168E17L,
-};
-#endif
-#if IBMPC
-static short y1n[] = {
-0x5b16,0xf7f8,0x0d7e,0xfbbd,0xc00f, XPD
-0x53e4,0x194c,0xbefa,0xbd19,0x4019, XPD
-0x7607,0xa687,0xaf0a,0xd892,0xc021, XPD
-0x5633,0xaa6b,0x79e5,0xe62c,0x4028, XPD
-0x69fd,0x1242,0xf62d,0xde75,0xc02e, XPD
-0x7f8b,0x4757,0x75bd,0xa196,0x4033, XPD
-0x3a10,0x0848,0x5930,0x9965,0xc035, XPD
-};
-static short y1d[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0xdd1a,0x3b8e,0xab73,0xdf28,0x4008, XPD
-0x298c,0x29ef,0x0630,0xe482,0x4011, XPD
-0x0e86,0x117b,0x36d6,0xa94a,0x401a, XPD
-0x57e0,0x1d92,0x90a9,0xbd99,0x4022, XPD
-0xaaf0,0x342b,0xd098,0x9ca5,0x402a, XPD
-0x8c6a,0x397e,0x0963,0xad7a,0x4031, XPD
-0x7302,0xb91b,0xde7e,0xc399,0x4037, XPD
-};
-#endif
-#if MIEEE
-static long y1n[21] = {
-0xc00f0000,0xfbbd0d7e,0xf7f85b16,
-0x40190000,0xbd19befa,0x194c53e4,
-0xc0210000,0xd892af0a,0xa6877607,
-0x40280000,0xe62c79e5,0xaa6b5633,
-0xc02e0000,0xde75f62d,0x124269fd,
-0x40330000,0xa19675bd,0x47577f8b,
-0xc0350000,0x99655930,0x08483a10,
-};
-static long y1d[21] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40080000,0xdf28ab73,0x3b8edd1a,
-0x40110000,0xe4820630,0x29ef298c,
-0x401a0000,0xa94a36d6,0x117b0e86,
-0x40220000,0xbd9990a9,0x1d9257e0,
-0x402a0000,0x9ca5d098,0x342baaf0,
-0x40310000,0xad7a0963,0x397e8c6a,
-0x40370000,0xc399de7e,0xb91b7302,
-};
-#endif
-/*
-y1(x) = (x-YZ1)(x-YZ2)(x-YZ3)(x-YZ4)R(x) P(z)/Q(z)
-z(x) = x
-4.5 <= x <= 9
-Absolute error
-n=9, d=10
-Peak error = 3.27e-22
-Relative error spread = 4.5e-2
-*/
-#if UNK
-static long double y159n[10] = {
--6.806634906054210550896E-1L,
- 4.306669585790359450532E1L,
--9.230477746767243316014E2L,
- 6.171186628598134035237E3L,
- 2.096869860275353982829E4L,
--1.238961670382216747944E5L,
--1.781314136808997406109E6L,
--1.803400156074242435454E6L,
--1.155761550219364178627E6L,
- 3.112221202330688509818E5L,
-};
-static long double y159d[10] = {
-/* 1.000000000000000000000E0L,*/
--6.181482377814679766978E1L,
- 2.238187927382180589099E3L,
--5.225317824142187494326E4L,
- 9.217235006983512475118E5L,
--1.183757638771741974521E7L,
- 1.208072488974110742912E8L,
--8.193431077523942651173E8L,
- 4.282669747880013349981E9L,
--1.171523459555524458808E9L,
- 1.078445545755236785692E8L,
-};
-#endif
-#if IBMPC
-static short y159n[] = {
-0xb5e5,0xbb42,0xf667,0xae3f,0xbffe, XPD
-0xfdf1,0x41e5,0x4beb,0xac44,0x4004, XPD
-0xe917,0x8486,0x0ebd,0xe6c3,0xc008, XPD
-0xdf40,0x226b,0x7e37,0xc0d9,0x400b, XPD
-0xb2bf,0x4296,0x65af,0xa3d1,0x400d, XPD
-0xa33b,0x8229,0x1561,0xf1fc,0xc00f, XPD
-0xcd43,0x2f50,0x1118,0xd972,0xc013, XPD
-0x3811,0xa3da,0x413f,0xdc24,0xc013, XPD
-0xf62f,0xd968,0x8c66,0x8d15,0xc013, XPD
-0x539b,0xf305,0xc3d8,0x97f6,0x4011, XPD
-};
-static short y159d[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
-0x1a6c,0x1c93,0x612a,0xf742,0xc004, XPD
-0xd0fe,0x2487,0x01c0,0x8be3,0x400a, XPD
-0xbed4,0x3ad5,0x2da1,0xcc1d,0xc00e, XPD
-0x3c4f,0xdc46,0xb802,0xe107,0x4012, XPD
-0xe5e5,0x4172,0x8863,0xb4a0,0xc016, XPD
-0x6de5,0xb797,0xea1c,0xe66b,0x4019, XPD
-0xa46a,0x0273,0xbc0f,0xc358,0xc01c, XPD
-0x8e0e,0xe148,0x5ab3,0xff44,0x401e, XPD
-0xb3ad,0x1c6d,0x0f07,0x8ba8,0xc01d, XPD
-0xa231,0x6ab0,0x7952,0xcdb2,0x4019, XPD
-};
-#endif
-#if MIEEE
-static long y159n[30] = {
-0xbffe0000,0xae3ff667,0xbb42b5e5,
-0x40040000,0xac444beb,0x41e5fdf1,
-0xc0080000,0xe6c30ebd,0x8486e917,
-0x400b0000,0xc0d97e37,0x226bdf40,
-0x400d0000,0xa3d165af,0x4296b2bf,
-0xc00f0000,0xf1fc1561,0x8229a33b,
-0xc0130000,0xd9721118,0x2f50cd43,
-0xc0130000,0xdc24413f,0xa3da3811,
-0xc0130000,0x8d158c66,0xd968f62f,
-0x40110000,0x97f6c3d8,0xf305539b,
-};
-static long y159d[30] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0040000,0xf742612a,0x1c931a6c,
-0x400a0000,0x8be301c0,0x2487d0fe,
-0xc00e0000,0xcc1d2da1,0x3ad5bed4,
-0x40120000,0xe107b802,0xdc463c4f,
-0xc0160000,0xb4a08863,0x4172e5e5,
-0x40190000,0xe66bea1c,0xb7976de5,
-0xc01c0000,0xc358bc0f,0x0273a46a,
-0x401e0000,0xff445ab3,0xe1488e0e,
-0xc01d0000,0x8ba80f07,0x1c6db3ad,
-0x40190000,0xcdb27952,0x6ab0a231,
-};
-#endif
-
-extern long double MAXNUML;
-/* #define MAXNUML 1.18973149535723176502e4932L */
-#define TWOOPI 6.36619772367581343075535e-1L
-#define THPIO4 2.35619449019234492885L
-#define Y1Z1 2.19714132603101703515e0L
-#define Y1Z2 5.42968104079413513277e0L
-#define Y1Z3 8.59600586833116892643e0L
-#define Y1Z4 1.17491548308398812434e1L
-
-long double y1l(x)
-long double x;
-{
-long double xx, y, z, modulus, phase;
-
-if( x < 0.0 )
- {
- return (-MAXNUML);
- }
-z = 1.0/x;
-xx = x * x;
-if( xx < 81.0L )
- {
- if( xx < 20.25L )
- {
- y = TWOOPI * (logl(x) * j1l(x) - z);
- y += x * polevll( xx, y1n, 6 ) / p1evll( xx, y1d, 7 );
- }
- else
- {
- y = (x - Y1Z1)*(x - Y1Z2)*(x - Y1Z3)*(x - Y1Z4);
- y *= polevll( x, y159n, 9 ) / p1evll( x, y159d, 10 );
- }
- return y;
- }
-
-xx = 1.0/xx;
-phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
-
-modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 8 );
-
-z = modulus * sinl( x - THPIO4L + z*phase) / sqrtl(x);
-return z;
-}
+++ /dev/null
-/* jnl.c
- *
- * Bessel function of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * int n;
- * long double x, y, jnl();
- *
- * y = jnl( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The ratio of jn(x) to j0(x) is computed by backward
- * recurrence. First the ratio jn/jn-1 is found by a
- * continued fraction expansion. Then the recurrence
- * relating successive orders is applied until j0 or j1 is
- * reached.
- *
- * If n = 0 or 1 the routine for j0 or j1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE -30, 30 5000 3.3e-19 4.7e-20
- *
- *
- * Not suitable for large n or x.
- *
- */
-\f
-/* jn.c
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-#include <math.h>
-
-extern long double MACHEPL;
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double j0l ( long double );
-extern long double j1l ( long double );
-#else
-long double fabsl(), j0l(), j1l();
-#endif
-
-long double jnl( n, x )
-int n;
-long double x;
-{
-long double pkm2, pkm1, pk, xk, r, ans;
-int k, sign;
-
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) == 0 ) /* -1**n */
- sign = 1;
- else
- sign = -1;
- }
-else
- sign = 1;
-
-if( x < 0.0L )
- {
- if( n & 1 )
- sign = -sign;
- x = -x;
- }
-
-
-if( n == 0 )
- return( sign * j0l(x) );
-if( n == 1 )
- return( sign * j1l(x) );
-if( n == 2 )
- return( sign * (2.0L * j1l(x) / x - j0l(x)) );
-
-if( x < MACHEPL )
- return( 0.0L );
-
-/* continued fraction */
-k = 53;
-pk = 2 * (n + k);
-ans = pk;
-xk = x * x;
-
-do
- {
- pk -= 2.0L;
- ans = pk - (xk/ans);
- }
-while( --k > 0 );
-ans = x/ans;
-
-/* backward recurrence */
-
-pk = 1.0L;
-pkm1 = 1.0L/ans;
-k = n-1;
-r = 2 * k;
-
-do
- {
- pkm2 = (pkm1 * r - pk * x) / x;
- pk = pkm1;
- pkm1 = pkm2;
- r -= 2.0L;
- }
-while( --k > 0 );
-
-if( fabsl(pk) > fabsl(pkm1) )
- ans = j1l(x)/pk;
-else
- ans = j0l(x)/pkm1;
-return( sign * ans );
-}
+++ /dev/null
-/* calc.c */
-/* Keyboard command interpreter */
-/* by Stephen L. Moshier */
-
-/* Include functions for IEEE special values */
-#define NANS 1
-
-/* length of command line: */
-#define LINLEN 128
-
-#define XON 0x11
-#define XOFF 0x13
-
-#define SALONE 1
-#define DECPDP 0
-#define INTLOGIN 0
-#define INTHELP 1
-#ifndef TRUE
-#define TRUE 1
-#endif
-
-/* Initialize squirrel printf: */
-#define INIPRINTF 0
-
-#if DECPDP
-#define TRUE 1
-#endif
-
-#include <stdio.h>
-#include <string.h>
-static char idterp[] = {
-"\n\nSteve Moshier's command interpreter V1.3\n"};
-#define ISLOWER(c) ((c >= 'a') && (c <= 'z'))
-#define ISUPPER(c) ((c >= 'A') && (c <= 'Z'))
-#define ISALPHA(c) (ISLOWER(c) || ISUPPER(c))
-#define ISDIGIT(c) ((c >= '0') && (c <= '9'))
-#define ISATF(c) (((c >= 'a')&&(c <= 'f')) || ((c >= 'A')&&(c <= 'F')))
-#define ISXDIGIT(c) (ISDIGIT(c) || ISATF(c))
-#define ISOCTAL(c) ((c >= '0') && (c < '8'))
-#define ISALNUM(c) (ISALPHA(c) || (ISDIGIT(c))
-FILE *fopen();
-
-#include "lcalc.h"
-#include "ehead.h"
-
-/* space for working precision numbers */
-static long double vs[22];
-
-/* the symbol table of temporary variables: */
-
-#define NTEMP 4
-struct varent temp[NTEMP] = {
-{"T", OPR | TEMP, &vs[14]},
-{"T", OPR | TEMP, &vs[15]},
-{"T", OPR | TEMP, &vs[16]},
-{"\0", OPR | TEMP, &vs[17]}
-};
-\f
-/* the symbol table of operators */
-/* EOL is interpreted on null, newline, or ; */
-struct symbol oprtbl[] = {
-{"BOL", OPR | BOL, 0},
-{"EOL", OPR | EOL, 0},
-{"-", OPR | UMINUS, 8},
-/*"~", OPR | COMP, 8,*/
-{",", OPR | EOE, 1},
-{"=", OPR | EQU, 2},
-/*"|", OPR | LOR, 3,*/
-/*"^", OPR | LXOR, 4,*/
-/*"&", OPR | LAND, 5,*/
-{"+", OPR | PLUS, 6},
-{"-", OPR | MINUS, 6},
-{"*", OPR | MULT, 7},
-{"/", OPR | DIV, 7},
-/*"%", OPR | MOD, 7,*/
-{"(", OPR | LPAREN, 11},
-{")", OPR | RPAREN, 11},
-{"\0", ILLEG, 0}
-};
-
-#define NOPR 8
-
-/* the symbol table of indirect variables: */
-extern long double PIL;
-struct varent indtbl[] = {
-{"t", VAR | IND, &vs[21]},
-{"u", VAR | IND, &vs[20]},
-{"v", VAR | IND, &vs[19]},
-{"w", VAR | IND, &vs[18]},
-{"x", VAR | IND, &vs[10]},
-{"y", VAR | IND, &vs[11]},
-{"z", VAR | IND, &vs[12]},
-{"pi", VAR | IND, &PIL},
-{"\0", ILLEG, 0}
-};
-\f
-/* the symbol table of constants: */
-
-#define NCONST 10
-struct varent contbl[NCONST] = {
-{"C",CONST,&vs[0]},
-{"C",CONST,&vs[1]},
-{"C",CONST,&vs[2]},
-{"C",CONST,&vs[3]},
-{"C",CONST,&vs[4]},
-{"C",CONST,&vs[5]},
-{"C",CONST,&vs[6]},
-{"C",CONST,&vs[7]},
-{"C",CONST,&vs[8]},
-{"\0",CONST,&vs[9]}
-};
-
-/* the symbol table of string variables: */
-
-static char strngs[160] = {0};
-
-#define NSTRNG 5
-struct strent strtbl[NSTRNG] = {
-{0, VAR | STRING, 0},
-{0, VAR | STRING, 0},
-{0, VAR | STRING, 0},
-{0, VAR | STRING, 0},
-{"\0",ILLEG,0},
-};
-\f
-
-/* Help messages */
-#if INTHELP
-static char *intmsg[] = {
-"?",
-"Unkown symbol",
-"Expression ends in illegal operator",
-"Precede ( by operator",
-")( is illegal",
-"Unmatched )",
-"Missing )",
-"Illegal left hand side",
-"Missing symbol",
-"Must assign to a variable",
-"Divide by zero",
-"Missing symbol",
-"Missing operator",
-"Precede quantity by operator",
-"Quantity preceded by )",
-"Function syntax",
-"Too many function args",
-"No more temps",
-"Arg list"
-};
-#endif
-
-/* the symbol table of functions: */
-#if SALONE
-long double hex(), cmdh(), cmdhlp();
-long double cmddm(), cmdtm(), cmdem();
-long double take(), mxit(), exit(), bits(), csys();
-long double cmddig(), prhlst(), abmac();
-long double ifrac(), xcmpl();
-long double floorl(), logl(), powl(), sqrtl(), tanhl(), expl();
-long double ellpel(), ellpkl(), incbetl(), incbil();
-long double stdtrl(), stdtril(), zstdtrl(), zstdtril();
-long double sinl(), cosl(), tanl(), asinl(), acosl(), atanl(), atan2l();
-long double tanhl(), atanhl();
-#ifdef NANS
-int isnanl(), isfinitel(), signbitl();
-long double zisnan(), zisfinite(), zsignbit();
-#endif
-
-struct funent funtbl[] = {
-{"h", OPR | FUNC, cmdh},
-{"help", OPR | FUNC, cmdhlp},
-{"hex", OPR | FUNC, hex},
-/*"view", OPR | FUNC, view,*/
-{"exp", OPR | FUNC, expl},
-{"floor", OPR | FUNC, floorl},
-{"log", OPR | FUNC, logl},
-{"pow", OPR | FUNC, powl},
-{"sqrt", OPR | FUNC, sqrtl},
-{"tanh", OPR | FUNC, tanhl},
-{"sin", OPR | FUNC, sinl},
-{"cos", OPR | FUNC, cosl},
-{"tan", OPR | FUNC, tanl},
-{"asin", OPR | FUNC, asinl},
-{"acos", OPR | FUNC, acosl},
-{"atan", OPR | FUNC, atanl},
-{"atantwo", OPR | FUNC, atan2l},
-{"tanh", OPR | FUNC, tanhl},
-{"atanh", OPR | FUNC, atanhl},
-{"ellpe", OPR | FUNC, ellpel},
-{"ellpk", OPR | FUNC, ellpkl},
-{"incbet", OPR | FUNC, incbetl},
-{"incbi", OPR | FUNC, incbil},
-{"stdtr", OPR | FUNC, zstdtrl},
-{"stdtri", OPR | FUNC, zstdtril},
-{"ifrac", OPR | FUNC, ifrac},
-{"cmp", OPR | FUNC, xcmpl},
-#ifdef NANS
-{"isnan", OPR | FUNC, zisnan},
-{"isfinite", OPR | FUNC, zisfinite},
-{"signbit", OPR | FUNC, zsignbit},
-#endif
-{"bits", OPR | FUNC, bits},
-{"digits", OPR | FUNC, cmddig},
-{"dm", OPR | FUNC, cmddm},
-{"tm", OPR | FUNC, cmdtm},
-{"em", OPR | FUNC, cmdem},
-{"take", OPR | FUNC | COMMAN, take},
-{"system", OPR | FUNC | COMMAN, csys},
-{"exit", OPR | FUNC, mxit},
-/*
-"remain", OPR | FUNC, eremain,
-*/
-{"\0", OPR | FUNC, 0}
-};
-
-/* the symbol table of key words */
-struct funent keytbl[] = {
-{"\0", ILLEG, 0}
-};
-#endif
-
-void zgets(), init();
-
-/* Number of decimals to display */
-#define DEFDIS 70
-static int ndigits = DEFDIS;
-
-/* Menu stack */
-struct funent *menstk[5] = {&funtbl[0], NULL, NULL, NULL, NULL};
-int menptr = 0;
-
-/* Take file stack */
-FILE *takstk[10] = {0};
-int takptr = -1;
-
-/* size of the expression scan list: */
-#define NSCAN 20
-
-/* previous token, saved for syntax checking: */
-struct symbol *lastok = 0;
-
-/* variables used by parser: */
-static char str[128] = {0};
-int uposs = 0; /* possible unary operator */
-static long double qnc;
-char lc[40] = { '\n' }; /* ASCII string of token symbol */
-static char line[LINLEN] = { '\n','\0' }; /* input command line */
-static char maclin[LINLEN] = { '\n','\0' }; /* macro command */
-char *interl = line; /* pointer into line */
-extern char *interl;
-static int maccnt = 0; /* number of times to execute macro command */
-static int comptr = 0; /* comma stack pointer */
-static long double comstk[5]; /* comma argument stack */
-static int narptr = 0; /* pointer to number of args */
-static int narstk[5] = {0}; /* stack of number of function args */
-\f
-/* main() */
-
-/* Entire program starts here */
-
-int main()
-{
-
-/* the scan table: */
-
-/* array of pointers to symbols which have been parsed: */
-struct symbol *ascsym[NSCAN];
-
-/* current place in ascsym: */
-register struct symbol **as;
-
-/* array of attributes of operators parsed: */
-int ascopr[NSCAN];
-
-/* current place in ascopr: */
-register int *ao;
-
-#if LARGEMEM
-/* array of precedence levels of operators: */
-long asclev[NSCAN];
-/* current place in asclev: */
-long *al;
-long symval; /* value of symbol just parsed */
-#else
-int asclev[NSCAN];
-int *al;
-int symval;
-#endif
-
-long double acc; /* the accumulator, for arithmetic */
-int accflg; /* flags accumulator in use */
-long double val; /* value to be combined into accumulator */
-register struct symbol *psym; /* pointer to symbol just parsed */
-struct varent *pvar; /* pointer to an indirect variable symbol */
-struct funent *pfun; /* pointer to a function symbol */
-struct strent *pstr; /* pointer to a string symbol */
-int att; /* attributes of symbol just parsed */
-int i; /* counter */
-int offset; /* parenthesis level */
-int lhsflg; /* kluge to detect illegal assignments */
-struct symbol *parser(); /* parser returns pointer to symbol */
-int errcod; /* for syntax error printout */
-\f
-
-/* Perform general initialization */
-
-init();
-
-menstk[0] = &funtbl[0];
-menptr = 0;
-cmdhlp(); /* print out list of symbols */
-\f
-
-/* Return here to get next command line to execute */
-getcmd:
-
-/* initialize registers and mutable symbols */
-
-accflg = 0; /* Accumulator not in use */
-acc = 0.0L; /* Clear the accumulator */
-offset = 0; /* Parenthesis level zero */
-comptr = 0; /* Start of comma stack */
-narptr = -1; /* Start of function arg counter stack */
-
-psym = (struct symbol *)&contbl[0];
-for( i=0; i<NCONST; i++ )
- {
- psym->attrib = CONST; /* clearing the busy bit */
- ++psym;
- }
-psym = (struct symbol *)&temp[0];
-for( i=0; i<NTEMP; i++ )
- {
- psym->attrib = VAR | TEMP; /* clearing the busy bit */
- ++psym;
- }
-
-pstr = &strtbl[0];
-for( i=0; i<NSTRNG; i++ )
- {
- pstr->spel = &strngs[ 40*i ];
- pstr->attrib = STRING | VAR;
- pstr->string = &strngs[ 40*i ];
- ++pstr;
- }
-
-/* List of scanned symbols is empty: */
-as = &ascsym[0];
-*as = 0;
---as;
-/* First item in scan list is Beginning of Line operator */
-ao = &ascopr[0];
-*ao = oprtbl[0].attrib & 0xf; /* BOL */
-/* value of first item: */
-al = &asclev[0];
-*al = oprtbl[0].sym;
-
-lhsflg = 0; /* illegal left hand side flag */
-psym = &oprtbl[0]; /* pointer to current token */
-\f
-/* get next token from input string */
-
-gettok:
-lastok = psym; /* last token = current token */
-psym = parser(); /* get a new current token */
-/*printf( "%s attrib %7o value %7o\n", psym->spel, psym->attrib & 0xffff,
- psym->sym );*/
-
-/* Examine attributes of the symbol returned by the parser */
-att = psym->attrib;
-if( att == ILLEG )
- {
- errcod = 1;
- goto synerr;
- }
-
-/* Push functions onto scan list without analyzing further */
-if( att & FUNC )
- {
- /* A command is a function whose argument is
- * a pointer to the rest of the input line.
- * A second argument is also passed: the address
- * of the last token parsed.
- */
- if( att & COMMAN )
- {
- pfun = (struct funent *)psym;
- ( *(pfun->fun))( interl, lastok );
- abmac(); /* scrub the input line */
- goto getcmd; /* and ask for more input */
- }
- ++narptr; /* offset to number of args */
- narstk[narptr] = 0;
- i = lastok->attrib & 0xffff; /* attrib=short, i=int */
- if( ((i & OPR) == 0)
- || (i == (OPR | RPAREN))
- || (i == (OPR | FUNC)) )
- {
- errcod = 15;
- goto synerr;
- }
-
- ++lhsflg;
- ++as;
- *as = psym;
- ++ao;
- *ao = FUNC;
- ++al;
- *al = offset + UMINUS;
- goto gettok;
- }
-
-/* deal with operators */
-if( att & OPR )
- {
- att &= 0xf;
- /* expression cannot end with an operator other than
- * (, ), BOL, or a function
- */
- if( (att == RPAREN) || (att == EOL) || (att == EOE))
- {
- i = lastok->attrib & 0xffff; /* attrib=short, i=int */
- if( (i & OPR)
- && (i != (OPR | RPAREN))
- && (i != (OPR | LPAREN))
- && (i != (OPR | FUNC))
- && (i != (OPR | BOL)) )
- {
- errcod = 2;
- goto synerr;
- }
- }
- ++lhsflg; /* any operator but ( and = is not a legal lhs */
-\f
-/* operator processing, continued */
-
- switch( att )
- {
- case EOE:
- lhsflg = 0;
- break;
- case LPAREN:
- /* ( must be preceded by an operator of some sort. */
- if( ((lastok->attrib & OPR) == 0) )
- {
- errcod = 3;
- goto synerr;
- }
- /* also, a preceding ) is illegal */
- if( (unsigned short )lastok->attrib == (OPR|RPAREN))
- {
- errcod = 4;
- goto synerr;
- }
- /* Begin looking for illegal left hand sides: */
- lhsflg = 0;
- offset += RPAREN; /* new parenthesis level */
- goto gettok;
- case RPAREN:
- offset -= RPAREN; /* parenthesis level */
- if( offset < 0 )
- {
- errcod = 5; /* parenthesis error */
- goto synerr;
- }
- goto gettok;
- case EOL:
- if( offset != 0 )
- {
- errcod = 6; /* parenthesis error */
- goto synerr;
- }
- break;
- case EQU:
- if( --lhsflg ) /* was incremented before switch{} */
- {
- errcod = 7;
- goto synerr;
- }
- case UMINUS:
- case COMP:
- goto pshopr; /* evaluate right to left */
- default: ;
- }
-\f
-
-/* evaluate expression whenever precedence is not increasing */
-
-symval = psym->sym + offset;
-
-while( symval <= *al )
- {
- /* if just starting, must fill accumulator with last
- * thing on the line
- */
- if( (accflg == 0) && (as >= ascsym) && (((*as)->attrib & FUNC) == 0 ))
- {
- pvar = (struct varent *)*as;
-/*
- if( pvar->attrib & STRING )
- strcpy( (char *)&acc, (char *)pvar->value );
- else
-*/
- acc = *pvar->value;
- --as;
- accflg = 1;
- }
-
-/* handle beginning of line type cases, where the symbol
- * list ascsym[] may be empty.
- */
- switch( *ao )
- {
- case BOL:
-/* printf( "%.16e\n", (double )acc ); */
-#if NE == 6
- e64toasc( &acc, str, 100 );
-#else
- e113toasc( &acc, str, 100 );
-#endif
- printf( "%s\n", str );
- goto getcmd; /* all finished */
- case UMINUS:
- acc = -acc;
- goto nochg;
-/*
- case COMP:
- acc = ~acc;
- goto nochg;
-*/
- default: ;
- }
-/* Now it is illegal for symbol list to be empty,
- * because we are going to need a symbol below.
- */
- if( as < &ascsym[0] )
- {
- errcod = 8;
- goto synerr;
- }
-/* get attributes and value of current symbol */
- att = (*as)->attrib;
- pvar = (struct varent *)*as;
- if( att & FUNC )
- val = 0.0L;
- else
- {
-/*
- if( att & STRING )
- strcpy( (char *)&val, (char *)pvar->value );
- else
-*/
- val = *pvar->value;
- }
-
-/* Expression evaluation, continued. */
-
- switch( *ao )
- {
- case FUNC:
- pfun = (struct funent *)*as;
- /* Call the function with appropriate number of args */
- i = narstk[ narptr ];
- --narptr;
- switch(i)
- {
- case 0:
- acc = ( *(pfun->fun) )(acc);
- break;
- case 1:
- acc = ( *(pfun->fun) )(acc, comstk[comptr-1]);
- break;
- case 2:
- acc = ( *(pfun->fun) )(acc, comstk[comptr-2],
- comstk[comptr-1]);
- break;
- case 3:
- acc = ( *(pfun->fun) )(acc, comstk[comptr-3],
- comstk[comptr-2], comstk[comptr-1]);
- break;
- default:
- errcod = 16;
- goto synerr;
- }
- comptr -= i;
- accflg = 1; /* in case at end of line */
- break;
- case EQU:
- if( ( att & TEMP) || ((att & VAR) == 0) || (att & STRING) )
- {
- errcod = 9;
- goto synerr; /* can only assign to a variable */
- }
- pvar = (struct varent *)*as;
- *pvar->value = acc;
- break;
- case PLUS:
- acc = acc + val; break;
- case MINUS:
- acc = val - acc; break;
- case MULT:
- acc = acc * val; break;
- case DIV:
- if( acc == 0.0L )
- {
-/*
-divzer:
-*/
- errcod = 10;
- goto synerr;
- }
- acc = val / acc; break;
-/*
- case MOD:
- if( acc == 0 )
- goto divzer;
- acc = val % acc; break;
- case LOR:
- acc |= val; break;
- case LXOR:
- acc ^= val; break;
- case LAND:
- acc &= val; break;
-*/
- case EOE:
- if( narptr < 0 )
- {
- errcod = 18;
- goto synerr;
- }
- narstk[narptr] += 1;
- comstk[comptr++] = acc;
-/* printf( "\ncomptr: %d narptr: %d %d\n", comptr, narptr, acc );*/
- acc = val;
- break;
- }
-\f
-
-/* expression evaluation, continued */
-
-/* Pop evaluated tokens from scan list: */
- /* make temporary variable not busy */
- if( att & TEMP )
- (*as)->attrib &= ~BUSY;
- if( as < &ascsym[0] ) /* can this happen? */
- {
- errcod = 11;
- goto synerr;
- }
- --as;
-nochg:
- --ao;
- --al;
- if( ao < &ascopr[0] ) /* can this happen? */
- {
- errcod = 12;
- goto synerr;
- }
-/* If precedence level will now increase, then */
-/* save accumulator in a temporary location */
- if( symval > *al )
- {
- /* find a free temp location */
- pvar = &temp[0];
- for( i=0; i<NTEMP; i++ )
- {
- if( (pvar->attrib & BUSY) == 0)
- goto temfnd;
- ++pvar;
- }
- errcod = 17;
- printf( "no more temps\n" );
- pvar = &temp[0];
- goto synerr;
-
- temfnd:
- pvar->attrib |= BUSY;
- *pvar->value = acc;
- /*printf( "temp %d\n", acc );*/
- accflg = 0;
- ++as; /* push the temp onto the scan list */
- *as = (struct symbol *)pvar;
- }
- } /* End of evaluation loop */
-\f
-
-/* Push operator onto scan list when precedence increases */
-
-pshopr:
- ++ao;
- *ao = psym->attrib & 0xf;
- ++al;
- *al = psym->sym + offset;
- goto gettok;
- } /* end of OPR processing */
-
-
-/* Token was not an operator. Push symbol onto scan list. */
-if( (lastok->attrib & OPR) == 0 )
- {
- errcod = 13;
- goto synerr; /* quantities must be preceded by an operator */
- }
-if( (unsigned short )lastok->attrib == (OPR | RPAREN) ) /* ...but not by ) */
- {
- errcod = 14;
- goto synerr;
- }
-++as;
-*as = psym;
-goto gettok;
-
-synerr:
-
-#if INTHELP
-printf( "%s ", intmsg[errcod] );
-#endif
-printf( " error %d\n", errcod );
-abmac(); /* flush the command line */
-goto getcmd;
-} /* end of program */
-\f
-/* parser() */
-
-/* Get token from input string and identify it. */
-
-
-static char number[128];
-
-struct symbol *parser( )
-{
-register struct symbol *psym;
-register char *pline;
-struct varent *pvar;
-struct strent *pstr;
-char *cp, *plc, *pn;
-long lnc;
-int i;
-long double tem;
-
-/* reference for old Whitesmiths compiler: */
-/*
- *extern FILE *stdout;
- */
-
-pline = interl; /* get current location in command string */
-
-
-/* If at beginning of string, must ask for more input */
-if( pline == line )
- {
-
- if( maccnt > 0 )
- {
- --maccnt;
- cp = maclin;
- plc = pline;
- while( (*plc++ = *cp++) != 0 )
- ;
- goto mstart;
- }
- if( takptr < 0 )
- { /* no take file active: prompt keyboard input */
- printf("* ");
- }
-/* Various ways of typing in a command line. */
-
-/*
- * Old Whitesmiths call to print "*" immediately
- * use RT11 .GTLIN to get command string
- * from command file or terminal
- */
-
-/*
- * fflush(stdout);
- * gtlin(line);
- */
-
-
- zgets( line, TRUE ); /* keyboard input for other systems: */
-\f
-
-mstart:
- uposs = 1; /* unary operators possible at start of line */
- }
-
-ignore:
-/* Skip over spaces */
-while( *pline == ' ' )
- ++pline;
-
-/* unary minus after operator */
-if( uposs && (*pline == '-') )
- {
- psym = &oprtbl[2]; /* UMINUS */
- ++pline;
- goto pdon3;
- }
- /* COMP */
-/*
-if( uposs && (*pline == '~') )
- {
- psym = &oprtbl[3];
- ++pline;
- goto pdon3;
- }
-*/
-if( uposs && (*pline == '+') ) /* ignore leading plus sign */
- {
- ++pline;
- goto ignore;
- }
-
-/* end of null terminated input */
-if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
- {
- pline = line;
- goto endlin;
- }
-if( *pline == ';' )
- {
- ++pline;
-endlin:
- psym = &oprtbl[1]; /* EOL */
- goto pdon2;
- }
-
-\f
-/* parser() */
-
-
-/* Test for numeric input */
-if( (ISDIGIT(*pline)) || (*pline == '.') )
- {
- lnc = 0; /* initialize numeric input to zero */
- qnc = 0.0L;
- if( *pline == '0' )
- { /* leading "0" may mean octal or hex radix */
- ++pline;
- if( *pline == '.' )
- goto decimal; /* 0.ddd */
- /* leading "0x" means hexadecimal radix */
- if( (*pline == 'x') || (*pline == 'X') )
- {
- ++pline;
- while( ISXDIGIT(*pline) )
- {
- i = *pline++ & 0xff;
- if( i >= 'a' )
- i -= 047;
- if( i >= 'A' )
- i -= 07;
- i -= 060;
- lnc = (lnc << 4) + i;
- qnc = lnc;
- }
- goto numdon;
- }
- else
- {
- while( ISOCTAL( *pline ) )
- {
- i = ((*pline++) & 0xff) - 060;
- lnc = (lnc << 3) + i;
- qnc = lnc;
- }
- goto numdon;
- }
- }
- else
- {
- /* no leading "0" means decimal radix */
-/******/
-decimal:
- pn = number;
- while( (ISDIGIT(*pline)) || (*pline == '.') )
- *pn++ = *pline++;
-/* get possible exponent field */
- if( (*pline == 'e') || (*pline == 'E') )
- *pn++ = *pline++;
- else
- goto numcvt;
- if( (*pline == '-') || (*pline == '+') )
- *pn++ = *pline++;
- while( ISDIGIT(*pline) )
- *pn++ = *pline++;
-numcvt:
- *pn++ = ' ';
- *pn++ = 0;
-#if NE == 6
- asctoe64( number, &qnc );
-#else
- asctoe113( number, &qnc );
-#endif
-/* sscanf( number, "%le", &nc ); */
- }
-/* output the number */
-numdon:
- /* search the symbol table of constants */
- pvar = &contbl[0];
- for( i=0; i<NCONST; i++ )
- {
- if( (pvar->attrib & BUSY) == 0 )
- goto confnd;
- tem = *pvar->value;
- if( tem == qnc )
- {
- psym = (struct symbol *)pvar;
- goto pdon2;
- }
- ++pvar;
- }
- printf( "no room for constant\n" );
- psym = (struct symbol *)&contbl[0];
- goto pdon2;
-
-confnd:
- pvar->spel= contbl[0].spel;
- pvar->attrib = CONST | BUSY;
- *pvar->value = qnc;
- psym = (struct symbol *)pvar;
- goto pdon2;
- }
-
-/* check for operators */
-psym = &oprtbl[3];
-for( i=0; i<NOPR; i++ )
- {
- if( *pline == *(psym->spel) )
- goto pdon1;
- ++psym;
- }
-\f
-/* if quoted, it is a string variable */
-if( *pline == '"' )
- {
- /* find an empty slot for the string */
- pstr = strtbl; /* string table */
- for( i=0; i<NSTRNG-1; i++ )
- {
- if( (pstr->attrib & BUSY) == 0 )
- goto fndstr;
- ++pstr;
- }
- printf( "No room for string\n" );
- pstr->attrib |= ILLEG;
- psym = (struct symbol *)pstr;
- goto pdon0;
-
-fndstr:
- pstr->attrib |= BUSY;
- plc = pstr->string;
- ++pline;
- for( i=0; i<39; i++ )
- {
- *plc++ = *pline;
- if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
- {
-illstr:
- pstr = &strtbl[NSTRNG-1];
- pstr->attrib |= ILLEG;
- printf( "Missing string terminator\n" );
- psym = (struct symbol *)pstr;
- goto pdon0;
- }
- if( *pline++ == '"' )
- goto finstr;
- }
-
- goto illstr; /* no terminator found */
-
-finstr:
- --plc;
- *plc = '\0';
- psym = (struct symbol *)pstr;
- goto pdon2;
- }
-/* If none of the above, search function and symbol tables: */
-
-/* copy character string to array lc[] */
-plc = &lc[0];
-while( ISALPHA(*pline) )
- {
- /* convert to lower case characters */
- if( ISUPPER( *pline ) )
- *pline += 040;
- *plc++ = *pline++;
- }
-*plc = 0; /* Null terminate the output string */
-\f
-/* parser() */
-
-psym = (struct symbol *)menstk[menptr]; /* function table */
-plc = &lc[0];
-cp = psym->spel;
-do
- {
- if( strcmp( plc, cp ) == 0 )
- goto pdon3; /* following unary minus is possible */
- ++psym;
- cp = psym->spel;
- }
-while( *cp != '\0' );
-
-psym = (struct symbol *)&indtbl[0]; /* indirect symbol table */
-plc = &lc[0];
-cp = psym->spel;
-do
- {
- if( strcmp( plc, cp ) == 0 )
- goto pdon2;
- ++psym;
- cp = psym->spel;
- }
-while( *cp != '\0' );
-
-pdon0:
-pline = line; /* scrub line if illegal symbol */
-goto pdon2;
-
-pdon1:
-++pline;
-if( (psym->attrib & 0xf) == RPAREN )
-pdon2: uposs = 0;
-else
-pdon3: uposs = 1;
-
-interl = pline;
-return( psym );
-} /* end of parser */
-\f
-/* exit from current menu */
-
-long double cmdex()
-{
-
-if( menptr == 0 )
- {
- printf( "Main menu is active.\n" );
- }
-else
- --menptr;
-
-cmdh();
-return(0.0L);
-}
-
-\f
-/* gets() */
-
-void zgets( gline, echo )
-char *gline;
-int echo;
-{
-register char *pline;
-register int i;
-
-
-scrub:
-pline = gline;
-getsl:
- if( (pline - gline) >= LINLEN )
- {
- printf( "\nLine too long\n *" );
- goto scrub;
- }
- if( takptr < 0 )
- { /* get character from keyboard */
-/*
-if DECPDP
- gtlin( gline );
- return(0);
-else
-*/
- *pline = getchar();
-/*endif*/
- }
- else
- { /* get a character from take file */
- i = fgetc( takstk[takptr] );
- if( i == -1 )
- { /* end of take file */
- if( takptr >= 0 )
- { /* close file and bump take stack */
- fclose( takstk[takptr] );
- takptr -= 1;
- }
- if( takptr < 0 ) /* no more take files: */
- printf( "*" ); /* prompt keyboard input */
- goto scrub; /* start a new input line */
- }
- *pline = i;
- }
-
- *pline &= 0x7f;
- /* xon or xoff characters need filtering out. */
- if ( *pline == XON || *pline == XOFF )
- goto getsl;
-
- /* control U or control C */
- if( (*pline == 025) || (*pline == 03) )
- {
- printf( "\n" );
- goto scrub;
- }
-
- /* Backspace or rubout */
- if( (*pline == 010) || (*pline == 0177) )
- {
- pline -= 1;
- if( pline >= gline )
- {
- if ( echo )
- printf( "\010\040\010" );
- goto getsl;
- }
- else
- goto scrub;
- }
- if ( echo )
- printf( "%c", *pline );
- if( (*pline != '\n') && (*pline != '\r') )
- {
- ++pline;
- goto getsl;
- }
- *pline = 0;
- if ( echo )
- printf( "%c", '\n' ); /* \r already echoed */
-}
-\f
-
-/* help function */
-long double cmdhlp()
-{
-
-printf( "%s", idterp );
-printf( "\nFunctions:\n" );
-prhlst( &funtbl[0] );
-printf( "\nVariables:\n" );
-prhlst( &indtbl[0] );
-printf( "\nOperators:\n" );
-prhlst( &oprtbl[2] );
-printf("\n");
-return(0.0L);
-}
-
-
-long double cmdh()
-{
-
-prhlst( menstk[menptr] );
-printf( "\n" );
-return(0.0L);
-}
-
-/* print keyword spellings */
-
-long double prhlst(ps)
-register struct symbol *ps;
-{
-register int j, k;
-int m;
-
-j = 0;
-while( *(ps->spel) != '\0' )
- {
- k = strlen( ps->spel ) - 1;
-/* size of a tab field is 2**3 chars */
- m = ((k >> 3) + 1) << 3;
- j += m;
- if( j > 72 )
- {
- printf( "\n" );
- j = m;
- }
- printf( "%s\t", ps->spel );
- ++ps;
- }
-return(0.0L);
-}
-
-
-#if SALONE
-void init(){}
-#endif
-\f
-
-/* macro commands */
-
-/* define macro */
-long double cmddm()
-{
-
-zgets( maclin, TRUE );
-return(0.0L);
-}
-
-/* type (i.e., display) macro */
-long double cmdtm()
-{
-
-printf( "%s\n", maclin );
-return(0.0L);
-}
-
-/* execute macro # times */
-long double cmdem( arg )
-long double arg;
-{
-long double f;
-long n;
-long double floorl();
-
-f = floorl(arg);
-n = f;
-if( n <= 0 )
- n = 1;
-maccnt = n;
-return(0.0L);
-}
-\f
-
-/* open a take file */
-
-long double take( fname )
-char *fname;
-{
-FILE *f;
-
-while( *fname == ' ' )
- fname += 1;
-f = fopen( fname, "r" );
-
-if( f == 0 )
- {
- printf( "Can't open take file %s\n", fname );
- takptr = -1; /* terminate all take file input */
- return(0.0L);
- }
-takptr += 1;
-takstk[ takptr ] = f;
-printf( "Running %s\n", fname );
-return(0.0L);
-}
-
-
-/* abort macro execution */
-long double abmac()
-{
-
-maccnt = 0;
-interl = line;
-return(0.0L);
-}
-
-
-/* display integer part in hex, octal, and decimal
- */
-long double hex(qx)
-long double qx;
-{
-long double f;
-long z;
-long double floorl();
-
-f = floorl(qx);
-z = f;
-printf( "0%lo 0x%lx %ld.\n", z, z, z );
-return(qx);
-}
-
-#define NASC 16
-
-long double bits( x )
-long double x;
-{
-int i, j;
-unsigned short dd[4], ee[10];
-char strx[40];
-unsigned short *p;
-
-p = (unsigned short *) &x;
-for( i=0; i<NE; i++ )
- ee[i] = *p++;
-
-j = 0;
-for( i=0; i<NE; i++ )
- {
- printf( "0x%04x,", ee[i] & 0xffff );
- if( ++j > 7 )
- {
- j = 0;
- printf( "\n" );
- }
- }
-printf( "\n" );
-
-/* double conversions
- */
-*((double *)dd) = x;
-printf( "double: " );
-for( i=0; i<4; i++ )
- printf( "0x%04x,", dd[i] & 0xffff );
-printf( "\n" );
-
-#if 1
-printf( "double -> long double: " );
-*(long double *)ee = *(double *)dd;
-for( i=0; i<6; i++ )
- printf( "0x%04x,", ee[i] & 0xffff );
-printf( "\n" );
-e53toasc( dd, strx, NASC );
-printf( "e53toasc: %s\n", strx );
-printf( "Native printf: %.17e\n", *(double *)dd );
-
-/* float conversions
- */
-*((float *)dd) = x;
-printf( "float: " );
-for( i=0; i<2; i++ )
- printf( "0x%04x,", dd[i] & 0xffff );
-printf( "\n" );
-e24toe( dd, ee );
-printf( "e24toe: " );
-for( i=0; i<NE; i++ )
- printf( "0x%04x,", ee[i] & 0xffff );
-printf( "\n" );
-e24toasc( dd, strx, NASC );
-printf( "e24toasc: %s\n", strx );
-/* printf( "Native printf: %.16e\n", (double) *(float *)dd ); */
-
-#ifdef DEC
-printf( "etodec: " );
-etodec( x, dd );
-for( i=0; i<4; i++ )
- printf( "0x%04x,", dd[i] & 0xffff );
-printf( "\n" );
-printf( "dectoe: " );
-dectoe( dd, ee );
-for( i=0; i<NE; i++ )
- printf( "0x%04x,", ee[i] & 0xffff );
-printf( "\n" );
-printf( "DEC printf: %.16e\n", *(double *)dd );
-#endif
-#endif /* 0 */
-return(x);
-}
-
-
-/* Exit to monitor. */
-long double mxit()
-{
-
-exit(0);
-return(0.0L);
-}
-
-
-long double cmddig( x )
-long double x;
-{
-long double f;
-long lx;
-
-f = floorl(x);
-lx = f;
-ndigits = lx;
-if( ndigits <= 0 )
- ndigits = DEFDIS;
-return(f);
-}
-
-
-long double csys(x)
-char *x;
-{
-void system();
-
-system( x+1 );
-cmdh();
-return(0.0L);
-}
-
-
-long double ifrac(x)
-long double x;
-{
-unsigned long lx;
-long double y, z;
-
-z = floorl(x);
-lx = z;
-y = x - z;
-printf( " int = %lx\n", lx );
-return(y);
-}
-
-long double xcmpl(x,y)
-long double x,y;
-{
-long double ans;
-char str[40];
-
-#if NE == 6
- e64toasc( &x, str, 100 );
- printf( "x = %s\n", str );
- e64toasc( &y, str, 100 );
- printf( "y = %s\n", str );
-#else
- e113toasc( &x, str, 100 );
- printf( "x = %s\n", str );
- e113toasc( &y, str, 100 );
- printf( "y = %s\n", str );
-#endif
-
-ans = -2.0;
-if( x == y )
- {
- printf( "x == y " );
- ans = 0.0;
- }
-if( x < y )
- {
- printf( "x < y" );
- ans = -1.0;
- }
-if( x > y )
- {
- printf( "x > y" );
- ans = 1.0;
- }
-return( ans );
-}
-
-long double zstdtrl(k,t)
-long double k, t;
-{
-int ki;
-long double y;
-ki = k;
-y = stdtrl(ki,t);
-return(y);
-}
-
-long double zstdtril(k,t)
-long double k, t;
-{
-int ki;
-long double y;
-ki = k;
-y = stdtril(ki,t);
-return(y);
-}
-
-#ifdef NANS
-long double zisnan(x)
-long double x;
-{
- long double y;
- int k;
- k = isnanl(x);
- y = k;
- return(y);
-}
-long double zisfinite(x)
-long double x;
-{
- long double y;
- int k;
- k = isfinitel(x);
- y = k;
- return(y);
-}
-long double zsignbit(x)
-long double x;
-{
- long double y;
- int k;
- k = signbitl(x);
- y = k;
- return(y);
-}
-#endif
+++ /dev/null
-/* calc.h
- * include file for calc.c
- */
-
-/* 32 bit memory addresses: */
-#ifndef LARGEMEM
-#define LARGEMEM 1
-#endif
-
-/* data structure of symbol table */
-struct symbol
- {
- char *spel;
- short attrib;
-#if LARGEMEM
- long sym;
-#else
- short sym;
-#endif
- };
-
-struct funent
- {
- char *spel;
- short attrib;
- long double (*fun )();
- };
-
-struct varent
- {
- char *spel;
- short attrib;
- long double *value;
- };
-
-struct strent
- {
- char *spel;
- short attrib;
- char *string;
- };
-
-
-/* general symbol attributes: */
-#define OPR 0x8000
-#define VAR 0x4000
-#define CONST 0x2000
-#define FUNC 0x1000
-#define ILLEG 0x800
-#define BUSY 0x400
-#define TEMP 0x200
-#define STRING 0x100
-#define COMMAN 0x80
-#define IND 0x1
-
-/* attributes of operators (ordered by precedence): */
-#define BOL 1
-#define EOL 2
-/* end of expression (comma): */
-#define EOE 3
-#define EQU 4
-#define PLUS 5
-#define MINUS 6
-#define MULT 7
-#define DIV 8
-#define UMINUS 9
-#define LPAREN 10
-#define RPAREN 11
-#define COMP 12
-#define MOD 13
-#define LAND 14
-#define LOR 15
-#define LXOR 16
-
-
-extern struct funent funtbl[];
-/*extern struct symbol symtbl[];*/
-extern struct varent indtbl[];
-
+++ /dev/null
-/* ldrand.c
- *
- * Pseudorandom number generator
- *
- *
- *
- * SYNOPSIS:
- *
- * double y;
- * int ldrand();
- *
- * ldrand( &y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Yields a random number 1.0 <= y < 2.0.
- *
- * The three-generator congruential algorithm by Brian
- * Wichmann and David Hill (BYTE magazine, March, 1987,
- * pp 127-8) is used.
- *
- * Versions invoked by the different arithmetic compile
- * time options IBMPC, and MIEEE, produce the same sequences.
- *
- */
-\f
-
-
-#include <math.h>
-#ifdef ANSIPROT
-int ranwh ( void );
-#else
-int ranwh();
-#endif
-#ifdef UNK
-#undef UNK
-#if BIGENDIAN
-#define MIEEE
-#else
-#define IBMPC
-#endif
-#endif
-
-/* Three-generator random number algorithm
- * of Brian Wichmann and David Hill
- * BYTE magazine, March, 1987 pp 127-8
- *
- * The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
- */
-
-static int sx = 1;
-static int sy = 10000;
-static int sz = 3000;
-
-static union {
- long double d;
- unsigned short s[8];
-} unkans;
-
-/* This function implements the three
- * congruential generators.
- */
-
-int ranwh()
-{
-int r, s;
-
-/* sx = sx * 171 mod 30269 */
-r = sx/177;
-s = sx - 177 * r;
-sx = 171 * s - 2 * r;
-if( sx < 0 )
- sx += 30269;
-
-
-/* sy = sy * 172 mod 30307 */
-r = sy/176;
-s = sy - 176 * r;
-sy = 172 * s - 35 * r;
-if( sy < 0 )
- sy += 30307;
-
-/* sz = 170 * sz mod 30323 */
-r = sz/178;
-s = sz - 178 * r;
-sz = 170 * s - 63 * r;
-if( sz < 0 )
- sz += 30323;
-/* The results are in static sx, sy, sz. */
-return 0;
-}
-\f
-/* ldrand.c
- *
- * Random double precision floating point number between 1 and 2.
- *
- * C callable:
- * drand( &x );
- */
-
-int ldrand( a )
-long double *a;
-{
-unsigned short r;
-
-/* This algorithm of Wichmann and Hill computes a floating point
- * result:
- */
-ranwh();
-unkans.d = sx/30269.0L + sy/30307.0L + sz/30323.0L;
-r = unkans.d;
-unkans.d -= r;
-unkans.d += 1.0L;
-
-if( sizeof(long double) == 16 )
- {
-#ifdef MIEEE
- ranwh();
- r = sx * sy + sz;
- unkans.s[7] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[6] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[5] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[4] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[3] = r;
-#endif
-#ifdef IBMPC
- ranwh();
- r = sx * sy + sz;
- unkans.s[0] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[1] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[2] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[3] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[4] = r;
-#endif
- }
-else
- {
-#ifdef MIEEE
- ranwh();
- r = sx * sy + sz;
- unkans.s[5] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[4] = r;
-#endif
-#ifdef IBMPC
- ranwh();
- r = sx * sy + sz;
- unkans.s[0] = r;
- ranwh();
- r = sx * sy + sz;
- unkans.s[1] = r;
-#endif
- }
-*a = unkans.d;
-return 0;
-}
+++ /dev/null
-/* log10l.c
- *
- * Common logarithm, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, log10l();
- *
- * y = log10l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 10 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20
- * IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns MINLOG
- * log domain: x < 0; returns MINLOG
- */
-\f
-/*
-Cephes Math Library Release 2.2: January, 1991
-Copyright 1984, 1991 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-static char fname[] = {"log10l"};
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 6.2e-22
- */
-#ifdef UNK
-static long double P[] = {
- 4.9962495940332550844739E-1L,
- 1.0767376367209449010438E1L,
- 7.7671073698359539859595E1L,
- 2.5620629828144409632571E2L,
- 4.2401812743503691187826E2L,
- 3.4258224542413922935104E2L,
- 1.0747524399916215149070E2L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0,*/
- 2.3479774160285863271658E1L,
- 1.9444210022760132894510E2L,
- 7.7952888181207260646090E2L,
- 1.6911722418503949084863E3L,
- 2.0307734695595183428202E3L,
- 1.2695660352705325274404E3L,
- 3.2242573199748645407652E2L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0xfe72,0xce22,0xd7b9,0xffce,0x3ffd, XPD
-0xb778,0x0e34,0x2c71,0xac47,0x4002, XPD
-0xea8b,0xc751,0x96f8,0x9b57,0x4005, XPD
-0xfeaf,0x6a02,0x67fb,0x801a,0x4007, XPD
-0x6b5a,0xf252,0x51ff,0xd402,0x4007, XPD
-0x39ce,0x9f76,0x8704,0xab4a,0x4007, XPD
-0x1b39,0x740b,0x532e,0xd6f3,0x4005, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003, XPD
-0x13c8,0x031a,0x2d7b,0xc271,0x4006, XPD
-0x449d,0x1993,0xd933,0xc2e1,0x4008, XPD
-0x5b65,0x574e,0x8301,0xd365,0x4009, XPD
-0xa65d,0x3bd2,0xc043,0xfdd8,0x4009, XPD
-0x3b21,0xffea,0x1cf5,0x9eb2,0x4009, XPD
-0x545c,0xd708,0x7e62,0xa136,0x4007, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3ffd0000,0xffced7b9,0xce22fe72,
-0x40020000,0xac472c71,0x0e34b778,
-0x40050000,0x9b5796f8,0xc751ea8b,
-0x40070000,0x801a67fb,0x6a02feaf,
-0x40070000,0xd40251ff,0xf2526b5a,
-0x40070000,0xab4a8704,0x9f7639ce,
-0x40050000,0xd6f3532e,0x740b1b39,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40030000,0xbbd693d5,0xbf262f3a,
-0x40060000,0xc2712d7b,0x031a13c8,
-0x40080000,0xc2e1d933,0x1993449d,
-0x40090000,0xd3658301,0x574e5b65,
-0x40090000,0xfdd8c043,0x3bd2a65d,
-0x40090000,0x9eb21cf5,0xffea3b21,
-0x40070000,0xa1367e62,0xd708545c,
-};
-#endif
-
-/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
- * where z = 2(x-1)/(x+1)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 6.16e-22
- */
-
-#ifdef UNK
-static long double R[4] = {
- 1.9757429581415468984296E-3L,
--7.1990767473014147232598E-1L,
- 1.0777257190312272158094E1L,
--3.5717684488096787370998E1L,
-};
-static long double S[4] = {
-/* 1.00000000000000000000E0L,*/
--2.6201045551331104417768E1L,
- 1.9361891836232102174846E2L,
--4.2861221385716144629696E2L,
-};
-/* log10(2) */
-#define L102A 0.3125L
-#define L102B -1.1470004336018804786261e-2L
-/* log10(e) */
-#define L10EA 0.5L
-#define L10EB -6.5705518096748172348871e-2L
-#endif
-#ifdef IBMPC
-static short R[] = {
-0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
-0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
-0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
-0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
-};
-static short S[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
-0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
-0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
-};
-static short LG102A[] = {0x0000,0x0000,0x0000,0xa000,0x3ffd, XPD};
-#define L102A *(long double *)LG102A
-static short LG102B[] = {0x0cee,0x8601,0xaf60,0xbbec,0xbff8, XPD};
-#define L102B *(long double *)LG102B
-static short LG10EA[] = {0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD};
-#define L10EA *(long double *)LG10EA
-static short LG10EB[] = {0x39ab,0x235e,0x9d5b,0x8690,0xbffb, XPD};
-#define L10EB *(long double *)LG10EB
-#endif
-
-#ifdef MIEEE
-static long R[12] = {
-0x3ff60000,0x817b7763,0xf9226ef4,
-0xbffe0000,0xb84bde8f,0x1af915fd,
-0x40020000,0xac6fa53c,0x4f8d8b96,
-0xc0040000,0x8edee8ae,0xb4e38932,
-};
-static long S[9] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0030000,0xd19bbdc5,0x1fc97ce4,
-0x40060000,0xc19e716f,0x0d100af3,
-0xc0070000,0xd64e5d06,0x0f554d7d,
-};
-static long LG102A[] = {0x3ffd0000,0xa0000000,0x00000000};
-#define L102A *(long double *)LG102A
-static long LG102B[] = {0xbff80000,0xbbecaf60,0x86010cee};
-#define L102B *(long double *)LG102B
-static long LG10EA[] = {0x3ffe0000,0x80000000,0x00000000};
-#define L10EA *(long double *)LG10EA
-static long LG10EB[] = {0xbffb0000,0x86909d5b,0x235e39ab};
-#define L10EB *(long double *)LG10EB
-#endif
-
-
-#define SQRTH 0.70710678118654752440L
-#ifdef ANSIPROT
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-#else
-long double frexpl(), ldexpl(), polevll(), p1evll(), isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double log10l(x)
-long double x;
-{
-long double y;
-VOLATILE long double z;
-int e;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-/* Test for domain */
-if( x <= 0.0L )
- {
- if( x == 0.0L )
- {
- mtherr( fname, SING );
-#ifdef INFINITIES
- return(-INFINITYL);
-#else
- return( -4.9314733889673399399914e3L );
-#endif
- }
- else
- {
- mtherr( fname, DOMAIN );
-#ifdef NANS
- return(NANL);
-#else
- return( -4.9314733889673399399914e3L );
-#endif
- }
- }
-#ifdef INFINITIES
-if( x == INFINITYL )
- return(INFINITYL);
-#endif
-/* separate mantissa from exponent */
-
-/* Note, frexp is used so that denormal numbers
- * will be handled properly.
- */
-x = frexpl( x, &e );
-
-
-/* logarithm using log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/x+1)
- */
-if( (e > 2) || (e < -2) )
-{
-if( x < SQRTH )
- { /* 2( 2x-1 )/( 2x+1 ) */
- e -= 1;
- z = x - 0.5L;
- y = 0.5L * z + 0.5L;
- }
-else
- { /* 2 (x-1)/(x+1) */
- z = x - 0.5L;
- z -= 0.5L;
- y = 0.5L * x + 0.5L;
- }
-x = z / y;
-z = x*x;
-y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
-goto done;
-}
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0L;
- }
-z = x*x;
-y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 7 ) );
-y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */
-
-done:
-
-/* Multiply log of fraction by log10(e)
- * and base 2 exponent by log10(2).
- *
- * ***CAUTION***
- *
- * This sequence of operations is critical and it may
- * be horribly defeated by some compiler optimizers.
- */
-z = y * (L10EB);
-z += x * (L10EB);
-z += e * (L102B);
-z += y * (L10EA);
-z += x * (L10EA);
-z += e * (L102A);
-
-return( z );
-}
+++ /dev/null
-/* log2l.c
- *
- * Base 2 logarithm, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, log2l();
- *
- * y = log2l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 2 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the (natural)
- * logarithm of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20
- * IEEE exp(+-10000) 70000 5.4e-20 2.3e-20
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITYL
- * log domain: x < 0; returns NANL
- */
-\f
-/*
-Cephes Math Library Release 2.8: May, 1998
-Copyright 1984, 1991, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 6.2e-22
- */
-#ifdef UNK
-static long double P[] = {
- 4.9962495940332550844739E-1L,
- 1.0767376367209449010438E1L,
- 7.7671073698359539859595E1L,
- 2.5620629828144409632571E2L,
- 4.2401812743503691187826E2L,
- 3.4258224542413922935104E2L,
- 1.0747524399916215149070E2L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0,*/
- 2.3479774160285863271658E1L,
- 1.9444210022760132894510E2L,
- 7.7952888181207260646090E2L,
- 1.6911722418503949084863E3L,
- 2.0307734695595183428202E3L,
- 1.2695660352705325274404E3L,
- 3.2242573199748645407652E2L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0xfe72,0xce22,0xd7b9,0xffce,0x3ffd, XPD
-0xb778,0x0e34,0x2c71,0xac47,0x4002, XPD
-0xea8b,0xc751,0x96f8,0x9b57,0x4005, XPD
-0xfeaf,0x6a02,0x67fb,0x801a,0x4007, XPD
-0x6b5a,0xf252,0x51ff,0xd402,0x4007, XPD
-0x39ce,0x9f76,0x8704,0xab4a,0x4007, XPD
-0x1b39,0x740b,0x532e,0xd6f3,0x4005, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003, XPD
-0x13c8,0x031a,0x2d7b,0xc271,0x4006, XPD
-0x449d,0x1993,0xd933,0xc2e1,0x4008, XPD
-0x5b65,0x574e,0x8301,0xd365,0x4009, XPD
-0xa65d,0x3bd2,0xc043,0xfdd8,0x4009, XPD
-0x3b21,0xffea,0x1cf5,0x9eb2,0x4009, XPD
-0x545c,0xd708,0x7e62,0xa136,0x4007, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3ffd0000,0xffced7b9,0xce22fe72,
-0x40020000,0xac472c71,0x0e34b778,
-0x40050000,0x9b5796f8,0xc751ea8b,
-0x40070000,0x801a67fb,0x6a02feaf,
-0x40070000,0xd40251ff,0xf2526b5a,
-0x40070000,0xab4a8704,0x9f7639ce,
-0x40050000,0xd6f3532e,0x740b1b39,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40030000,0xbbd693d5,0xbf262f3a,
-0x40060000,0xc2712d7b,0x031a13c8,
-0x40080000,0xc2e1d933,0x1993449d,
-0x40090000,0xd3658301,0x574e5b65,
-0x40090000,0xfdd8c043,0x3bd2a65d,
-0x40090000,0x9eb21cf5,0xffea3b21,
-0x40070000,0xa1367e62,0xd708545c,
-};
-#endif
-
-/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
- * where z = 2(x-1)/(x+1)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 6.16e-22
- */
-#ifdef UNK
-static long double R[4] = {
- 1.9757429581415468984296E-3L,
--7.1990767473014147232598E-1L,
- 1.0777257190312272158094E1L,
--3.5717684488096787370998E1L,
-};
-static long double S[4] = {
-/* 1.00000000000000000000E0L,*/
--2.6201045551331104417768E1L,
- 1.9361891836232102174846E2L,
--4.2861221385716144629696E2L,
-};
-/* log2(e) - 1 */
-#define LOG2EA 4.4269504088896340735992e-1L
-#endif
-#ifdef IBMPC
-static short R[] = {
-0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
-0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
-0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
-0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
-};
-static short S[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
-0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
-0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
-};
-static short LG2EA[] = {0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, XPD};
-#define LOG2EA *(long double *)LG2EA
-#endif
-
-#ifdef MIEEE
-static long R[12] = {
-0x3ff60000,0x817b7763,0xf9226ef4,
-0xbffe0000,0xb84bde8f,0x1af915fd,
-0x40020000,0xac6fa53c,0x4f8d8b96,
-0xc0040000,0x8edee8ae,0xb4e38932,
-};
-static long S[9] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0030000,0xd19bbdc5,0x1fc97ce4,
-0x40060000,0xc19e716f,0x0d100af3,
-0xc0070000,0xd64e5d06,0x0f554d7d,
-};
-static long LG2EA[] = {0x3ffd0000,0xe2a8eca5,0x705fc2ef};
-#define LOG2EA *(long double *)LG2EA
-#endif
-
-
-#define SQRTH 0.70710678118654752440L
-extern long double MINLOGL;
-#ifdef ANSIPROT
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-#else
-long double frexpl(), ldexpl(), polevll(), p1evll();
-extern int isnanl ();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double log2l(x)
-long double x;
-{
-VOLATILE long double z;
-long double y;
-int e;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITYL )
- return(x);
-#endif
-/* Test for domain */
-if( x <= 0.0L )
- {
- if( x == 0.0L )
- {
-#ifdef INFINITIES
- return( -INFINITYL );
-#else
- mtherr( "log2l", SING );
- return( -16384.0L );
-#endif
- }
- else
- {
-#ifdef NANS
- return( NANL );
-#else
- mtherr( "log2l", DOMAIN );
- return( -16384.0L );
-#endif
- }
- }
-
-/* separate mantissa from exponent */
-
-/* Note, frexp is used so that denormal numbers
- * will be handled properly.
- */
-x = frexpl( x, &e );
-
-
-/* logarithm using log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/x+1)
- */
-if( (e > 2) || (e < -2) )
-{
-if( x < SQRTH )
- { /* 2( 2x-1 )/( 2x+1 ) */
- e -= 1;
- z = x - 0.5L;
- y = 0.5L * z + 0.5L;
- }
-else
- { /* 2 (x-1)/(x+1) */
- z = x - 0.5L;
- z -= 0.5L;
- y = 0.5L * x + 0.5L;
- }
-x = z / y;
-z = x*x;
-y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
-goto done;
-}
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0L;
- }
-z = x*x;
-y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 7 ) );
-y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */
-
-done:
-
-/* Multiply log of fraction by log2(e)
- * and base 2 exponent by 1
- *
- * ***CAUTION***
- *
- * This sequence of operations is critical and it may
- * be horribly defeated by some compiler optimizers.
- */
-z = y * LOG2EA;
-z += x * LOG2EA;
-z += y;
-z += x;
-z += e;
-return( z );
-}
-
+++ /dev/null
-/* logl.c
- *
- * Natural logarithm, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, logl();
- *
- * y = logl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base e (2.718...) logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z**3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20
- * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITYL
- * log domain: x < 0; returns NANL
- */
-\f
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1990, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 2.32e-20
- */
-#ifdef UNK
-static long double P[] = {
- 4.5270000862445199635215E-5L,
- 4.9854102823193375972212E-1L,
- 6.5787325942061044846969E0L,
- 2.9911919328553073277375E1L,
- 6.0949667980987787057556E1L,
- 5.7112963590585538103336E1L,
- 2.0039553499201281259648E1L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0,*/
- 1.5062909083469192043167E1L,
- 8.3047565967967209469434E1L,
- 2.2176239823732856465394E2L,
- 3.0909872225312059774938E2L,
- 2.1642788614495947685003E2L,
- 6.0118660497603843919306E1L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0x51b9,0x9cae,0x4b15,0xbde0,0x3ff0, XPD
-0x19cf,0xf0d4,0xc507,0xff40,0x3ffd, XPD
-0x9942,0xa7d2,0xfa37,0xd284,0x4001, XPD
-0x4add,0x65ce,0x9c5c,0xef4b,0x4003, XPD
-0x8445,0x619a,0x75c3,0xf3cc,0x4004, XPD
-0x81ab,0x3cd0,0xacba,0xe473,0x4004, XPD
-0x4cbf,0xcc18,0x016c,0xa051,0x4003, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0xb8b7,0x81f1,0xacf4,0xf101,0x4002, XPD
-0xbc31,0x09a4,0x5a91,0xa618,0x4005, XPD
-0xaeec,0xe7da,0x2c87,0xddc3,0x4006, XPD
-0x2bde,0x4845,0xa2ee,0x9a8c,0x4007, XPD
-0x3120,0x4703,0x89f2,0xd86d,0x4006, XPD
-0x7347,0x3224,0x8223,0xf079,0x4004, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3ff00000,0xbde04b15,0x9cae51b9,
-0x3ffd0000,0xff40c507,0xf0d419cf,
-0x40010000,0xd284fa37,0xa7d29942,
-0x40030000,0xef4b9c5c,0x65ce4add,
-0x40040000,0xf3cc75c3,0x619a8445,
-0x40040000,0xe473acba,0x3cd081ab,
-0x40030000,0xa051016c,0xcc184cbf,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40020000,0xf101acf4,0x81f1b8b7,
-0x40050000,0xa6185a91,0x09a4bc31,
-0x40060000,0xddc32c87,0xe7daaeec,
-0x40070000,0x9a8ca2ee,0x48452bde,
-0x40060000,0xd86d89f2,0x47033120,
-0x40040000,0xf0798223,0x32247347,
-};
-#endif
-
-/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
- * where z = 2(x-1)/(x+1)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 6.16e-22
- */
-
-#ifdef UNK
-static long double R[4] = {
- 1.9757429581415468984296E-3L,
--7.1990767473014147232598E-1L,
- 1.0777257190312272158094E1L,
--3.5717684488096787370998E1L,
-};
-static long double S[4] = {
-/* 1.00000000000000000000E0L,*/
--2.6201045551331104417768E1L,
- 1.9361891836232102174846E2L,
--4.2861221385716144629696E2L,
-};
-static long double C1 = 6.9314575195312500000000E-1L;
-static long double C2 = 1.4286068203094172321215E-6L;
-#endif
-#ifdef IBMPC
-static short R[] = {
-0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
-0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
-0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
-0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
-};
-static short S[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
-0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
-0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
-};
-static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD};
-#define C1 (*(long double *)sc1)
-static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD};
-#define C2 (*(long double *)sc2)
-#endif
-#ifdef MIEEE
-static long R[12] = {
-0x3ff60000,0x817b7763,0xf9226ef4,
-0xbffe0000,0xb84bde8f,0x1af915fd,
-0x40020000,0xac6fa53c,0x4f8d8b96,
-0xc0040000,0x8edee8ae,0xb4e38932,
-};
-static long S[9] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0xc0030000,0xd19bbdc5,0x1fc97ce4,
-0x40060000,0xc19e716f,0x0d100af3,
-0xc0070000,0xd64e5d06,0x0f554d7d,
-};
-static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
-#define C1 (*(long double *)sc1)
-static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
-#define C2 (*(long double *)sc2)
-#endif
-
-
-#define SQRTH 0.70710678118654752440L
-extern long double MINLOGL;
-#ifdef ANSIPROT
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern int isnanl ( long double );
-#else
-long double frexpl(), ldexpl(), polevll(), p1evll(), isnanl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double logl(x)
-long double x;
-{
-long double y, z;
-int e;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == INFINITYL )
- return(x);
-#endif
-/* Test for domain */
-if( x <= 0.0L )
- {
- if( x == 0.0L )
- {
-#ifdef INFINITIES
- return( -INFINITYL );
-#else
- mtherr( "logl", SING );
- return( MINLOGL );
-#endif
- }
- else
- {
-#ifdef NANS
- return( NANL );
-#else
- mtherr( "logl", DOMAIN );
- return( MINLOGL );
-#endif
- }
- }
-
-/* separate mantissa from exponent */
-
-/* Note, frexp is used so that denormal numbers
- * will be handled properly.
- */
-x = frexpl( x, &e );
-
-/* logarithm using log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/x+1)
- */
-if( (e > 2) || (e < -2) )
-{
-if( x < SQRTH )
- { /* 2( 2x-1 )/( 2x+1 ) */
- e -= 1;
- z = x - 0.5L;
- y = 0.5L * z + 0.5L;
- }
-else
- { /* 2 (x-1)/(x+1) */
- z = x - 0.5L;
- z -= 0.5L;
- y = 0.5L * x + 0.5L;
- }
-x = z / y;
-z = x*x;
-z = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
-z = z + e * C2;
-z = z + x;
-z = z + e * C1;
-return( z );
-}
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
-if( x < SQRTH )
- {
- e -= 1;
- x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
- }
-else
- {
- x = x - 1.0L;
- }
-z = x*x;
-y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 6 ) );
-y = y + e * C2;
-z = y - ldexpl( z, -1 ); /* y - 0.5 * z */
-/* Note, the sum of above terms does not exceed x/4,
- * so it contributes at most about 1/4 lsb to the error.
- */
-z = z + x;
-z = z + e * C1; /* This sum has an error of 1/2 lsb. */
-return( z );
-}
+++ /dev/null
-/* A C version of Kahan's Floating Point Test "Paranoia"
-
- Thos Sumner, UCSF, Feb. 1985
- David Gay, BTL, Jan. 1986
-
- This is a rewrite from the Pascal version by
-
- B. A. Wichmann, 18 Jan. 1985
-
- (and does NOT exhibit good C programming style).
-
-(C) Apr 19 1983 in BASIC version by:
- Professor W. M. Kahan,
- 567 Evans Hall
- Electrical Engineering & Computer Science Dept.
- University of California
- Berkeley, California 94720
- USA
-
-converted to Pascal by:
- B. A. Wichmann
- National Physical Laboratory
- Teddington Middx
- TW11 OLW
- UK
-
-converted to C by:
-
- David M. Gay and Thos Sumner
- AT&T Bell Labs Computer Center, Rm. U-76
- 600 Mountainn Avenue University of California
- Murray Hill, NJ 07974 San Francisco, CA 94143
- USA USA
-
-with simultaneous corrections to the Pascal source (reflected
-in the Pascal source available over netlib).
-
-Reports of results on various systems from all the versions
-of Paranoia are being collected by Richard Karpinski at the
-same address as Thos Sumner. This includes sample outputs,
-bug reports, and criticisms.
-
-You may copy this program freely if you acknowledge its source.
-Comments on the Pascal version to NPL, please.
-
-
-The C version catches signals from floating-point exceptions.
-If signal(SIGFPE,...) is unavailable in your environment, you may
-#define NOSIGNAL to comment out the invocations of signal.
-
-This source file is too big for some C compilers, but may be split
-into pieces. Comments containing "SPLIT" suggest convenient places
-for this splitting. At the end of these comments is an "ed script"
-(for the UNIX(tm) editor ed) that will do this splitting.
-
-By #defining Single when you compile this source, you may obtain
-a single-precision C version of Paranoia.
-
-
-The following is from the introductory commentary from Wichmann's work:
-
-The BASIC program of Kahan is written in Microsoft BASIC using many
-facilities which have no exact analogy in Pascal. The Pascal
-version below cannot therefore be exactly the same. Rather than be
-a minimal transcription of the BASIC program, the Pascal coding
-follows the conventional style of block-structured languages. Hence
-the Pascal version could be useful in producing versions in other
-structured languages.
-
-Rather than use identifiers of minimal length (which therefore have
-little mnemonic significance), the Pascal version uses meaningful
-identifiers as follows [Note: A few changes have been made for C]:
-
-
-BASIC C BASIC C BASIC C
-
- A J S StickyBit
- A1 AInverse J0 NoErrors T
- B Radix [Failure] T0 Underflow
- B1 BInverse J1 NoErrors T2 ThirtyTwo
- B2 RadixD2 [SeriousDefect] T5 OneAndHalf
- B9 BMinusU2 J2 NoErrors T7 TwentySeven
- C [Defect] T8 TwoForty
- C1 CInverse J3 NoErrors U OneUlp
- D [Flaw] U0 UnderflowThreshold
- D4 FourD K PageNo U1
- E0 L Milestone U2
- E1 M V
- E2 Exp2 N V0
- E3 N1 V8
- E5 MinSqEr O Zero V9
- E6 SqEr O1 One W
- E7 MaxSqEr O2 Two X
- E8 O3 Three X1
- E9 O4 Four X8
- F1 MinusOne O5 Five X9 Random1
- F2 Half O8 Eight Y
- F3 Third O9 Nine Y1
- F6 P Precision Y2
- F9 Q Y9 Random2
- G1 GMult Q8 Z
- G2 GDiv Q9 Z0 PseudoZero
- G3 GAddSub R Z1
- H R1 RMult Z2
- H1 HInverse R2 RDiv Z9
- I R3 RAddSub
- IO NoTrials R4 RSqrt
- I3 IEEE R9 Random9
-
- SqRWrng
-
-All the variables in BASIC are true variables and in consequence,
-the program is more difficult to follow since the "constants" must
-be determined (the glossary is very helpful). The Pascal version
-uses Real constants, but checks are added to ensure that the values
-are correctly converted by the compiler.
-
-The major textual change to the Pascal version apart from the
-identifiersis that named procedures are used, inserting parameters
-wherehelpful. New procedures are also introduced. The
-correspondence is as follows:
-
-
-BASIC Pascal
-lines
-
- 90- 140 Pause
- 170- 250 Instructions
- 380- 460 Heading
- 480- 670 Characteristics
- 690- 870 History
-2940-2950 Random
-3710-3740 NewD
-4040-4080 DoesYequalX
-4090-4110 PrintIfNPositive
-4640-4850 TestPartialUnderflow
-
-=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
-
-Below is an "ed script" that splits para.c into 10 files
-of the form part[1-8].c, subs.c, and msgs.c, plus a header
-file, paranoia.h, that these files require.
-r paranoia.c
-$
-?SPLIT
-+,$w msgs.c
-.,$d
-?SPLIT
-.d
-+d
--,$w subs.c
--,$d
-?part8
-+d
-?include
-.,$w part8.c
-.,$d
--d
-?part7
-+d
-?include
-.,$w part7.c
-.,$d
--d
-?part6
-+d
-?include
-.,$w part6.c
-.,$d
--d
-?part5
-+d
-?include
-.,$w part5.c
-.,$d
--d
-?part4
-+d
-?include
-.,$w part4.c
-.,$d
--d
-?part3
-+d
-?include
-.,$w part3.c
-.,$d
--d
-?part2
-+d
-?include
-.,$w part2.c
-.,$d
-?SPLIT
-.d
-1,/^#include/-1d
-1,$w part1.c
-/Computed constants/,$d
-1,$s/^int/extern &/
-1,$s/^FLOAT/extern &/
-1,$s! = .*!;!
-/^Guard/,/^Round/s/^/extern /
-/^jmp_buf/s/^/extern /
-/^Sig_type/s/^/extern /
-a
-extern int sigfpe();
-.
-w paranoia.h
-q
-
-*/
-
-#include <stdio.h>
-#ifndef NOSIGNAL
-#include <signal.h>
-#endif
-#include <setjmp.h>
-
-#define Ldouble
-/*#define Single*/
-
-#ifdef Single
-#define NPRT 2
-extern double fabs(), floor(), log(), pow(), sqrt();
-#define FLOAT float
-#define FABS(x) (float)fabs((double)(x))
-#define FLOOR(x) (float)floor((double)(x))
-#define LOG(x) (float)log((double)(x))
-#define POW(x,y) (float)pow((double)(x),(double)(y))
-#define SQRT(x) (float)sqrt((double)(x))
-#define FSETUP sprec
-/*sprec() { }*/
-#else
-#ifdef Ldouble
-#define NPRT 6
-extern long double fabsl(), floorl(), logl(), powl(), sqrtl();
-#define FLOAT long double
-#define FABS(x) fabsl(x)
-#define FLOOR(x) floorl(x)
-#define LOG(x) logl(x)
-#define POW(x,y) powl(x,y)
-#define SQRT(x) sqrtl(x)
-#define FSETUP ldprec
-#else
-#define NPRT 4
-extern double fabs(), floor(), log(), pow(), sqrt();
-#define FLOAT double
-#define FABS(x) fabs(x)
-#define FLOOR(x) floor(x)
-#define LOG(x) log(x)
-#define POW(x,y) pow(x,y)
-#define SQRT(x) sqrt(x)
-/*double __sqrtdf2();
-#define SQRT(x) __sqrtdf2(x)
-*/
-#define FSETUP dprec
-/* dprec() { } */
-#endif
-#endif
-
-jmp_buf ovfl_buf;
-typedef int (*Sig_type)();
-Sig_type sigsave;
-
-#define KEYBOARD 0
-
-FLOAT Radix, BInvrse, RadixD2, BMinusU2;
-FLOAT Sign(), Random();
-
-/*Small floating point constants.*/
-FLOAT Zero = 0.0;
-FLOAT Half = 0.5;
-FLOAT One = 1.0;
-FLOAT Two = 2.0;
-FLOAT Three = 3.0;
-FLOAT Four = 4.0;
-FLOAT Five = 5.0;
-FLOAT Eight = 8.0;
-FLOAT Nine = 9.0;
-FLOAT TwentySeven = 27.0;
-FLOAT ThirtyTwo = 32.0;
-FLOAT TwoForty = 240.0;
-FLOAT MinusOne = -1.0;
-FLOAT OneAndHalf = 1.5;
-/*Integer constants*/
-int NoTrials = 20; /*Number of tests for commutativity. */
-#define False 0
-#define True 1
-
-/* Definitions for declared types
- Guard == (Yes, No);
- Rounding == (Chopped, Rounded, Other);
- Message == packed array [1..40] of char;
- Class == (Flaw, Defect, Serious, Failure);
- */
-#define Yes 1
-#define No 0
-#define Chopped 2
-#define Rounded 1
-#define Other 0
-#define Flaw 3
-#define Defect 2
-#define Serious 1
-#define Failure 0
-typedef int Guard, Rounding, Class;
-typedef char Message;
-
-/* Declarations of Variables */
-int Indx;
-char ch[8];
-FLOAT AInvrse, A1;
-FLOAT C, CInvrse;
-FLOAT D, FourD;
-static FLOAT E0, E1, Exp2, E3, MinSqEr;
-FLOAT SqEr, MaxSqEr, E9;
-FLOAT Third;
-FLOAT F6, F9;
-FLOAT H, HInvrse;
-int I;
-FLOAT StickyBit, J;
-FLOAT MyZero;
-FLOAT Precision;
-FLOAT Q, Q9;
-FLOAT R, Random9;
-FLOAT T, Underflow, S;
-FLOAT OneUlp, UfThold, U1, U2;
-FLOAT V, V0, V9;
-FLOAT W;
-FLOAT X, X1, X2, X8, Random1;
-static FLOAT Y, Y1, Y2, Random2;
-FLOAT Z, PseudoZero, Z1, Z2, Z9;
-int ErrCnt[4];
-int fpecount;
-int Milestone;
-int PageNo;
-int M, N, N1;
-Guard GMult, GDiv, GAddSub;
-Rounding RMult, RDiv, RAddSub, RSqrt;
-int Break, Done, NotMonot, Monot, Anomaly, IEEE,
- SqRWrng, UfNGrad;
-/* Computed constants. */
-/*U1 gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */
-/*U2 gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */
-
-/* floating point exception receiver */
-sigfpe()
-{
- fpecount++;
- printf("\n* * * FLOATING-POINT ERROR * * *\n");
- fflush(stdout);
- if (sigsave) {
-#ifndef NOSIGNAL
- signal(SIGFPE, sigsave);
-#endif
- sigsave = 0;
- longjmp(ovfl_buf, 1);
- }
- abort();
-}
-
-
-FLOAT Ptemp;
-
-pnum( x )
-FLOAT *x;
-{
-char str[30];
-double d;
-unsigned short *p;
-int i;
-
-p = (unsigned short *)x;
-for( i=0; i<NPRT; i++ )
- printf( "%04x ", *p++ & 0xffff );
-#ifdef Ldouble
-e64toasc( x, str, 20 );
-#else
-#ifdef Single
-e24toasc( x, str, 20 );
-#else
-e53toasc( x, str, 20 );
-#endif
-#endif
-printf( " = %s\n", str );
-/*
-d = *x;
-printf( " = %.16e\n", d );
-*/
-}
-
-
-
-main()
-{
-/* noexcept(); */
- FSETUP();
- /* First two assignments use integer right-hand sides. */
- Zero = 0;
- One = 1;
- Two = One + One;
- Three = Two + One;
- Four = Three + One;
- Five = Four + One;
- Eight = Four + Four;
- Nine = Three * Three;
- TwentySeven = Nine * Three;
- ThirtyTwo = Four * Eight;
- TwoForty = Four * Five * Three * Four;
- MinusOne = -One;
- Half = One / Two;
- OneAndHalf = One + Half;
- ErrCnt[Failure] = 0;
- ErrCnt[Serious] = 0;
- ErrCnt[Defect] = 0;
- ErrCnt[Flaw] = 0;
- PageNo = 1;
- /*=============================================*/
- Milestone = 0;
- /*=============================================*/
-#ifndef NOSIGNAL
- signal(SIGFPE, sigfpe);
-#endif
- Instructions();
- Pause();
- Heading();
- Pause();
- Characteristics();
- Pause();
- History();
- Pause();
- /*=============================================*/
- Milestone = 7;
- /*=============================================*/
- printf("Program is now RUNNING tests on small integers:\n");
-
- TstCond (Failure, (Zero + Zero == Zero) && (One - One == Zero)
- && (One > Zero) && (One + One == Two),
- "0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2");
- Z = - Zero;
- if (Z == 0.0) {
- U1 = 0.001;
- Radix = 1;
- TstPtUf();
- }
- else {
- ErrCnt[Failure] = ErrCnt[Failure] + 1;
- printf("Comparison alleges that -0.0 is Non-zero!\n");
- }
- TstCond (Failure, (Three == Two + One) && (Four == Three + One)
- && (Four + Two * (- Two) == Zero)
- && (Four - Three - One == Zero),
- "3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0");
- TstCond (Failure, (MinusOne == (0 - One))
- && (MinusOne + One == Zero ) && (One + MinusOne == Zero)
- && (MinusOne + FABS(One) == Zero)
- && (MinusOne + MinusOne * MinusOne == Zero),
- "-1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0");
- TstCond (Failure, Half + MinusOne + Half == Zero,
- "1/2 + (-1) + 1/2 != 0");
- /*=============================================*/
- /*SPLIT
- part2();
- part3();
- part4();
- part5();
- part6();
- part7();
- part8();
- }
-#include "paranoia.h"
-part2(){
-*/
- Milestone = 10;
- /*=============================================*/
- TstCond (Failure, (Nine == Three * Three)
- && (TwentySeven == Nine * Three) && (Eight == Four + Four)
- && (ThirtyTwo == Eight * Four)
- && (ThirtyTwo - TwentySeven - Four - One == Zero),
- "9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0");
- TstCond (Failure, (Five == Four + One) &&
- (TwoForty == Four * Five * Three * Four)
- && (TwoForty / Three - Four * Four * Five == Zero)
- && ( TwoForty / Four - Five * Three * Four == Zero)
- && ( TwoForty / Five - Four * Three * Four == Zero),
- "5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48");
- if (ErrCnt[Failure] == 0) {
- printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n");
- printf("\n");
- }
- printf("Searching for Radix and Precision.\n");
- W = One;
- do {
- W = W + W;
- Y = W + One;
- Z = Y - W;
- Y = Z - One;
- } while (MinusOne + FABS(Y) < Zero);
- /*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
- Precision = Zero;
- Y = One;
- do {
- Radix = W + Y;
- Y = Y + Y;
- Radix = Radix - W;
- } while ( Radix == Zero);
- if (Radix < Two) Radix = One;
- printf("Radix = " );
- pnum( &Radix );
- if (Radix != 1) {
- W = One;
- do {
- Precision = Precision + One;
- W = W * Radix;
- Y = W + One;
- } while ((Y - W) == One);
- }
- /*... now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1
- ...*/
- U1 = One / W;
- U2 = Radix * U1;
- printf("Closest relative separation found is U1 = " );
- pnum( &U1 );
- printf("U2 = ");
- pnum( &U2 );
- printf("Recalculating radix and precision.");
-
- /*save old values*/
- E0 = Radix;
- E1 = U1;
- E9 = U2;
- E3 = Precision;
-
- X = Four / Three;
- Third = X - One;
- F6 = Half - Third;
- X = F6 + F6;
- X = FABS(X - Third);
- if (X < U2) X = U2;
-
- /*... now X = (unknown no.) ulps of 1+...*/
- do {
- U2 = X;
- Y = Half * U2 + ThirtyTwo * U2 * U2;
- Y = One + Y;
- X = Y - One;
- } while ( ! ((U2 <= X) || (X <= Zero)));
-
- /*... now U2 == 1 ulp of 1 + ... */
- X = Two / Three;
- F6 = X - Half;
- Third = F6 + F6;
- X = Third - Half;
- X = FABS(X + F6);
- if (X < U1) X = U1;
-
- /*... now X == (unknown no.) ulps of 1 -... */
- do {
- U1 = X;
- Y = Half * U1 + ThirtyTwo * U1 * U1;
- Y = Half - Y;
- X = Half + Y;
- Y = Half - X;
- X = Half + Y;
- } while ( ! ((U1 <= X) || (X <= Zero)));
- /*... now U1 == 1 ulp of 1 - ... */
- if (U1 == E1) printf("confirms closest relative separation U1 .\n");
- else
- {
- printf("gets better closest relative separation U1 = " );
- pnum( &U1 );
- }
- W = One / U1;
- F9 = (Half - U1) + Half;
- Radix = FLOOR(0.01 + U2 / U1);
- if (Radix == E0) printf("Radix confirmed.\n");
- else
- {
- printf("MYSTERY: recalculated Radix = " );
- pnum( &Radix );
- }
- TstCond (Defect, Radix <= Eight + Eight,
- "Radix is too big: roundoff problems");
- TstCond (Flaw, (Radix == Two) || (Radix == 10)
- || (Radix == One), "Radix is not as good as 2 or 10");
- /*=============================================*/
- Milestone = 20;
- /*=============================================*/
- TstCond (Failure, F9 - Half < Half,
- "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?");
- X = F9;
- I = 1;
- Y = X - Half;
- Z = Y - Half;
- TstCond (Failure, (X != One)
- || (Z == Zero), "Comparison is fuzzy,X=1 but X-1/2-1/2 != 0");
- X = One + U2;
- I = 0;
- /*=============================================*/
- Milestone = 25;
- /*=============================================*/
- /*... BMinusU2 = nextafter(Radix, 0) */
- BMinusU2 = Radix - One;
- BMinusU2 = (BMinusU2 - U2) + One;
- /* Purify Integers */
- if (Radix != One) {
- X = - TwoForty * LOG(U1) / LOG(Radix);
- Y = FLOOR(Half + X);
- if (FABS(X - Y) * Four < One) X = Y;
- Precision = X / TwoForty;
- Y = FLOOR(Half + Precision);
- if (FABS(Precision - Y) * TwoForty < Half) Precision = Y;
- }
- if ((Precision != FLOOR(Precision)) || (Radix == One)) {
- printf("Precision cannot be characterized by an Integer number\n");
- printf("of significant digits but, by itself, this is a minor flaw.\n");
- }
- if (Radix == One)
- printf("logarithmic encoding has precision characterized solely by U1.\n");
- else
- {
- printf("The number of significant digits of the Radix is " );
- pnum( &Precision );
- }
- TstCond (Serious, U2 * Nine * Nine * TwoForty < One,
- "Precision worse than 5 decimal figures ");
- /*=============================================*/
- Milestone = 30;
- /*=============================================*/
- /* Test for extra-precise subepressions */
- X = FABS(((Four / Three - One) - One / Four) * Three - One / Four);
- do {
- Z2 = X;
- X = (One + (Half * Z2 + ThirtyTwo * Z2 * Z2)) - One;
- } while ( ! ((Z2 <= X) || (X <= Zero)));
- X = Y = Z = FABS((Three / Four - Two / Three) * Three - One / Four);
- do {
- Z1 = Z;
- Z = (One / Two - ((One / Two - (Half * Z1 + ThirtyTwo * Z1 * Z1))
- + One / Two)) + One / Two;
- } while ( ! ((Z1 <= Z) || (Z <= Zero)));
- do {
- do {
- Y1 = Y;
- Y = (Half - ((Half - (Half * Y1 + ThirtyTwo * Y1 * Y1)) + Half
- )) + Half;
- } while ( ! ((Y1 <= Y) || (Y <= Zero)));
- X1 = X;
- X = ((Half * X1 + ThirtyTwo * X1 * X1) - F9) + F9;
- } while ( ! ((X1 <= X) || (X <= Zero)));
- if ((X1 != Y1) || (X1 != Z1)) {
- BadCond(Serious, "Disagreements among the values X1, Y1, Z1,\n");
- printf("respectively " );
- pnum( &X1 );
- pnum( &Y1 );
- pnum( &Z1 );
- printf("are symptoms of inconsistencies introduced\n");
- printf("by extra-precise evaluation of arithmetic subexpressions.\n");
- notify("Possibly some part of this");
- if ((X1 == U1) || (Y1 == U1) || (Z1 == U1)) printf(
- "That feature is not tested further by this program.\n") ;
- }
- else {
- if ((Z1 != U1) || (Z2 != U2)) {
- if ((Z1 >= U1) || (Z2 >= U2)) {
- BadCond(Failure, "");
- notify("Precision");
- printf("\tU1 = " );
- pnum( &U1 );
- printf( "Z1 - U1 = " );
- Ptemp = Z1-U1;
- pnum( &Ptemp );
- printf("\tU2 = " );
- pnum( &U2 );
- Ptemp = Z2-U2;
- printf( "Z2 - U2 = " );
- pnum( &Ptemp );
- }
- else {
- if ((Z1 <= Zero) || (Z2 <= Zero)) {
- printf("Because of unusual Radix = ");
- pnum( &Radix );
- printf(", or exact rational arithmetic a result\n");
- printf("Z1 = " );
- pnum( &Z1 );
- printf( "or Z2 = " );
- pnum( &Z2 );
- notify("of an\nextra-precision");
- }
- if (Z1 != Z2 || Z1 > Zero) {
- X = Z1 / U1;
- Y = Z2 / U2;
- if (Y > X) X = Y;
- Q = - LOG(X);
- printf("Some subexpressions appear to be calculated extra\n");
- printf("precisely with about" );
- Ptemp = Q / LOG(Radix);
- pnum( &Ptemp );
- printf( "extra B-digits, i.e.\n" );
- Ptemp = Q / LOG(10.);
- printf("roughly " );
- pnum( &Ptemp );
- printf( "extra significant decimals.\n");
- }
- printf("That feature is not tested further by this program.\n");
- }
- }
- }
- Pause();
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part3(){
-*/
- Milestone = 35;
- /*=============================================*/
- if (Radix >= Two) {
- X = W / (Radix * Radix);
- Y = X + One;
- Z = Y - X;
- T = Z + U2;
- X = T - Z;
- TstCond (Failure, X == U2,
- "Subtraction is not normalized X=Y,X+Z != Y+Z!");
- if (X == U2) printf(
- "Subtraction appears to be normalized, as it should be.");
- }
- printf("\nChecking for guard digit in *, /, and -.\n");
- Y = F9 * One;
- Z = One * F9;
- X = F9 - Half;
- Y = (Y - Half) - X;
- Z = (Z - Half) - X;
- X = One + U2;
- T = X * Radix;
- R = Radix * X;
- X = T - Radix;
- X = X - Radix * U2;
- T = R - Radix;
- T = T - Radix * U2;
- X = X * (Radix - One);
- T = T * (Radix - One);
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)) GMult = Yes;
- else {
- GMult = No;
- TstCond (Serious, False,
- "* lacks a Guard Digit, so 1*X != X");
- }
- Z = Radix * U2;
- X = One + Z;
- Y = FABS((X + Z) - X * X) - U2;
- X = One - U2;
- Z = FABS((X - U2) - X * X) - U1;
- TstCond (Failure, (Y <= Zero)
- && (Z <= Zero), "* gets too many final digits wrong.\n");
- Y = One - U2;
- X = One + U2;
- Z = One / Y;
- Y = Z - X;
- X = One / Three;
- Z = Three / Nine;
- X = X - Z;
- T = Nine / TwentySeven;
- Z = Z - T;
- TstCond(Defect, X == Zero && Y == Zero && Z == Zero,
- "Division lacks a Guard Digit, so error can exceed 1 ulp\n\
-or 1/3 and 3/9 and 9/27 may disagree");
- Y = F9 / One;
- X = F9 - Half;
- Y = (Y - Half) - X;
- X = One + U2;
- T = X / One;
- X = T - X;
- if ((X == Zero) && (Y == Zero) && (Z == Zero)) GDiv = Yes;
- else {
- GDiv = No;
- TstCond (Serious, False,
- "Division lacks a Guard Digit, so X/1 != X");
- }
- X = One / (One + U2);
- Y = X - Half - Half;
- TstCond (Serious, Y < Zero,
- "Computed value of 1/1.000..1 >= 1");
- X = One - U2;
- Y = One + Radix * U2;
- Z = X * Radix;
- T = Y * Radix;
- R = Z / Radix;
- StickyBit = T / Radix;
- X = R - X;
- Y = StickyBit - Y;
- TstCond (Failure, X == Zero && Y == Zero,
- "* and/or / gets too many last digits wrong");
- Y = One - U1;
- X = One - F9;
- Y = One - Y;
- T = Radix - U2;
- Z = Radix - BMinusU2;
- T = Radix - T;
- if ((X == U1) && (Y == U1) && (Z == U2) && (T == U2)) GAddSub = Yes;
- else {
- GAddSub = No;
- TstCond (Serious, False,
- "- lacks Guard Digit, so cancellation is obscured");
- }
- if (F9 != One && F9 - One >= Zero) {
- BadCond(Serious, "comparison alleges (1-U1) < 1 although\n");
- printf(" subtration yields (1-U1) - 1 = 0 , thereby vitiating\n");
- printf(" such precautions against division by zero as\n");
- printf(" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
- }
- if (GMult == Yes && GDiv == Yes && GAddSub == Yes) printf(
- " *, /, and - appear to have guard digits, as they should.\n");
- /*=============================================*/
- Milestone = 40;
- /*=============================================*/
- Pause();
- printf("Checking rounding on multiply, divide and add/subtract.\n");
- RMult = Other;
- RDiv = Other;
- RAddSub = Other;
- RadixD2 = Radix / Two;
- A1 = Two;
- Done = False;
- do {
- AInvrse = Radix;
- do {
- X = AInvrse;
- AInvrse = AInvrse / A1;
- } while ( ! (FLOOR(AInvrse) != AInvrse));
- Done = (X == One) || (A1 > Three);
- if (! Done) A1 = Nine + One;
- } while ( ! (Done));
- if (X == One) A1 = Radix;
- AInvrse = One / A1;
- X = A1;
- Y = AInvrse;
- Done = False;
- do {
- Z = X * Y - Half;
- TstCond (Failure, Z == Half,
- "X * (1/X) differs from 1");
- Done = X == Radix;
- X = Radix;
- Y = One / X;
- } while ( ! (Done));
- Y2 = One + U2;
- Y1 = One - U2;
- X = OneAndHalf - U2;
- Y = OneAndHalf + U2;
- Z = (X - U2) * Y2;
- T = Y * Y1;
- Z = Z - X;
- T = T - X;
- X = X * Y2;
- Y = (Y + U2) * Y1;
- X = X - OneAndHalf;
- Y = Y - OneAndHalf;
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T <= Zero)) {
- printf("Y2 = ");
- pnum( &Y2 );
- printf("Y1 = ");
- pnum( &Y1 );
- printf("U2 = ");
- pnum( &U2 );
- X = (OneAndHalf + U2) * Y2;
- Y = OneAndHalf - U2 - U2;
- Z = OneAndHalf + U2 + U2;
- T = (OneAndHalf - U2) * Y1;
- X = X - (Z + U2);
- StickyBit = Y * Y1;
- S = Z * Y2;
- T = T - Y;
- Y = (U2 - Y) + StickyBit;
- Z = S - (Z + U2 + U2);
- StickyBit = (Y2 + U2) * Y1;
- Y1 = Y2 * Y1;
- StickyBit = StickyBit - Y2;
- Y1 = Y1 - Half;
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
- && ( StickyBit == Zero) && (Y1 == Half)) {
- RMult = Rounded;
- printf("Multiplication appears to round correctly.\n");
- }
- else if ((X + U2 == Zero) && (Y < Zero) && (Z + U2 == Zero)
- && (T < Zero) && (StickyBit + U2 == Zero)
- && (Y1 < Half)) {
- RMult = Chopped;
- printf("Multiplication appears to chop.\n");
- }
- else printf("* is neither chopped nor correctly rounded.\n");
- if ((RMult == Rounded) && (GMult == No)) notify("Multiplication");
- }
- else printf("* is neither chopped nor correctly rounded.\n");
- /*=============================================*/
- Milestone = 45;
- /*=============================================*/
- Y2 = One + U2;
- Y1 = One - U2;
- Z = OneAndHalf + U2 + U2;
- X = Z / Y2;
- T = OneAndHalf - U2 - U2;
- Y = (T - U2) / Y1;
- Z = (Z + U2) / Y2;
- X = X - OneAndHalf;
- Y = Y - T;
- T = T / Y1;
- Z = Z - (OneAndHalf + U2);
- T = (U2 - OneAndHalf) + T;
- if (! ((X > Zero) || (Y > Zero) || (Z > Zero) || (T > Zero))) {
- X = OneAndHalf / Y2;
- Y = OneAndHalf - U2;
- Z = OneAndHalf + U2;
- X = X - Y;
- T = OneAndHalf / Y1;
- Y = Y / Y1;
- T = T - (Z + U2);
- Y = Y - Z;
- Z = Z / Y2;
- Y1 = (Y2 + U2) / Y2;
- Z = Z - OneAndHalf;
- Y2 = Y1 - Y2;
- Y1 = (F9 - U1) / F9;
- if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
- && (Y2 == Zero) && (Y2 == Zero)
- && (Y1 - Half == F9 - Half )) {
- RDiv = Rounded;
- printf("Division appears to round correctly.\n");
- if (GDiv == No) notify("Division");
- }
- else if ((X < Zero) && (Y < Zero) && (Z < Zero) && (T < Zero)
- && (Y2 < Zero) && (Y1 - Half < F9 - Half)) {
- RDiv = Chopped;
- printf("Division appears to chop.\n");
- }
- }
- if (RDiv == Other) printf("/ is neither chopped nor correctly rounded.\n");
- BInvrse = One / Radix;
- TstCond (Failure, (BInvrse * Radix - Half == Half),
- "Radix * ( 1 / Radix ) differs from 1");
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part4(){
-*/
- Milestone = 50;
- /*=============================================*/
- TstCond (Failure, ((F9 + U1) - Half == Half)
- && ((BMinusU2 + U2 ) - One == Radix - One),
- "Incomplete carry-propagation in Addition");
- X = One - U1 * U1;
- Y = One + U2 * (One - U2);
- Z = F9 - Half;
- X = (X - Half) - Z;
- Y = Y - One;
- if ((X == Zero) && (Y == Zero)) {
- RAddSub = Chopped;
- printf("Add/Subtract appears to be chopped.\n");
- }
- if (GAddSub == Yes) {
- X = (Half + U2) * U2;
- Y = (Half - U2) * U2;
- X = One + X;
- Y = One + Y;
- X = (One + U2) - X;
- Y = One - Y;
- if ((X == Zero) && (Y == Zero)) {
- X = (Half + U2) * U1;
- Y = (Half - U2) * U1;
- X = One - X;
- Y = One - Y;
- X = F9 - X;
- Y = One - Y;
- if ((X == Zero) && (Y == Zero)) {
- RAddSub = Rounded;
- printf("Addition/Subtraction appears to round correctly.\n");
- if (GAddSub == No) notify("Add/Subtract");
- }
- else printf("Addition/Subtraction neither rounds nor chops.\n");
- }
- else printf("Addition/Subtraction neither rounds nor chops.\n");
- }
- else printf("Addition/Subtraction neither rounds nor chops.\n");
- S = One;
- X = One + Half * (One + Half);
- Y = (One + U2) * Half;
- Z = X - Y;
- T = Y - X;
- StickyBit = Z + T;
- if (StickyBit != Zero) {
- S = Zero;
- BadCond(Flaw, "(X - Y) + (Y - X) is non zero!\n");
- }
- StickyBit = Zero;
- if ((GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
- && (RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (FLOOR(RadixD2) == RadixD2)) {
- printf("Checking for sticky bit.\n");
- X = (Half + U1) * U2;
- Y = Half * U2;
- Z = One + Y;
- T = One + X;
- if ((Z - One <= Zero) && (T - One >= U2)) {
- Z = T + Y;
- Y = Z - X;
- if ((Z - T >= U2) && (Y - T == Zero)) {
- X = (Half + U1) * U1;
- Y = Half * U1;
- Z = One - Y;
- T = One - X;
- if ((Z - One == Zero) && (T - F9 == Zero)) {
- Z = (Half - U1) * U1;
- T = F9 - Z;
- Q = F9 - Y;
- if ((T - F9 == Zero) && (F9 - U1 - Q == Zero)) {
- Z = (One + U2) * OneAndHalf;
- T = (OneAndHalf + U2) - Z + U2;
- X = One + Half / Radix;
- Y = One + Radix * U2;
- Z = X * Y;
- if (T == Zero && X + Radix * U2 - Z == Zero) {
- if (Radix != Two) {
- X = Two + U2;
- Y = X / Two;
- if ((Y - One == Zero)) StickyBit = S;
- }
- else StickyBit = S;
- }
- }
- }
- }
- }
- }
- if (StickyBit == One) printf("Sticky bit apparently used correctly.\n");
- else printf("Sticky bit used incorrectly or not at all.\n");
- TstCond (Flaw, !(GMult == No || GDiv == No || GAddSub == No ||
- RMult == Other || RDiv == Other || RAddSub == Other),
- "lack(s) of guard digits or failure(s) to correctly round or chop\n\
-(noted above) count as one flaw in the final tally below");
- /*=============================================*/
- Milestone = 60;
- /*=============================================*/
- printf("\n");
- printf("Does Multiplication commute? ");
- printf("Testing on %d random pairs.\n", NoTrials);
- Ptemp = 3.0;
- Random9 = SQRT(Ptemp);
- Random1 = Third;
- I = 1;
- do {
- X = Random();
- Y = Random();
- Z9 = Y * X;
- Z = X * Y;
- Z9 = Z - Z9;
- I = I + 1;
- } while ( ! ((I > NoTrials) || (Z9 != Zero)));
- if (I == NoTrials) {
- Random1 = One + Half / Three;
- Random2 = (U2 + U1) + One;
- Z = Random1 * Random2;
- Y = Random2 * Random1;
- Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
- Three) * ((U2 + U1) + One);
- }
- if (! ((I == NoTrials) || (Z9 == Zero)))
- BadCond(Defect, "X * Y == Y * X trial fails.\n");
- else printf(" No failures found in %d integer pairs.\n", NoTrials);
- /*=============================================*/
- Milestone = 70;
- /*=============================================*/
- printf("\nRunning test of square root(x).\n");
- TstCond (Failure, (Zero == SQRT(Zero))
- && (- Zero == SQRT(- Zero))
- && (One == SQRT(One)), "Square root of 0.0, -0.0 or 1.0 wrong");
- MinSqEr = Zero;
- MaxSqEr = Zero;
- J = Zero;
- X = Radix;
- OneUlp = U2;
- SqXMinX (Serious);
- X = BInvrse;
- OneUlp = BInvrse * U1;
- SqXMinX (Serious);
- X = U1;
- OneUlp = U1 * U1;
- SqXMinX (Serious);
- if (J != Zero) Pause();
- printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
- J = Zero;
- X = Two;
- Y = Radix;
- if ((Radix != One)) do {
- X = Y;
- Y = Radix * Y;
- } while ( ! ((Y - X >= NoTrials)));
- OneUlp = X * U2;
- I = 1;
- while (I < 10) {
- X = X + One;
- SqXMinX (Defect);
- if (J > Zero) break;
- I = I + 1;
- }
- printf("Test for sqrt monotonicity.\n");
- I = - 1;
- X = BMinusU2;
- Y = Radix;
- Z = Radix + Radix * U2;
- NotMonot = False;
- Monot = False;
- while ( ! (NotMonot || Monot)) {
- I = I + 1;
- X = SQRT(X);
- Q = SQRT(Y);
- Z = SQRT(Z);
- if ((X > Q) || (Q > Z)) NotMonot = True;
- else {
- Q = FLOOR(Q + Half);
- if ((I > 0) || (Radix == Q * Q)) Monot = True;
- else if (I > 0) {
- if (I > 1) Monot = True;
- else {
- Y = Y * BInvrse;
- X = Y - U1;
- Z = Y + U1;
- }
- }
- else {
- Y = Q;
- X = Y - U2;
- Z = Y + U2;
- }
- }
- }
- if (Monot) printf("sqrt has passed a test for Monotonicity.\n");
- else {
- BadCond(Defect, "");
- printf("sqrt(X) is non-monotonic for X near " );
- pnum( &Y );
- }
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part5(){
-*/
- Milestone = 80;
- /*=============================================*/
- MinSqEr = MinSqEr + Half;
- MaxSqEr = MaxSqEr - Half;
- Y = (SQRT(One + U2) - One) / U2;
- SqEr = (Y - One) + U2 / Eight;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- SqEr = Y + U2 / Eight;
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- Y = ((SQRT(F9) - U2) - (One - U2)) / U1;
- SqEr = Y + U1 / Eight;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- SqEr = (Y + One) + U1 / Eight;
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- OneUlp = U2;
- X = OneUlp;
- for( Indx = 1; Indx <= 3; ++Indx) {
- Y = SQRT((X + U1 + X) + F9);
- Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;
- Z = ((U1 - X) + F9) * Half * X * X / OneUlp;
- SqEr = (Y + Half) + Z;
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- SqEr = (Y - Half) + Z;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- if (((Indx == 1) || (Indx == 3)))
- X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));
- else {
- OneUlp = U1;
- X = - OneUlp;
- }
- }
- /*=============================================*/
- Milestone = 85;
- /*=============================================*/
- SqRWrng = False;
- Anomaly = False;
- if (Radix != One) {
- printf("Testing whether sqrt is rounded or chopped.\n");
- D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));
- /* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
- X = D / Radix;
- Y = D / A1;
- if ((X != FLOOR(X)) || (Y != FLOOR(Y))) {
- Anomaly = True;
- }
- else {
- X = Zero;
- Z2 = X;
- Y = One;
- Y2 = Y;
- Z1 = Radix - One;
- FourD = Four * D;
- do {
- if (Y2 > Z2) {
- Q = Radix;
- Y1 = Y;
- do {
- X1 = FABS(Q + FLOOR(Half - Q / Y1) * Y1);
- Q = Y1;
- Y1 = X1;
- } while ( ! (X1 <= Zero));
- if (Q <= One) {
- Z2 = Y2;
- Z = Y;
- }
- }
- Y = Y + Two;
- X = X + Eight;
- Y2 = Y2 + X;
- if (Y2 >= FourD) Y2 = Y2 - FourD;
- } while ( ! (Y >= D));
- X8 = FourD - Z2;
- Q = (X8 + Z * Z) / FourD;
- X8 = X8 / Eight;
- if (Q != FLOOR(Q)) Anomaly = True;
- else {
- Break = False;
- do {
- X = Z1 * Z;
- X = X - FLOOR(X / Radix) * Radix;
- if (X == One)
- Break = True;
- else
- Z1 = Z1 - One;
- } while ( ! (Break || (Z1 <= Zero)));
- if ((Z1 <= Zero) && (! Break)) Anomaly = True;
- else {
- if (Z1 > RadixD2) Z1 = Z1 - Radix;
- do {
- NewD();
- } while ( ! (U2 * D >= F9));
- if (D * Radix - D != W - D) Anomaly = True;
- else {
- Z2 = D;
- I = 0;
- Y = D + (One + Z) * Half;
- X = D + Z + Q;
- SR3750();
- Y = D + (One - Z) * Half + D;
- X = D - Z + D;
- X = X + Q + X;
- SR3750();
- NewD();
- if (D - Z2 != W - Z2) Anomaly = True;
- else {
- Y = (D - Z2) + (Z2 + (One - Z) * Half);
- X = (D - Z2) + (Z2 - Z + Q);
- SR3750();
- Y = (One + Z) * Half;
- X = Q;
- SR3750();
- if (I == 0) Anomaly = True;
- }
- }
- }
- }
- }
- if ((I == 0) || Anomaly) {
- BadCond(Failure, "Anomalous arithmetic with Integer < ");
- printf("Radix^Precision = " );
- pnum( &W );
- printf(" fails test whether sqrt rounds or chops.\n");
- SqRWrng = True;
- }
- }
- if (! Anomaly) {
- if (! ((MinSqEr < Zero) || (MaxSqEr > Zero))) {
- RSqrt = Rounded;
- printf("Square root appears to be correctly rounded.\n");
- }
- else {
- if ((MaxSqEr + U2 > U2 - Half) || (MinSqEr > Half)
- || (MinSqEr + Radix < Half)) SqRWrng = True;
- else {
- RSqrt = Chopped;
- printf("Square root appears to be chopped.\n");
- }
- }
- }
- if (SqRWrng) {
- printf("Square root is neither chopped nor correctly rounded.\n");
- printf("Observed errors run from " );
- Ptemp = MinSqEr - Half;
- pnum( &Ptemp );
- printf("to %.7e ulps.\n");
- Ptemp = Half + MaxSqEr;
- pnum( &Ptemp );
- TstCond (Serious, MaxSqEr - MinSqEr < Radix * Radix,
- "sqrt gets too many last digits wrong");
- }
- /*=============================================*/
- Milestone = 90;
- /*=============================================*/
- Pause();
- printf("Testing powers Z^i for small Integers Z and i.\n");
- N = 0;
- /* ... test powers of zero. */
- I = 0;
- Z = -Zero;
- M = 3.0;
- Break = False;
- do {
- X = One;
- SR3980();
- if (I <= 10) {
- I = 1023;
- SR3980();
- }
- if (Z == MinusOne) Break = True;
- else {
- Z = MinusOne;
- PrintIfNPositive();
- N = 0;
- /* .. if(-1)^N is invalid, replace MinusOne by One. */
- I = - 4;
- }
- } while ( ! Break);
- PrintIfNPositive();
- N1 = N;
- N = 0;
- Z = A1;
- M = FLOOR(Two * LOG(W) / LOG(A1));
- Break = False;
- do {
- X = Z;
- I = 1;
- SR3980();
- if (Z == AInvrse) Break = True;
- else Z = AInvrse;
- } while ( ! (Break));
- /*=============================================*/
- Milestone = 100;
- /*=============================================*/
- /* Powers of Radix have been tested, */
- /* next try a few primes */
- M = NoTrials;
- Z = Three;
- do {
- X = Z;
- I = 1;
- SR3980();
- do {
- Z = Z + Two;
- } while ( Three * FLOOR(Z / Three) == Z );
- } while ( Z < Eight * Three );
- if (N > 0) {
- printf("Errors like this may invalidate financial calculations\n");
- printf("\tinvolving interest rates.\n");
- }
- PrintIfNPositive();
- N += N1;
- if (N == 0) printf("... no discrepancis found.\n");
- if (N > 0) Pause();
- else printf("\n");
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part6(){
-*/
- Milestone = 110;
- /*=============================================*/
- printf("Seeking Underflow thresholds UfThold and E0.\n");
- D = U1;
- if (Precision != FLOOR(Precision)) {
- D = BInvrse;
- X = Precision;
- do {
- D = D * BInvrse;
- X = X - One;
- } while ( X > Zero);
- }
- Y = One;
- Z = D;
- /* ... D is power of 1/Radix < 1. */
- do {
- C = Y;
- Y = Z;
- Z = Y * Y;
- } while ((Y > Z) && (Z + Z > Z));
- Y = C;
- Z = Y * D;
- do {
- C = Y;
- Y = Z;
- Z = Y * D;
- } while ((Y > Z) && (Z + Z > Z));
- if (Radix < Two) HInvrse = Two;
- else HInvrse = Radix;
- H = One / HInvrse;
- /* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
- CInvrse = One / C;
- E0 = C;
- Z = E0 * H;
- /* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
- do {
- Y = E0;
- E0 = Z;
- Z = E0 * H;
- } while ((E0 > Z) && (Z + Z > Z));
- UfThold = E0;
- E1 = Zero;
- Q = Zero;
- E9 = U2;
- S = One + E9;
- D = C * S;
- if (D <= C) {
- E9 = Radix * U2;
- S = One + E9;
- D = C * S;
- if (D <= C) {
- BadCond(Failure, "multiplication gets too many last digits wrong.\n");
- Underflow = E0;
- Y1 = Zero;
- PseudoZero = Z;
- Pause();
- }
- }
- else {
- Underflow = D;
- PseudoZero = Underflow * H;
- UfThold = Zero;
- do {
- Y1 = Underflow;
- Underflow = PseudoZero;
- if (E1 + E1 <= E1) {
- Y2 = Underflow * HInvrse;
- E1 = FABS(Y1 - Y2);
- Q = Y1;
- if ((UfThold == Zero) && (Y1 != Y2)) UfThold = Y1;
- }
- PseudoZero = PseudoZero * H;
- } while ((Underflow > PseudoZero)
- && (PseudoZero + PseudoZero > PseudoZero));
- }
- /* Comment line 4530 .. 4560 */
- if (PseudoZero != Zero) {
- printf("\n");
- Z = PseudoZero;
- /* ... Test PseudoZero for "phoney- zero" violates */
- /* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
- ... */
- if (PseudoZero <= Zero) {
- BadCond(Failure, "Positive expressions can underflow to an\n");
- printf("allegedly negative value\n");
- printf("PseudoZero that prints out as: " );
- pnum( &PseudoZero );
- X = - PseudoZero;
- if (X <= Zero) {
- printf("But -PseudoZero, which should be\n");
- printf("positive, isn't; it prints out as " );
- pnum( &X );
- }
- }
- else {
- BadCond(Flaw, "Underflow can stick at an allegedly positive\n");
- printf("value PseudoZero that prints out as ");
- pnum( &PseudoZero );
- }
- TstPtUf();
- }
- /*=============================================*/
- Milestone = 120;
- /*=============================================*/
- if (CInvrse * Y > CInvrse * Y1) {
- S = H * S;
- E0 = Underflow;
- }
- if (! ((E1 == Zero) || (E1 == E0))) {
- BadCond(Defect, "");
- if (E1 < E0) {
- printf("Products underflow at a higher");
- printf(" threshold than differences.\n");
- if (PseudoZero == Zero)
- E0 = E1;
- }
- else {
- printf("Difference underflows at a higher");
- printf(" threshold than products.\n");
- }
- }
- printf("Smallest strictly positive number found is E0 = ");
- Pause();
- pnum( &E0 );
- Z = E0;
- TstPtUf();
- Underflow = E0;
- if (N == 1) Underflow = Y;
- I = 4;
- if (E1 == Zero) I = 3;
- if (UfThold == Zero) I = I - 2;
- UfNGrad = True;
- switch (I) {
- case 1:
- UfThold = Underflow;
- if ((CInvrse * Q) != ((CInvrse * Y) * S)) {
- UfThold = Y;
- BadCond(Failure, "Either accuracy deteriorates as numbers\n");
- printf("approach a threshold = ");
- pnum( &UfThold );
- printf(" coming down from " );
- pnum( &C );
- printf(" or else multiplication gets too many last digits wrong.\n");
- }
- Pause();
- break;
-
- case 2:
- BadCond(Failure, "Underflow confuses Comparison which alleges that\n");
- printf("Q == Y while denying that |Q - Y| == 0; these values\n");
- printf("print out as Q = " );
- pnum( &Q );
- printf( "Y = " );
- pnum( &Y );
- printf ("|Q - Y| = " );
- Ptemp = FABS(Q - Y2);
- pnum( &Ptemp );
- UfThold = Q;
- break;
-
- case 3:
- X = X;
- break;
-
- case 4:
- if ((Q == UfThold) && (E1 == E0)
- && (FABS( UfThold - E1 / E9) <= E1)) {
- UfNGrad = False;
- printf("Underflow is gradual; it incurs Absolute Error =\n");
- printf("(roundoff in UfThold) < E0.\n");
- Y = E0 * CInvrse;
- Y = Y * (OneAndHalf + U2);
- X = CInvrse * (One + U2);
- Y = Y / X;
- IEEE = (Y == E0);
- }
- }
- if (UfNGrad) {
- printf("\n");
- R = SQRT(Underflow / UfThold);
- if (R <= H) {
- Z = R * UfThold;
- X = Z * (One + R * H * (One + H));
- }
- else {
- Z = UfThold;
- X = Z * (One + H * H * (One + H));
- }
- if (! ((X == Z) || (X - Z != Zero))) {
- BadCond(Flaw, "");
- printf("X = " );
- pnum( &X );
- printf( "is not equal to Z = ");
- pnum( &Z );
- Z9 = X - Z;
- printf("yet X - Z yields " );
- pnum( &Z9 );
- printf(" Should this NOT signal Underflow, ");
- printf("this is a SERIOUS DEFECT\nthat causes ");
- printf("confusion when innocent statements like\n");;
- printf(" if (X == Z) ... else");
- printf(" ... (f(X) - f(Z)) / (X - Z) ...\n");
- printf("encounter Division by Zero although actually\n");
- printf("X / Z = 1 + ");
- Ptemp = (X / Z - Half) - Half;
- pnum( &Ptemp );
- }
- }
- printf("The Underflow threshold is ");
- pnum( &UfThold );
- printf("below which calculation may suffer larger Relative error than ");
- printf("merely roundoff.\n");
- Y2 = U1 * U1;
- Y = Y2 * Y2;
- Y2 = Y * U1;
- if (Y2 <= UfThold) {
- if (Y > E0) {
- BadCond(Defect, "");
- I = 5;
- }
- else {
- BadCond(Serious, "");
- I = 4;
- }
- printf("Range is too narrow; U1^%d Underflows.\n", I);
- }
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part7(){
-*/
- Milestone = 130;
- /*=============================================*/
- Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;
- Y2 = Y - One;
- printf("Since underflow occurs below the threshold\n");
- printf("UfThold = ");
- pnum( &HInvrse );
- printf( ") ^ (Y=" );
- pnum( &Y );
- printf( ")\nonly underflow " );
- printf("should afflict the expression HInvrse^(Y+1).\n");
- pnum( &HInvrse );
- pnum( &Y2 );
- V9 = POW(HInvrse, Y2);
- printf("actually calculating yields: ");
- pnum( &V9 );
- if (! ((V9 >= Zero) && (V9 <= (Radix + Radix + E9) * UfThold))) {
- BadCond(Serious, "this is not between 0 and underflow\n");
- printf(" threshold = ");
- pnum( &UfThold );
- }
- else if (! (V9 > UfThold * (One + E9)))
- printf("This computed value is O.K.\n");
- else {
- BadCond(Defect, "this is not between 0 and underflow\n");
- printf(" threshold = ");
- pnum( &UfThold);
- }
- /*=============================================*/
- Milestone = 140;
- /*=============================================*/
- printf("\n");
- /* ...calculate Exp2 == exp(2) == 7.389056099... */
- X = Zero;
- I = 2;
- Y = Two * Three;
- Q = Zero;
- N = 0;
- do {
- Z = X;
- I = I + 1;
- Y = Y / (I + I);
- R = Y + Q;
- X = Z + R;
- Q = (Z - X) + R;
- } while(X > Z);
- Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);
- X = Z * Z;
- Exp2 = X * X;
- X = F9;
- Y = X - U1;
- printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = ");
- pnum( &Exp2 );
- printf( "as X -> 1.\n");
- for(I = 1;;) {
- Z = X - BInvrse;
- Z = (X + One) / (Z - (One - BInvrse));
- Q = POW(X, Z) - Exp2;
- if (FABS(Q) > TwoForty * U2) {
- N = 1;
- V9 = (X - BInvrse) - (One - BInvrse);
- BadCond(Defect, "Calculated");
- Ptemp = POW(X,Z);
- pnum(&Ptemp);
- printf("for (1 + (" );
- pnum( &V9 );
- printf( ") ^ (" );
- pnum( &Z );
- printf(") differs from correct value by ");
- pnum( &Q );
- printf("\tThis much error may spoil financial\n");
- printf("\tcalculations involving tiny interest rates.\n");
- break;
- }
- else {
- Z = (Y - X) * Two + Y;
- X = Y;
- Y = Z;
- Z = One + (X - F9)*(X - F9);
- if (Z > One && I < NoTrials) I++;
- else {
- if (X > One) {
- if (N == 0)
- printf("Accuracy seems adequate.\n");
- break;
- }
- else {
- X = One + U2;
- Y = U2 + U2;
- Y += X;
- I = 1;
- }
- }
- }
- }
- /*=============================================*/
- Milestone = 150;
- /*=============================================*/
- printf("Testing powers Z^Q at four nearly extreme values.\n");
- N = 0;
- Z = A1;
- Q = FLOOR(Half - LOG(C) / LOG(A1));
- Break = False;
- do {
- X = CInvrse;
- Y = POW(Z, Q);
- IsYeqX();
- Q = - Q;
- X = C;
- Y = POW(Z, Q);
- IsYeqX();
- if (Z < One) Break = True;
- else Z = AInvrse;
- } while ( ! (Break));
- PrintIfNPositive();
- if (N == 0) printf(" ... no discrepancies found.\n");
- printf("\n");
-
- /*=============================================*/
- Milestone = 160;
- /*=============================================*/
- Pause();
- printf("Searching for Overflow threshold:\n");
- printf("This may generate an error.\n");
- sigsave = sigfpe;
- I = 0;
- Y = - CInvrse;
- V9 = HInvrse * Y;
- if (setjmp(ovfl_buf)) goto overflow;
- do {
- V = Y;
- Y = V9;
- V9 = HInvrse * Y;
- } while(V9 < Y);
- I = 1;
-overflow:
- Z = V9;
- printf("Can `Z = -Y' overflow?\n");
- printf("Trying it on Y = " );
- pnum( &Y );
- V9 = - Y;
- V0 = V9;
- if (V - Y == V + V0) printf("Seems O.K.\n");
- else {
- printf("finds a ");
- BadCond(Flaw, "-(-Y) differs from Y.\n");
- }
-#if 0
-/* this doesn't handle infinity. */
- if (Z != Y) {
- BadCond(Serious, "");
- printf("overflow past " );
- pnum( &Y );
- printf( "shrinks to " );
- pnum( &Z );
- }
-#endif
- Y = V * (HInvrse * U2 - HInvrse);
- Z = Y + ((One - HInvrse) * U2) * V;
- if (Z < V0) Y = Z;
- if (Y < V0) V = Y;
- if (V0 - V < V0) V = V0;
- printf("Overflow threshold is V = " );
- pnum( &V );
- if (I)
- {
- printf("Overflow saturates at V0 = " );
- pnum( &V0 );
- }
- else printf("There is no saturation value because the system traps on overflow.\n");
- V9 = V * One;
- printf("No Overflow should be signaled for V * 1 = " );
- pnum( &V9 );
- V9 = V / One;
- printf(" nor for V / 1 = " );
- pnum( &V9 );
- printf("Any overflow signal separating this * from the one\n");
- printf("above is a DEFECT.\n");
- /*=============================================*/
- Milestone = 170;
- /*=============================================*/
- if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
- BadCond(Failure, "Comparisons involving ");
- printf("+-" );
- pnum( &V );
- printf( ", +- " );
- pnum( &V0 );
- printf( "and +- " );
- pnum( &UfThold );
- printf( "are confused by Overflow." );
- }
- /*=============================================*/
- Milestone = 175;
- /*=============================================*/
- printf("\n");
- for(Indx = 1; Indx <= 3; ++Indx) {
- switch (Indx) {
- case 1: Z = UfThold; break;
- case 2: Z = E0; break;
- case 3: Z = PseudoZero; break;
- }
- if (Z != Zero) {
- V9 = SQRT(Z);
- Y = V9 * V9;
- if (Y / (One - Radix * E9) < Z
- || Y > (One + Radix + E9) * Z) {
- if (V9 > U1) BadCond(Serious, "");
- else BadCond(Defect, "");
- printf("Comparison alleges that what prints as Z =" );
- pnum( &Z );
- printf(" is too far from sqrt(Z) ^ 2 = ");
- pnum( &Y );
- }
- }
- }
- /*=============================================*/
- Milestone = 180;
- /*=============================================*/
- for(Indx = 1; Indx <= 2; ++Indx) {
- if (Indx == 1) Z = V;
- else Z = V0;
- V9 = SQRT(Z);
- X = (One - Radix * E9) * V9;
- V9 = V9 * X;
- if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
- Y = V9;
- if (X < W) BadCond(Serious, "");
- else BadCond(Defect, "");
- printf("Comparison alleges that Z = ");
- pnum( &Z );
- printf(" is too far from sqrt(Z) ^ 2 " );
- pnum( &Y );
- }
- }
- /*=============================================*/
- /*SPLIT
- }
-#include "paranoia.h"
-part8(){
-*/
- Milestone = 190;
- /*=============================================*/
- Pause();
- X = UfThold * V;
- Y = Radix * Radix;
- if (X*Y < One || X > Y) {
- if (X * Y < U1 || X > Y/U1) BadCond(Defect, "Badly");
- else BadCond(Flaw, "");
-
- printf(" unbalanced range; UfThold * V = " );
- pnum( &X );
- printf( "is too far from 1.\n");
- }
- /*=============================================*/
- Milestone = 200;
- /*=============================================*/
- for (Indx = 1; Indx <= 5; ++Indx) {
- X = F9;
- switch (Indx) {
- case 2: X = One + U2; break;
- case 3: X = V; break;
- case 4: X = UfThold; break;
- case 5: X = Radix;
- }
- Y = X;
- sigsave = sigfpe;
- if (setjmp(ovfl_buf))
- {
- printf(" X / X traps when X = ");
- pnum( &X );
- }
- else {
- V9 = (Y / X - Half) - Half;
- if (V9 == Zero) continue;
- if (V9 == - U1 && Indx < 5) BadCond(Flaw, "");
- else BadCond(Serious, "");
- printf(" X / X differs from 1 when X =");
- pnum( &X );
- printf(" instead, X / X - 1/2 - 1/2 = ");
- pnum( &V9 );
- }
- }
- /*=============================================*/
- Milestone = 210;
- /*=============================================*/
- MyZero = Zero;
- printf("\n");
- printf("What message and/or values does Division by Zero produce?\n") ;
-#ifndef NOPAUSE
- printf("This can interupt your program. You can ");
- printf("skip this part if you wish.\n");
- printf("Do you wish to compute 1 / 0? ");
- fflush(stdout);
- read (KEYBOARD, ch, 8);
- if ((ch[0] == 'Y') || (ch[0] == 'y')) {
-#endif
- sigsave = sigfpe;
- printf(" Trying to compute 1 / 0 produces ...");
- if (!setjmp(ovfl_buf))
- {
- Ptemp = One / MyZero;
- pnum( &Ptemp );
- }
-#ifndef NOPAUSE
- }
- else printf("O.K.\n");
- printf("\nDo you wish to compute 0 / 0? ");
- fflush(stdout);
- read (KEYBOARD, ch, 80);
- if ((ch[0] == 'Y') || (ch[0] == 'y')) {
-#endif
- sigsave = sigfpe;
- printf("\n Trying to compute 0 / 0 produces ...");
- if (!setjmp(ovfl_buf))
- {
- Ptemp = Zero / MyZero;
- pnum( &Ptemp );
- }
-#ifndef NOPAUSE
- }
- else printf("O.K.\n");
-#endif
- /*=============================================*/
- Milestone = 220;
- /*=============================================*/
- Pause();
- printf("\n");
- {
- static char *msg[] = {
- "FAILUREs encountered =",
- "SERIOUS DEFECTs discovered =",
- "DEFECTs discovered =",
- "FLAWs discovered =" };
- int i;
- for(i = 0; i < 4; i++) if (ErrCnt[i])
- printf("The number of %-29s %d.\n",
- msg[i], ErrCnt[i]);
- }
- printf("\n");
- if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
- + ErrCnt[Flaw]) > 0) {
- if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
- Defect] == 0) && (ErrCnt[Flaw] > 0)) {
- printf("The arithmetic diagnosed seems ");
- printf("satisfactory though flawed.\n");
- }
- if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
- && ( ErrCnt[Defect] > 0)) {
- printf("The arithmetic diagnosed may be acceptable\n");
- printf("despite inconvenient Defects.\n");
- }
- if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
- printf("The arithmetic diagnosed has ");
- printf("unacceptable serious defects.\n");
- }
- if (ErrCnt[Failure] > 0) {
- printf("Fatal FAILURE may have spoiled this");
- printf(" program's subsequent diagnoses.\n");
- }
- }
- else {
- printf("No failures, defects nor flaws have been discovered.\n");
- if (! ((RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (RSqrt == Rounded)))
- printf("The arithmetic diagnosed seems satisfactory.\n");
- else {
- if (StickyBit >= One &&
- (Radix - Two) * (Radix - Nine - One) == Zero) {
- printf("Rounding appears to conform to ");
- printf("the proposed IEEE standard P");
- if ((Radix == Two) &&
- ((Precision - Four * Three * Two) *
- ( Precision - TwentySeven -
- TwentySeven + One) == Zero))
- printf("754");
- else printf("854");
- if (IEEE) printf(".\n");
- else {
- printf(",\nexcept for possibly Double Rounding");
- printf(" during Gradual Underflow.\n");
- }
- }
- printf("The arithmetic diagnosed appears to be excellent!\n");
- }
- }
- if (fpecount)
- printf("\nA total of %d floating point exceptions were registered.\n",
- fpecount);
- printf("END OF TEST.\n");
- }
-
-/*SPLIT subs.c
-#include "paranoia.h"
-*/
-
-/* Sign */
-
-FLOAT Sign (X)
-FLOAT X;
-{ return X >= 0. ? 1.0 : -1.0; }
-
-/* Pause */
-
-Pause()
-{
- char ch[8];
-
-#ifndef NOPAUSE
- printf("\nTo continue, press RETURN");
- fflush(stdout);
- read(KEYBOARD, ch, 8);
-#endif
- printf("\nDiagnosis resumes after milestone Number %d", Milestone);
- printf(" Page: %d\n\n", PageNo);
- ++Milestone;
- ++PageNo;
- }
-
- /* TstCond */
-
-TstCond (K, Valid, T)
-int K, Valid;
-char *T;
-{ if (! Valid) { BadCond(K,T); printf(".\n"); } }
-
-BadCond(K, T)
-int K;
-char *T;
-{
- static char *msg[] = { "FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW" };
-
- ErrCnt [K] = ErrCnt [K] + 1;
- printf("%s: %s", msg[K], T);
- }
-
-/* Random */
-/* Random computes
- X = (Random1 + Random9)^5
- Random1 = X - FLOOR(X) + 0.000005 * X;
- and returns the new value of Random1
-*/
-
-FLOAT Random()
-{
- FLOAT X, Y;
-
- X = Random1 + Random9;
- Y = X * X;
- Y = Y * Y;
- X = X * Y;
- Y = X - FLOOR(X);
- Random1 = Y + X * 0.000005;
- return(Random1);
- }
-
-/* SqXMinX */
-
-SqXMinX (ErrKind)
-int ErrKind;
-{
- FLOAT XA, XB;
-
- XB = X * BInvrse;
- XA = X - XB;
- SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;
- if (SqEr != Zero) {
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- J = J + 1.0;
- BadCond(ErrKind, "\n");
- printf("sqrt( ");
- Ptemp = X * X;
- pnum( &Ptemp );
- printf( ") - " );
- pnum( &X );
- printf(" = " );
- Ptemp = OneUlp * SqEr;
- pnum( &Ptemp );
- printf("\tinstead of correct value 0 .\n");
- }
- }
-
-/* NewD */
-
-NewD()
-{
- X = Z1 * Q;
- X = FLOOR(Half - X / Radix) * Radix + X;
- Q = (Q - X * Z) / Radix + X * X * (D / Radix);
- Z = Z - Two * X * D;
- if (Z <= Zero) {
- Z = - Z;
- Z1 = - Z1;
- }
- D = Radix * D;
- }
-
-/* SR3750 */
-
-SR3750()
-{
- if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {
- I = I + 1;
- X2 = SQRT(X * D);
- Y2 = (X2 - Z2) - (Y - Z2);
- X2 = X8 / (Y - Half);
- X2 = X2 - Half * X2 * X2;
- SqEr = (Y2 + Half) + (Half - X2);
- if (SqEr < MinSqEr) MinSqEr = SqEr;
- SqEr = Y2 - X2;
- if (SqEr > MaxSqEr) MaxSqEr = SqEr;
- }
- }
-
-/* IsYeqX */
-
-IsYeqX()
-{
- if (Y != X) {
- if (N <= 0) {
- if (Z == Zero && Q <= Zero)
- printf("WARNING: computing\n");
- else BadCond(Defect, "computing\n");
- printf("\t(");
- pnum( &Z );
- printf( ") ^ (" );
- pnum( &Q );
- printf("\tyielded " );
- pnum( &Y );
- printf("\twhich compared unequal to correct " );
- pnum( &X );
- printf("\t\tthey differ by " );
- Ptemp = Y - X;
- pnum( &Ptemp );
- }
- N = N + 1; /* ... count discrepancies. */
- }
- }
-
-/* SR3980 */
-
-SR3980()
-{
- do {
- Q = (FLOAT) I;
- Y = POW(Z, Q);
- IsYeqX();
- if (++I > M) break;
- X = Z * X;
- } while ( X < W );
- }
-
-/* PrintIfNPositive */
-
-PrintIfNPositive()
-{
- if (N > 0) printf("Similar discrepancies have occurred %d times.\n", N);
- }
-
-/* TstPtUf */
-
-TstPtUf()
-{
- N = 0;
- if (Z != Zero) {
- printf("Since comparison denies Z = 0, evaluating ");
- printf("(Z + Z) / Z should be safe.\n");
- sigsave = sigfpe;
- if (setjmp(ovfl_buf)) goto very_serious;
- Q9 = (Z + Z) / Z;
- printf("What the machine gets for (Z + Z) / Z is " );
- pnum( &Q9 );
- if (FABS(Q9 - Two) < Radix * U2) {
- printf("This is O.K., provided Over/Underflow");
- printf(" has NOT just been signaled.\n");
- }
- else {
- if ((Q9 < One) || (Q9 > Two)) {
-very_serious:
- N = 1;
- ErrCnt [Serious] = ErrCnt [Serious] + 1;
- printf("This is a VERY SERIOUS DEFECT!\n");
- }
- else {
- N = 1;
- ErrCnt [Defect] = ErrCnt [Defect] + 1;
- printf("This is a DEFECT!\n");
- }
- }
- V9 = Z * One;
- Random1 = V9;
- V9 = One * Z;
- Random2 = V9;
- V9 = Z / One;
- if ((Z == Random1) && (Z == Random2) && (Z == V9)) {
- if (N > 0) Pause();
- }
- else {
- N = 1;
- BadCond(Defect, "What prints as Z = ");
- pnum( &Z );
- printf("\tcompares different from ");
- if (Z != Random1)
- {
- printf("Z * 1 = " );
- pnum( &Random1 );
- }
- if (! ((Z == Random2)
- || (Random2 == Random1)))
- {
- printf("1 * Z == " );
- pnum( &Random2 );
- }
- if (! (Z == V9))
- {
- printf("Z / 1 = ");
- pnum( &V9 );
- }
- if (Random2 != Random1) {
- ErrCnt [Defect] = ErrCnt [Defect] + 1;
- BadCond(Defect, "Multiplication does not commute!\n");
- printf("\tComparison alleges that 1 * Z = ");
- pnum( &Random2 );
- printf("\tdiffers from Z * 1 = ");
- pnum( &Random1 );
- }
- Pause();
- }
- }
- }
-
-notify(s)
-char *s;
-{
- printf("%s test appears to be inconsistent...\n", s);
- printf(" PLEASE NOTIFY KARPINKSI!\n");
- }
-
-/*SPLIT msgs.c */
-
-/* Instructions */
-
-msglist(s)
-char **s;
-{ while(*s) printf("%s\n", *s++); }
-
-Instructions()
-{
- static char *instr[] = {
- "Lest this program stop prematurely, i.e. before displaying\n",
- " `END OF TEST',\n",
- "try to persuade the computer NOT to terminate execution when an",
- "error like Over/Underflow or Division by Zero occurs, but rather",
- "to persevere with a surrogate value after, perhaps, displaying some",
- "warning. If persuasion avails naught, don't despair but run this",
- "program anyway to see how many milestones it passes, and then",
- "amend it to make further progress.\n",
- "Answer questions with Y, y, N or n (unless otherwise indicated).\n",
- 0};
-
- msglist(instr);
- }
-
-/* Heading */
-
-Heading()
-{
- static char *head[] = {
- "Users are invited to help debug and augment this program so it will",
- "cope with unanticipated and newly uncovered arithmetic pathologies.\n",
- "Please send suggestions and interesting results to",
- "\tRichard Karpinski",
- "\tComputer Center U-76",
- "\tUniversity of California",
- "\tSan Francisco, CA 94143-0704, USA\n",
- "In doing so, please include the following information:",
-#ifdef Single
- "\tPrecision:\tsingle;",
-#else
- "\tPrecision:\tdouble;",
-#endif
- "\tVersion:\t27 January 1986;",
- "\tComputer:\n",
- "\tCompiler:\n",
- "\tOptimization level:\n",
- "\tOther relevant compiler options:",
- 0};
-
- msglist(head);
- }
-
-/* Characteristics */
-
-Characteristics()
-{
- static char *chars[] = {
- "Running this program should reveal these characteristics:",
- " Radix = 1, 2, 4, 8, 10, 16, 100, 256 ...",
- " Precision = number of significant digits carried.",
- " U2 = Radix/Radix^Precision = One Ulp",
- "\t(OneUlpnit in the Last Place) of 1.000xxx .",
- " U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 .",
- " Adequacy of guard digits for Mult., Div. and Subt.",
- " Whether arithmetic is chopped, correctly rounded, or something else",
- "\tfor Mult., Div., Add/Subt. and Sqrt.",
- " Whether a Sticky Bit used correctly for rounding.",
- " UnderflowThreshold = an underflow threshold.",
- " E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy.",
- " V = an overflow threshold, roughly.",
- " V0 tells, roughly, whether Infinity is represented.",
- " Comparisions are checked for consistency with subtraction",
- "\tand for contamination with pseudo-zeros.",
- " Sqrt is tested. Y^X is not tested.",
- " Extra-precise subexpressions are revealed but NOT YET tested.",
- " Decimal-Binary conversion is NOT YET tested for accuracy.",
- 0};
-
- msglist(chars);
- }
-
-History()
-
-{ /* History */
- /* Converted from Brian Wichmann's Pascal version to C by Thos Sumner,
- with further massaging by David M. Gay. */
-
- static char *hist[] = {
- "The program attempts to discriminate among",
- " FLAWs, like lack of a sticky bit,",
- " Serious DEFECTs, like lack of a guard digit, and",
- " FAILUREs, like 2+2 == 5 .",
- "Failures may confound subsequent diagnoses.\n",
- "The diagnostic capabilities of this program go beyond an earlier",
- "program called `MACHAR', which can be found at the end of the",
- "book `Software Manual for the Elementary Functions' (1980) by",
- "W. J. Cody and W. Waite. Although both programs try to discover",
- "the Radix, Precision and range (over/underflow thresholds)",
- "of the arithmetic, this program tries to cope with a wider variety",
- "of pathologies, and to say how well the arithmetic is implemented.",
- "\nThe program is based upon a conventional radix representation for",
- "floating-point numbers, but also allows logarithmic encoding",
- "as used by certain early WANG machines.\n",
- "BASIC version of this program (C) 1983 by Prof. W. M. Kahan;",
- "see source comments for more history.",
- 0};
-
- msglist(hist);
- }
+++ /dev/null
-
-/* monot.c
- Floating point function test vectors.
-
- Arguments and function values are synthesized for NPTS points in
- the vicinity of each given tabulated test point. The points are
- chosen to be near and on either side of the likely function algorithm
- domain boundaries. Since the function programs change their methods
- at these points, major coding errors or monotonicity failures might be
- detected.
-
- August, 1998
- S. L. Moshier */
-
-
-#include <stdio.h>
-
-/* Avoid including math.h. */
-long double frexpl (long double, int *);
-long double ldexpl (long double, int);
-
-/* Number of test points to generate on each side of tabulated point. */
-#define NPTS 100
-
-/* Functions of one variable. */
-long double expl (long double);
-long double logl (long double);
-long double sinl (long double);
-long double cosl (long double);
-long double tanl (long double);
-long double atanl (long double);
-long double asinl (long double);
-long double acosl (long double);
-long double sinhl (long double);
-long double coshl (long double);
-long double tanhl (long double);
-long double asinhl (long double);
-long double acoshl (long double);
-long double atanhl (long double);
-long double gammal (long double);
-long double fabsl (long double);
-long double floorl (long double);
-
-struct oneargument
- {
- char *name; /* Name of the function. */
- long double (*func) (long double);
- long double arg1; /* Function argument, assumed exact. */
- long double answer1; /* Exact, close to function value. */
- long double answer2; /* answer1 + answer2 has extended precision. */
- long double derivative; /* dy/dx evaluated at x = arg1. */
- int thresh; /* Error report threshold. 2 = 1 ULP approx. */
- };
-
-/* Add this to error threshold test[i].thresh. */
-#define OKERROR 2
-
-/* Unit of relative error in test[i].thresh. */
-static long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
-
-/* extern double MACHEP; */
-
-
-struct oneargument test1[] =
-{
- {"exp", expl, 1.0L, 2.7182769775390625L,
- 4.85091998273536028747e-6L, 2.71828182845904523536L, 1},
- {"exp", expl, -1.0L, 3.678741455078125e-1L,
- 5.29566362982159552377e-6L, 3.678794411714423215955e-1L, 1},
- {"exp", expl, 0.5L, 1.648712158203125L,
- 9.1124970031468486507878e-6L, 1.64872127070012814684865L, 1},
- {"exp", expl, -0.5L, 6.065216064453125e-1L,
- 9.0532673209236037995e-6L, 6.0653065971263342360e-1L, 1},
- {"exp", expl, 2.0L, 7.3890533447265625L,
- 2.75420408772723042746e-6L, 7.38905609893065022723L, 1},
- {"exp", expl, -2.0L, 1.353302001953125e-1L,
- 5.08304130019189399949e-6L, 1.3533528323661269189e-1L, 1},
- {"log", logl, 1.41421356237309492343L, 3.465728759765625e-1L,
- 7.1430341006605745676897e-7L, 7.0710678118654758708668e-1L, 1},
- {"log", logl, 7.07106781186547461715e-1L, -3.46588134765625e-1L,
- 1.45444856522566402246e-5L, 1.41421356237309517417L, 1},
- {"sin", sinl, 7.85398163397448278999e-1L, 7.0709228515625e-1L,
- 1.4496030297502751942956e-5L, 7.071067811865475460497e-1L, 1},
- {"sin", sinl, -7.85398163397448501044e-1L, -7.071075439453125e-1L,
- 7.62758764840238811175e-7L, 7.07106781186547389040e-1L, 1},
- {"sin", sinl, 1.570796326794896558L, 9.999847412109375e-1L,
- 1.52587890625e-5L, 6.12323399573676588613e-17L, 1},
- {"sin", sinl, -1.57079632679489678004L, -1.0L,
- 1.29302922820150306903e-32L, -1.60812264967663649223e-16L, 1},
- {"sin", sinl, 4.712388980384689674L, -1.0L,
- 1.68722975549458979398e-32L, -1.83697019872102976584e-16L, 1},
- {"sin", sinl, -4.71238898038468989604L, 9.999847412109375e-1L,
- 1.52587890625e-5L, 3.83475850529283315008e-17L, 1},
- {"cos", cosl, 3.92699081698724139500E-1L, 9.23873901367187500000E-1L,
- 5.63114409926198633370E-6L, -3.82683432365089757586E-1L, 1},
- {"cos", cosl, 7.85398163397448278999E-1L, 7.07092285156250000000E-1L,
- 1.44960302975460497458E-5L, -7.07106781186547502752E-1L, 1},
- {"cos", cosl, 1.17809724509617241850E0L, 3.82675170898437500000E-1L,
- 8.26146665231415693919E-6L, -9.23879532511286738554E-1L, 1},
- {"cos", cosl, 1.96349540849362069750E0L, -3.82690429687500000000E-1L,
- 6.99732241029898567203E-6L, -9.23879532511286785419E-1L, 1},
- {"cos", cosl, 2.35619449019234483700E0L, -7.07107543945312500000E-1L,
- 7.62758765040545859856E-7L, -7.07106781186547589348E-1L, 1},
- {"cos", cosl, 2.74889357189106897650E0L, -9.23889160156250000000E-1L,
- 9.62764496328487887036E-6L, -3.82683432365089870728E-1L, 1},
- {"cos", cosl, 3.14159265358979311600E0L, -1.00000000000000000000E0L,
- 7.49879891330928797323E-33L, -1.22464679914735317723E-16L, 1},
- {"tan", tanl, 7.85398163397448278999E-1L, 9.999847412109375e-1L,
- 1.52587890624387676600E-5L, 1.99999999999999987754E0L, 1},
- {"tan", tanl, 1.17809724509617241850E0L, 2.41419982910156250000E0L,
- 1.37332715322352112604E-5L, 6.82842712474618858345E0L, 1},
- {"tan", tanl, 1.96349540849362069750E0L, -2.41421508789062500000E0L,
- 1.52551752942854759743E-6L, 6.82842712474619262118E0L, 1},
- {"tan", tanl, 2.35619449019234483700E0L, -1.00001525878906250000E0L,
- 1.52587890623163029801E-5L, 2.00000000000000036739E0L, 1},
- {"tan", tanl, 2.74889357189106897650E0L, -4.14215087890625000000E-1L,
- 1.52551752982565655126E-6L, 1.17157287525381000640E0L, 1},
- {"atan", atanl, 4.14213562373094923430E-1L, 3.92684936523437500000E-1L,
- 1.41451752865477964149E-5L, 8.53553390593273837869E-1L, 1},
- {"atan", atanl, 1.0L, 7.85385131835937500000E-1L,
- 1.30315615108096156608E-5L, 0.5L, 1},
- {"atan", atanl, 2.41421356237309492343E0L, 1.17808532714843750000E0L,
- 1.19179477349460632350E-5L, 1.46446609406726250782E-1L, 1},
- {"atan", atanl, -2.41421356237309514547E0L, -1.17810058593750000000E0L,
- 3.34084132752141908545E-6L, 1.46446609406726227789E-1L, 1},
- {"atan", atanl, -1.0L, -7.85400390625000000000E-1L,
- 2.22722755169038433915E-6L, 0.5L, 1},
- {"atan", atanl, -4.14213562373095145475E-1L, -3.92700195312500000000E-1L,
- 1.11361377576267665972E-6L, 8.53553390593273703853E-1L, 1},
- {"asin", asinl, 3.82683432365089615246E-1L, 3.92684936523437500000E-1L,
- 1.41451752864854321970E-5L, 1.08239220029239389286E0L, 1},
- {"asin", asinl, 0.5L, 5.23590087890625000000E-1L,
- 8.68770767387307710723E-6L, 1.15470053837925152902E0L, 1},
- {"asin", asinl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
- 1.30315615107209645016E-5L, 1.41421356237309492343E0L, 1},
- {"asin", asinl, 9.23879532511286738483E-1L, 1.17808532714843750000E0L,
- 1.19179477349183147612E-5L, 2.61312592975275276483E0L, 1},
- {"asin", asinl, -0.5L, -5.23605346679687500000E-1L,
- 6.57108138862692289277E-6L, 1.15470053837925152902E0L, 1},
- {"acos", acosl, 1.95090322016128192573E-1L, 1.37443542480468750000E0L,
- 1.13611408471185777914E-5L, -1.01959115820831832232E0L, 1},
- {"acos", acosl, 3.82683432365089615246E-1L, 1.17808532714843750000E0L,
- 1.19179477351337991247E-5L, -1.08239220029239389286E0L, 1},
- {"acos", acosl, 0.5L, 1.04719543457031250000E0L,
- 2.11662628524615421446E-6L, -1.15470053837925152902E0L, 1},
- {"acos", acosl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
- 1.30315615108982668201E-5L, -1.41421356237309492343E0L, 1},
- {"acos", acosl, 9.23879532511286738483E-1L, 3.92684936523437500000E-1L,
- 1.41451752867009165605E-5L, -2.61312592975275276483E0L, 1},
- {"acos", acosl, 9.80785280403230430579E-1L, 1.96334838867187500000E-1L,
- 1.47019821746724723933E-5L, -5.12583089548300990774E0L, 1},
- {"acos", acosl, -0.5L, 2.09439086914062500000E0L,
- 4.23325257049230842892E-6L, -1.15470053837925152902E0L, 1},
- {"sinh", sinhl, 1.0L, 1.17518615722656250000E0L,
- 1.50364172389568823819E-5L, 1.54308063481524377848E0L, 1},
- {"sinh", sinhl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
- 4.25947714184369757620E208L, 4.49423283712885057274E307L, 1},
- {"sinh", sinhl, 2.22044604925031308085E-16L, 0.00000000000000000000E0L,
- 2.22044604925031308085E-16L, 1.00000000000000000000E0L, 1},
- {"cosh", coshl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
- 4.25947714184369757620E208L, 4.49423283712885057274E307L, 1},
- {"cosh", coshl, 1.0L, 1.54307556152343750000E0L,
- 5.07329180627847790562E-6L, 1.17520119364380145688E0L, 1},
- {"cosh", coshl, 0.5L, 1.12762451171875000000E0L,
- 1.45348763078522622516E-6L, 5.21095305493747361622E-1L, 1},
- {"tanh", tanhl, 0.5L, 4.62112426757812500000E-1L,
- 4.73050219725850231848E-6L, 7.86447732965927410150E-1L, 1},
- {"tanh", tanhl, 5.49306144334054780032E-1L, 4.99984741210937500000E-1L,
- 1.52587890624507506378E-5L, 7.50000000000000049249E-1L, 1},
- {"tanh", tanhl, 0.625L, 5.54595947265625000000E-1L,
- 3.77508375729399903910E-6L, 6.92419147969988069631E-1L, 1},
- {"asinh", asinhl, 0.5L, 4.81201171875000000000E-1L,
- 1.06531846034474977589E-5L, 8.94427190999915878564E-1L, 1},
- {"asinh", asinhl, 1.0L, 8.81362915039062500000E-1L,
- 1.06719804805252326093E-5L, 7.07106781186547524401E-1L, 1},
- {"asinh", asinhl, 2.0L, 1.44363403320312500000E0L,
- 1.44197568534249327674E-6L, 4.47213595499957939282E-1L, 1},
- {"acosh", acoshl, 2.0L, 1.31695556640625000000E0L,
- 2.33051856670862504635E-6L, 5.77350269189625764509E-1L, 1},
- {"acosh", acoshl, 1.5L, 9.62417602539062500000E-1L,
- 6.04758014439499551783E-6L, 8.94427190999915878564E-1L, 1},
- {"acosh", acoshl, 1.03125L, 2.49343872070312500000E-1L,
- 9.62177257298785143908E-6L, 3.96911150685467059809E0L, 1},
- {"atanh", atanhl, 0.5L, 5.49301147460937500000E-1L,
- 4.99687311734569762262E-6L, 1.33333333333333333333E0L, 1},
-#if 0
- {"gamma", gammal, 1.0L, 1.0L,
- 0.0L, -5.772156649015328606e-1L, 1},
- {"gamma", gammal, 2.0L, 1.0L,
- 0.0L, 4.2278433509846713939e-1L, 1},
- {"gamma", gammal, 3.0L, 2.0L,
- 0.0L, 1.845568670196934279L, 1},
- {"gamma", gammal, 4.0L, 6.0L,
- 0.0L, 7.536706010590802836L, 1},
-#endif
- {"null", NULL, 0.0L, 0.0L, 0.0L, 1},
-};
-
-/* These take care of extra-precise floating point register problems. */
-volatile long double volat1;
-volatile long double volat2;
-
-
-/* Return the next nearest floating point value to X
- in the direction of UPDOWN (+1 or -1).
- (Fails if X is denormalized.) */
-
-long double
-nextval (x, updown)
- long double x;
- int updown;
-{
- long double m;
- int i;
-
- volat1 = x;
- m = 0.25L * MACHEPL * volat1 * updown;
- volat2 = volat1 + m;
- if (volat2 != volat1)
- printf ("successor failed\n");
-
- for (i = 2; i < 10; i++)
- {
- volat2 = volat1 + i * m;
- if (volat1 != volat2)
- return volat2;
- }
-
- printf ("nextval failed\n");
- return volat1;
-}
-
-
-
-
-int
-main ()
-{
- long double (*fun1) (long double);
- int i, j, errs, tests;
- long double x, x0, y, dy, err;
-
- errs = 0;
- tests = 0;
- i = 0;
-
- for (;;)
- {
- fun1 = test1[i].func;
- if (fun1 == NULL)
- break;
- volat1 = test1[i].arg1;
- x0 = volat1;
- x = volat1;
- for (j = 0; j <= NPTS; j++)
- {
- volat1 = x - x0;
- dy = volat1 * test1[i].derivative;
- dy = test1[i].answer2 + dy;
- volat1 = test1[i].answer1 + dy;
- volat2 = (*(fun1)) (x);
- if (volat2 != volat1)
- {
- /* Report difference between program result
- and extended precision function value. */
- err = volat2 - test1[i].answer1;
- err = err - dy;
- err = err / volat1;
- if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL))
- {
- printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
- j, test1[i].name, x, volat2, err);
- errs += 1;
- }
- }
- x = nextval (x, 1);
- tests += 1;
- }
-
- x = x0;
- x = nextval (x, -1);
- for (j = 1; j < NPTS; j++)
- {
- volat1 = x - x0;
- dy = volat1 * test1[i].derivative;
- dy = test1[i].answer2 + dy;
- volat1 = test1[i].answer1 + dy;
- volat2 = (*(fun1)) (x);
- if (volat2 != volat1)
- {
- err = volat2 - test1[i].answer1;
- err = err - dy;
- err = err / volat1;
- if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL))
- {
- printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
- j, test1[i].name, x, volat2, err);
- errs += 1;
- }
- }
- x = nextval (x, -1);
- tests += 1;
- }
- i += 1;
- }
- printf ("%d errors in %d tests\n", errs, tests);
-}
+++ /dev/null
-/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * int mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file mconf.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * mconf.h
- *
- */
-\f
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <stdio.h>
-#include <math.h>
-
-int merror = 0;
-
-/* Notice: the order of appearance of the following
- * messages is bound to the error codes defined
- * in mconf.h.
- */
-static char *ermsg[7] = {
-"unknown", /* error code 0 */
-"domain", /* error code 1 */
-"singularity", /* et seq. */
-"overflow",
-"underflow",
-"total loss of precision",
-"partial loss of precision"
-};
-
-
-int mtherr( name, code )
-char *name;
-int code;
-{
-
-/* Display string passed by calling program,
- * which is supposed to be the name of the
- * function in which the error occurred:
- */
-printf( "\n%s ", name );
-
-/* Set global error message word */
-merror = code;
-
-/* Display error message defined
- * by the code argument.
- */
-if( (code <= 0) || (code >= 7) )
- code = 0;
-printf( "%s error\n", ermsg[code] );
-
-/* Return to calling
- * program
- */
-return( 0 );
-}
+++ /dev/null
-/* mtst.c
- Consistency tests for math functions.
-
- With NTRIALS=10000, the following are typical results for
- an alleged IEEE long double precision arithmetic:
-
-Consistency test of math functions.
-Max and rms errors for 10000 random arguments.
-A = absolute error criterion (but relative if >1):
-Otherwise, estimate is of relative error
-x = cbrt( cube(x) ): max = 7.65E-20 rms = 4.39E-21
-x = atan( tan(x) ): max = 2.01E-19 rms = 3.96E-20
-x = sin( asin(x) ): max = 2.15E-19 rms = 3.00E-20
-x = sqrt( square(x) ): max = 0.00E+00 rms = 0.00E+00
-x = log( exp(x) ): max = 5.42E-20 A rms = 1.87E-21 A
-x = log2( exp2(x) ): max = 1.08E-19 A rms = 3.37E-21 A
-x = log10( exp10(x) ): max = 2.71E-20 A rms = 6.76E-22 A
-x = acosh( cosh(x) ): max = 3.13E-18 A rms = 3.21E-20 A
-x = pow( pow(x,a),1/a ): max = 1.25E-17 rms = 1.70E-19
-x = tanh( atanh(x) ): max = 1.08E-19 rms = 1.16E-20
-x = asinh( sinh(x) ): max = 1.03E-19 rms = 2.94E-21
-x = cos( acos(x) ): max = 1.63E-19 A rms = 4.37E-20 A
-lgam(x) = log(gamma(x)): max = 2.31E-19 A rms = 5.93E-20 A
-x = ndtri( ndtr(x) ): max = 5.07E-17 rms = 7.03E-19
-Legendre ellpk, ellpe: max = 7.59E-19 A rms = 1.72E-19 A
-Absolute error and only 2000 trials:
-Wronksian of Yn, Jn: max = 6.40E-18 A rms = 1.49E-19 A
-Relative error and only 100 trials:
-x = stdtri(stdtr(k,x) ): max = 6.73E-19 rms = 2.46E-19
-*/
-
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1984, 1987, 1988, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-/* C9X spells lgam lgamma. */
-#define GLIBC2 0
-
-#define NTRIALS 10000
-#define WTRIALS (NTRIALS/5)
-#define STRTST 0
-
-/* Note, fabsl may be an intrinsic function. */
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double sqrtl ( long double );
-extern long double cbrtl ( long double );
-extern long double expl ( long double );
-extern long double logl ( long double );
-extern long double tanl ( long double );
-extern long double atanl ( long double );
-extern long double sinl ( long double );
-extern long double asinl ( long double );
-extern long double cosl ( long double );
-extern long double acosl ( long double );
-extern long double powl ( long double, long double );
-extern long double tanhl ( long double );
-extern long double atanhl ( long double );
-extern long double sinhl ( long double );
-extern long double asinhl ( long double );
-extern long double coshl ( long double );
-extern long double acoshl ( long double );
-extern long double exp2l ( long double );
-extern long double log2l ( long double );
-extern long double exp10l ( long double );
-extern long double log10l ( long double );
-extern long double gammal ( long double );
-extern long double lgaml ( long double );
-extern long double jnl ( int, long double );
-extern long double ynl ( int, long double );
-extern long double ndtrl ( long double );
-extern long double ndtril ( long double );
-extern long double stdtrl ( int, long double );
-extern long double stdtril ( int, long double );
-extern long double ellpel ( long double );
-extern long double ellpkl ( long double );
-extern void exit (int);
-#else
-long double fabsl(), sqrtl();
-long double cbrtl(), expl(), logl(), tanl(), atanl();
-long double sinl(), asinl(), cosl(), acosl(), powl();
-long double tanhl(), atanhl(), sinhl(), asinhl(), coshl(), acoshl();
-long double exp2l(), log2l(), exp10l(), log10l();
-long double gammal(), lgaml(), jnl(), ynl(), ndtrl(), ndtril();
-long double stdtrl(), stdtril(), ellpel(), ellpkl();
-void exit ();
-#endif
-extern int merror;
-#if GLIBC2
-long double lgammal(long double);
-#endif
-/*
-NYI:
-double iv(), kn();
-*/
-
-/* Provide inverses for square root and cube root: */
-long double squarel(x)
-long double x;
-{
-return( x * x );
-}
-
-long double cubel(x)
-long double x;
-{
-return( x * x * x );
-}
-
-/* lookup table for each function */
-struct fundef
- {
- char *nam1; /* the function */
- long double (*name )();
- char *nam2; /* its inverse */
- long double (*inv )();
- int nargs; /* number of function arguments */
- int tstyp; /* type code of the function */
- long ctrl; /* relative error flag */
- long double arg1w; /* width of domain for 1st arg */
- long double arg1l; /* lower bound domain 1st arg */
- long arg1f; /* flags, e.g. integer arg */
- long double arg2w; /* same info for args 2, 3, 4 */
- long double arg2l;
- long arg2f;
-/*
- double arg3w;
- double arg3l;
- long arg3f;
- double arg4w;
- double arg4l;
- long arg4f;
-*/
- };
-
-
-/* fundef.ctrl bits: */
-#define RELERR 1
-#define EXPSCAL 4
-
-/* fundef.tstyp test types: */
-#define POWER 1
-#define ELLIP 2
-#define GAMMA 3
-#define WRONK1 4
-#define WRONK2 5
-#define WRONK3 6
-#define STDTR 7
-
-/* fundef.argNf argument flag bits: */
-#define INT 2
-
-extern long double MINLOGL;
-extern long double MAXLOGL;
-extern long double PIL;
-extern long double PIO2L;
-/*
-define MINLOG -170.0
-define MAXLOG +170.0
-define PI 3.14159265358979323846
-define PIO2 1.570796326794896619
-*/
-
-#define NTESTS 17
-struct fundef defs[NTESTS] = {
-{" cube", cubel, " cbrt", cbrtl, 1, 0, 1, 2000.0L, -1000.0L, 0,
-0.0, 0.0, 0},
-{" tan", tanl, " atan", atanl, 1, 0, 1, 0.0L, 0.0L, 0,
-0.0, 0.0, 0},
-{" asin", asinl, " sin", sinl, 1, 0, 1, 2.0L, -1.0L, 0,
-0.0, 0.0, 0},
-{"square", squarel, " sqrt", sqrtl, 1, 0, 1, 170.0L, -85.0L, EXPSCAL,
-0.0, 0.0, 0},
-{" exp", expl, " log", logl, 1, 0, 0, 340.0L, -170.0L, 0,
-0.0, 0.0, 0},
-{" exp2", exp2l, " log2", log2l, 1, 0, 0, 340.0L, -170.0L, 0,
-0.0, 0.0, 0},
-{" exp10", exp10l, " log10", log10l, 1, 0, 0, 340.0L, -170.0L, 0,
-0.0, 0.0, 0},
-{" cosh", coshl, " acosh", acoshl, 1, 0, 0, 340.0L, 0.0L, 0,
-0.0, 0.0, 0},
-{"pow", powl, "pow", powl, 2, POWER, 1, 25.0L, 0.0L, 0,
-50.0, -25.0, 0},
-{" atanh", atanhl, " tanh", tanhl, 1, 0, 1, 2.0L, -1.0L, 0,
-0.0, 0.0, 0},
-{" sinh", sinhl, " asinh", asinhl, 1, 0, 1, 340.0L, 0.0L, 0,
-0.0, 0.0, 0},
-{" acos", acosl, " cos", cosl, 1, 0, 0, 2.0L, -1.0L, 0,
-0.0, 0.0, 0},
-#if GLIBC2
- /*
-{ "gamma", gammal, "lgammal", lgammal, 1, GAMMA, 0, 34.0, 0.0, 0,
-0.0, 0.0, 0},
-*/
-#else
-{ "gamma", gammal, "lgam", lgaml, 1, GAMMA, 0, 34.0, 0.0, 0,
-0.0, 0.0, 0},
-{ " ndtr", ndtrl, " ndtri", ndtril, 1, 0, 1, 10.0L, -10.0L, 0,
-0.0, 0.0, 0},
-{" ellpe", ellpel, " ellpk", ellpkl, 1, ELLIP, 0, 1.0L, 0.0L, 0,
-0.0, 0.0, 0},
-{ "stdtr", stdtrl, "stdtri", stdtril, 2, STDTR, 1, 4.0L, -2.0L, 0,
-30.0, 1.0, INT},
-{ " Jn", jnl, " Yn", ynl, 2, WRONK1, 0, 30.0, 0.1, 0,
-40.0, -20.0, INT},
-#endif
-};
-
-static char *headrs[] = {
-"x = %s( %s(x) ): ",
-"x = %s( %s(x,a),1/a ): ", /* power */
-"Legendre %s, %s: ", /* ellip */
-"%s(x) = log(%s(x)): ", /* gamma */
-"Wronksian of %s, %s: ", /* wronk1 */
-"Wronksian of %s, %s: ", /* wronk2 */
-"Wronksian of %s, %s: ", /* wronk3 */
-"x = %s(%s(k,x) ): ", /* stdtr */
-};
-
-static long double y1 = 0.0;
-static long double y2 = 0.0;
-static long double y3 = 0.0;
-static long double y4 = 0.0;
-static long double a = 0.0;
-static long double x = 0.0;
-static long double y = 0.0;
-static long double z = 0.0;
-static long double e = 0.0;
-static long double max = 0.0;
-static long double rmsa = 0.0;
-static long double rms = 0.0;
-static long double ave = 0.0;
-static double da, db, dc, dd;
-
-int ldrand();
-int printf();
-
-int
-main()
-{
-long double (*fun )();
-long double (*ifun )();
-struct fundef *d;
-int i, k, itst;
-int m, ntr;
-
-ntr = NTRIALS;
-printf( "Consistency test of math functions.\n" );
-printf( "Max and rms errors for %d random arguments.\n",
- ntr );
-printf( "A = absolute error criterion (but relative if >1):\n" );
-printf( "Otherwise, estimate is of relative error\n" );
-
-/* Initialize machine dependent parameters to test near the
- * largest an smallest possible arguments. To compare different
- * machines, use the same test intervals for all systems.
- */
-defs[1].arg1w = PIL;
-defs[1].arg1l = -PIL/2.0;
-/*
-defs[3].arg1w = MAXLOGL;
-defs[3].arg1l = -MAXLOGL/2.0;
-defs[4].arg1w = 2.0*MAXLOGL;
-defs[4].arg1l = -MAXLOGL;
-defs[6].arg1w = 2.0*MAXLOGL;
-defs[6].arg1l = -MAXLOGL;
-defs[7].arg1w = MAXLOGL;
-defs[7].arg1l = 0.0;
-*/
-
-/* Outer loop, on the test number: */
-
-for( itst=STRTST; itst<NTESTS; itst++ )
-{
-d = &defs[itst];
-m = 0;
-max = 0.0L;
-rmsa = 0.0L;
-ave = 0.0L;
-fun = d->name;
-ifun = d->inv;
-
-/* Smaller number of trials for Wronksians
- * (put them at end of list)
- */
-if( d->tstyp == WRONK1 )
- {
- ntr = WTRIALS;
- printf( "Absolute error and only %d trials:\n", ntr );
- }
-else if( d->tstyp == STDTR )
- {
- ntr = NTRIALS/100;
- printf( "Relative error and only %d trials:\n", ntr );
- }
-/*
-y1 = d->arg1l;
-y2 = d->arg1w;
-da = y1;
-db = y2;
-printf( "arg1l = %.4e, arg1w = %.4e\n", da, db );
-*/
-printf( headrs[d->tstyp], d->nam2, d->nam1 );
-
-for( i=0; i<ntr; i++ )
-{
-m++;
-k = 0;
-/* make random number(s) in desired range(s) */
-switch( d->nargs )
-{
-
-default:
-goto illegn;
-
-case 2:
-ldrand( &a );
-a = d->arg2w * ( a - 1.0L ) + d->arg2l;
-if( d->arg2f & EXPSCAL )
- {
- a = expl(a);
- ldrand( &y2 );
- a -= 1.0e-13L * a * (y2 - 1.0L);
- }
-if( d->arg2f & INT )
- {
- k = a + 0.25L;
- a = k;
- }
-
-case 1:
-ldrand( &x );
-y1 = d->arg1l;
-y2 = d->arg1w;
-x = y2 * ( x - 1.0L ) + y1;
-if( x < y1 )
- x = y1;
-y1 += y2;
-if( x > y1 )
- x = y1;
-if( d->arg1f & EXPSCAL )
- {
- x = expl(x);
- ldrand( &y2 );
- x += 1.0e-13L * x * (y2 - 1.0L);
- }
-}
-
-/* compute function under test */
-switch( d->nargs )
- {
- case 1:
- switch( d->tstyp )
- {
- case ELLIP:
- y1 = ( *(fun) )(x);
- y2 = ( *(fun) )(1.0L-x);
- y3 = ( *(ifun) )(x);
- y4 = ( *(ifun) )(1.0L-x);
- break;
-#if 1
- case GAMMA:
- y = lgaml(x);
- x = logl( gammal(x) );
- break;
-#endif
- default:
- z = ( *(fun) )(x);
- y = ( *(ifun) )(z);
- }
-/*
-if( merror )
- {
- printf( "error: x = %.15e, z = %.15e, y = %.15e\n",
- (double )x, (double )z, (double )y );
- }
-*/
- break;
-
- case 2:
- if( d->arg2f & INT )
- {
- switch( d->tstyp )
- {
- case WRONK1:
- y1 = (*fun)( k, x ); /* jn */
- y2 = (*fun)( k+1, x );
- y3 = (*ifun)( k, x ); /* yn */
- y4 = (*ifun)( k+1, x );
- break;
-
- case WRONK2:
- y1 = (*fun)( a, x ); /* iv */
- y2 = (*fun)( a+1.0L, x );
- y3 = (*ifun)( k, x ); /* kn */
- y4 = (*ifun)( k+1, x );
- break;
-
- default:
- z = (*fun)( k, x );
- y = (*ifun)( k, z );
- }
- }
- else
- {
- if( d->tstyp == POWER )
- {
- z = (*fun)( x, a );
- y = (*ifun)( z, 1.0L/a );
- }
- else
- {
- z = (*fun)( a, x );
- y = (*ifun)( a, z );
- }
- }
- break;
-
-
- default:
-illegn:
- printf( "Illegal nargs= %d", d->nargs );
- exit(1);
- }
-
-switch( d->tstyp )
- {
- case WRONK1:
- /* Jn, Yn */
-/* e = (y2*y3 - y1*y4) - 2.0L/(PIL*x);*/
- e = x*(y2*y3 - y1*y4) - 2.0L/PIL;
- break;
-
- case WRONK2:
-/* In, Kn */
-/* e = (y2*y3 + y1*y4) - 1.0L/x; */
- e = x*(y2*y3 + y1*y4) - 1.0L;
- break;
-
- case ELLIP:
- e = (y1-y3)*y4 + y3*y2 - PIO2L;
- break;
-
- default:
- e = y - x;
- break;
- }
-
-if( d->ctrl & RELERR )
- {
- if( x != 0.0L )
- e /= x;
- else
- printf( "warning, x == 0\n" );
- }
-else
- {
- if( fabsl(x) > 1.0L )
- e /= x;
- }
-
-ave += e;
-/* absolute value of error */
-if( e < 0 )
- e = -e;
-
-/* peak detect the error */
-if( e > max )
- {
- max = e;
-
- if( e > 1.0e-10L )
- {
-da = x;
-db = z;
-dc = y;
-dd = max;
- printf("x %.6E z %.6E y %.6E max %.4E\n",
- da, db, dc, dd );
-/*
- if( d->tstyp >= WRONK1 )
- {
- printf( "y1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
- (double )y1, (double )y2, (double )y3,
- (double )y4, k, (double )x );
- }
-*/
- }
-
-/*
- printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
- printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
- printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
- printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
- printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
- a, b, c, x, y, max, n);
-*/
- }
-
-/* accumulate rms error */
-e *= 1.0e16L; /* adjust range */
-rmsa += e * e; /* accumulate the square of the error */
-}
-
-/* report after NTRIALS trials */
-rms = 1.0e-16L * sqrtl( rmsa/m );
-da = max;
-db = rms;
-if(d->ctrl & RELERR)
- printf(" max = %.2E rms = %.2E\n", da, db );
-else
- printf(" max = %.2E A rms = %.2E A\n", da, db );
-} /* loop on itst */
-
-exit (0);
-return 0;
-}
-
+++ /dev/null
-#include <stdio.h>
-long double inf = 1.0f/0.0f;
-long double nnn = 1.0f/0.0f - 1.0f/0.0f;
-long double fin = 1.0f;
-long double neg = -1.0f;
-long double nn2;
-
-int isnanl(), isfinitel(), signbitl();
-void abort (void);
-void exit (int);
-
-void pvalue (char *str, long double x)
-{
-union
- {
- long double f;
- unsigned int i[3];
- }u;
-int k;
-
-printf("%s ", str);
-u.f = x;
-for (k = 0; k < 3; k++)
- printf("%08x ", u.i[k]);
-printf ("\n");
-}
-
-
-int
-main()
-{
-
-if (!isnanl(nnn))
- abort();
-pvalue("nnn", nnn);
-pvalue("inf", inf);
-nn2 = inf - inf;
-pvalue("inf - inf", nn2);
-if (isnanl(fin))
- abort();
-if (isnanl(inf))
- abort();
-if (!isfinitel(fin))
- abort();
-if (isfinitel(nnn))
- abort();
-if (isfinitel(inf))
- abort();
-if (!signbitl(neg))
- abort();
-if (signbitl(fin))
- abort();
-if (signbitl(inf))
- abort();
-/*
-if (signbitf(nnn))
- abort();
- */
-exit (0);
-return 0;
-}
+++ /dev/null
-/* nbdtrl.c
- *
- * Negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, nbdtrl();
- *
- * y = nbdtrl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms 0 through k of the negative
- * binomial distribution:
- *
- * k
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=0
- *
- * In a sequence of Bernoulli trials, this is the probability
- * that k or fewer failures precede the nth success.
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at random points (k,n,p) with k and n between 1 and 10,000
- * and p between 0 and 1.
- *
- * arithmetic domain # trials peak rms
- * Absolute error:
- * IEEE 0,10000 10000 9.8e-15 2.1e-16
- *
- */
-\f/* nbdtrcl.c
- *
- * Complemented negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, nbdtrcl();
- *
- * y = nbdtrcl( k, n, p );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the negative
- * binomial distribution:
- *
- * inf
- * -- ( n+j-1 ) n j
- * > ( ) p (1-p)
- * -- ( j )
- * j=k+1
- *
- * The terms are not computed individually; instead the incomplete
- * beta integral is employed, according to the formula
- *
- * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
- *
- * The arguments must be positive, with p ranging from 0 to 1.
- *
- *
- *
- * ACCURACY:
- *
- * See incbetl.c.
- *
- */
-\f/* nbdtril
- *
- * Functional inverse of negative binomial distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k, n;
- * long double p, y, nbdtril();
- *
- * p = nbdtril( k, n, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the argument p such that nbdtr(k,n,p) is equal to y.
- *
- * ACCURACY:
- *
- * Tested at random points (a,b,y), with y between 0 and 1.
- *
- * a,b Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,100
- * See also incbil.c.
- */
-\f
-/*
-Cephes Math Library Release 2.3: January,1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double incbetl ( long double, long double, long double );
-extern long double powl ( long double, long double );
-extern long double incbil ( long double, long double, long double );
-#else
-long double incbetl(), powl(), incbil();
-#endif
-
-long double nbdtrcl( k, n, p )
-int k, n;
-long double p;
-{
-long double dk, dn;
-
-if( (p < 0.0L) || (p > 1.0L) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtrl", DOMAIN );
- return( 0.0L );
- }
-dn = n;
-if( k == 0 )
- return( 1.0L - powl( p, dn ) );
-
-dk = k+1;
-return( incbetl( dk, dn, 1.0L - p ) );
-}
-
-
-
-long double nbdtrl( k, n, p )
-int k, n;
-long double p;
-{
-long double dk, dn;
-
-if( (p < 0.0L) || (p > 1.0L) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtrl", DOMAIN );
- return( 0.0L );
- }
-dn = n;
-if( k == 0 )
- return( powl( p, dn ) );
-
-dk = k+1;
-return( incbetl( dn, dk, p ) );
-}
-
-
-long double nbdtril( k, n, p )
-int k, n;
-long double p;
-{
-long double dk, dn, w;
-
-if( (p < 0.0L) || (p > 1.0L) )
- goto domerr;
-if( k < 0 )
- {
-domerr:
- mtherr( "nbdtrl", DOMAIN );
- return( 0.0L );
- }
-dk = k+1;
-dn = n;
-w = incbil( dn, dk, p );
-return( w );
-}
+++ /dev/null
-/* ndtril.c
- *
- * Inverse of Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, ndtril();
- *
- * x = ndtril( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2 log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z) .
- * For larger arguments, x/sqrt(2 pi) = w + w^3 R(w^2)/S(w^2)) ,
- * where w = y - 0.5 .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * Arguments uniformly distributed:
- * IEEE 0, 1 5000 7.8e-19 9.9e-20
- * Arguments exponentially distributed:
- * IEEE exp(-11355),-1 30000 1.7e-19 4.3e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtril domain x <= 0 -MAXNUML
- * ndtril domain x >= 1 MAXNUML
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: January, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-extern long double MAXNUML;
-
-/* ndtri(y+0.5)/sqrt(2 pi) = y + y^3 R(y^2)
- 0 <= y <= 3/8
- Peak relative error 6.8e-21. */
-#if UNK
-/* sqrt(2pi) */
-static long double s2pi = 2.506628274631000502416E0L;
-static long double P0[8] = {
- 8.779679420055069160496E-3L,
--7.649544967784380691785E-1L,
- 2.971493676711545292135E0L,
--4.144980036933753828858E0L,
- 2.765359913000830285937E0L,
--9.570456817794268907847E-1L,
- 1.659219375097958322098E-1L,
--1.140013969885358273307E-2L,
-};
-static long double Q0[7] = {
-/* 1.000000000000000000000E0L, */
--5.303846964603721860329E0L,
- 9.908875375256718220854E0L,
--9.031318655459381388888E0L,
- 4.496118508523213950686E0L,
--1.250016921424819972516E0L,
- 1.823840725000038842075E-1L,
--1.088633151006419263153E-2L,
-};
-#endif
-#if IBMPC
-static unsigned short s2p[] = {
-0x2cb3,0xb138,0x98ff,0xa06c,0x4000, XPD
-};
-#define s2pi *(long double *)s2p
-static short P0[] = {
-0xb006,0x9fc1,0xa4fe,0x8fd8,0x3ff8, XPD
-0x6f8a,0x976e,0x0ed2,0xc3d4,0xbffe, XPD
-0xf1f1,0x6fcc,0xf3d0,0xbe2c,0x4000, XPD
-0xccfb,0xa681,0xad2c,0x84a3,0xc001, XPD
-0x9a0d,0x0082,0xa825,0xb0fb,0x4000, XPD
-0x13d1,0x054a,0xf220,0xf500,0xbffe, XPD
-0xcee9,0x2c92,0x70bd,0xa9e7,0x3ffc, XPD
-0x5fee,0x4a42,0xa6cb,0xbac7,0xbff8, XPD
-};
-static short Q0[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0x841e,0xfec7,0x1d44,0xa9b9,0xc001, XPD
-0x97e6,0xcde0,0xc0e7,0x9e8a,0x4002, XPD
-0x66f9,0x8f3e,0x47fd,0x9080,0xc002, XPD
-0x212f,0x2185,0x33ec,0x8fe0,0x4001, XPD
-0x8e73,0x7bac,0x8df2,0xa000,0xbfff, XPD
-0xc143,0xcb94,0xe3ea,0xbac2,0x3ffc, XPD
-0x25d9,0xc8f3,0x9573,0xb25c,0xbff8, XPD
-};
-#endif
-#if MIEEE
-static unsigned long s2p[] = {
-0x40000000,0xa06c98ff,0xb1382cb3,
-};
-#define s2pi *(long double *)s2p
-static long P0[24] = {
-0x3ff80000,0x8fd8a4fe,0x9fc1b006,
-0xbffe0000,0xc3d40ed2,0x976e6f8a,
-0x40000000,0xbe2cf3d0,0x6fccf1f1,
-0xc0010000,0x84a3ad2c,0xa681ccfb,
-0x40000000,0xb0fba825,0x00829a0d,
-0xbffe0000,0xf500f220,0x054a13d1,
-0x3ffc0000,0xa9e770bd,0x2c92cee9,
-0xbff80000,0xbac7a6cb,0x4a425fee,
-};
-static long Q0[21] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0xc0010000,0xa9b91d44,0xfec7841e,
-0x40020000,0x9e8ac0e7,0xcde097e6,
-0xc0020000,0x908047fd,0x8f3e66f9,
-0x40010000,0x8fe033ec,0x2185212f,
-0xbfff0000,0xa0008df2,0x7bac8e73,
-0x3ffc0000,0xbac2e3ea,0xcb94c143,
-0xbff80000,0xb25c9573,0xc8f325d9,
-};
-#endif
-
-/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
- */
-/* ndtri(p) = z - ln(z)/z - 1/z P1(1/z)/Q1(1/z)
- z = sqrt(-2 ln(p))
- 2 <= z <= 8, i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
- Peak relative error 5.3e-21 */
-#if UNK
-static long double P1[10] = {
- 4.302849750435552180717E0L,
- 4.360209451837096682600E1L,
- 9.454613328844768318162E1L,
- 9.336735653151873871756E1L,
- 5.305046472191852391737E1L,
- 1.775851836288460008093E1L,
- 3.640308340137013109859E0L,
- 3.691354900171224122390E-1L,
- 1.403530274998072987187E-2L,
- 1.377145111380960566197E-4L,
-};
-static long double Q1[9] = {
-/* 1.000000000000000000000E0L, */
- 2.001425109170530136741E1L,
- 7.079893963891488254284E1L,
- 8.033277265194672063478E1L,
- 5.034715121553662712917E1L,
- 1.779820137342627204153E1L,
- 3.845554944954699547539E0L,
- 3.993627390181238962857E-1L,
- 1.526870689522191191380E-2L,
- 1.498700676286675466900E-4L,
-};
-#endif
-#if IBMPC
-static short P1[] = {
-0x6105,0xb71e,0xf1f5,0x89b0,0x4001, XPD
-0x461d,0x2604,0x8b77,0xae68,0x4004, XPD
-0x8b33,0x4a47,0x9ec8,0xbd17,0x4005, XPD
-0xa0b2,0xc1b0,0x1627,0xbabc,0x4005, XPD
-0x9901,0x28f7,0xad06,0xd433,0x4004, XPD
-0xddcb,0x5009,0x7213,0x8e11,0x4003, XPD
-0x2432,0x0fa6,0xcfd5,0xe8fa,0x4000, XPD
-0x3e24,0xd53c,0x53b2,0xbcff,0x3ffd, XPD
-0x4058,0x3d75,0x5393,0xe5f4,0x3ff8, XPD
-0x1789,0xf50a,0x7524,0x9067,0x3ff2, XPD
-};
-static short Q1[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0xd901,0x2673,0x2fad,0xa01d,0x4003, XPD
-0x24f5,0xc93c,0x0e9d,0x8d99,0x4005, XPD
-0x8cda,0x523a,0x612d,0xa0aa,0x4005, XPD
-0x602c,0xb5fc,0x7b9b,0xc963,0x4004, XPD
-0xac72,0xd3e7,0xb766,0x8e62,0x4003, XPD
-0x048e,0xe34c,0x927c,0xf61d,0x4000, XPD
-0x6d88,0xa5cc,0x45de,0xcc79,0x3ffd, XPD
-0xe6d1,0x199a,0x9931,0xfa29,0x3ff8, XPD
-0x4c7d,0x3675,0x70a0,0x9d26,0x3ff2, XPD
-};
-#endif
-#if MIEEE
-static long P1[30] = {
-0x40010000,0x89b0f1f5,0xb71e6105,
-0x40040000,0xae688b77,0x2604461d,
-0x40050000,0xbd179ec8,0x4a478b33,
-0x40050000,0xbabc1627,0xc1b0a0b2,
-0x40040000,0xd433ad06,0x28f79901,
-0x40030000,0x8e117213,0x5009ddcb,
-0x40000000,0xe8facfd5,0x0fa62432,
-0x3ffd0000,0xbcff53b2,0xd53c3e24,
-0x3ff80000,0xe5f45393,0x3d754058,
-0x3ff20000,0x90677524,0xf50a1789,
-};
-static long Q1[27] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40030000,0xa01d2fad,0x2673d901,
-0x40050000,0x8d990e9d,0xc93c24f5,
-0x40050000,0xa0aa612d,0x523a8cda,
-0x40040000,0xc9637b9b,0xb5fc602c,
-0x40030000,0x8e62b766,0xd3e7ac72,
-0x40000000,0xf61d927c,0xe34c048e,
-0x3ffd0000,0xcc7945de,0xa5cc6d88,
-0x3ff80000,0xfa299931,0x199ae6d1,
-0x3ff20000,0x9d2670a0,0x36754c7d,
-};
-#endif
-
-/* ndtri(x) = z - ln(z)/z - 1/z P2(1/z)/Q2(1/z)
- z = sqrt(-2 ln(y))
- 8 <= z <= 32
- i.e., y between exp(-32) = 1.27e-14 and exp(-512) = 4.38e-223
- Peak relative error 1.0e-21 */
-#if UNK
-static long double P2[8] = {
- 3.244525725312906932464E0L,
- 6.856256488128415760904E0L,
- 3.765479340423144482796E0L,
- 1.240893301734538935324E0L,
- 1.740282292791367834724E-1L,
- 9.082834200993107441750E-3L,
- 1.617870121822776093899E-4L,
- 7.377405643054504178605E-7L,
-};
-static long double Q2[7] = {
-/* 1.000000000000000000000E0L, */
- 6.021509481727510630722E0L,
- 3.528463857156936773982E0L,
- 1.289185315656302878699E0L,
- 1.874290142615703609510E-1L,
- 9.867655920899636109122E-3L,
- 1.760452434084258930442E-4L,
- 8.028288500688538331773E-7L,
-};
-#endif
-#if IBMPC
-static short P2[] = {
-0xafb1,0x4ff9,0x4f3a,0xcfa6,0x4000, XPD
-0xbd81,0xaffa,0x7401,0xdb66,0x4001, XPD
-0x3a32,0x3863,0x9d0f,0xf0fd,0x4000, XPD
-0x300e,0x633d,0x977a,0x9ed5,0x3fff, XPD
-0xea3a,0x56b6,0x74c5,0xb234,0x3ffc, XPD
-0x38c6,0x49d2,0x2af6,0x94d0,0x3ff8, XPD
-0xc85d,0xe17d,0x5ed1,0xa9a5,0x3ff2, XPD
-0x536c,0x808b,0x2542,0xc609,0x3fea, XPD
-};
-static short Q2[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0xaabd,0x125a,0x34a7,0xc0b0,0x4001, XPD
-0x0ded,0xe6da,0x5a11,0xe1d2,0x4000, XPD
-0xc742,0x9d16,0x0640,0xa504,0x3fff, XPD
-0xea1e,0x4cc2,0x643a,0xbfed,0x3ffc, XPD
-0x7a9b,0xfaff,0xf2dd,0xa1ab,0x3ff8, XPD
-0xfd90,0x4688,0xc902,0xb898,0x3ff2, XPD
-0xf003,0x032a,0xfa7e,0xd781,0x3fea, XPD
-};
-#endif
-#if MIEEE
-static long P2[24] = {
-0x40000000,0xcfa64f3a,0x4ff9afb1,
-0x40010000,0xdb667401,0xaffabd81,
-0x40000000,0xf0fd9d0f,0x38633a32,
-0x3fff0000,0x9ed5977a,0x633d300e,
-0x3ffc0000,0xb23474c5,0x56b6ea3a,
-0x3ff80000,0x94d02af6,0x49d238c6,
-0x3ff20000,0xa9a55ed1,0xe17dc85d,
-0x3fea0000,0xc6092542,0x808b536c,
-};
-static long Q2[21] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40010000,0xc0b034a7,0x125aaabd,
-0x40000000,0xe1d25a11,0xe6da0ded,
-0x3fff0000,0xa5040640,0x9d16c742,
-0x3ffc0000,0xbfed643a,0x4cc2ea1e,
-0x3ff80000,0xa1abf2dd,0xfaff7a9b,
-0x3ff20000,0xb898c902,0x4688fd90,
-0x3fea0000,0xd781fa7e,0x032af003,
-};
-#endif
-
-/* ndtri(x) = z - ln(z)/z - 1/z P3(1/z)/Q3(1/z)
- 32 < z < 2048/13
- Peak relative error 1.4e-20 */
-#if UNK
-static long double P3[8] = {
- 2.020331091302772535752E0L,
- 2.133020661587413053144E0L,
- 2.114822217898707063183E-1L,
--6.500909615246067985872E-3L,
--7.279315200737344309241E-4L,
--1.275404675610280787619E-5L,
--6.433966387613344714022E-8L,
--7.772828380948163386917E-11L,
-};
-static long double Q3[7] = {
-/* 1.000000000000000000000E0L, */
- 2.278210997153449199574E0L,
- 2.345321838870438196534E-1L,
--6.916708899719964982855E-3L,
--7.908542088737858288849E-4L,
--1.387652389480217178984E-5L,
--7.001476867559193780666E-8L,
--8.458494263787680376729E-11L,
-};
-#endif
-#if IBMPC
-static short P3[] = {
-0x87b2,0x0f31,0x1ac7,0x814d,0x4000, XPD
-0x491c,0xcd74,0x6917,0x8883,0x4000, XPD
-0x935e,0x1776,0xcba9,0xd88e,0x3ffc, XPD
-0xbafd,0x8abb,0x9518,0xd505,0xbff7, XPD
-0xc87e,0x2ed3,0xa84a,0xbed2,0xbff4, XPD
-0x0094,0xa402,0x36b5,0xd5fa,0xbfee, XPD
-0xbc53,0x0fc3,0x1ab2,0x8a2b,0xbfe7, XPD
-0x30b4,0x71c0,0x223d,0xaaed,0xbfdd, XPD
-};
-static short Q3[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0xdfc1,0x8a57,0x357f,0x91ce,0x4000, XPD
-0xcc4f,0x9e03,0x346e,0xf029,0x3ffc, XPD
-0x38b1,0x9788,0x8f42,0xe2a5,0xbff7, XPD
-0xb281,0x2117,0x53da,0xcf51,0xbff4, XPD
-0xf2ab,0x1d42,0x3760,0xe8cf,0xbfee, XPD
-0x741b,0xf14f,0x06b0,0x965b,0xbfe7, XPD
-0x37c2,0xa91f,0x16ea,0xba01,0xbfdd, XPD
-};
-#endif
-#if MIEEE
-static long P3[24] = {
-0x40000000,0x814d1ac7,0x0f3187b2,
-0x40000000,0x88836917,0xcd74491c,
-0x3ffc0000,0xd88ecba9,0x1776935e,
-0xbff70000,0xd5059518,0x8abbbafd,
-0xbff40000,0xbed2a84a,0x2ed3c87e,
-0xbfee0000,0xd5fa36b5,0xa4020094,
-0xbfe70000,0x8a2b1ab2,0x0fc3bc53,
-0xbfdd0000,0xaaed223d,0x71c030b4,
-};
-static long Q3[21] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40000000,0x91ce357f,0x8a57dfc1,
-0x3ffc0000,0xf029346e,0x9e03cc4f,
-0xbff70000,0xe2a58f42,0x978838b1,
-0xbff40000,0xcf5153da,0x2117b281,
-0xbfee0000,0xe8cf3760,0x1d42f2ab,
-0xbfe70000,0x965b06b0,0xf14f741b,
-0xbfdd0000,0xba0116ea,0xa91f37c2,
-};
-#endif
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double logl ( long double );
-extern long double sqrtl ( long double );
-#else
-long double polevll(), p1evll(), logl(), sqrtl();
-#endif
-
-long double ndtril(y0)
-long double y0;
-{
-long double x, y, z, y2, x0, x1;
-int code;
-
-if( y0 <= 0.0L )
- {
- mtherr( "ndtril", DOMAIN );
- return( -MAXNUML );
- }
-if( y0 >= 1.0L )
- {
- mtherr( "ndtri", DOMAIN );
- return( MAXNUML );
- }
-code = 1;
-y = y0;
-if( y > (1.0L - 0.13533528323661269189L) ) /* 0.135... = exp(-2) */
- {
- y = 1.0L - y;
- code = 0;
- }
-
-if( y > 0.13533528323661269189L )
- {
- y = y - 0.5L;
- y2 = y * y;
- x = y + y * (y2 * polevll( y2, P0, 7 )/p1evll( y2, Q0, 7 ));
- x = x * s2pi;
- return(x);
- }
-
-x = sqrtl( -2.0L * logl(y) );
-x0 = x - logl(x)/x;
-z = 1.0L/x;
-if( x < 8.0L )
- x1 = z * polevll( z, P1, 9 )/p1evll( z, Q1, 9 );
-else if( x < 32.0L )
- x1 = z * polevll( z, P2, 7 )/p1evll( z, Q2, 7 );
-else
- x1 = z * polevll( z, P3, 7 )/p1evll( z, Q3, 7 );
-x = x0 - x1;
-if( code != 0 )
- x = -x;
-return( x );
-}
+++ /dev/null
-/* ndtrl.c
- *
- * Normal distribution function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, ndtrl();
- *
- * y = ndtrl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the area under the Gaussian probability density
- * function, integrated from minus infinity to x:
- *
- * x
- * -
- * 1 | | 2
- * ndtr(x) = --------- | exp( - t /2 ) dt
- * sqrt(2pi) | |
- * -
- * -inf.
- *
- * = ( 1 + erf(z) ) / 2
- * = erfc(z) / 2
- *
- * where z = x/sqrt(2). Computation is via the functions
- * erf and erfc.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -13,0 30000 1.6e-17 2.9e-18
- * IEEE -150.7,0 2000 1.6e-15 3.8e-16
- * Accuracy is limited by error amplification in computing exp(-x^2).
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfcl underflow x^2 / 2 > MAXLOGL 0.0
- *
- */
-\f/* erfl.c
- *
- * Error function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, erfl();
- *
- * y = erfl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * The integral is
- *
- * x
- * -
- * 2 | | 2
- * erf(x) = -------- | exp( - t ) dt.
- * sqrt(pi) | |
- * -
- * 0
- *
- * The magnitude of x is limited to about 106.56 for IEEE
- * arithmetic; 1 or -1 is returned outside this range.
- *
- * For 0 <= |x| < 1, erf(x) = x * P6(x^2)/Q6(x^2); otherwise
- * erf(x) = 1 - erfc(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 50000 2.0e-19 5.7e-20
- *
- */
-\f/* erfcl.c
- *
- * Complementary error function
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, erfcl();
- *
- * y = erfcl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * 1 - erf(x) =
- *
- * inf.
- * -
- * 2 | | 2
- * erfc(x) = -------- | exp( - t ) dt
- * sqrt(pi) | |
- * -
- * x
- *
- *
- * For small x, erfc(x) = 1 - erf(x); otherwise rational
- * approximations are computed.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,13 20000 7.0e-18 1.8e-18
- * IEEE 0,106.56 10000 4.4e-16 1.2e-16
- * Accuracy is limited by error amplification in computing exp(-x^2).
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * erfcl underflow x^2 > MAXLOGL 0.0
- *
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: January, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-extern long double MAXLOGL;
-static long double SQRTHL = 7.071067811865475244008e-1L;
-
-/* erfc(x) = exp(-x^2) P(1/x)/Q(1/x)
- 1/8 <= 1/x <= 1
- Peak relative error 5.8e-21 */
-#if UNK
-static long double P[10] = {
- 1.130609921802431462353E9L,
- 2.290171954844785638925E9L,
- 2.295563412811856278515E9L,
- 1.448651275892911637208E9L,
- 6.234814405521647580919E8L,
- 1.870095071120436715930E8L,
- 3.833161455208142870198E7L,
- 4.964439504376477951135E6L,
- 3.198859502299390825278E5L,
--9.085943037416544232472E-6L,
-};
-static long double Q[10] = {
-/* 1.000000000000000000000E0L, */
- 1.130609910594093747762E9L,
- 3.565928696567031388910E9L,
- 5.188672873106859049556E9L,
- 4.588018188918609726890E9L,
- 2.729005809811924550999E9L,
- 1.138778654945478547049E9L,
- 3.358653716579278063988E8L,
- 6.822450775590265689648E7L,
- 8.799239977351261077610E6L,
- 5.669830829076399819566E5L,
-};
-#endif
-#if IBMPC
-static short P[] = {
-0x4bf0,0x9ad8,0x7a03,0x86c7,0x401d, XPD
-0xdf23,0xd843,0x4032,0x8881,0x401e, XPD
-0xd025,0xcfd5,0x8494,0x88d3,0x401e, XPD
-0xb6d0,0xc92b,0x5417,0xacb1,0x401d, XPD
-0xada8,0x356a,0x4982,0x94a6,0x401c, XPD
-0x4e13,0xcaee,0x9e31,0xb258,0x401a, XPD
-0x5840,0x554d,0x37a3,0x9239,0x4018, XPD
-0x3b58,0x3da2,0xaf02,0x9780,0x4015, XPD
-0x0144,0x489e,0xbe68,0x9c31,0x4011, XPD
-0x333b,0xd9e6,0xd404,0x986f,0xbfee, XPD
-};
-static short Q[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0x0e43,0x302d,0x79ed,0x86c7,0x401d, XPD
-0xf817,0x9128,0xc0f8,0xd48b,0x401e, XPD
-0x8eae,0x8dad,0x6eb4,0x9aa2,0x401f, XPD
-0x00e7,0x7595,0xcd06,0x88bb,0x401f, XPD
-0x4991,0xcfda,0x52f1,0xa2a9,0x401e, XPD
-0xc39d,0xe415,0xc43d,0x87c0,0x401d, XPD
-0xa75d,0x436f,0x30dd,0xa027,0x401b, XPD
-0xc4cb,0x305a,0xbf78,0x8220,0x4019, XPD
-0x3708,0x33b1,0x07fa,0x8644,0x4016, XPD
-0x24fa,0x96f6,0x7153,0x8a6c,0x4012, XPD
-};
-#endif
-#if MIEEE
-static long P[30] = {
-0x401d0000,0x86c77a03,0x9ad84bf0,
-0x401e0000,0x88814032,0xd843df23,
-0x401e0000,0x88d38494,0xcfd5d025,
-0x401d0000,0xacb15417,0xc92bb6d0,
-0x401c0000,0x94a64982,0x356aada8,
-0x401a0000,0xb2589e31,0xcaee4e13,
-0x40180000,0x923937a3,0x554d5840,
-0x40150000,0x9780af02,0x3da23b58,
-0x40110000,0x9c31be68,0x489e0144,
-0xbfee0000,0x986fd404,0xd9e6333b,
-};
-static long Q[30] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x401d0000,0x86c779ed,0x302d0e43,
-0x401e0000,0xd48bc0f8,0x9128f817,
-0x401f0000,0x9aa26eb4,0x8dad8eae,
-0x401f0000,0x88bbcd06,0x759500e7,
-0x401e0000,0xa2a952f1,0xcfda4991,
-0x401d0000,0x87c0c43d,0xe415c39d,
-0x401b0000,0xa02730dd,0x436fa75d,
-0x40190000,0x8220bf78,0x305ac4cb,
-0x40160000,0x864407fa,0x33b13708,
-0x40120000,0x8a6c7153,0x96f624fa,
-};
-#endif
-
-/* erfc(x) = exp(-x^2) 1/x R(1/x^2) / S(1/x^2)
- 1/128 <= 1/x < 1/8
- Peak relative error 1.9e-21 */
-#if UNK
-static long double R[5] = {
- 3.621349282255624026891E0L,
- 7.173690522797138522298E0L,
- 3.445028155383625172464E0L,
- 5.537445669807799246891E-1L,
- 2.697535671015506686136E-2L,
-};
-static long double S[5] = {
-/* 1.000000000000000000000E0L, */
- 1.072884067182663823072E1L,
- 1.533713447609627196926E1L,
- 6.572990478128949439509E0L,
- 1.005392977603322982436E0L,
- 4.781257488046430019872E-2L,
-};
-#endif
-#if IBMPC
-static short R[] = {
-0x260a,0xab95,0x2fc7,0xe7c4,0x4000, XPD
-0x4761,0x613e,0xdf6d,0xe58e,0x4001, XPD
-0x0615,0x4b00,0x575f,0xdc7b,0x4000, XPD
-0x521d,0x8527,0x3435,0x8dc2,0x3ffe, XPD
-0x22cf,0xc711,0x6c5b,0xdcfb,0x3ff9, XPD
-};
-static short S[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0x5de6,0x17d7,0x54d6,0xaba9,0x4002, XPD
-0x55d5,0xd300,0xe71e,0xf564,0x4002, XPD
-0xb611,0x8f76,0xf020,0xd255,0x4001, XPD
-0x3684,0x3798,0xb793,0x80b0,0x3fff, XPD
-0xf5af,0x2fb2,0x1e57,0xc3d7,0x3ffa, XPD
-};
-#endif
-#if MIEEE
-static long R[15] = {
-0x40000000,0xe7c42fc7,0xab95260a,
-0x40010000,0xe58edf6d,0x613e4761,
-0x40000000,0xdc7b575f,0x4b000615,
-0x3ffe0000,0x8dc23435,0x8527521d,
-0x3ff90000,0xdcfb6c5b,0xc71122cf,
-};
-static long S[15] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40020000,0xaba954d6,0x17d75de6,
-0x40020000,0xf564e71e,0xd30055d5,
-0x40010000,0xd255f020,0x8f76b611,
-0x3fff0000,0x80b0b793,0x37983684,
-0x3ffa0000,0xc3d71e57,0x2fb2f5af,
-};
-#endif
-
-/* erf(x) = x P(x^2)/Q(x^2)
- 0 <= x <= 1
- Peak relative error 7.6e-23 */
-#if UNK
-static long double T[7] = {
- 1.097496774521124996496E-1L,
- 5.402980370004774841217E0L,
- 2.871822526820825849235E2L,
- 2.677472796799053019985E3L,
- 4.825977363071025440855E4L,
- 1.549905740900882313773E5L,
- 1.104385395713178565288E6L,
-};
-static long double U[6] = {
-/* 1.000000000000000000000E0L, */
- 4.525777638142203713736E1L,
- 9.715333124857259246107E2L,
- 1.245905812306219011252E4L,
- 9.942956272177178491525E4L,
- 4.636021778692893773576E5L,
- 9.787360737578177599571E5L,
-};
-#endif
-#if IBMPC
-static short T[] = {
-0xfd7a,0x3a1a,0x705b,0xe0c4,0x3ffb, XPD
-0x3128,0xc337,0x3716,0xace5,0x4001, XPD
-0x9517,0x4e93,0x540e,0x8f97,0x4007, XPD
-0x6118,0x6059,0x9093,0xa757,0x400a, XPD
-0xb954,0xa987,0xc60c,0xbc83,0x400e, XPD
-0x7a56,0xe45a,0xa4bd,0x975b,0x4010, XPD
-0xc446,0x6bab,0x0b2a,0x86d0,0x4013, XPD
-};
-static short U[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
-0x3453,0x1f8e,0xf688,0xb507,0x4004, XPD
-0x71ac,0xb12f,0x21ca,0xf2e2,0x4008, XPD
-0xffe8,0x9cac,0x3b84,0xc2ac,0x400c, XPD
-0x481d,0x445b,0xc807,0xc232,0x400f, XPD
-0x9ad5,0x1aef,0x45b1,0xe25e,0x4011, XPD
-0x71a7,0x1cad,0x012e,0xeef3,0x4012, XPD
-};
-#endif
-#if MIEEE
-static long T[21] = {
-0x3ffb0000,0xe0c4705b,0x3a1afd7a,
-0x40010000,0xace53716,0xc3373128,
-0x40070000,0x8f97540e,0x4e939517,
-0x400a0000,0xa7579093,0x60596118,
-0x400e0000,0xbc83c60c,0xa987b954,
-0x40100000,0x975ba4bd,0xe45a7a56,
-0x40130000,0x86d00b2a,0x6babc446,
-};
-static long U[18] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40040000,0xb507f688,0x1f8e3453,
-0x40080000,0xf2e221ca,0xb12f71ac,
-0x400c0000,0xc2ac3b84,0x9cacffe8,
-0x400f0000,0xc232c807,0x445b481d,
-0x40110000,0xe25e45b1,0x1aef9ad5,
-0x40120000,0xeef3012e,0x1cad71a7,
-};
-#endif
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double expl ( long double );
-extern long double logl ( long double );
-extern long double erfl ( long double );
-extern long double erfcl ( long double );
-extern long double fabsl ( long double );
-#else
-long double polevll(), p1evll(), expl(), logl(), erfl(), erfcl(), fabsl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-
-long double ndtrl(a)
-long double a;
-{
-long double x, y, z;
-
-x = a * SQRTHL;
-z = fabsl(x);
-
-if( z < SQRTHL )
- y = 0.5L + 0.5L * erfl(x);
-
-else
- {
- y = 0.5L * erfcl(z);
-
- if( x > 0.0L )
- y = 1.0L - y;
- }
-
-return(y);
-}
-
-
-long double erfcl(a)
-long double a;
-{
-long double p,q,x,y,z;
-
-#ifdef INFINITIES
-if( a == INFINITYL )
- return(0.0L);
-if( a == -INFINITYL )
- return(2.0L);
-#endif
-if( a < 0.0L )
- x = -a;
-else
- x = a;
-
-if( x < 1.0L )
- return( 1.0L - erfl(a) );
-
-z = -a * a;
-
-if( z < -MAXLOGL )
- {
-under:
- mtherr( "erfcl", UNDERFLOW );
- if( a < 0 )
- return( 2.0L );
- else
- return( 0.0L );
- }
-
-z = expl(z);
-y = 1.0L/x;
-
-if( x < 8.0L )
- {
- p = polevll( y, P, 9 );
- q = p1evll( y, Q, 10 );
- }
-else
- {
- q = y * y;
- p = y * polevll( q, R, 4 );
- q = p1evll( q, S, 5 );
- }
-y = (z * p)/q;
-
-if( a < 0.0L )
- y = 2.0L - y;
-
-if( y == 0.0L )
- goto under;
-
-return(y);
-}
-
-
-
-long double erfl(x)
-long double x;
-{
-long double y, z;
-
-#if MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-#ifdef INFINITIES
-if( x == -INFINITYL )
- return(-1.0L);
-if( x == INFINITYL )
- return(1.0L);
-#endif
-if( fabsl(x) > 1.0L )
- return( 1.0L - erfcl(x) );
-
-z = x * x;
-y = x * polevll( z, T, 6 ) / p1evll( z, U, 6 );
-return( y );
-}
+++ /dev/null
-/* pdtrl.c
- *
- * Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * long double m, y, pdtrl();
- *
- * y = pdtrl( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the first k terms of the Poisson
- * distribution:
- *
- * k j
- * -- -m m
- * > e --
- * -- j!
- * j=0
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the relation
- *
- * y = pdtr( k, m ) = igamc( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igamc().
- *
- */
-\f/* pdtrcl()
- *
- * Complemented poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * long double m, y, pdtrcl();
- *
- * y = pdtrcl( k, m );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the sum of the terms k+1 to infinity of the Poisson
- * distribution:
- *
- * inf. j
- * -- -m m
- * > e --
- * -- j!
- * j=k+1
- *
- * The terms are not summed directly; instead the incomplete
- * gamma integral is employed, according to the formula
- *
- * y = pdtrc( k, m ) = igam( k+1, m ).
- *
- * The arguments must both be positive.
- *
- *
- *
- * ACCURACY:
- *
- * See igam.c.
- *
- */
-\f/* pdtril()
- *
- * Inverse Poisson distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * int k;
- * long double m, y, pdtrl();
- *
- * m = pdtril( k, y );
- *
- *
- *
- *
- * DESCRIPTION:
- *
- * Finds the Poisson variable x such that the integral
- * from 0 to x of the Poisson density is equal to the
- * given probability y.
- *
- * This is accomplished using the inverse gamma integral
- * function and the relation
- *
- * m = igami( k+1, y ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * See igami.c.
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pdtri domain y < 0 or y >= 1 0.0
- * k < 0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern long double igaml ( long double, long double );
-extern long double igamcl ( long double, long double );
-extern long double igamil ( long double, long double );
-#else
-long double igaml(), igamcl(), igamil();
-#endif
-
-long double pdtrcl( k, m )
-int k;
-long double m;
-{
-long double v;
-
-if( (k < 0) || (m <= 0.0L) )
- {
- mtherr( "pdtrcl", DOMAIN );
- return( 0.0L );
- }
-v = k+1;
-return( igaml( v, m ) );
-}
-
-
-
-long double pdtrl( k, m )
-int k;
-long double m;
-{
-long double v;
-
-if( (k < 0) || (m <= 0.0L) )
- {
- mtherr( "pdtrl", DOMAIN );
- return( 0.0L );
- }
-v = k+1;
-return( igamcl( v, m ) );
-}
-
-
-long double pdtril( k, y )
-int k;
-long double y;
-{
-long double v;
-
-if( (k < 0) || (y < 0.0L) || (y >= 1.0L) )
- {
- mtherr( "pdtril", DOMAIN );
- return( 0.0L );
- }
-v = k+1;
-v = igamil( v, y );
-return( v );
-}
+++ /dev/null
-/* polevll.c
- * p1evll.c
- *
- * Evaluate polynomial
- *
- *
- *
- * SYNOPSIS:
- *
- * int N;
- * long double x, y, coef[N+1], polevl[];
- *
- * y = polevll( x, coef, N );
- *
- *
- *
- * DESCRIPTION:
- *
- * Evaluates polynomial of degree N:
- *
- * 2 N
- * y = C + C x + C x +...+ C x
- * 0 1 2 N
- *
- * Coefficients are stored in reverse order:
- *
- * coef[0] = C , ..., coef[N] = C .
- * N 0
- *
- * The function p1evll() assumes that coef[N] = 1.0 and is
- * omitted from the array. Its calling arguments are
- * otherwise the same as polevll().
- *
- * This module also contains the following globally declared constants:
- * MAXNUML = 1.189731495357231765021263853E4932L;
- * MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
- * MAXLOGL = 1.1356523406294143949492E4L;
- * MINLOGL = -1.1355137111933024058873E4L;
- * LOGE2L = 6.9314718055994530941723E-1L;
- * LOG2EL = 1.4426950408889634073599E0L;
- * PIL = 3.1415926535897932384626L;
- * PIO2L = 1.5707963267948966192313L;
- * PIO4L = 7.8539816339744830961566E-1L;
- *
- * SPEED:
- *
- * In the interest of speed, there are no checks for out
- * of bounds arithmetic. This routine is used by most of
- * the functions in the library. Depending on available
- * equipment features, the user may wish to rewrite the
- * program in microcode or assembly language.
- *
- */
-\f
-
-/*
-Cephes Math Library Release 2.2: July, 1992
-Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-#include <math.h>
-
-#if UNK
-/* almost 2^16384 */
-long double MAXNUML = 1.189731495357231765021263853E4932L;
-/* 2^-64 */
-long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
-/* log( MAXNUML ) */
-long double MAXLOGL = 1.1356523406294143949492E4L;
-#ifdef DENORMAL
-/* log(smallest denormal number = 2^-16446) */
-long double MINLOGL = -1.13994985314888605586758E4L;
-#else
-/* log( underflow threshold = 2^(-16382) ) */
-long double MINLOGL = -1.1355137111933024058873E4L;
-#endif
-long double LOGE2L = 6.9314718055994530941723E-1L;
-long double LOG2EL = 1.4426950408889634073599E0L;
-long double PIL = 3.1415926535897932384626L;
-long double PIO2L = 1.5707963267948966192313L;
-long double PIO4L = 7.8539816339744830961566E-1L;
-#ifdef INFINITIES
-long double NANL = 0.0L / 0.0L;
-long double INFINITYL = 1.0L / 0.0L;
-#else
-long double INFINITYL = 1.189731495357231765021263853E4932L;
-long double NANL = 0.0L;
-#endif
-#endif
-#if IBMPC
-short MAXNUML[] = {0xffff,0xffff,0xffff,0xffff,0x7ffe, XPD};
-short MAXLOGL[] = {0x79ab,0xd1cf,0x17f7,0xb172,0x400c, XPD};
-#ifdef INFINITIES
-short INFINITYL[] = {0,0,0,0x8000,0x7fff, XPD};
-short NANL[] = {0,0,0,0xc000,0x7fff, XPD};
-#else
-short INFINITYL[] = {0xffff,0xffff,0xffff,0xffff,0x7ffe, XPD};
-long double NANL = 0.0L;
-#endif
-#ifdef DENORMAL
-short MINLOGL[] = {0xbaaa,0x09e2,0xfe7f,0xb21d,0xc00c, XPD};
-#else
-short MINLOGL[] = {0xeb2f,0x1210,0x8c67,0xb16c,0xc00c, XPD};
-#endif
-short MACHEPL[] = {0x0000,0x0000,0x0000,0x8000,0x3fbf, XPD};
-short LOGE2L[] = {0x79ac,0xd1cf,0x17f7,0xb172,0x3ffe, XPD};
-short LOG2EL[] = {0xf0bc,0x5c17,0x3b29,0xb8aa,0x3fff, XPD};
-short PIL[] = {0xc235,0x2168,0xdaa2,0xc90f,0x4000, XPD};
-short PIO2L[] = {0xc235,0x2168,0xdaa2,0xc90f,0x3fff, XPD};
-short PIO4L[] = {0xc235,0x2168,0xdaa2,0xc90f,0x3ffe, XPD};
-#endif
-#if MIEEE
-long MAXNUML[] = {0x7ffe0000,0xffffffff,0xffffffff};
-long MAXLOGL[] = {0x400c0000,0xb17217f7,0xd1cf79ab};
-#ifdef INFINITIES
-long INFINITY[] = {0x7fff0000,0x80000000,0x00000000};
-long NANL[] = {0x7fff0000,0xffffffff,0xffffffff};
-#else
-long INFINITYL[] = {0x7ffe0000,0xffffffff,0xffffffff};
-long double NANL = 0.0L;
-#endif
-#ifdef DENORMAL
-long MINLOGL[] = {0xc00c0000,0xb21dfe7f,0x09e2baaa};
-#else
-long MINLOGL[] = {0xc00c0000,0xb16c8c67,0x1210eb2f};
-#endif
-long MACHEPL[] = {0x3fbf0000,0x80000000,0x00000000};
-long LOGE2L[] = {0x3ffe0000,0xb17217f7,0xd1cf79ac};
-long LOG2EL[] = {0x3fff0000,0xb8aa3b29,0x5c17f0bc};
-long PIL[] = {0x40000000,0xc90fdaa2,0x2168c235};
-long PIO2L[] = {0x3fff0000,0xc90fdaa2,0x2168c235};
-long PIO4L[] = {0x3ffe0000,0xc90fdaa2,0x2168c235};
-#endif
-
-#ifdef MINUSZERO
-long double NEGZEROL = -0.0L;
-#else
-long double NEGZEROL = 0.0L;
-#endif
-
-/* Polynomial evaluator:
- * P[0] x^n + P[1] x^(n-1) + ... + P[n]
- */
-long double polevll( x, p, n )
-long double x;
-void *p;
-int n;
-{
-register long double y;
-register long double *P = (long double *)p;
-
-y = *P++;
-do
- {
- y = y * x + *P++;
- }
-while( --n );
-return(y);
-}
-
-
-
-/* Polynomial evaluator:
- * x^n + P[0] x^(n-1) + P[1] x^(n-2) + ... + P[n]
- */
-long double p1evll( x, p, n )
-long double x;
-void *p;
-int n;
-{
-register long double y;
-register long double *P = (long double *)p;
-
-n -= 1;
-y = x + *P++;
-do
- {
- y = y * x + *P++;
- }
-while( --n );
-return( y );
-}
+++ /dev/null
-/* powil.c
- *
- * Real raised to integer power, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, powil();
- * int n;
- *
- * y = powil( x, n );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns argument x raised to the nth power.
- * The routine efficiently decomposes n as a sum of powers of
- * two. The desired power is a product of two-to-the-kth
- * powers of x. Thus to compute the 32767 power of x requires
- * 28 multiplications instead of 32767 multiplications.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic x domain n domain # trials peak rms
- * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18
- * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
- * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
- *
- * Returns MAXNUM on overflow, zero on underflow.
- *
- */
-\f
-/* powil.c */
-
-/*
-Cephes Math Library Release 2.2: December, 1990
-Copyright 1984, 1990 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern long double MAXNUML, MAXLOGL, MINLOGL;
-extern long double LOGE2L;
-#ifdef ANSIPROT
-extern long double frexpl ( long double, int * );
-#else
-long double frexpl();
-#endif
-
-long double powil( x, nn )
-long double x;
-int nn;
-{
-long double w, y;
-long double s;
-int n, e, sign, asign, lx;
-
-if( x == 0.0L )
- {
- if( nn == 0 )
- return( 1.0L );
- else if( nn < 0 )
- return( MAXNUML );
- else
- return( 0.0L );
- }
-
-if( nn == 0 )
- return( 1.0L );
-
-
-if( x < 0.0L )
- {
- asign = -1;
- x = -x;
- }
-else
- asign = 0;
-
-
-if( nn < 0 )
- {
- sign = -1;
- n = -nn;
- }
-else
- {
- sign = 1;
- n = nn;
- }
-
-/* Overflow detection */
-
-/* Calculate approximate logarithm of answer */
-s = x;
-s = frexpl( s, &lx );
-e = (lx - 1)*n;
-if( (e == 0) || (e > 64) || (e < -64) )
- {
- s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
- s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L;
- }
-else
- {
- s = LOGE2L * e;
- }
-
-if( s > MAXLOGL )
- {
- mtherr( "powil", OVERFLOW );
- y = MAXNUML;
- goto done;
- }
-
-if( s < MINLOGL )
- {
- mtherr( "powil", UNDERFLOW );
- return(0.0L);
- }
-/* Handle tiny denormal answer, but with less accuracy
- * since roundoff error in 1.0/x will be amplified.
- * The precise demarcation should be the gradual underflow threshold.
- */
-if( s < (-MAXLOGL+2.0L) )
- {
- x = 1.0L/x;
- sign = -sign;
- }
-
-/* First bit of the power */
-if( n & 1 )
- y = x;
-
-else
- {
- y = 1.0L;
- asign = 0;
- }
-
-w = x;
-n >>= 1;
-while( n )
- {
- w = w * w; /* arg to the 2-to-the-kth power */
- if( n & 1 ) /* if that bit is set, then include in product */
- y *= w;
- n >>= 1;
- }
-
-
-done:
-
-if( asign )
- y = -y; /* odd power of negative number */
-if( sign < 0 )
- y = 1.0L/y;
-return(y);
-}
+++ /dev/null
-/* powl.c
- *
- * Power function, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, z, powl();
- *
- * z = powl( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/32 and pseudo extended precision arithmetic to
- * obtain several extra bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * The relative error of pow(x,y) can be estimated
- * by y dl ln(2), where dl is the absolute error of
- * the internally computed base 2 logarithm. At the ends
- * of the approximation interval the logarithm equal 1/32
- * and its relative error is about 1 lsb = 1.1e-19. Hence
- * the predicted relative error in the result is 2.3e-21 y .
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- *
- * IEEE +-1000 40000 2.8e-18 3.7e-19
- * .001 < x < 1000, with log(x) uniformly distributed.
- * -1000 < y < 1000, y uniformly distributed.
- *
- * IEEE 0,8700 60000 6.5e-18 1.0e-18
- * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pow overflow x**y > MAXNUM INFINITY
- * pow underflow x**y < 1/MAXNUM 0.0
- * pow domain x<0 and y noninteger 0.0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1991, 1998 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-static char fname[] = {"powl"};
-
-/* Table size */
-#define NXT 32
-/* log2(Table size) */
-#define LNXT 5
-
-#ifdef UNK
-/* log(1+x) = x - .5x^2 + x^3 * P(z)/Q(z)
- * on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1
- */
-static long double P[] = {
- 8.3319510773868690346226E-4L,
- 4.9000050881978028599627E-1L,
- 1.7500123722550302671919E0L,
- 1.4000100839971580279335E0L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
- 5.2500282295834889175431E0L,
- 8.4000598057587009834666E0L,
- 4.2000302519914740834728E0L,
-};
-/* A[i] = 2^(-i/32), rounded to IEEE long double precision.
- * If i is even, A[i] + B[i/2] gives additional accuracy.
- */
-static long double A[33] = {
- 1.0000000000000000000000E0L,
- 9.7857206208770013448287E-1L,
- 9.5760328069857364691013E-1L,
- 9.3708381705514995065011E-1L,
- 9.1700404320467123175367E-1L,
- 8.9735453750155359320742E-1L,
- 8.7812608018664974155474E-1L,
- 8.5930964906123895780165E-1L,
- 8.4089641525371454301892E-1L,
- 8.2287773907698242225554E-1L,
- 8.0524516597462715409607E-1L,
- 7.8799042255394324325455E-1L,
- 7.7110541270397041179298E-1L,
- 7.5458221379671136985669E-1L,
- 7.3841307296974965571198E-1L,
- 7.2259040348852331001267E-1L,
- 7.0710678118654752438189E-1L,
- 6.9195494098191597746178E-1L,
- 6.7712777346844636413344E-1L,
- 6.6261832157987064729696E-1L,
- 6.4841977732550483296079E-1L,
- 6.3452547859586661129850E-1L,
- 6.2092890603674202431705E-1L,
- 6.0762367999023443907803E-1L,
- 5.9460355750136053334378E-1L,
- 5.8186242938878875689693E-1L,
- 5.6939431737834582684856E-1L,
- 5.5719337129794626814472E-1L,
- 5.4525386633262882960438E-1L,
- 5.3357020033841180906486E-1L,
- 5.2213689121370692017331E-1L,
- 5.1094857432705833910408E-1L,
- 5.0000000000000000000000E-1L,
-};
-static long double B[17] = {
- 0.0000000000000000000000E0L,
- 2.6176170809902549338711E-20L,
--1.0126791927256478897086E-20L,
- 1.3438228172316276937655E-21L,
- 1.2207982955417546912101E-20L,
--6.3084814358060867200133E-21L,
- 1.3164426894366316434230E-20L,
--1.8527916071632873716786E-20L,
- 1.8950325588932570796551E-20L,
- 1.5564775779538780478155E-20L,
- 6.0859793637556860974380E-21L,
--2.0208749253662532228949E-20L,
- 1.4966292219224761844552E-20L,
- 3.3540909728056476875639E-21L,
--8.6987564101742849540743E-22L,
--1.2327176863327626135542E-20L,
- 0.0000000000000000000000E0L,
-};
-
-/* 2^x = 1 + x P(x),
- * on the interval -1/32 <= x <= 0
- */
-static long double R[] = {
- 1.5089970579127659901157E-5L,
- 1.5402715328927013076125E-4L,
- 1.3333556028915671091390E-3L,
- 9.6181291046036762031786E-3L,
- 5.5504108664798463044015E-2L,
- 2.4022650695910062854352E-1L,
- 6.9314718055994530931447E-1L,
-};
-
-#define douba(k) A[k]
-#define doubb(k) B[k]
-#define MEXP (NXT*16384.0L)
-/* The following if denormal numbers are supported, else -MEXP: */
-#ifdef DENORMAL
-#define MNEXP (-NXT*(16384.0L+64.0L))
-#else
-#define MNEXP (-NXT*16384.0L)
-#endif
-/* log2(e) - 1 */
-#define LOG2EA 0.44269504088896340735992L
-#endif
-
-
-#ifdef IBMPC
-static short P[] = {
-0xb804,0xa8b7,0xc6f4,0xda6a,0x3ff4, XPD
-0x7de9,0xcf02,0x58c0,0xfae1,0x3ffd, XPD
-0x405a,0x3722,0x67c9,0xe000,0x3fff, XPD
-0xcd99,0x6b43,0x87ca,0xb333,0x3fff, XPD
-};
-static short Q[] = {
-/* 0x0000,0x0000,0x0000,0x8000,0x3fff, */
-0x6307,0xa469,0x3b33,0xa800,0x4001, XPD
-0xfec2,0x62d7,0xa51c,0x8666,0x4002, XPD
-0xda32,0xd072,0xa5d7,0x8666,0x4001, XPD
-};
-static short A[] = {
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-0x033a,0x722a,0xb2db,0xfa83,0x3ffe, XPD
-0xcc2c,0x2486,0x7d15,0xf525,0x3ffe, XPD
-0xf5cb,0xdcda,0xb99b,0xefe4,0x3ffe, XPD
-0x392f,0xdd24,0xc6e7,0xeac0,0x3ffe, XPD
-0x48a8,0x7c83,0x06e7,0xe5b9,0x3ffe, XPD
-0xe111,0x2a94,0xdeec,0xe0cc,0x3ffe, XPD
-0x3755,0xdaf2,0xb797,0xdbfb,0x3ffe, XPD
-0x6af4,0xd69d,0xfcca,0xd744,0x3ffe, XPD
-0xe45a,0xf12a,0x1d91,0xd2a8,0x3ffe, XPD
-0x80e4,0x1f84,0x8c15,0xce24,0x3ffe, XPD
-0x27a3,0x6e2f,0xbd86,0xc9b9,0x3ffe, XPD
-0xdadd,0x5506,0x2a11,0xc567,0x3ffe, XPD
-0x9456,0x6670,0x4cca,0xc12c,0x3ffe, XPD
-0x36bf,0x580c,0xa39f,0xbd08,0x3ffe, XPD
-0x9ee9,0x62fb,0xaf47,0xb8fb,0x3ffe, XPD
-0x6484,0xf9de,0xf333,0xb504,0x3ffe, XPD
-0x2590,0xd2ac,0xf581,0xb123,0x3ffe, XPD
-0x4ac6,0x42a1,0x3eea,0xad58,0x3ffe, XPD
-0x0ef8,0xea7c,0x5ab4,0xa9a1,0x3ffe, XPD
-0x38ea,0xb151,0xd6a9,0xa5fe,0x3ffe, XPD
-0x6819,0x0c49,0x4303,0xa270,0x3ffe, XPD
-0x11ae,0x91a1,0x3260,0x9ef5,0x3ffe, XPD
-0x5539,0xd54e,0x39b9,0x9b8d,0x3ffe, XPD
-0xa96f,0x8db8,0xf051,0x9837,0x3ffe, XPD
-0x0961,0xfef7,0xefa8,0x94f4,0x3ffe, XPD
-0xc336,0xab11,0xd373,0x91c3,0x3ffe, XPD
-0x53c0,0x45cd,0x398b,0x8ea4,0x3ffe, XPD
-0xd6e7,0xea8b,0xc1e3,0x8b95,0x3ffe, XPD
-0x8527,0x92da,0x0e80,0x8898,0x3ffe, XPD
-0x7b15,0xcc48,0xc367,0x85aa,0x3ffe, XPD
-0xa1d7,0xac2b,0x8698,0x82cd,0x3ffe, XPD
-0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD
-};
-static short B[] = {
-0x0000,0x0000,0x0000,0x0000,0x0000, XPD
-0x1f87,0xdb30,0x18f5,0xf73a,0x3fbd, XPD
-0xac15,0x3e46,0x2932,0xbf4a,0xbfbc, XPD
-0x7944,0xba66,0xa091,0xcb12,0x3fb9, XPD
-0xff78,0x40b4,0x2ee6,0xe69a,0x3fbc, XPD
-0xc895,0x5069,0xe383,0xee53,0xbfbb, XPD
-0x7cde,0x9376,0x4325,0xf8ab,0x3fbc, XPD
-0xa10c,0x25e0,0xc093,0xaefd,0xbfbd, XPD
-0x7d3e,0xea95,0x1366,0xb2fb,0x3fbd, XPD
-0x5d89,0xeb34,0x5191,0x9301,0x3fbd, XPD
-0x80d9,0xb883,0xfb10,0xe5eb,0x3fbb, XPD
-0x045d,0x288c,0xc1ec,0xbedd,0xbfbd, XPD
-0xeded,0x5c85,0x4630,0x8d5a,0x3fbd, XPD
-0x9d82,0xe5ac,0x8e0a,0xfd6d,0x3fba, XPD
-0x6dfd,0xeb58,0xaf14,0x8373,0xbfb9, XPD
-0xf938,0x7aac,0x91cf,0xe8da,0xbfbc, XPD
-0x0000,0x0000,0x0000,0x0000,0x0000, XPD
-};
-static short R[] = {
-0xa69b,0x530e,0xee1d,0xfd2a,0x3fee, XPD
-0xc746,0x8e7e,0x5960,0xa182,0x3ff2, XPD
-0x63b6,0xadda,0xfd6a,0xaec3,0x3ff5, XPD
-0xc104,0xfd99,0x5b7c,0x9d95,0x3ff8, XPD
-0xe05e,0x249d,0x46b8,0xe358,0x3ffa, XPD
-0x5d1d,0x162c,0xeffc,0xf5fd,0x3ffc, XPD
-0x79aa,0xd1cf,0x17f7,0xb172,0x3ffe, XPD
-};
-
-/* 10 byte sizes versus 12 byte */
-#define douba(k) (*(long double *)(&A[(sizeof( long double )/2)*(k)]))
-#define doubb(k) (*(long double *)(&B[(sizeof( long double )/2)*(k)]))
-#define MEXP (NXT*16384.0L)
-#ifdef DENORMAL
-#define MNEXP (-NXT*(16384.0L+64.0L))
-#else
-#define MNEXP (-NXT*16384.0L)
-#endif
-static short L[] = {0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, XPD};
-#define LOG2EA (*(long double *)(&L[0]))
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3ff40000,0xda6ac6f4,0xa8b7b804,
-0x3ffd0000,0xfae158c0,0xcf027de9,
-0x3fff0000,0xe00067c9,0x3722405a,
-0x3fff0000,0xb33387ca,0x6b43cd99,
-};
-static long Q[] = {
-/* 0x3fff0000,0x80000000,0x00000000, */
-0x40010000,0xa8003b33,0xa4696307,
-0x40020000,0x8666a51c,0x62d7fec2,
-0x40010000,0x8666a5d7,0xd072da32,
-};
-static long A[] = {
-0x3fff0000,0x80000000,0x00000000,
-0x3ffe0000,0xfa83b2db,0x722a033a,
-0x3ffe0000,0xf5257d15,0x2486cc2c,
-0x3ffe0000,0xefe4b99b,0xdcdaf5cb,
-0x3ffe0000,0xeac0c6e7,0xdd24392f,
-0x3ffe0000,0xe5b906e7,0x7c8348a8,
-0x3ffe0000,0xe0ccdeec,0x2a94e111,
-0x3ffe0000,0xdbfbb797,0xdaf23755,
-0x3ffe0000,0xd744fcca,0xd69d6af4,
-0x3ffe0000,0xd2a81d91,0xf12ae45a,
-0x3ffe0000,0xce248c15,0x1f8480e4,
-0x3ffe0000,0xc9b9bd86,0x6e2f27a3,
-0x3ffe0000,0xc5672a11,0x5506dadd,
-0x3ffe0000,0xc12c4cca,0x66709456,
-0x3ffe0000,0xbd08a39f,0x580c36bf,
-0x3ffe0000,0xb8fbaf47,0x62fb9ee9,
-0x3ffe0000,0xb504f333,0xf9de6484,
-0x3ffe0000,0xb123f581,0xd2ac2590,
-0x3ffe0000,0xad583eea,0x42a14ac6,
-0x3ffe0000,0xa9a15ab4,0xea7c0ef8,
-0x3ffe0000,0xa5fed6a9,0xb15138ea,
-0x3ffe0000,0xa2704303,0x0c496819,
-0x3ffe0000,0x9ef53260,0x91a111ae,
-0x3ffe0000,0x9b8d39b9,0xd54e5539,
-0x3ffe0000,0x9837f051,0x8db8a96f,
-0x3ffe0000,0x94f4efa8,0xfef70961,
-0x3ffe0000,0x91c3d373,0xab11c336,
-0x3ffe0000,0x8ea4398b,0x45cd53c0,
-0x3ffe0000,0x8b95c1e3,0xea8bd6e7,
-0x3ffe0000,0x88980e80,0x92da8527,
-0x3ffe0000,0x85aac367,0xcc487b15,
-0x3ffe0000,0x82cd8698,0xac2ba1d7,
-0x3ffe0000,0x80000000,0x00000000,
-};
-static long B[51] = {
-0x00000000,0x00000000,0x00000000,
-0x3fbd0000,0xf73a18f5,0xdb301f87,
-0xbfbc0000,0xbf4a2932,0x3e46ac15,
-0x3fb90000,0xcb12a091,0xba667944,
-0x3fbc0000,0xe69a2ee6,0x40b4ff78,
-0xbfbb0000,0xee53e383,0x5069c895,
-0x3fbc0000,0xf8ab4325,0x93767cde,
-0xbfbd0000,0xaefdc093,0x25e0a10c,
-0x3fbd0000,0xb2fb1366,0xea957d3e,
-0x3fbd0000,0x93015191,0xeb345d89,
-0x3fbb0000,0xe5ebfb10,0xb88380d9,
-0xbfbd0000,0xbeddc1ec,0x288c045d,
-0x3fbd0000,0x8d5a4630,0x5c85eded,
-0x3fba0000,0xfd6d8e0a,0xe5ac9d82,
-0xbfb90000,0x8373af14,0xeb586dfd,
-0xbfbc0000,0xe8da91cf,0x7aacf938,
-0x00000000,0x00000000,0x00000000,
-};
-static long R[] = {
-0x3fee0000,0xfd2aee1d,0x530ea69b,
-0x3ff20000,0xa1825960,0x8e7ec746,
-0x3ff50000,0xaec3fd6a,0xadda63b6,
-0x3ff80000,0x9d955b7c,0xfd99c104,
-0x3ffa0000,0xe35846b8,0x249de05e,
-0x3ffc0000,0xf5fdeffc,0x162c5d1d,
-0x3ffe0000,0xb17217f7,0xd1cf79aa,
-};
-
-#define douba(k) (*(long double *)&A[3*(k)])
-#define doubb(k) (*(long double *)&B[3*(k)])
-#define MEXP (NXT*16384.0L)
-#ifdef DENORMAL
-#define MNEXP (-NXT*(16384.0L+64.0L))
-#else
-#define MNEXP (-NXT*16382.0L)
-#endif
-static long L[3] = {0x3ffd0000,0xe2a8eca5,0x705fc2ef};
-#define LOG2EA (*(long double *)(&L[0]))
-#endif
-
-
-#define F W
-#define Fa Wa
-#define Fb Wb
-#define G W
-#define Ga Wa
-#define Gb u
-#define H W
-#define Ha Wb
-#define Hb Wb
-
-extern long double MAXNUML;
-static VOLATILE long double z;
-static long double w, W, Wa, Wb, ya, yb, u;
-#ifdef ANSIPROT
-extern long double floorl ( long double );
-extern long double fabsl ( long double );
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double powil ( long double, int );
-extern int isnanl ( long double );
-extern int isfinitel ( long double );
-static long double reducl( long double );
-extern int signbitl ( long double );
-#else
-long double floorl(), fabsl(), frexpl(), ldexpl();
-long double polevll(), p1evll(), powil();
-static long double reducl();
-int isnanl(), isfinitel(), signbitl();
-#endif
-
-#ifdef INFINITIES
-extern long double INFINITYL;
-#else
-#define INFINITYL MAXNUML
-#endif
-
-#ifdef NANS
-extern long double NANL;
-#endif
-#ifdef MINUSZERO
-extern long double NEGZEROL;
-#endif
-
-long double powl( x, y )
-long double x, y;
-{
-/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
-int i, nflg, iyflg, yoddint;
-long e;
-
-if( y == 0.0L )
- return( 1.0L );
-
-#ifdef NANS
-if( isnanl(x) )
- return( x );
-if( isnanl(y) )
- return( y );
-#endif
-
-if( y == 1.0L )
- return( x );
-
-#ifdef INFINITIES
-if( !isfinitel(y) && (x == -1.0L || x == 1.0L) )
- {
- mtherr( "powl", DOMAIN );
-#ifdef NANS
- return( NANL );
-#else
- return( INFINITYL );
-#endif
- }
-#endif
-
-if( x == 1.0L )
- return( 1.0L );
-
-if( y >= MAXNUML )
- {
-#ifdef INFINITIES
- if( x > 1.0L )
- return( INFINITYL );
-#else
- if( x > 1.0L )
- return( MAXNUML );
-#endif
- if( x > 0.0L && x < 1.0L )
- return( 0.0L );
-#ifdef INFINITIES
- if( x < -1.0L )
- return( INFINITYL );
-#else
- if( x < -1.0L )
- return( MAXNUML );
-#endif
- if( x > -1.0L && x < 0.0L )
- return( 0.0L );
- }
-if( y <= -MAXNUML )
- {
- if( x > 1.0L )
- return( 0.0L );
-#ifdef INFINITIES
- if( x > 0.0L && x < 1.0L )
- return( INFINITYL );
-#else
- if( x > 0.0L && x < 1.0L )
- return( MAXNUML );
-#endif
- if( x < -1.0L )
- return( 0.0L );
-#ifdef INFINITIES
- if( x > -1.0L && x < 0.0L )
- return( INFINITYL );
-#else
- if( x > -1.0L && x < 0.0L )
- return( MAXNUML );
-#endif
- }
-if( x >= MAXNUML )
- {
-#if INFINITIES
- if( y > 0.0L )
- return( INFINITYL );
-#else
- if( y > 0.0L )
- return( MAXNUML );
-#endif
- return( 0.0L );
- }
-
-w = floorl(y);
-/* Set iyflg to 1 if y is an integer. */
-iyflg = 0;
-if( w == y )
- iyflg = 1;
-
-/* Test for odd integer y. */
-yoddint = 0;
-if( iyflg )
- {
- ya = fabsl(y);
- ya = floorl(0.5L * ya);
- yb = 0.5L * fabsl(w);
- if( ya != yb )
- yoddint = 1;
- }
-
-if( x <= -MAXNUML )
- {
- if( y > 0.0L )
- {
-#ifdef INFINITIES
- if( yoddint )
- return( -INFINITYL );
- return( INFINITYL );
-#else
- if( yoddint )
- return( -MAXNUML );
- return( MAXNUML );
-#endif
- }
- if( y < 0.0L )
- {
-#ifdef MINUSZERO
- if( yoddint )
- return( NEGZEROL );
-#endif
- return( 0.0 );
- }
- }
-
-
-nflg = 0; /* flag = 1 if x<0 raised to integer power */
-if( x <= 0.0L )
- {
- if( x == 0.0L )
- {
- if( y < 0.0 )
- {
-#ifdef MINUSZERO
- if( signbitl(x) && yoddint )
- return( -INFINITYL );
-#endif
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- return( MAXNUML );
-#endif
- }
- if( y > 0.0 )
- {
-#ifdef MINUSZERO
- if( signbitl(x) && yoddint )
- return( NEGZEROL );
-#endif
- return( 0.0 );
- }
- if( y == 0.0L )
- return( 1.0L ); /* 0**0 */
- else
- return( 0.0L ); /* 0**y */
- }
- else
- {
- if( iyflg == 0 )
- { /* noninteger power of negative number */
- mtherr( fname, DOMAIN );
-#ifdef NANS
- return(NANL);
-#else
- return(0.0L);
-#endif
- }
- nflg = 1;
- }
- }
-
-/* Integer power of an integer. */
-
-if( iyflg )
- {
- i = w;
- w = floorl(x);
- if( (w == x) && (fabsl(y) < 32768.0) )
- {
- w = powil( x, (int) y );
- return( w );
- }
- }
-
-
-if( nflg )
- x = fabsl(x);
-
-/* separate significand from exponent */
-x = frexpl( x, &i );
-e = i;
-
-/* find significand in antilog table A[] */
-i = 1;
-if( x <= douba(17) )
- i = 17;
-if( x <= douba(i+8) )
- i += 8;
-if( x <= douba(i+4) )
- i += 4;
-if( x <= douba(i+2) )
- i += 2;
-if( x >= douba(1) )
- i = -1;
-i += 1;
-
-
-/* Find (x - A[i])/A[i]
- * in order to compute log(x/A[i]):
- *
- * log(x) = log( a x/a ) = log(a) + log(x/a)
- *
- * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
- */
-x -= douba(i);
-x -= doubb(i/2);
-x /= douba(i);
-
-
-/* rational approximation for log(1+v):
- *
- * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
- */
-z = x*x;
-w = x * ( z * polevll( x, P, 3 ) / p1evll( x, Q, 3 ) );
-w = w - ldexpl( z, -1 ); /* w - 0.5 * z */
-
-/* Convert to base 2 logarithm:
- * multiply by log2(e) = 1 + LOG2EA
- */
-z = LOG2EA * w;
-z += w;
-z += LOG2EA * x;
-z += x;
-
-/* Compute exponent term of the base 2 logarithm. */
-w = -i;
-w = ldexpl( w, -LNXT ); /* divide by NXT */
-w += e;
-/* Now base 2 log of x is w + z. */
-
-/* Multiply base 2 log by y, in extended precision. */
-
-/* separate y into large part ya
- * and small part yb less than 1/NXT
- */
-ya = reducl(y);
-yb = y - ya;
-
-/* (w+z)(ya+yb)
- * = w*ya + w*yb + z*y
- */
-F = z * y + w * yb;
-Fa = reducl(F);
-Fb = F - Fa;
-
-G = Fa + w * ya;
-Ga = reducl(G);
-Gb = G - Ga;
-
-H = Fb + Gb;
-Ha = reducl(H);
-w = ldexpl( Ga+Ha, LNXT );
-
-/* Test the power of 2 for overflow */
-if( w > MEXP )
- {
-/* printf( "w = %.4Le ", w ); */
- mtherr( fname, OVERFLOW );
- return( MAXNUML );
- }
-
-if( w < MNEXP )
- {
-/* printf( "w = %.4Le ", w ); */
- mtherr( fname, UNDERFLOW );
- return( 0.0L );
- }
-
-e = w;
-Hb = H - Ha;
-
-if( Hb > 0.0L )
- {
- e += 1;
- Hb -= (1.0L/NXT); /*0.0625L;*/
- }
-
-/* Now the product y * log2(x) = Hb + e/NXT.
- *
- * Compute base 2 exponential of Hb,
- * where -0.0625 <= Hb <= 0.
- */
-z = Hb * polevll( Hb, R, 6 ); /* z = 2**Hb - 1 */
-
-/* Express e/NXT as an integer plus a negative number of (1/NXT)ths.
- * Find lookup table entry for the fractional power of 2.
- */
-if( e < 0 )
- i = 0;
-else
- i = 1;
-i = e/NXT + i;
-e = NXT*i - e;
-w = douba( e );
-z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
-z = z + w;
-z = ldexpl( z, i ); /* multiply by integer power of 2 */
-
-if( nflg )
- {
-/* For negative x,
- * find out if the integer exponent
- * is odd or even.
- */
- w = ldexpl( y, -1 );
- w = floorl(w);
- w = ldexpl( w, 1 );
- if( w != y )
- z = -z; /* odd exponent */
- }
-
-return( z );
-}
-
-
-/* Find a multiple of 1/NXT that is within 1/NXT of x. */
-static long double reducl(x)
-long double x;
-{
-long double t;
-
-t = ldexpl( x, LNXT );
-t = floorl( t );
-t = ldexpl( t, -LNXT );
-return(t);
-}
+++ /dev/null
-/* sinhl.c
- *
- * Hyperbolic sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, sinhl();
- *
- * y = sinhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic sine of argument in the range MINLOGL to
- * MAXLOGL.
- *
- * The range is partitioned into two segments. If |x| <= 1, a
- * rational function of the form x + x**3 P(x)/Q(x) is employed.
- * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -2,2 10000 1.5e-19 3.9e-20
- * IEEE +-10000 30000 1.1e-19 2.8e-20
- *
- */
-\f
-/*
-Cephes Math Library Release 2.7: January, 1998
-Copyright 1984, 1991, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
- 1.7550769032975377032681E-6L,
- 4.1680702175874268714539E-4L,
- 3.0993532520425419002409E-2L,
- 9.9999999999999999998002E-1L,
-};
-static long double Q[] = {
- 1.7453965448620151484660E-8L,
--5.9116673682651952419571E-6L,
- 1.0599252315677389339530E-3L,
--1.1403880487744749056675E-1L,
- 6.0000000000000000000200E0L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0xec6a,0xd942,0xfbb3,0xeb8f,0x3feb, XPD
-0x365e,0xb30a,0xe437,0xda86,0x3ff3, XPD
-0x8890,0x01f6,0x2612,0xfde6,0x3ff9, XPD
-0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
-};
-static short Q[] = {
-0x4edd,0x4c21,0xad09,0x95ed,0x3fe5, XPD
-0x4376,0x9b70,0xd605,0xc65c,0xbfed, XPD
-0xc8ad,0x5d21,0x3069,0x8aed,0x3ff5, XPD
-0x9c32,0x6374,0x2d4b,0xe98d,0xbffb, XPD
-0x0000,0x0000,0x0000,0xc000,0x4001, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0x3feb0000,0xeb8ffbb3,0xd942ec6a,
-0x3ff30000,0xda86e437,0xb30a365e,
-0x3ff90000,0xfde62612,0x01f68890,
-0x3fff0000,0x80000000,0x00000000,
-};
-static long Q[] = {
-0x3fe50000,0x95edad09,0x4c214edd,
-0xbfed0000,0xc65cd605,0x9b704376,
-0x3ff50000,0x8aed3069,0x5d21c8ad,
-0xbffb0000,0xe98d2d4b,0x63749c32,
-0x40010000,0xc0000000,0x00000000,
-};
-#endif
-
-extern long double MAXNUML, MAXLOGL, MINLOGL, LOGE2L;
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double expl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-#else
-long double fabsl(), expl(), polevll(), p1evll();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double sinhl(x)
-long double x;
-{
-long double a;
-
-#ifdef MINUSZERO
-if( x == 0.0 )
- return(x);
-#endif
-a = fabsl(x);
-if( (x > (MAXLOGL + LOGE2L)) || (x > -(MINLOGL-LOGE2L) ) )
- {
- mtherr( "sinhl", DOMAIN );
-#ifdef INFINITIES
- if( x > 0.0L )
- return( INFINITYL );
- else
- return( -INFINITYL );
-#else
- if( x > 0.0L )
- return( MAXNUML );
- else
- return( -MAXNUML );
-#endif
- }
-if( a > 1.0L )
- {
- if( a >= (MAXLOGL - LOGE2L) )
- {
- a = expl(0.5L*a);
- a = (0.5L * a) * a;
- if( x < 0.0L )
- a = -a;
- return(a);
- }
- a = expl(a);
- a = 0.5L*a - (0.5L/a);
- if( x < 0.0L )
- a = -a;
- return(a);
- }
-
-a *= a;
-return( x + x * a * (polevll(a,P,3)/polevll(a,Q,4)) );
-}
+++ /dev/null
-/* sinl.c
- *
- * Circular sine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, sinl();
- *
- * y = sinl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the sine is approximated by the Cody
- * and Waite polynomial form
- * x + x**3 P(x**2) .
- * Between pi/4 and pi/2 the cosine is represented as
- * 1 - .5 x**2 + x**4 Q(x**2) .
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-5.5e11 200,000 1.2e-19 2.9e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sin total loss x > 2**39 0.0
- *
- * Loss of precision occurs for x > 2**39 = 5.49755813888e11.
- * The routine as implemented flags a TLOSS error for
- * x > 2**39 and returns 0.0.
- */
-\f/* cosl.c
- *
- * Circular cosine, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, cosl();
- *
- * y = cosl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Range reduction is into intervals of pi/4. The reduction
- * error is nearly eliminated by contriving an extended precision
- * modular arithmetic.
- *
- * Two polynomial approximating functions are employed.
- * Between 0 and pi/4 the cosine is approximated by
- * 1 - .5 x**2 + x**4 Q(x**2) .
- * Between pi/4 and pi/2 the sine is represented by the Cody
- * and Waite polynomial form
- * x + x**3 P(x**2) .
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-5.5e11 50000 1.2e-19 2.9e-20
- */
-\f
-/* sin.c */
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1985, 1990, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static long double sincof[7] = {
--7.5785404094842805756289E-13L,
- 1.6058363167320443249231E-10L,
--2.5052104881870868784055E-8L,
- 2.7557319214064922217861E-6L,
--1.9841269841254799668344E-4L,
- 8.3333333333333225058715E-3L,
--1.6666666666666666640255E-1L,
-};
-static long double coscof[7] = {
- 4.7377507964246204691685E-14L,
--1.1470284843425359765671E-11L,
- 2.0876754287081521758361E-9L,
--2.7557319214999787979814E-7L,
- 2.4801587301570552304991E-5L,
--1.3888888888888872993737E-3L,
- 4.1666666666666666609054E-2L,
-};
-static long double DP1 = 7.853981554508209228515625E-1L;
-static long double DP2 = 7.946627356147928367136046290398E-9L;
-static long double DP3 = 3.061616997868382943065164830688E-17L;
-#endif
-
-#ifdef IBMPC
-static short sincof[] = {
-0x4e27,0xe1d6,0x2389,0xd551,0xbfd6, XPD
-0x64d7,0xe706,0x4623,0xb090,0x3fde, XPD
-0x01b1,0xbf34,0x2946,0xd732,0xbfe5, XPD
-0xc8f7,0x9845,0x1d29,0xb8ef,0x3fec, XPD
-0x6514,0x0c53,0x00d0,0xd00d,0xbff2, XPD
-0x569a,0x8888,0x8888,0x8888,0x3ff8, XPD
-0xaa97,0xaaaa,0xaaaa,0xaaaa,0xbffc, XPD
-};
-static short coscof[] = {
-0x7436,0x6f99,0x8c3a,0xd55e,0x3fd2, XPD
-0x2f37,0x58f4,0x920f,0xc9c9,0xbfda, XPD
-0x5350,0x659e,0xc648,0x8f76,0x3fe2, XPD
-0x4d2b,0xf5c6,0x7dba,0x93f2,0xbfe9, XPD
-0x53ed,0x0c66,0x00d0,0xd00d,0x3fef, XPD
-0x7b67,0x0b60,0x60b6,0xb60b,0xbff5, XPD
-0xaa9a,0xaaaa,0xaaaa,0xaaaa,0x3ffa, XPD
-};
-static short P1[] = {0x0000,0x0000,0xda80,0xc90f,0x3ffe, XPD};
-static short P2[] = {0x0000,0x0000,0xa300,0x8885,0x3fe4, XPD};
-static short P3[] = {0x3707,0xa2e0,0x3198,0x8d31,0x3fc8, XPD};
-#define DP1 *(long double *)P1
-#define DP2 *(long double *)P2
-#define DP3 *(long double *)P3
-#endif
-
-#ifdef MIEEE
-static long sincof[] = {
-0xbfd60000,0xd5512389,0xe1d64e27,
-0x3fde0000,0xb0904623,0xe70664d7,
-0xbfe50000,0xd7322946,0xbf3401b1,
-0x3fec0000,0xb8ef1d29,0x9845c8f7,
-0xbff20000,0xd00d00d0,0x0c536514,
-0x3ff80000,0x88888888,0x8888569a,
-0xbffc0000,0xaaaaaaaa,0xaaaaaa97,
-};
-static long coscof[] = {
-0x3fd20000,0xd55e8c3a,0x6f997436,
-0xbfda0000,0xc9c9920f,0x58f42f37,
-0x3fe20000,0x8f76c648,0x659e5350,
-0xbfe90000,0x93f27dba,0xf5c64d2b,
-0x3fef0000,0xd00d00d0,0x0c6653ed,
-0xbff50000,0xb60b60b6,0x0b607b67,
-0x3ffa0000,0xaaaaaaaa,0xaaaaaa9a,
-};
-static long P1[] = {0x3ffe0000,0xc90fda80,0x00000000};
-static long P2[] = {0x3fe40000,0x8885a300,0x00000000};
-static long P3[] = {0x3fc80000,0x8d313198,0xa2e03707};
-#define DP1 *(long double *)P1
-#define DP2 *(long double *)P2
-#define DP3 *(long double *)P3
-#endif
-
-static long double lossth = 5.49755813888e11L; /* 2^39 */
-extern long double PIO4L;
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double floorl ( long double );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-extern int isfinitel ( long double );
-#else
-long double polevll(), floorl(), ldexpl(), isnanl(), isfinitel();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double sinl(x)
-long double x;
-{
-long double y, z, zz;
-int j, sign;
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-#ifdef MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-#ifdef NANS
-if( !isfinitel(x) )
- {
- mtherr( "sinl", DOMAIN );
-#ifdef NANS
- return(NANL);
-#else
- return(0.0L);
-#endif
- }
-#endif
-/* make argument positive but save the sign */
-sign = 1;
-if( x < 0 )
- {
- x = -x;
- sign = -1;
- }
-
-if( x > lossth )
- {
- mtherr( "sinl", TLOSS );
- return(0.0L);
- }
-
-y = floorl( x/PIO4L ); /* integer part of x/PIO4 */
-
-/* strip high bits of integer part to prevent integer overflow */
-z = ldexpl( y, -4 );
-z = floorl(z); /* integer part of y/8 */
-z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
-
-j = z; /* convert to integer for tests on the phase angle */
-/* map zeros to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0L;
- }
-j = j & 07; /* octant modulo 360 degrees */
-/* reflect in x axis */
-if( j > 3)
- {
- sign = -sign;
- j -= 4;
- }
-
-/* Extended precision modular arithmetic */
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-if( (j==1) || (j==2) )
- {
- y = 1.0L - ldexpl(zz,-1) + zz * zz * polevll( zz, coscof, 6 );
- }
-else
- {
- y = z + z * (zz * polevll( zz, sincof, 6 ));
- }
-
-if(sign < 0)
- y = -y;
-
-return(y);
-}
-
-
-
-
-
-long double cosl(x)
-long double x;
-{
-long double y, z, zz;
-long i;
-int j, sign;
-
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-#ifdef INFINITIES
-if( !isfinitel(x) )
- {
- mtherr( "cosl", DOMAIN );
-#ifdef NANS
- return(NANL);
-#else
- return(0.0L);
-#endif
- }
-#endif
-
-/* make argument positive */
-sign = 1;
-if( x < 0 )
- x = -x;
-
-if( x > lossth )
- {
- mtherr( "cosl", TLOSS );
- return(0.0L);
- }
-
-y = floorl( x/PIO4L );
-z = ldexpl( y, -4 );
-z = floorl(z); /* integer part of y/8 */
-z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
-
-/* integer and fractional part modulo one octant */
-i = z;
-if( i & 1 ) /* map zeros to origin */
- {
- i += 1;
- y += 1.0L;
- }
-j = i & 07;
-if( j > 3)
- {
- j -=4;
- sign = -sign;
- }
-
-if( j > 1 )
- sign = -sign;
-
-/* Extended precision modular arithmetic */
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-if( (j==1) || (j==2) )
- {
- y = z + z * (zz * polevll( zz, sincof, 6 ));
- }
-else
- {
- y = 1.0L - ldexpl(zz,-1) + zz * zz * polevll( zz, coscof, 6 );
- }
-
-if(sign < 0)
- y = -y;
-
-return(y);
-}
+++ /dev/null
-/* sqrtl.c
- *
- * Square root, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, sqrtl();
- *
- * y = sqrtl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the square root of x.
- *
- * Range reduction involves isolating the power of two of the
- * argument and using a polynomial approximation to obtain
- * a rough value for the square root. Then Heron's iteration
- * is used three times to converge to an accurate value.
- *
- * Note, some arithmetic coprocessors such as the 8087 and
- * 68881 produce correctly rounded square roots, which this
- * routine will not.
- *
- * ACCURACY:
- *
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,10 30000 8.1e-20 3.1e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * sqrt domain x < 0 0.0
- *
- */
-\f
-/*
-Cephes Math Library Release 2.2: December, 1990
-Copyright 1984, 1990 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-#define SQRT2 1.4142135623730950488017E0L
-#ifdef ANSIPROT
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-#else
-long double frexpl(), ldexpl();
-#endif
-
-long double sqrtl(x)
-long double x;
-{
-int e;
-long double z, w;
-#ifndef UNK
-short *q;
-#endif
-
-if( x <= 0.0 )
- {
- if( x < 0.0 )
- mtherr( "sqrtl", DOMAIN );
- return( 0.0 );
- }
-w = x;
-/* separate exponent and significand */
-#ifdef UNK
-z = frexpl( x, &e );
-#endif
-
-/* Note, frexp and ldexp are used in order to
- * handle denormal numbers properly.
- */
-#ifdef IBMPC
-z = frexpl( x, &e );
-q = (short *)&x; /* point to the exponent word */
-q += 4;
-/*
-e = ((*q >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x000f;
-*q |= 0x3fe0;
-z = x;
-*/
-#endif
-#ifdef MIEEE
-z = frexpl( x, &e );
-q = (short *)&x;
-/*
-e = ((*q >> 4) & 0x0fff) - 0x3fe;
-*q &= 0x000f;
-*q |= 0x3fe0;
-z = x;
-*/
-#endif
-
-/* approximate square root of number between 0.5 and 1
- * relative error of linear approximation = 7.47e-3
- */
-/*
-x = 0.4173075996388649989089L + 0.59016206709064458299663L * z;
-*/
-
-/* quadratic approximation, relative error 6.45e-4 */
-x = ( -0.20440583154734771959904L * z
- + 0.89019407351052789754347L) * z
- + 0.31356706742295303132394L;
-
-/* adjust for odd powers of 2 */
-if( (e & 1) != 0 )
- x *= SQRT2;
-
-/* re-insert exponent */
-#ifdef UNK
-x = ldexpl( x, (e >> 1) );
-#endif
-#ifdef IBMPC
-x = ldexpl( x, (e >> 1) );
-/*
-*q += ((e >>1) & 0x7ff) << 4;
-*q &= 077777;
-*/
-#endif
-#ifdef MIEEE
-x = ldexpl( x, (e >> 1) );
-/*
-*q += ((e >>1) & 0x7ff) << 4;
-*q &= 077777;
-*/
-#endif
-
-/* Newton iterations: */
-#ifdef UNK
-x += w/x;
-x = ldexpl( x, -1 ); /* divide by 2 */
-x += w/x;
-x = ldexpl( x, -1 );
-x += w/x;
-x = ldexpl( x, -1 );
-#endif
-
-/* Note, assume the square root cannot be denormal,
- * so it is safe to use integer exponent operations here.
- */
-#ifdef IBMPC
-x += w/x;
-*q -= 1;
-x += w/x;
-*q -= 1;
-x += w/x;
-*q -= 1;
-#endif
-#ifdef MIEEE
-x += w/x;
-*q -= 1;
-x += w/x;
-*q -= 1;
-x += w/x;
-*q -= 1;
-#endif
-
-return(x);
-}
+++ /dev/null
-/* stdtrl.c
- *
- * Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double p, t, stdtrl();
- * int k;
- *
- * p = stdtrl( k, t );
- *
- *
- * DESCRIPTION:
- *
- * Computes the integral from minus infinity to t of the Student
- * t distribution with integer k > 0 degrees of freedom:
- *
- * t
- * -
- * | |
- * - | 2 -(k+1)/2
- * | ( (k+1)/2 ) | ( x )
- * ---------------------- | ( 1 + --- ) dx
- * - | ( k )
- * sqrt( k pi ) | ( k/2 ) |
- * | |
- * -
- * -inf.
- *
- * Relation to incomplete beta integral:
- *
- * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
- * where
- * z = k/(k + t**2).
- *
- * For t < -1.6, this is the method of computation. For higher t,
- * a direct method is derived from integration by parts.
- * Since the function is symmetric about t=0, the area under the
- * right tail of the density is found by calling the function
- * with -t instead of t.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 100. The "domain" refers to t.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -100,-1.6 10000 5.7e-18 9.8e-19
- * IEEE -1.6,100 10000 3.8e-18 1.0e-19
- */
-\f
-/* stdtril.c
- *
- * Functional inverse of Student's t distribution
- *
- *
- *
- * SYNOPSIS:
- *
- * long double p, t, stdtril();
- * int k;
- *
- * t = stdtril( k, p );
- *
- *
- * DESCRIPTION:
- *
- * Given probability p, finds the argument t such that stdtrl(k,t)
- * is equal to p.
- *
- * ACCURACY:
- *
- * Tested at random 1 <= k <= 100. The "domain" refers to p:
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,1 3500 4.2e-17 4.1e-18
- */
-\f
-
-/*
-Cephes Math Library Release 2.3: January, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern long double PIL, MACHEPL, MAXNUML;
-#ifdef ANSIPROT
-extern long double sqrtl ( long double );
-extern long double atanl ( long double );
-extern long double incbetl ( long double, long double, long double );
-extern long double incbil ( long double, long double, long double );
-extern long double fabsl ( long double );
-#else
-long double sqrtl(), atanl(), incbetl(), incbil(), fabsl();
-#endif
-
-long double stdtrl( k, t )
-int k;
-long double t;
-{
-long double x, rk, z, f, tz, p, xsqk;
-int j;
-
-if( k <= 0 )
- {
- mtherr( "stdtrl", DOMAIN );
- return(0.0L);
- }
-
-if( t == 0.0L )
- return( 0.5L );
-
-if( t < -1.6L )
- {
- rk = k;
- z = rk / (rk + t * t);
- p = 0.5L * incbetl( 0.5L*rk, 0.5L, z );
- return( p );
- }
-
-/* compute integral from -t to + t */
-
-if( t < 0.0L )
- x = -t;
-else
- x = t;
-
-rk = k; /* degrees of freedom */
-z = 1.0L + ( x * x )/rk;
-
-/* test if k is odd or even */
-if( (k & 1) != 0)
- {
-
- /* computation for odd k */
-
- xsqk = x/sqrtl(rk);
- p = atanl( xsqk );
- if( k > 1 )
- {
- f = 1.0L;
- tz = 1.0L;
- j = 3;
- while( (j<=(k-2)) && ( (tz/f) > MACHEPL ) )
- {
- tz *= (j-1)/( z * j );
- f += tz;
- j += 2;
- }
- p += f * xsqk/z;
- }
- p *= 2.0L/PIL;
- }
-
-
-else
- {
-
- /* computation for even k */
-
- f = 1.0L;
- tz = 1.0L;
- j = 2;
-
- while( ( j <= (k-2) ) && ( (tz/f) > MACHEPL ) )
- {
- tz *= (j - 1)/( z * j );
- f += tz;
- j += 2;
- }
- p = f * x/sqrtl(z*rk);
- }
-
-/* common exit */
-
-
-if( t < 0.0L )
- p = -p; /* note destruction of relative accuracy */
-
- p = 0.5L + 0.5L * p;
-return(p);
-}
-
-
-long double stdtril( k, p )
-int k;
-long double p;
-{
-long double t, rk, z;
-int rflg;
-
-if( k <= 0 || p <= 0.0L || p >= 1.0L )
- {
- mtherr( "stdtril", DOMAIN );
- return(0.0L);
- }
-
-rk = k;
-
-if( p > 0.25L && p < 0.75L )
- {
- if( p == 0.5L )
- return( 0.0L );
- z = 1.0L - 2.0L * p;
- z = incbil( 0.5L, 0.5L*rk, fabsl(z) );
- t = sqrtl( rk*z/(1.0L-z) );
- if( p < 0.5L )
- t = -t;
- return( t );
- }
-rflg = -1;
-if( p >= 0.5L)
- {
- p = 1.0L - p;
- rflg = 1;
- }
-z = incbil( 0.5L*rk, 0.5L, 2.0L*p );
-
-if( MAXNUML * z < rk )
- return(rflg* MAXNUML);
-t = sqrtl( rk/z - rk );
-return( rflg * t );
-}
+++ /dev/null
-/* tanhl.c
- *
- * Hyperbolic tangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, tanhl();
- *
- * y = tanhl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns hyperbolic tangent of argument in the range MINLOGL to
- * MAXLOGL.
- *
- * A rational function is used for |x| < 0.625. The form
- * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
- * Otherwise,
- * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -2,2 30000 1.3e-19 2.4e-20
- *
- */
-\f
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1987, 1989, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
--6.8473739392677100872869E-5L,
--9.5658283111794641589011E-1L,
--8.4053568599672284488465E1L,
--1.3080425704712825945553E3L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
- 9.6259501838840336946872E1L,
- 1.8218117903645559060232E3L,
- 3.9241277114138477845780E3L,
-};
-#endif
-
-#ifdef IBMPC
-static short P[] = {
-0xd2a4,0x1b0c,0x8f15,0x8f99,0xbff1, XPD
-0x5959,0x9111,0x9cc7,0xf4e2,0xbffe, XPD
-0xb576,0xef5e,0x6d57,0xa81b,0xc005, XPD
-0xe3be,0xbfbd,0x5cbc,0xa381,0xc009, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x687f,0xce24,0xdd6c,0xc084,0x4005, XPD
-0x3793,0xc95f,0xfa2f,0xe3b9,0x4009, XPD
-0xd5a2,0x1f9c,0x0b1b,0xf542,0x400a, XPD
-};
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0xbff10000,0x8f998f15,0x1b0cd2a4,
-0xbffe0000,0xf4e29cc7,0x91115959,
-0xc0050000,0xa81b6d57,0xef5eb576,
-0xc0090000,0xa3815cbc,0xbfbde3be,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x40050000,0xc084dd6c,0xce24687f,
-0x40090000,0xe3b9fa2f,0xc95f3793,
-0x400a0000,0xf5420b1b,0x1f9cd5a2,
-};
-#endif
-
-extern long double MAXLOGL;
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double expl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-#else
-long double fabsl(), expl(), polevll(), p1evll();
-#endif
-
-long double tanhl(x)
-long double x;
-{
-long double s, z;
-
-#ifdef MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-z = fabsl(x);
-if( z > 0.5L * MAXLOGL )
- {
- if( x > 0 )
- return( 1.0L );
- else
- return( -1.0L );
- }
-if( z >= 0.625L )
- {
- s = expl(2.0*z);
- z = 1.0L - 2.0/(s + 1.0L);
- if( x < 0 )
- z = -z;
- }
-else
- {
- s = x * x;
- z = polevll( s, P, 3 )/p1evll(s, Q, 3);
- z = x * s * z;
- z = x + z;
- }
-return( z );
-}
+++ /dev/null
-/* tanl.c
- *
- * Circular tangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, tanl();
- *
- * y = tanl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular tangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-1.07e9 30000 1.9e-19 4.8e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * tan total loss x > 2^39 0.0
- *
- */
-\f/* cotl.c
- *
- * Circular cotangent, long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, cotl();
- *
- * y = cotl( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the circular cotangent of the radian argument x.
- *
- * Range reduction is modulo pi/4. A rational function
- * x + x**3 P(x**2)/Q(x**2)
- * is employed in the basic interval [0, pi/4].
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE +-1.07e9 30000 1.9e-19 5.1e-20
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * cot total loss x > 2^39 0.0
- * cot singularity x = 0 INFINITYL
- *
- */
-\f
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1984, 1990, 1998 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef UNK
-static long double P[] = {
--1.3093693918138377764608E4L,
- 1.1535166483858741613983E6L,
--1.7956525197648487798769E7L,
-};
-static long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
- 1.3681296347069295467845E4L,
--1.3208923444021096744731E6L,
- 2.5008380182335791583922E7L,
--5.3869575592945462988123E7L,
-};
-static long double DP1 = 7.853981554508209228515625E-1L;
-static long double DP2 = 7.946627356147928367136046290398E-9L;
-static long double DP3 = 3.061616997868382943065164830688E-17L;
-#endif
-
-
-#ifdef IBMPC
-static short P[] = {
-0xbc1c,0x79f9,0xc692,0xcc96,0xc00c, XPD
-0xe5b1,0xe4ee,0x652f,0x8ccf,0x4013, XPD
-0xaf9a,0x4c8b,0x5699,0x88ff,0xc017, XPD
-};
-static short Q[] = {
-/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
-0x8ed4,0x9b2b,0x2f75,0xd5c5,0x400c, XPD
-0xadcd,0x55e4,0xe2c1,0xa13d,0xc013, XPD
-0x7adf,0x56c7,0x7e17,0xbecc,0x4017, XPD
-0x86f6,0xf2d1,0x01e5,0xcd7f,0xc018, XPD
-};
-static short P1[] = {0x0000,0x0000,0xda80,0xc90f,0x3ffe, XPD};
-static short P2[] = {0x0000,0x0000,0xa300,0x8885,0x3fe4, XPD};
-static short P3[] = {0x3707,0xa2e0,0x3198,0x8d31,0x3fc8, XPD};
-#define DP1 *(long double *)P1
-#define DP2 *(long double *)P2
-#define DP3 *(long double *)P3
-#endif
-
-#ifdef MIEEE
-static long P[] = {
-0xc00c0000,0xcc96c692,0x79f9bc1c,
-0x40130000,0x8ccf652f,0xe4eee5b1,
-0xc0170000,0x88ff5699,0x4c8baf9a,
-};
-static long Q[] = {
-/*0x3fff0000,0x80000000,0x00000000,*/
-0x400c0000,0xd5c52f75,0x9b2b8ed4,
-0xc0130000,0xa13de2c1,0x55e4adcd,
-0x40170000,0xbecc7e17,0x56c77adf,
-0xc0180000,0xcd7f01e5,0xf2d186f6,
-};
-static long P1[] = {0x3ffe0000,0xc90fda80,0x00000000};
-static long P2[] = {0x3fe40000,0x8885a300,0x00000000};
-static long P3[] = {0x3fc80000,0x8d313198,0xa2e03707};
-#define DP1 *(long double *)P1
-#define DP2 *(long double *)P2
-#define DP3 *(long double *)P3
-#endif
-
-static long double lossth = 5.49755813888e11L; /* 2^39 */
-extern long double PIO4L;
-extern long double MAXNUML;
-
-#ifdef ANSIPROT
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-extern long double floorl ( long double );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-extern int isfinitel ( long double );
-static long double tancotl( long double, int );
-#else
-long double polevll(), p1evll(), floorl(), ldexpl(), isnanl(), isfinitel();
-static long double tancotl();
-#endif
-#ifdef INFINITIES
-extern long double INFINITYL;
-#endif
-#ifdef NANS
-extern long double NANL;
-#endif
-
-long double tanl(x)
-long double x;
-{
-
-#ifdef NANS
-if( isnanl(x) )
- return(x);
-#endif
-#ifdef MINUSZERO
-if( x == 0.0L )
- return(x);
-#endif
-#ifdef NANS
-if( !isfinitel(x) )
- {
- mtherr( "tanl", DOMAIN );
- return(NANL);
- }
-#endif
-return( tancotl(x,0) );
-}
-
-
-long double cotl(x)
-long double x;
-{
-
-if( x == 0.0L )
- {
- mtherr( "cotl", SING );
-#ifdef INFINITIES
- return( INFINITYL );
-#else
- return( MAXNUML );
-#endif
- }
-return( tancotl(x,1) );
-}
-
-
-static long double tancotl( xx, cotflg )
-long double xx;
-int cotflg;
-{
-long double x, y, z, zz;
-int j, sign;
-
-/* make argument positive but save the sign */
-if( xx < 0.0L )
- {
- x = -xx;
- sign = -1;
- }
-else
- {
- x = xx;
- sign = 1;
- }
-
-if( x > lossth )
- {
- if( cotflg )
- mtherr( "cotl", TLOSS );
- else
- mtherr( "tanl", TLOSS );
- return(0.0L);
- }
-
-/* compute x mod PIO4 */
-y = floorl( x/PIO4L );
-
-/* strip high bits of integer part */
-z = ldexpl( y, -4 );
-z = floorl(z); /* integer part of y/16 */
-z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
-
-/* integer and fractional part modulo one octant */
-j = z;
-
-/* map zeros and singularities to origin */
-if( j & 1 )
- {
- j += 1;
- y += 1.0L;
- }
-
-z = ((x - y * DP1) - y * DP2) - y * DP3;
-
-zz = z * z;
-
-if( zz > 1.0e-20L )
- y = z + z * (zz * polevll( zz, P, 2 )/p1evll(zz, Q, 4));
-else
- y = z;
-
-if( j & 2 )
- {
- if( cotflg )
- y = -y;
- else
- y = -1.0L/y;
- }
-else
- {
- if( cotflg )
- y = 1.0L/y;
- }
-
-if( sign < 0 )
- y = -y;
-
-return( y );
-}
+++ /dev/null
-
-/* Test vectors for math functions.
- See C9X section F.9.
-
- On some systems it may be necessary to modify the default exception
- settings of the floating point arithmetic unit. */
-
-/*
-Cephes Math Library Release 2.7: May, 1998
-Copyright 1998 by Stephen L. Moshier
-*/
-
-#include <stdio.h>
-int isfinitel (long double);
-
-/* Some compilers will not accept these expressions. */
-
-#define ZINF 1
-#define ZMINF 2
-#define ZNANL 3
-#define ZPIL 4
-#define ZPIO2L 4
-
-extern long double INFINITYL, NANL, NEGZEROL;
-long double MINFL;
-extern long double PIL, PIO2L, PIO4L, MACHEPL;
-long double MPIL;
-long double MPIO2L;
-long double MPIO4L;
-long double THPIO4L = 2.35619449019234492884698L;
-long double MTHPIO4L = -2.35619449019234492884698L;
-long double SQRT2L = 1.414213562373095048802E0L;
-long double SQRTHL = 7.071067811865475244008E-1L;
-long double ZEROL = 0.0L;
-long double HALFL = 0.5L;
-long double MHALFL = -0.5L;
-long double ONEL = 1.0L;
-long double MONEL = -1.0L;
-long double TWOL = 2.0L;
-long double MTWOL = -2.0L;
-long double THREEL = 3.0L;
-long double MTHREEL = -3.0L;
-
-/* Functions of one variable. */
-long double logl (long double);
-long double expl (long double);
-long double atanl (long double);
-long double sinl (long double);
-long double cosl (long double);
-long double tanl (long double);
-long double acosl (long double);
-long double asinl (long double);
-long double acoshl (long double);
-long double asinhl (long double);
-long double atanhl (long double);
-long double sinhl (long double);
-long double coshl (long double);
-long double tanhl (long double);
-long double exp2l (long double);
-long double expm1l (long double);
-long double log10l (long double);
-long double log1pl (long double);
-long double log2l (long double);
-long double fabsl (long double);
-long double erfl (long double);
-long double erfcl (long double);
-long double gammal (long double);
-long double lgaml (long double);
-long double floorl (long double);
-long double ceill (long double);
-long double cbrtl (long double);
-
-struct oneargument
- {
- char *name; /* Name of the function. */
- long double (*func) (long double);
- long double *arg1;
- long double *answer;
- int thresh; /* Error report threshold. */
- };
-
-#if 0
- {"sinl", sinl, 32767.L, 1.8750655394138942394239E-1L, 0},
- {"cosl", cosl, 32767.L, 9.8226335176928229845654E-1L, 0},
- {"tanl", tanl, 32767.L, 1.9089234430221485740826E-1L, 0},
- {"sinl", sinl, 8388607.L, 9.9234509376961249835628E-1L, 0},
- {"cosl", cosl, 8388607.L, -1.2349580912475928183718E-1L, 0},
- {"tanl", tanl, 8388607.L, -8.0354556223613614748329E0L, 0},
- {"sinl", sinl, 2147483647.L, -7.2491655514455639054829E-1L, 0},
- {"cosl", cosl, 2147483647.L, -6.8883669187794383467976E-1L, 0},
- {"tanl", tanl, 2147483647.L, 1.0523779637351339136698E0L, 0},
- {"sinl", sinl, PIO4L, 7.0710678118654752440084E-1L, 0},
- {"cosl", cosl, PIO2L, -2.50827880633416613471e-20L, 0},
-#endif
-
-struct oneargument test1[] =
-{
- {"atanl", atanl, &ONEL, &PIO4L, 0},
- {"sinl", sinl, &PIO2L, &ONEL, 0},
- {"cosl", cosl, &PIO4L, &SQRTHL, 0},
- {"acosl", acosl, &NANL, &NANL, 0},
- {"acosl", acosl, &ONEL, &ZEROL, 0},
- {"acosl", acosl, &TWOL, &NANL, 0},
- {"acosl", acosl, &MTWOL, &NANL, 0},
- {"asinl", asinl, &NANL, &NANL, 0},
- {"asinl", asinl, &ZEROL, &ZEROL, 0},
- {"asinl", asinl, &NEGZEROL, &NEGZEROL, 0},
- {"asinl", asinl, &TWOL, &NANL, 0},
- {"asinl", asinl, &MTWOL, &NANL, 0},
- {"atanl", atanl, &NANL, &NANL, 0},
- {"atanl", atanl, &ZEROL, &ZEROL, 0},
- {"atanl", atanl, &NEGZEROL, &NEGZEROL, 0},
- {"atanl", atanl, &INFINITYL, &PIO2L, 0},
- {"atanl", atanl, &MINFL, &MPIO2L, 0},
- {"cosl", cosl, &NANL, &NANL, 0},
- {"cosl", cosl, &ZEROL, &ONEL, 0},
- {"cosl", cosl, &NEGZEROL, &ONEL, 0},
- {"cosl", cosl, &INFINITYL, &NANL, 0},
- {"cosl", cosl, &MINFL, &NANL, 0},
- {"sinl", sinl, &NANL, &NANL, 0},
- {"sinl", sinl, &NEGZEROL, &NEGZEROL, 0},
- {"sinl", sinl, &ZEROL, &ZEROL, 0},
- {"sinl", sinl, &INFINITYL, &NANL, 0},
- {"sinl", sinl, &MINFL, &NANL, 0},
- {"tanl", tanl, &NANL, &NANL, 0},
- {"tanl", tanl, &ZEROL, &ZEROL, 0},
- {"tanl", tanl, &NEGZEROL, &NEGZEROL, 0},
- {"tanl", tanl, &INFINITYL, &NANL, 0},
- {"tanl", tanl, &MINFL, &NANL, 0},
- {"acoshl", acoshl, &NANL, &NANL, 0},
- {"acoshl", acoshl, &ONEL, &ZEROL, 0},
- {"acoshl", acoshl, &INFINITYL, &INFINITYL, 0},
- {"acoshl", acoshl, &HALFL, &NANL, 0},
- {"acoshl", acoshl, &MONEL, &NANL, 0},
- {"asinhl", asinhl, &NANL, &NANL, 0},
- {"asinhl", asinhl, &ZEROL, &ZEROL, 0},
- {"asinhl", asinhl, &NEGZEROL, &NEGZEROL, 0},
- {"asinhl", asinhl, &INFINITYL, &INFINITYL, 0},
- {"asinhl", asinhl, &MINFL, &MINFL, 0},
- {"atanhl", atanhl, &NANL, &NANL, 0},
- {"atanhl", atanhl, &ZEROL, &ZEROL, 0},
- {"atanhl", atanhl, &NEGZEROL, &NEGZEROL, 0},
- {"atanhl", atanhl, &ONEL, &INFINITYL, 0},
- {"atanhl", atanhl, &MONEL, &MINFL, 0},
- {"atanhl", atanhl, &TWOL, &NANL, 0},
- {"atanhl", atanhl, &MTWOL, &NANL, 0},
- {"coshl", coshl, &NANL, &NANL, 0},
- {"coshl", coshl, &ZEROL, &ONEL, 0},
- {"coshl", coshl, &NEGZEROL, &ONEL, 0},
- {"coshl", coshl, &INFINITYL, &INFINITYL, 0},
- {"coshl", coshl, &MINFL, &INFINITYL, 0},
- {"sinhl", sinhl, &NANL, &NANL, 0},
- {"sinhl", sinhl, &ZEROL, &ZEROL, 0},
- {"sinhl", sinhl, &NEGZEROL, &NEGZEROL, 0},
- {"sinhl", sinhl, &INFINITYL, &INFINITYL, 0},
- {"sinhl", sinhl, &MINFL, &MINFL, 0},
- {"tanhl", tanhl, &NANL, &NANL, 0},
- {"tanhl", tanhl, &ZEROL, &ZEROL, 0},
- {"tanhl", tanhl, &NEGZEROL, &NEGZEROL, 0},
- {"tanhl", tanhl, &INFINITYL, &ONEL, 0},
- {"tanhl", tanhl, &MINFL, &MONEL, 0},
- {"expl", expl, &NANL, &NANL, 0},
- {"expl", expl, &ZEROL, &ONEL, 0},
- {"expl", expl, &NEGZEROL, &ONEL, 0},
- {"expl", expl, &INFINITYL, &INFINITYL, 0},
- {"expl", expl, &MINFL, &ZEROL, 0},
- {"exp2l", exp2l, &NANL, &NANL, 0},
- {"exp2l", exp2l, &ZEROL, &ONEL, 0},
- {"exp2l", exp2l, &NEGZEROL, &ONEL, 0},
- {"exp2l", exp2l, &INFINITYL, &INFINITYL, 0},
- {"exp2l", exp2l, &MINFL, &ZEROL, 0},
- {"expm1l", expm1l, &NANL, &NANL, 0},
- {"expm1l", expm1l, &ZEROL, &ZEROL, 0},
- {"expm1l", expm1l, &NEGZEROL, &NEGZEROL, 0},
- {"expm1l", expm1l, &INFINITYL, &INFINITYL, 0},
- {"expm1l", expm1l, &MINFL, &MONEL, 0},
- {"logl", logl, &NANL, &NANL, 0},
- {"logl", logl, &ZEROL, &MINFL, 0},
- {"logl", logl, &NEGZEROL, &MINFL, 0},
- {"logl", logl, &ONEL, &ZEROL, 0},
- {"logl", logl, &MONEL, &NANL, 0},
- {"logl", logl, &INFINITYL, &INFINITYL, 0},
- {"log10l", log10l, &NANL, &NANL, 0},
- {"log10l", log10l, &ZEROL, &MINFL, 0},
- {"log10l", log10l, &NEGZEROL, &MINFL, 0},
- {"log10l", log10l, &ONEL, &ZEROL, 0},
- {"log10l", log10l, &MONEL, &NANL, 0},
- {"log10l", log10l, &INFINITYL, &INFINITYL, 0},
- {"log1pl", log1pl, &NANL, &NANL, 0},
- {"log1pl", log1pl, &ZEROL, &ZEROL, 0},
- {"log1pl", log1pl, &NEGZEROL, &NEGZEROL, 0},
- {"log1pl", log1pl, &MONEL, &MINFL, 0},
- {"log1pl", log1pl, &MTWOL, &NANL, 0},
- {"log1pl", log1pl, &INFINITYL, &INFINITYL, 0},
- {"log2l", log2l, &NANL, &NANL, 0},
- {"log2l", log2l, &ZEROL, &MINFL, 0},
- {"log2l", log2l, &NEGZEROL, &MINFL, 0},
- {"log2l", log2l, &MONEL, &NANL, 0},
- {"log2l", log2l, &INFINITYL, &INFINITYL, 0},
- /* {"fabsl", fabsl, &NANL, &NANL, 0}, */
- {"fabsl", fabsl, &ONEL, &ONEL, 0},
- {"fabsl", fabsl, &MONEL, &ONEL, 0},
- {"fabsl", fabsl, &ZEROL, &ZEROL, 0},
- {"fabsl", fabsl, &NEGZEROL, &ZEROL, 0},
- {"fabsl", fabsl, &INFINITYL, &INFINITYL, 0},
- {"fabsl", fabsl, &MINFL, &INFINITYL, 0},
- {"cbrtl", cbrtl, &NANL, &NANL, 0},
- {"cbrtl", cbrtl, &ZEROL, &ZEROL, 0},
- {"cbrtl", cbrtl, &NEGZEROL, &NEGZEROL, 0},
- {"cbrtl", cbrtl, &INFINITYL, &INFINITYL, 0},
- {"cbrtl", cbrtl, &MINFL, &MINFL, 0},
- {"erfl", erfl, &NANL, &NANL, 0},
- {"erfl", erfl, &ZEROL, &ZEROL, 0},
- {"erfl", erfl, &NEGZEROL, &NEGZEROL, 0},
- {"erfl", erfl, &INFINITYL, &ONEL, 0},
- {"erfl", erfl, &MINFL, &MONEL, 0},
- {"erfcl", erfcl, &NANL, &NANL, 0},
- {"erfcl", erfcl, &INFINITYL, &ZEROL, 0},
- {"erfcl", erfcl, &MINFL, &TWOL, 0},
- {"gammal", gammal, &NANL, &NANL, 0},
- {"gammal", gammal, &INFINITYL, &INFINITYL, 0},
- {"gammal", gammal, &MONEL, &NANL, 0},
- {"gammal", gammal, &ZEROL, &NANL, 0},
- {"gammal", gammal, &MINFL, &NANL, 0},
- {"lgaml", lgaml, &NANL, &NANL, 0},
- {"lgaml", lgaml, &INFINITYL, &INFINITYL, 0},
- {"lgaml", lgaml, &MONEL, &INFINITYL, 0},
- {"lgaml", lgaml, &ZEROL, &INFINITYL, 0},
- {"lgaml", lgaml, &MINFL, &INFINITYL, 0},
- {"ceill", ceill, &NANL, &NANL, 0},
- {"ceill", ceill, &ZEROL, &ZEROL, 0},
- {"ceill", ceill, &NEGZEROL, &NEGZEROL, 0},
- {"ceill", ceill, &INFINITYL, &INFINITYL, 0},
- {"ceill", ceill, &MINFL, &MINFL, 0},
- {"floorl", floorl, &NANL, &NANL, 0},
- {"floorl", floorl, &ZEROL, &ZEROL, 0},
- {"floorl", floorl, &NEGZEROL, &NEGZEROL, 0},
- {"floorl", floorl, &INFINITYL, &INFINITYL, 0},
- {"floorl", floorl, &MINFL, &MINFL, 0},
- {"null", NULL, &ZEROL, &ZEROL, 0},
-};
-
-/* Functions of two variables. */
-long double atan2l (long double, long double);
-long double powl (long double, long double);
-
-struct twoarguments
- {
- char *name; /* Name of the function. */
- long double (*func) (long double, long double);
- long double *arg1;
- long double *arg2;
- long double *answer;
- int thresh;
- };
-
-struct twoarguments test2[] =
-{
- {"atan2l", atan2l, &ZEROL, &ONEL, &ZEROL, 0},
- {"atan2l", atan2l, &NEGZEROL, &ONEL,&NEGZEROL, 0},
- {"atan2l", atan2l, &ZEROL, &ZEROL, &ZEROL, 0},
- {"atan2l", atan2l, &NEGZEROL, &ZEROL, &NEGZEROL, 0},
- {"atan2l", atan2l, &ZEROL, &MONEL, &PIL, 0},
- {"atan2l", atan2l, &NEGZEROL, &MONEL, &MPIL, 0},
- {"atan2l", atan2l, &ZEROL, &NEGZEROL, &PIL, 0},
- {"atan2l", atan2l, &NEGZEROL, &NEGZEROL, &MPIL, 0},
- {"atan2l", atan2l, &ONEL, &ZEROL, &PIO2L, 0},
- {"atan2l", atan2l, &ONEL, &NEGZEROL, &PIO2L, 0},
- {"atan2l", atan2l, &MONEL, &ZEROL, &MPIO2L, 0},
- {"atan2l", atan2l, &MONEL, &NEGZEROL, &MPIO2L, 0},
- {"atan2l", atan2l, &ONEL, &INFINITYL, &ZEROL, 0},
- {"atan2l", atan2l, &MONEL, &INFINITYL, &NEGZEROL, 0},
- {"atan2l", atan2l, &INFINITYL, &ONEL, &PIO2L, 0},
- {"atan2l", atan2l, &INFINITYL, &MONEL, &PIO2L, 0},
- {"atan2l", atan2l, &MINFL, &ONEL, &MPIO2L, 0},
- {"atan2l", atan2l, &MINFL, &MONEL, &MPIO2L, 0},
- {"atan2l", atan2l, &ONEL, &MINFL, &PIL, 0},
- {"atan2l", atan2l, &MONEL, &MINFL, &MPIL, 0},
- {"atan2l", atan2l, &INFINITYL, &INFINITYL, &PIO4L, 0},
- {"atan2l", atan2l, &MINFL, &INFINITYL, &MPIO4L, 0},
- {"atan2l", atan2l, &INFINITYL, &MINFL, &THPIO4L, 0},
- {"atan2l", atan2l, &MINFL, &MINFL, &MTHPIO4L, 0},
- {"atan2l", atan2l, &ONEL, &ONEL, &PIO4L, 0},
- {"atan2l", atan2l, &NANL, &ONEL, &NANL, 0},
- {"atan2l", atan2l, &ONEL, &NANL, &NANL, 0},
- {"atan2l", atan2l, &NANL, &NANL, &NANL, 0},
- {"powl", powl, &ONEL, &ZEROL, &ONEL, 0},
- {"powl", powl, &ONEL, &NEGZEROL, &ONEL, 0},
- {"powl", powl, &MONEL, &ZEROL, &ONEL, 0},
- {"powl", powl, &MONEL, &NEGZEROL, &ONEL, 0},
- {"powl", powl, &INFINITYL, &ZEROL, &ONEL, 0},
- {"powl", powl, &INFINITYL, &NEGZEROL, &ONEL, 0},
- {"powl", powl, &NANL, &ZEROL, &ONEL, 0},
- {"powl", powl, &NANL, &NEGZEROL, &ONEL, 0},
- {"powl", powl, &TWOL, &INFINITYL, &INFINITYL, 0},
- {"powl", powl, &MTWOL, &INFINITYL, &INFINITYL, 0},
- {"powl", powl, &HALFL, &INFINITYL, &ZEROL, 0},
- {"powl", powl, &MHALFL, &INFINITYL, &ZEROL, 0},
- {"powl", powl, &TWOL, &MINFL, &ZEROL, 0},
- {"powl", powl, &MTWOL, &MINFL, &ZEROL, 0},
- {"powl", powl, &HALFL, &MINFL, &INFINITYL, 0},
- {"powl", powl, &MHALFL, &MINFL, &INFINITYL, 0},
- {"powl", powl, &INFINITYL, &HALFL, &INFINITYL, 0},
- {"powl", powl, &INFINITYL, &TWOL, &INFINITYL, 0},
- {"powl", powl, &INFINITYL, &MHALFL, &ZEROL, 0},
- {"powl", powl, &INFINITYL, &MTWOL, &ZEROL, 0},
- {"powl", powl, &MINFL, &THREEL, &MINFL, 0},
- {"powl", powl, &MINFL, &TWOL, &INFINITYL, 0},
- {"powl", powl, &MINFL, &MTHREEL, &NEGZEROL, 0},
- {"powl", powl, &MINFL, &MTWOL, &ZEROL, 0},
- {"powl", powl, &NANL, &ONEL, &NANL, 0},
- {"powl", powl, &ONEL, &NANL, &NANL, 0},
- {"powl", powl, &NANL, &NANL, &NANL, 0},
- {"powl", powl, &ONEL, &INFINITYL, &NANL, 0},
- {"powl", powl, &MONEL, &INFINITYL, &NANL, 0},
- {"powl", powl, &ONEL, &MINFL, &NANL, 0},
- {"powl", powl, &MONEL, &MINFL, &NANL, 0},
- {"powl", powl, &MTWOL, &HALFL, &NANL, 0},
- {"powl", powl, &ZEROL, &MTHREEL, &INFINITYL, 0},
- {"powl", powl, &NEGZEROL, &MTHREEL, &MINFL, 0},
- {"powl", powl, &ZEROL, &MHALFL, &INFINITYL, 0},
- {"powl", powl, &NEGZEROL, &MHALFL, &INFINITYL, 0},
- {"powl", powl, &ZEROL, &THREEL, &ZEROL, 0},
- {"powl", powl, &NEGZEROL, &THREEL, &NEGZEROL, 0},
- {"powl", powl, &ZEROL, &HALFL, &ZEROL, 0},
- {"powl", powl, &NEGZEROL, &HALFL, &ZEROL, 0},
- {"null", NULL, &ZEROL, &ZEROL, &ZEROL, 0},
-};
-
-/* Integer functions of one variable. */
-
-int isnanl (long double);
-int signbitl (long double);
-
-struct intans
- {
- char *name; /* Name of the function. */
- int (*func) (long double);
- long double *arg1;
- int ianswer;
- };
-
-struct intans test3[] =
-{
- {"isfinitel", isfinitel, &ZEROL, 1},
- {"isfinitel", isfinitel, &INFINITYL, 0},
- {"isfinitel", isfinitel, &MINFL, 0},
- {"isnanl", isnanl, &NANL, 1},
- {"isnanl", isnanl, &INFINITYL, 0},
- {"isnanl", isnanl, &ZEROL, 0},
- {"isnanl", isnanl, &NEGZEROL, 0},
- {"signbitl", signbitl, &NEGZEROL, 1},
- {"signbitl", signbitl, &MONEL, 1},
- {"signbitl", signbitl, &ZEROL, 0},
- {"signbitl", signbitl, &ONEL, 0},
- {"signbitl", signbitl, &MINFL, 1},
- {"signbitl", signbitl, &INFINITYL, 0},
- {"null", NULL, &ZEROL, 0},
-};
-
-static volatile long double x1;
-static volatile long double x2;
-static volatile long double y;
-static volatile long double answer;
-
-int
-main ()
-{
- int i, nerrors, k, ianswer, ntests;
- long double (*fun1) (long double);
- long double (*fun2) (long double, long double);
- int (*fun3) (long double);
- long double e;
- union
- {
- long double d;
- char c[12];
- } u, v;
-
- /* This masks off fpu exceptions on i386. */
- /* setfpu(0x137f); */
- nerrors = 0;
- ntests = 0;
- MINFL = -INFINITYL;
- MPIL = -PIL;
- MPIO2L = -PIO2L;
- MPIO4L = -PIO4L;
- i = 0;
- for (;;)
- {
- fun1 = test1[i].func;
- if (fun1 == NULL)
- break;
- x1 = *(test1[i].arg1);
- y = (*(fun1)) (x1);
- answer = *(test1[i].answer);
- if (test1[i].thresh == 0)
- {
- v.d = answer;
- u.d = y;
- if (memcmp(u.c, v.c, 10) != 0)
- {
- /* O.K. if both are NaNs of some sort. */
- if (isnanl(v.d) && isnanl(u.d))
- goto nxttest1;
- goto wrongone;
- }
- else
- goto nxttest1;
- }
- if (y != answer)
- {
- e = y - answer;
- if (answer != 0.0L)
- e = e / answer;
- if (e < 0)
- e = -e;
- if (e > test1[i].thresh * MACHEPL)
- {
-wrongone:
- printf ("%s (%.20Le) = %.20Le\n should be %.20Le\n",
- test1[i].name, x1, y, answer);
- nerrors += 1;
- }
- }
-nxttest1:
- ntests += 1;
- i += 1;
- }
-
- i = 0;
- for (;;)
- {
- fun2 = test2[i].func;
- if (fun2 == NULL)
- break;
- x1 = *(test2[i].arg1);
- x2 = *(test2[i].arg2);
- y = (*(fun2)) (x1, x2);
- answer = *(test2[i].answer);
- if (test2[i].thresh == 0)
- {
- v.d = answer;
- u.d = y;
- if (memcmp(u.c, v.c, 10) != 0)
- {
- /* O.K. if both are NaNs of some sort. */
- if (isnanl(v.d) && isnanl(u.d))
- goto nxttest2;
- goto wrongtwo;
- }
- else
- goto nxttest2;
- }
- if (y != answer)
- {
- e = y - answer;
- if (answer != 0.0L)
- e = e / answer;
- if (e < 0)
- e = -e;
- if (e > test2[i].thresh * MACHEPL)
- {
-wrongtwo:
- printf ("%s (%.20Le, %.20Le) = %.20Le\n should be %.20Le\n",
- test2[i].name, x1, x2, y, answer);
- nerrors += 1;
- }
- }
-nxttest2:
- ntests += 1;
- i += 1;
- }
-
-
- i = 0;
- for (;;)
- {
- fun3 = test3[i].func;
- if (fun3 == NULL)
- break;
- x1 = *(test3[i].arg1);
- k = (*(fun3)) (x1);
- ianswer = test3[i].ianswer;
- if (k != ianswer)
- {
- printf ("%s (%.20Le) = %d\n should be. %d\n",
- test3[i].name, x1, k, ianswer);
- nerrors += 1;
- }
- ntests += 1;
- i += 1;
- }
-
- printf ("testvect: %d errors in %d tests\n", nerrors, ntests);
- exit (0);
-}
+++ /dev/null
-/* unityl.c
- *
- * Relative error approximations for function arguments near
- * unity.
- *
- * log1p(x) = log(1+x)
- * expm1(x) = exp(x) - 1
- * cosm1(x) = cos(x) - 1
- *
- */
-
-
-/* log1p(x) = log(1 + x)
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2 30000 1.4e-19 4.1e-20
- *
- */
-
-#include <math.h>
-/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 2.32e-20
- */
-static long double LP[] = {
- 4.5270000862445199635215E-5L,
- 4.9854102823193375972212E-1L,
- 6.5787325942061044846969E0L,
- 2.9911919328553073277375E1L,
- 6.0949667980987787057556E1L,
- 5.7112963590585538103336E1L,
- 2.0039553499201281259648E1L,
-};
-static long double LQ[] = {
-/* 1.0000000000000000000000E0L,*/
- 1.5062909083469192043167E1L,
- 8.3047565967967209469434E1L,
- 2.2176239823732856465394E2L,
- 3.0909872225312059774938E2L,
- 2.1642788614495947685003E2L,
- 6.0118660497603843919306E1L,
-};
-
-#define SQRTH 0.70710678118654752440L
-#define SQRT2 1.41421356237309504880L
-#ifdef ANSIPROT
-extern long double logl ( long double );
-extern long double expl ( long double );
-extern long double cosl ( long double );
-extern long double polevll ( long double, void *, int );
-extern long double p1evll ( long double, void *, int );
-#else
-long double logl(), expl(), cosl(), polevll(), p1evll();
-#endif
-
-long double log1pl(x)
-long double x;
-{
-long double z;
-
-z = 1.0L + x;
-if( (z < SQRTH) || (z > SQRT2) )
- return( logl(z) );
-z = x*x;
-z = -0.5L * z + x * ( z * polevll( x, LP, 6 ) / p1evll( x, LQ, 6 ) );
-return (x + z);
-}
-
-
-
-/* expm1(x) = exp(x) - 1 */
-
-/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
- * -0.5 <= x <= 0.5
- */
-
-static long double EP[3] = {
- 1.2617719307481059087798E-4L,
- 3.0299440770744196129956E-2L,
- 9.9999999999999999991025E-1L,
-};
-static long double EQ[4] = {
- 3.0019850513866445504159E-6L,
- 2.5244834034968410419224E-3L,
- 2.2726554820815502876593E-1L,
- 2.0000000000000000000897E0L,
-};
-
-long double expm1l(x)
-long double x;
-{
-long double r, xx;
-
-if( (x < -0.5L) || (x > 0.5L) )
- return( expl(x) - 1.0L );
-xx = x * x;
-r = x * polevll( xx, EP, 2 );
-r = r/( polevll( xx, EQ, 3 ) - r );
-return (r + r);
-}
-
-
-
-/* cosm1(x) = cos(x) - 1 */
-
-static long double coscof[7] = {
- 4.7377507964246204691685E-14L,
--1.1470284843425359765671E-11L,
- 2.0876754287081521758361E-9L,
--2.7557319214999787979814E-7L,
- 2.4801587301570552304991E-5L,
--1.3888888888888872993737E-3L,
- 4.1666666666666666609054E-2L,
-};
-
-extern long double PIO4L;
-
-long double cosm1l(x)
-long double x;
-{
-long double xx;
-
-if( (x < -PIO4L) || (x > PIO4L) )
- return( cosl(x) - 1.0L );
-xx = x * x;
-xx = -0.5L*xx + xx * xx * polevll( xx, coscof, 6 );
-return xx;
-}
+++ /dev/null
-/* Wronksian test for Bessel functions. */
-
-long double jnl (), ynl (), floorl ();
-#define PI 3.14159265358979323846L
-
-long double y, Jn, Jnp1, Jmn, Jmnp1, Yn, Ynp1;
-long double w1, w2, err1, max1, err2, max2;
-void wronk ();
-
-main ()
-{
- long double x, delta;
- int n, i, j;
-
- max1 = 0.0L;
- max2 = 0.0L;
- delta = 0.6 / PI;
- for (n = -30; n <= 30; n++)
- {
- x = -30.0;
- while (x < 30.0)
- {
- wronk (n, x);
- x += delta;
- }
- delta += .00123456;
- }
-}
-
-void
-wronk (n, x)
- int n;
- long double x;
-{
-
- Jnp1 = jnl (n + 1, x);
- Jmn = jnl (-n, x);
- Jn = jnl (n, x);
- Jmnp1 = jnl (-(n + 1), x);
- /* This should be trivially zero. */
- err1 = Jnp1 * Jmn + Jn * Jmnp1;
- if (err1 < 0.0)
- err1 = -err1;
- if (err1 > max1)
- {
- max1 = err1;
- printf ("1 %3d %.5Le %.3Le\n", n, x, max1);
- }
- if (x < 0.0)
- {
- x = -x;
- Jn = jnl (n, x);
- Jnp1 = jnl (n + 1, x);
- }
- Yn = ynl (n, x);
- Ynp1 = ynl (n + 1, x);
- /* The Wronksian. */
- w1 = Jnp1 * Yn - Jn * Ynp1;
- /* What the Wronksian should be. */
- w2 = 2.0 / (PI * x);
- err2 = w1 - w2;
- if (err2 > max2)
- {
- max2 = err2;
- printf ("2 %3d %.5Le %.3Le\n", n, x, max2);
- }
-}
+++ /dev/null
-/* ynl.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, ynl();
- * int n;
- *
- * y = ynl( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0l() and y1l().
- *
- * If n = 0 or 1 the routine for y0l or y1l is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative error when y > 1.
- * x >= 0, -30 <= n <= +30.
- * arithmetic domain # trials peak rms
- * IEEE -30, 30 10000 1.3e-18 1.8e-19
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ynl singularity x = 0 MAXNUML
- * ynl overflow MAXNUML
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
-\f
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-extern long double MAXNUML;
-#ifdef ANSIPROT
-extern long double y0l ( long double );
-extern long double y1l ( long double );
-#else
-long double y0l(), y1l();
-#endif
-
-long double ynl( n, x )
-int n;
-long double x;
-{
-long double an, anm1, anm2, r;
-int k, sign;
-
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) == 0 ) /* -1**n */
- sign = 1;
- else
- sign = -1;
- }
-else
- sign = 1;
-
-
-if( n == 0 )
- return( sign * y0l(x) );
-if( n == 1 )
- return( sign * y1l(x) );
-
-/* test for overflow */
-if( x <= 0.0L )
- {
- mtherr( "ynl", SING );
- return( -MAXNUML );
- }
-
-/* forward recurrence on n */
-
-anm2 = y0l(x);
-anm1 = y1l(x);
-k = 1;
-r = 2 * k;
-do
- {
- an = r * anm1 / x - anm2;
- anm2 = anm1;
- anm1 = an;
- r += 2.0L;
- ++k;
- }
-while( k < n );
-
-
-return( sign * an );
-}
--- /dev/null
+#if defined(__ppc__)
+/*******************************************************************************
+* *
+* File logb.c, *
+* Functions logb. *
+* Implementation of logb for the PowerPC. *
+* *
+* Copyright © 1991 Apple Computer, Inc. All rights reserved. *
+* *
+* Written by Ali Sazegari, started on June 1991, *
+* *
+* August 26 1991: removed CFront Version 1.1d17 warnings. *
+* August 27 1991: no errors reported by the test suite. *
+* November 11 1991: changed CLASSEXTENDED to the macro CLASSIFY and *
+* + or - infinity to constants. *
+* November 18 1991: changed the macro CLASSIFY to CLASSEXTENDEDint to *
+* improve performance. *
+* February 07 1992: changed bit operations to macros ( object size is *
+* unchanged ). *
+* September24 1992: took the "#include support.h" out. *
+* December 03 1992: first rs/6000 port. *
+* August 30 1992: set the divide by zero for the zero argument case. *
+* October 05 1993: corrected the environment. *
+* October 17 1994: replaced all environmental functions with __setflm. *
+* May 28 1997: made speed improvements. *
+* April 30 2001: forst mac os x port using gcc. *
+* *
+********************************************************************************
+* The C math library offers a similar function called "frexp". It is *
+* different in details from logb, but similar in spirit. This current *
+* implementation of logb follows the recommendation in IEEE Standard 854 *
+* which is different in its handling of denormalized numbers from the IEEE *
+* Standard 754. *
+*******************************************************************************/
+
+typedef union
+ {
+ struct {
+#if defined(__BIG_ENDIAN__)
+ unsigned long int hi;
+ unsigned long int lo;
+#else
+ unsigned long int lo;
+ unsigned long int hi;
+#endif
+ } words;
+ double dbl;
+ } DblInHex;
+
+static const double twoTo52 = 4.50359962737049600e15; // 0x1p52
+static const double klTod = 4503601774854144.0; // 0x1.000008p52
+static const unsigned long int signMask = 0x80000000ul;
+static const DblInHex minusInf = {{ 0xFFF00000, 0x00000000 }};
+
+
+/*******************************************************************************
+********************************************************************************
+* L O G B *
+********************************************************************************
+*******************************************************************************/
+
+double logb ( double x )
+ {
+ DblInHex xInHex;
+ long int shiftedExp;
+
+ xInHex.dbl = x;
+ shiftedExp = ( xInHex.words.hi & 0x7ff00000UL ) >> 20;
+
+ if ( shiftedExp == 2047 )
+ { // NaN or INF
+ if ( ( ( xInHex.words.hi & signMask ) == 0 ) || ( x != x ) )
+ return x; // NaN or +INF return x
+ else
+ return -x; // -INF returns +INF
+ }
+
+ if ( shiftedExp != 0 ) // normal number
+ shiftedExp -= 1023; // unbias exponent
+
+ else if ( x == 0.0 )
+ { // zero
+ xInHex.words.hi = 0x0UL; // return -infinity
+ return ( minusInf.dbl );
+ }
+
+ else
+ { // subnormal number
+ xInHex.dbl *= twoTo52; // scale up
+ shiftedExp = ( xInHex.words.hi & 0x7ff00000UL ) >> 20;
+ shiftedExp -= 1075; // unbias exponent
+ }
+
+ if ( shiftedExp == 0 ) // zero result
+ return ( 0.0 );
+
+ else
+ { // nonzero result
+ xInHex.dbl = klTod;
+ xInHex.words.lo += shiftedExp;
+ return ( xInHex.dbl - klTod );
+ }
+ }
+#endif /* __ppc__ */
--- /dev/null
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/*
+ * from: @(#)fdlibm.h 5.1 93/09/24
+ * $Id: math_private.h,v 1.1 2001/11/22 14:01:05 andersen Exp $
+ */
+
+#ifndef _MATH_PRIVATE_H_
+#define _MATH_PRIVATE_H_
+
+#include <endian.h>
+#include <sys/types.h>
+
+/* The original fdlibm code used statements like:
+ n0 = ((*(int*)&one)>>29)^1; * index of high word *
+ ix0 = *(n0+(int*)&x); * high word of x *
+ ix1 = *((1-n0)+(int*)&x); * low word of x *
+ to dig two 32 bit words out of the 64 bit IEEE floating point
+ value. That is non-ANSI, and, moreover, the gcc instruction
+ scheduler gets it wrong. We instead use the following macros.
+ Unlike the original code, we determine the endianness at compile
+ time, not at run time; I don't see much benefit to selecting
+ endianness at run time. */
+
+/* A union which permits us to convert between a double and two 32 bit
+ ints. */
+
+/*
+ * Math on arm is little endian except for the FP word order which is
+ * big endian.
+ */
+
+#if (__BYTE_ORDER == __BIG_ENDIAN) || defined(__arm__)
+
+typedef union
+{
+ double value;
+ struct
+ {
+ u_int32_t msw;
+ u_int32_t lsw;
+ } parts;
+} ieee_double_shape_type;
+
+#endif
+
+#if (__BYTE_ORDER == __LITTLE_ENDIAN) && !defined(__arm__)
+
+typedef union
+{
+ double value;
+ struct
+ {
+ u_int32_t lsw;
+ u_int32_t msw;
+ } parts;
+} ieee_double_shape_type;
+
+#endif
+
+/* Get two 32 bit ints from a double. */
+
+#define EXTRACT_WORDS(ix0,ix1,d) \
+do { \
+ ieee_double_shape_type ew_u; \
+ ew_u.value = (d); \
+ (ix0) = ew_u.parts.msw; \
+ (ix1) = ew_u.parts.lsw; \
+} while (0)
+
+/* Get the more significant 32 bit int from a double. */
+
+#define GET_HIGH_WORD(i,d) \
+do { \
+ ieee_double_shape_type gh_u; \
+ gh_u.value = (d); \
+ (i) = gh_u.parts.msw; \
+} while (0)
+
+/* Get the less significant 32 bit int from a double. */
+
+#define GET_LOW_WORD(i,d) \
+do { \
+ ieee_double_shape_type gl_u; \
+ gl_u.value = (d); \
+ (i) = gl_u.parts.lsw; \
+} while (0)
+
+/* Set a double from two 32 bit ints. */
+
+#define INSERT_WORDS(d,ix0,ix1) \
+do { \
+ ieee_double_shape_type iw_u; \
+ iw_u.parts.msw = (ix0); \
+ iw_u.parts.lsw = (ix1); \
+ (d) = iw_u.value; \
+} while (0)
+
+/* Set the more significant 32 bits of a double from an int. */
+
+#define SET_HIGH_WORD(d,v) \
+do { \
+ ieee_double_shape_type sh_u; \
+ sh_u.value = (d); \
+ sh_u.parts.msw = (v); \
+ (d) = sh_u.value; \
+} while (0)
+
+/* Set the less significant 32 bits of a double from an int. */
+
+#define SET_LOW_WORD(d,v) \
+do { \
+ ieee_double_shape_type sl_u; \
+ sl_u.value = (d); \
+ sl_u.parts.lsw = (v); \
+ (d) = sl_u.value; \
+} while (0)
+
+/* A union which permits us to convert between a float and a 32 bit
+ int. */
+
+typedef union
+{
+ float value;
+ u_int32_t word;
+} ieee_float_shape_type;
+
+/* Get a 32 bit int from a float. */
+
+#define GET_FLOAT_WORD(i,d) \
+do { \
+ ieee_float_shape_type gf_u; \
+ gf_u.value = (d); \
+ (i) = gf_u.word; \
+} while (0)
+
+/* Set a float from a 32 bit int. */
+
+#define SET_FLOAT_WORD(d,i) \
+do { \
+ ieee_float_shape_type sf_u; \
+ sf_u.word = (i); \
+ (d) = sf_u.value; \
+} while (0)
+
+/* ieee style elementary functions */
+extern double __ieee754_sqrt __P((double));
+extern double __ieee754_acos __P((double));
+extern double __ieee754_acosh __P((double));
+extern double __ieee754_log __P((double));
+extern double __ieee754_atanh __P((double));
+extern double __ieee754_asin __P((double));
+extern double __ieee754_atan2 __P((double,double));
+extern double __ieee754_exp __P((double));
+extern double __ieee754_cosh __P((double));
+extern double __ieee754_fmod __P((double,double));
+extern double __ieee754_pow __P((double,double));
+extern double __ieee754_lgamma_r __P((double,int *));
+extern double __ieee754_gamma_r __P((double,int *));
+extern double __ieee754_lgamma __P((double));
+extern double __ieee754_gamma __P((double));
+extern double __ieee754_log10 __P((double));
+extern double __ieee754_sinh __P((double));
+extern double __ieee754_hypot __P((double,double));
+extern double __ieee754_j0 __P((double));
+extern double __ieee754_j1 __P((double));
+extern double __ieee754_y0 __P((double));
+extern double __ieee754_y1 __P((double));
+extern double __ieee754_jn __P((int,double));
+extern double __ieee754_yn __P((int,double));
+extern double __ieee754_remainder __P((double,double));
+extern int __ieee754_rem_pio2 __P((double,double*));
+#if defined(_SCALB_INT)
+extern double __ieee754_scalb __P((double,int));
+#else
+extern double __ieee754_scalb __P((double,double));
+#endif
+
+/* fdlibm kernel function */
+extern double __kernel_standard __P((double,double,int));
+extern double __kernel_sin __P((double,double,int));
+extern double __kernel_cos __P((double,double));
+extern double __kernel_tan __P((double,double,int));
+extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));
+
+
+/* ieee style elementary float functions */
+extern float __ieee754_sqrtf __P((float));
+extern float __ieee754_acosf __P((float));
+extern float __ieee754_acoshf __P((float));
+extern float __ieee754_logf __P((float));
+extern float __ieee754_atanhf __P((float));
+extern float __ieee754_asinf __P((float));
+extern float __ieee754_atan2f __P((float,float));
+extern float __ieee754_expf __P((float));
+extern float __ieee754_coshf __P((float));
+extern float __ieee754_fmodf __P((float,float));
+extern float __ieee754_powf __P((float,float));
+extern float __ieee754_lgammaf_r __P((float,int *));
+extern float __ieee754_gammaf_r __P((float,int *));
+extern float __ieee754_lgammaf __P((float));
+extern float __ieee754_gammaf __P((float));
+extern float __ieee754_log10f __P((float));
+extern float __ieee754_sinhf __P((float));
+extern float __ieee754_hypotf __P((float,float));
+extern float __ieee754_j0f __P((float));
+extern float __ieee754_j1f __P((float));
+extern float __ieee754_y0f __P((float));
+extern float __ieee754_y1f __P((float));
+extern float __ieee754_jnf __P((int,float));
+extern float __ieee754_ynf __P((int,float));
+extern float __ieee754_remainderf __P((float,float));
+extern int __ieee754_rem_pio2f __P((float,float*));
+extern float __ieee754_scalbf __P((float,float));
+
+/* float versions of fdlibm kernel functions */
+extern float __kernel_sinf __P((float,float,int));
+extern float __kernel_cosf __P((float,float));
+extern float __kernel_tanf __P((float,float,int));
+extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*));
+
+#endif /* _MATH_PRIVATE_H_ */
--- /dev/null
+/*******************************************************************************
+** File: rndint.c
+**
+** Contains: C source code for implementations of floating-point
+** functions which round to integral value or format, as
+** defined in header <fp.h>. In particular, this file
+** contains implementations of functions rint, nearbyint,
+** rinttol, round, roundtol, trunc, modf and modfl. This file
+** targets PowerPC or Power platforms.
+**
+** Written by: A. Sazegari, Apple AltiVec Group
+** Created originally by Jon Okada, Apple Numerics Group
+**
+** Copyright: © 1992-2001 by Apple Computer, Inc., all rights reserved
+**
+** Change History (most recent first):
+**
+** 13 Jul 01 ram replaced --setflm calls with inline assembly
+** 03 Mar 01 ali first port to os x using gcc, added the crucial __setflm
+** definition.
+** 1. removed double_t, put in double for now.
+** 2. removed iclass from nearbyint.
+** 3. removed wrong comments intrunc.
+** 4.
+** 13 May 97 ali made performance improvements in rint, rinttol, roundtol
+** and trunc by folding some of the taligent ideas into this
+** implementation. nearbyint is faster than the one in taligent,
+** rint is more elegant, but slower by %30 than the taligent one.
+** 09 Apr 97 ali deleted modfl and deferred to AuxiliaryDD.c
+** 15 Sep 94 ali Major overhaul and performance improvements of all functions.
+** 20 Jul 94 PAF New faster version
+** 16 Jul 93 ali Added the modfl function.
+** 18 Feb 93 ali Changed the return value of fenv functions
+** feclearexcept and feraiseexcept to their new
+** NCEG X3J11.1/93-001 definitions.
+** 16 Dec 92 JPO Removed __itrunc implementation to a
+** separate file.
+** 15 Dec 92 JPO Added __itrunc implementation and modified
+** rinttol to include conversion from double
+** to long int format. Modified roundtol to
+** call __itrunc.
+** 10 Dec 92 JPO Added modf (double) implementation.
+** 04 Dec 92 JPO First created.
+**
+*******************************************************************************/
+
+#include <limits.h>
+#include <math.h>
+
+#if !defined(__ppc__)
+#define asm(x)
+#endif
+
+#define SET_INVALID 0x01000000UL
+
+typedef union
+ {
+ struct {
+#if defined(__BIG_ENDIAN__)
+ unsigned long int hi;
+ unsigned long int lo;
+#else
+ unsigned long int lo;
+ unsigned long int hi;
+#endif
+ } words;
+ double dbl;
+ } DblInHex;
+
+static const unsigned long int signMask = 0x80000000ul;
+static const double twoTo52 = 4503599627370496.0;
+static const double doubleToLong = 4503603922337792.0; // 2^52
+static const DblInHex Huge = {{ 0x7FF00000, 0x00000000 }};
+static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }};
+
+/*******************************************************************************
+* *
+* The function rint rounds its double argument to integral value *
+* according to the current rounding direction and returns the result in *
+* double format. This function signals inexact if an ordered return *
+* value is not equal to the operand. *
+* *
+********************************************************************************
+* *
+* This function calls: fabs. *
+* *
+*******************************************************************************/
+
+/*******************************************************************************
+* First, an elegant implementation. *
+********************************************************************************
+*
+*double rint ( double x )
+* {
+* double y;
+*
+* y = twoTo52.fval;
+*
+* if ( fabs ( x ) >= y ) // huge case is exact
+* return x;
+* if ( x < 0 ) y = -y; // negative case
+* y = ( x + y ) - y; // force rounding
+* if ( y == 0.0 ) // zero results mirror sign of x
+* y = copysign ( y, x );
+* return ( y );
+* }
+********************************************************************************
+* Now a bit twidling version that is about %30 faster. *
+*******************************************************************************/
+
+#if defined(__ppc__)
+double rint ( double x )
+ {
+ DblInHex argument;
+ register double y;
+ unsigned long int xHead;
+ register long int target;
+
+ argument.dbl = x;
+ xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x|
+ target = ( argument.words.hi < signMask ); // flags positive sign
+
+ if ( xHead < 0x43300000ul )
+/*******************************************************************************
+* Is |x| < 2.0^52? *
+*******************************************************************************/
+ {
+ if ( xHead < 0x3ff00000ul )
+/*******************************************************************************
+* Is |x| < 1.0? *
+*******************************************************************************/
+ {
+ if ( target )
+ y = ( x + twoTo52 ) - twoTo52; // round at binary point
+ else
+ y = ( x - twoTo52 ) + twoTo52; // round at binary point
+ if ( y == 0.0 )
+ { // fix sign of zero result
+ if ( target )
+ return ( 0.0 );
+ else
+ return ( -0.0 );
+ }
+ return y;
+ }
+
+/*******************************************************************************
+* Is 1.0 < |x| < 2.0^52? *
+*******************************************************************************/
+
+ if ( target )
+ return ( ( x + twoTo52 ) - twoTo52 ); // round at binary pt.
+ else
+ return ( ( x - twoTo52 ) + twoTo52 );
+ }
+
+/*******************************************************************************
+* |x| >= 2.0^52 or x is a NaN. *
+*******************************************************************************/
+ return ( x );
+ }
+#endif /* __ppc__ */
+
+/*******************************************************************************
+* *
+* The function nearbyint rounds its double argument to integral value *
+* according to the current rounding direction and returns the result in *
+* double format. This function does not signal inexact. *
+* *
+********************************************************************************
+* *
+* This function calls fabs and copysign. *
+* *
+*******************************************************************************/
+
+double nearbyint ( double x )
+ {
+ double y, OldEnvironment;
+
+ y = twoTo52;
+
+ asm ("mffs %0" : "=f" (OldEnvironment)); /* get the environement */
+
+ if ( fabs ( x ) >= y ) /* huge case is exact */
+ return x;
+ if ( x < 0 ) y = -y; /* negative case */
+ y = ( x + y ) - y; /* force rounding */
+ if ( y == 0.0 ) /* zero results mirror sign of x */
+ y = copysign ( y, x );
+// restore old flags
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment ));
+ return ( y );
+ }
+
+/*******************************************************************************
+* *
+* The function rinttol converts its double argument to integral value *
+* according to the current rounding direction and returns the result in *
+* long int format. This conversion signals invalid if the argument is a *
+* NaN or the rounded intermediate result is out of range of the *
+* destination long int format, and it delivers an unspecified result in *
+* this case. This function signals inexact if the rounded result is *
+* within range of the long int format but unequal to the operand. *
+* *
+*******************************************************************************/
+
+long int rinttol ( double x )
+ {
+ register double y;
+ DblInHex argument, OldEnvironment;
+ unsigned long int xHead;
+ register long int target;
+
+ argument.dbl = x;
+ target = ( argument.words.hi < signMask ); // flag positive sign
+ xHead = argument.words.hi & 0x7ffffffful; // high 32 bits of x
+
+ if ( target )
+/*******************************************************************************
+* Sign of x is positive. *
+*******************************************************************************/
+ {
+ if ( xHead < 0x41dffffful )
+ { // x is safely in long range
+ y = ( x + twoTo52 ) - twoTo52; // round at binary point
+ argument.dbl = y + doubleToLong; // force result into argument.words.lo
+ return ( ( long ) argument.words.lo );
+ }
+
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
+
+ if ( xHead > 0x41dffffful )
+ { // x is safely out of long range
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( LONG_MAX );
+ }
+
+/*******************************************************************************
+* x > 0.0 and may or may not be out of range of long. *
+*******************************************************************************/
+
+ y = ( x + twoTo52 ) - twoTo52; // do rounding
+ if ( y > ( double ) LONG_MAX )
+ { // out of range of long
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( LONG_MAX );
+ }
+ argument.dbl = y + doubleToLong; // in range
+ return ( ( long ) argument.words.lo ); // return result & flags
+ }
+
+/*******************************************************************************
+* Sign of x is negative. *
+*******************************************************************************/
+ if ( xHead < 0x41e00000ul )
+ { // x is safely in long range
+ y = ( x - twoTo52 ) + twoTo52;
+ argument.dbl = y + doubleToLong;
+ return ( ( long ) argument.words.lo );
+ }
+
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
+
+ if ( xHead > 0x41e00000ul )
+ { // x is safely out of long range
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( LONG_MIN );
+ }
+
+/*******************************************************************************
+* x < 0.0 and may or may not be out of range of long. *
+*******************************************************************************/
+
+ y = ( x - twoTo52 ) + twoTo52; // do rounding
+ if ( y < ( double ) LONG_MIN )
+ { // out of range of long
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( LONG_MIN );
+ }
+ argument.dbl = y + doubleToLong; // in range
+ return ( ( long ) argument.words.lo ); // return result & flags
+ }
+
+/*******************************************************************************
+* *
+* The function round rounds its double argument to integral value *
+* according to the "add half to the magnitude and truncate" rounding of *
+* Pascal's Round function and FORTRAN's ANINT function and returns the *
+* result in double format. This function signals inexact if an ordered *
+* return value is not equal to the operand. *
+* *
+*******************************************************************************/
+
+double round ( double x )
+ {
+ DblInHex argument, OldEnvironment;
+ register double y, z;
+ register unsigned long int xHead;
+ register long int target;
+
+ argument.dbl = x;
+ xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x|
+ target = ( argument.words.hi < signMask ); // flag positive sign
+
+ if ( xHead < 0x43300000ul )
+/*******************************************************************************
+* Is |x| < 2.0^52? *
+*******************************************************************************/
+ {
+ if ( xHead < 0x3ff00000ul )
+/*******************************************************************************
+* Is |x| < 1.0? *
+*******************************************************************************/
+ {
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
+ if ( xHead < 0x3fe00000ul )
+/*******************************************************************************
+* Is |x| < 0.5? *
+*******************************************************************************/
+ {
+ if ( ( xHead | argument.words.lo ) != 0ul )
+ OldEnvironment.words.lo |= 0x02000000ul;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ if ( target )
+ return ( 0.0 );
+ else
+ return ( -0.0 );
+ }
+/*******************************************************************************
+* Is 0.5 ² |x| < 1.0? *
+*******************************************************************************/
+ OldEnvironment.words.lo |= 0x02000000ul;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ if ( target )
+ return ( 1.0 );
+ else
+ return ( -1.0 );
+ }
+/*******************************************************************************
+* Is 1.0 < |x| < 2.0^52? *
+*******************************************************************************/
+ if ( target )
+ { // positive x
+ y = ( x + twoTo52 ) - twoTo52; // round at binary point
+ if ( y == x ) // exact case
+ return ( x );
+ z = x + 0.5; // inexact case
+ y = ( z + twoTo52 ) - twoTo52; // round at binary point
+ if ( y > z )
+ return ( y - 1.0 );
+ else
+ return ( y );
+ }
+
+/*******************************************************************************
+* Is x < 0? *
+*******************************************************************************/
+ else
+ {
+ y = ( x - twoTo52 ) + twoTo52; // round at binary point
+ if ( y == x )
+ return ( x );
+ z = x - 0.5;
+ y = ( z - twoTo52 ) + twoTo52; // round at binary point
+ if ( y < z )
+ return ( y + 1.0 );
+ else
+ return ( y );
+ }
+ }
+/*******************************************************************************
+* |x| >= 2.0^52 or x is a NaN. *
+*******************************************************************************/
+ return ( x );
+ }
+
+/*******************************************************************************
+* *
+* The function roundtol converts its double argument to integral format *
+* according to the "add half to the magnitude and chop" rounding mode of *
+* Pascal's Round function and FORTRAN's NINT function. This conversion *
+* signals invalid if the argument is a NaN or the rounded intermediate *
+* result is out of range of the destination long int format, and it *
+* delivers an unspecified result in this case. This function signals *
+* inexact if the rounded result is within range of the long int format but *
+* unequal to the operand. *
+* *
+*******************************************************************************/
+
+long int roundtol ( double x )
+ {
+ register double y, z;
+ DblInHex argument, OldEnvironment;
+ register unsigned long int xhi;
+ register long int target;
+ const DblInHex kTZ = {{ 0x0, 0x1 }};
+ const DblInHex kUP = {{ 0x0, 0x2 }};
+
+ argument.dbl = x;
+ xhi = argument.words.hi & 0x7ffffffful; // high 32 bits of x
+ target = ( argument.words.hi < signMask ); // flag positive sign
+
+ if ( xhi > 0x41e00000ul )
+/*******************************************************************************
+* Is x is out of long range or NaN? *
+*******************************************************************************/
+ {
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ if ( target ) // pin result
+ return ( LONG_MAX );
+ else
+ return ( LONG_MIN );
+ }
+
+ if ( target )
+/*******************************************************************************
+* Is sign of x is "+"? *
+*******************************************************************************/
+ {
+ if ( x < 2147483647.5 )
+/*******************************************************************************
+* x is in the range of a long. *
+*******************************************************************************/
+ {
+ y = ( x + doubleToLong ) - doubleToLong; // round at binary point
+ if ( y != x )
+ { // inexact case
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kTZ.dbl )); // truncate rounding
+ z = x + 0.5; // truncate x + 0.5
+ argument.dbl = z + doubleToLong;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( ( long ) argument.words.lo );
+ }
+
+ argument.dbl = y + doubleToLong; // force result into argument.words.lo
+ return ( ( long ) argument.words.lo ); // return long result
+ }
+/*******************************************************************************
+* Rounded positive x is out of the range of a long. *
+*******************************************************************************/
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( LONG_MAX ); // return pinned result
+ }
+/*******************************************************************************
+* x < 0.0 and may or may not be out of the range of a long. *
+*******************************************************************************/
+ if ( x > -2147483648.5 )
+/*******************************************************************************
+* x is in the range of a long. *
+*******************************************************************************/
+ {
+ y = ( x + doubleToLong ) - doubleToLong; // round at binary point
+ if ( y != x )
+ { // inexact case
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kUP.dbl )); // round up
+ z = x - 0.5; // truncate x - 0.5
+ argument.dbl = z + doubleToLong;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( ( long ) argument.words.lo );
+ }
+
+ argument.dbl = y + doubleToLong;
+ return ( ( long ) argument.words.lo ); // return long result
+ }
+/*******************************************************************************
+* Rounded negative x is out of the range of a long. *
+*******************************************************************************/
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+ OldEnvironment.words.lo |= SET_INVALID;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ return ( LONG_MIN ); // return pinned result
+ }
+
+/*******************************************************************************
+* *
+* The function trunc truncates its double argument to integral value *
+* and returns the result in double format. This function signals *
+* inexact if an ordered return value is not equal to the operand. *
+* *
+*******************************************************************************/
+
+double trunc ( double x )
+ {
+ DblInHex argument,OldEnvironment;
+ register double y;
+ register unsigned long int xhi;
+ register long int target;
+
+ argument.dbl = x;
+ xhi = argument.words.hi & 0x7fffffffUL; // xhi <- high half of |x|
+ target = ( argument.words.hi < signMask ); // flag positive sign
+
+ if ( xhi < 0x43300000ul )
+/*******************************************************************************
+* Is |x| < 2.0^53? *
+*******************************************************************************/
+ {
+ if ( xhi < 0x3ff00000ul )
+/*******************************************************************************
+* Is |x| < 1.0? *
+*******************************************************************************/
+ {
+ if ( ( xhi | argument.words.lo ) != 0ul )
+ { // raise deserved INEXACT
+ asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+ OldEnvironment.words.lo |= 0x02000000ul;
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+ }
+ if ( target ) // return properly signed zero
+ return ( 0.0 );
+ else
+ return ( -0.0 );
+ }
+/*******************************************************************************
+* Is 1.0 < |x| < 2.0^52? *
+*******************************************************************************/
+ if ( target )
+ {
+ y = ( x + twoTo52 ) - twoTo52; // round at binary point
+ if ( y > x )
+ return ( y - 1.0 );
+ else
+ return ( y );
+ }
+
+ else
+ {
+ y = ( x - twoTo52 ) + twoTo52; // round at binary point.
+ if ( y < x )
+ return ( y + 1.0 );
+ else
+ return ( y );
+ }
+ }
+/*******************************************************************************
+* Is |x| >= 2.0^52 or x is a NaN. *
+*******************************************************************************/
+ return ( x );
+ }
+
+/*******************************************************************************
+* The modf family of functions separate a floating-point number into its *
+* fractional and integral parts, returning the fractional part and writing *
+* the integral part in floating-point format to the object pointed to by a *
+* pointer argument. If the input argument is integral or infinite in *
+* value, the return value is a zero with the sign of the input argument. *
+* The modf family of functions raises no floating-point exceptions. older *
+* implemenation set the INVALID flag due to signaling NaN input. *
+* *
+*******************************************************************************/
+
+/*******************************************************************************
+* modf is the double implementation. *
+*******************************************************************************/
+
+#if defined(__ppc__)
+double modf ( double x, double *iptr )
+ {
+ register double OldEnvironment, xtrunc;
+ register unsigned long int xHead, signBit;
+ DblInHex argument;
+
+ argument.dbl = x;
+ xHead = argument.words.hi & 0x7ffffffful; // |x| high bit pattern
+ signBit = ( argument.words.hi & 0x80000000ul ); // isolate sign bit
+ if (xHead == 0x7ff81fe0)
+ signBit = signBit | 0;
+
+ if ( xHead < 0x43300000ul )
+/*******************************************************************************
+* Is |x| < 2.0^53? *
+*******************************************************************************/
+ {
+ if ( xHead < 0x3ff00000ul )
+/*******************************************************************************
+* Is |x| < 1.0? *
+*******************************************************************************/
+ {
+ argument.words.hi = signBit; // truncate to zero
+ argument.words.lo = 0ul;
+ *iptr = argument.dbl;
+ return ( x );
+ }
+/*******************************************************************************
+* Is 1.0 < |x| < 2.0^52? *
+*******************************************************************************/
+ asm ("mffs %0" : "=f" (OldEnvironment)); // save environment
+ // round toward zero
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( TOWARDZERO.dbl ));
+ if ( signBit == 0ul ) // truncate to integer
+ xtrunc = ( x + twoTo52 ) - twoTo52;
+ else
+ xtrunc = ( x - twoTo52 ) + twoTo52;
+ // restore caller's env
+ asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment ));
+ *iptr = xtrunc; // store integral part
+ if ( x != xtrunc ) // nonzero fraction
+ return ( x - xtrunc );
+ else
+ { // zero with x's sign
+ argument.words.hi = signBit;
+ argument.words.lo = 0ul;
+ return ( argument.dbl );
+ }
+ }
+
+ *iptr = x; // x is integral or NaN
+ if ( x != x ) // NaN is returned
+ return x;
+ else
+ { // zero with x's sign
+ argument.words.hi = signBit;
+ argument.words.lo = 0ul;
+ return ( argument.dbl );
+ }
+ }
+#endif /* __ppc__ */
--- /dev/null
+/* @(#)s_asinh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
+#endif
+
+/* asinh(x)
+ * Method :
+ * Based on
+ * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
+ * we have
+ * asinh(x) := x if 1+x*x=1,
+ * := sign(x)*(log(x)+ln2)) for large |x|, else
+ * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
+ * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+huge= 1.00000000000000000000e+300;
+
+#ifdef __STDC__
+ double asinh(double x)
+#else
+ double asinh(x)
+ double x;
+#endif
+{
+ double t,w;
+ int32_t hx,ix;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
+ if(ix< 0x3e300000) { /* |x|<2**-28 */
+ if(huge+x>one) return x; /* return x inexact except 0 */
+ }
+ if(ix>0x41b00000) { /* |x| > 2**28 */
+ w = __ieee754_log(fabs(x))+ln2;
+ } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
+ t = fabs(x);
+ w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
+ } else { /* 2.0 > |x| > 2**-28 */
+ t = x*x;
+ w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
+ }
+ if(hx>0) return w; else return -w;
+}
--- /dev/null
+/* @(#)s_atan.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $";
+#endif
+
+/* atan(x)
+ * Method
+ * 1. Reduce x to positive by atan(x) = -atan(-x).
+ * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ * is further reduced to one of the following intervals and the
+ * arctangent of t is evaluated by the corresponding formula:
+ *
+ * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double atanhi[] = {
+#else
+static double atanhi[] = {
+#endif
+ 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+ 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+ 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+ 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+};
+
+#ifdef __STDC__
+static const double atanlo[] = {
+#else
+static double atanlo[] = {
+#endif
+ 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+ 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+ 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+ 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+};
+
+#ifdef __STDC__
+static const double aT[] = {
+#else
+static double aT[] = {
+#endif
+ 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
+ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+ 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
+ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+ 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
+ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+ 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
+ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+ 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
+ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+ 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
+};
+
+#ifdef __STDC__
+ static const double
+#else
+ static double
+#endif
+one = 1.0,
+huge = 1.0e300;
+
+#ifdef __STDC__
+ double atan(double x)
+#else
+ double atan(x)
+ double x;
+#endif
+{
+ double w,s1,s2,z;
+ int32_t ix,hx,id;
+
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x44100000) { /* if |x| >= 2^66 */
+ u_int32_t low;
+ GET_LOW_WORD(low,x);
+ if(ix>0x7ff00000||
+ (ix==0x7ff00000&&(low!=0)))
+ return x+x; /* NaN */
+ if(hx>0) return atanhi[3]+atanlo[3];
+ else return -atanhi[3]-atanlo[3];
+ } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
+ if (ix < 0x3e200000) { /* |x| < 2^-29 */
+ if(huge+x>one) return x; /* raise inexact */
+ }
+ id = -1;
+ } else {
+ x = fabs(x);
+ if (ix < 0x3ff30000) { /* |x| < 1.1875 */
+ if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
+ id = 0; x = (2.0*x-one)/(2.0+x);
+ } else { /* 11/16<=|x|< 19/16 */
+ id = 1; x = (x-one)/(x+one);
+ }
+ } else {
+ if (ix < 0x40038000) { /* |x| < 2.4375 */
+ id = 2; x = (x-1.5)/(one+1.5*x);
+ } else { /* 2.4375 <= |x| < 2^66 */
+ id = 3; x = -1.0/x;
+ }
+ }}
+ /* end of argument reduction */
+ z = x*x;
+ w = z*z;
+ /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+ s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+ s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+ if (id<0) return x - x*(s1+s2);
+ else {
+ z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+ return (hx<0)? -z:z;
+ }
+}
--- /dev/null
+/* @(#)s_cbrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+/* cbrt(x)
+ * Return cube root of x
+ */
+#ifdef __STDC__
+static const u_int32_t
+#else
+static u_int32_t
+#endif
+ B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
+ B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
+D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
+E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
+F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
+G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
+
+#ifdef __STDC__
+ double cbrt(double x)
+#else
+ double cbrt(x)
+ double x;
+#endif
+{
+ int32_t hx;
+ double r,s,t=0.0,w;
+ u_int32_t sign;
+ u_int32_t high,low;
+
+ GET_HIGH_WORD(hx,x);
+ sign=hx&0x80000000; /* sign= sign(x) */
+ hx ^=sign;
+ if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
+ GET_LOW_WORD(low,x);
+ if((hx|low)==0)
+ return(x); /* cbrt(0) is itself */
+
+ SET_HIGH_WORD(x,hx); /* x <- |x| */
+ /* rough cbrt to 5 bits */
+ if(hx<0x00100000) /* subnormal number */
+ {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
+ t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
+ }
+ else
+ SET_HIGH_WORD(t,hx/3+B1);
+
+
+ /* new cbrt to 23 bits, may be implemented in single precision */
+ r=t*t/x;
+ s=C+r*t;
+ t*=G+F/(s+E+D/s);
+
+ /* chopped to 20 bits and make it larger than cbrt(x) */
+ GET_HIGH_WORD(high,t);
+ INSERT_WORDS(t,high+0x00000001,0);
+
+
+ /* one step newton iteration to 53 bits with error less than 0.667 ulps */
+ s=t*t; /* t*t is exact */
+ r=x/s;
+ w=t+t;
+ r=(r-t)/(w+r); /* r-s is exact */
+ t=t+t*r;
+
+ /* retore the sign bit */
+ GET_HIGH_WORD(high,t);
+ SET_HIGH_WORD(t,high|sign);
+ return(t);
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_ceil.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_ceil.c,v 1.8 1995/05/10 20:46:53 jtc Exp $";
+#endif
+
+/*
+ * ceil(x)
+ * Return x rounded toward -inf to integral value
+ * Method:
+ * Bit twiddling.
+ * Exception:
+ * Inexact flag raised if x not equal to ceil(x).
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double huge = 1.0e300;
+#else
+static double huge = 1.0e300;
+#endif
+
+#ifdef __STDC__
+ double ceil(double x)
+#else
+ double ceil(x)
+ double x;
+#endif
+{
+ int32_t i0,i1,j0;
+ u_int32_t i,j;
+ EXTRACT_WORDS(i0,i1,x);
+ j0 = ((i0>>20)&0x7ff)-0x3ff;
+ if(j0<20) {
+ if(j0<0) { /* raise inexact if x != 0 */
+ if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
+ if(i0<0) {i0=0x80000000;i1=0;}
+ else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
+ }
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0>0) i0 += (0x00100000)>>j0;
+ i0 &= (~i); i1=0;
+ }
+ }
+ } else if (j0>51) {
+ if(j0==0x400) return x+x; /* inf or NaN */
+ else return x; /* x is integral */
+ } else {
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0>0) {
+ if(j0==20) i0+=1;
+ else {
+ j = i1 + (1<<(52-j0));
+ if(j<i1) i0+=1; /* got a carry */
+ i1 = j;
+ }
+ }
+ i1 &= (~i);
+ }
+ }
+ INSERT_WORDS(x,i0,i1);
+ return x;
+}
+#endif /* !__ppc__ */
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_copysign.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $";
+#endif
+
+/*
+ * copysign(double x, double y)
+ * copysign(x,y) returns a value with the magnitude of x and
+ * with the sign bit of y.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double copysign(double x, double y)
+#else
+ double copysign(x,y)
+ double x,y;
+#endif
+{
+ u_int32_t hx,hy;
+ GET_HIGH_WORD(hx,x);
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000));
+ return x;
+}
+#endif
--- /dev/null
+/* @(#)s_cos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $";
+#endif
+
+/* cos(x)
+ * Return cosine function of x.
+ *
+ * kernel function:
+ * __kernel_sin ... sine function on [-pi/4,pi/4]
+ * __kernel_cos ... cosine function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double cos(double x)
+#else
+ double cos(x)
+ double x;
+#endif
+{
+ double y[2],z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix,x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
+
+ /* cos(Inf or NaN) is NaN */
+ else if (ix>=0x7ff00000) return x-x;
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2(x,y);
+ switch(n&3) {
+ case 0: return __kernel_cos(y[0],y[1]);
+ case 1: return -__kernel_sin(y[0],y[1],1);
+ case 2: return -__kernel_cos(y[0],y[1]);
+ default:
+ return __kernel_sin(y[0],y[1],1);
+ }
+ }
+}
--- /dev/null
+/* @(#)s_erf.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $";
+#endif
+
+/* double erf(double x)
+ * double erfc(double x)
+ * x
+ * 2 |\
+ * erf(x) = --------- | exp(-t*t)dt
+ * sqrt(pi) \|
+ * 0
+ *
+ * erfc(x) = 1-erf(x)
+ * Note that
+ * erf(-x) = -erf(x)
+ * erfc(-x) = 2 - erfc(x)
+ *
+ * Method:
+ * 1. For |x| in [0, 0.84375]
+ * erf(x) = x + x*R(x^2)
+ * erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
+ * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
+ * where R = P/Q where P is an odd poly of degree 8 and
+ * Q is an odd poly of degree 10.
+ * -57.90
+ * | R - (erf(x)-x)/x | <= 2
+ *
+ *
+ * Remark. The formula is derived by noting
+ * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
+ * and that
+ * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
+ * is close to one. The interval is chosen because the fix
+ * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
+ * near 0.6174), and by some experiment, 0.84375 is chosen to
+ * guarantee the error is less than one ulp for erf.
+ *
+ * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
+ * c = 0.84506291151 rounded to single (24 bits)
+ * erf(x) = sign(x) * (c + P1(s)/Q1(s))
+ * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
+ * 1+(c+P1(s)/Q1(s)) if x < 0
+ * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
+ * Remark: here we use the taylor series expansion at x=1.
+ * erf(1+s) = erf(1) + s*Poly(s)
+ * = 0.845.. + P1(s)/Q1(s)
+ * That is, we use rational approximation to approximate
+ * erf(1+s) - (c = (single)0.84506291151)
+ * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
+ * where
+ * P1(s) = degree 6 poly in s
+ * Q1(s) = degree 6 poly in s
+ *
+ * 3. For x in [1.25,1/0.35(~2.857143)],
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
+ * erf(x) = 1 - erfc(x)
+ * where
+ * R1(z) = degree 7 poly in z, (z=1/x^2)
+ * S1(z) = degree 8 poly in z
+ *
+ * 4. For x in [1/0.35,28]
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
+ * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
+ * = 2.0 - tiny (if x <= -6)
+ * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
+ * erf(x) = sign(x)*(1.0 - tiny)
+ * where
+ * R2(z) = degree 6 poly in z, (z=1/x^2)
+ * S2(z) = degree 7 poly in z
+ *
+ * Note1:
+ * To compute exp(-x*x-0.5625+R/S), let s be a single
+ * precision number and s := x; then
+ * -x*x = -s*s + (s-x)*(s+x)
+ * exp(-x*x-0.5626+R/S) =
+ * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
+ * Note2:
+ * Here 4 and 5 make use of the asymptotic series
+ * exp(-x*x)
+ * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
+ * x*sqrt(pi)
+ * We use rational approximation to approximate
+ * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
+ * Here is the error bound for R1/S1 and R2/S2
+ * |R1/S1 - f(x)| < 2**(-62.57)
+ * |R2/S2 - f(x)| < 2**(-61.52)
+ *
+ * 5. For inf > x >= 28
+ * erf(x) = sign(x) *(1 - tiny) (raise inexact)
+ * erfc(x) = tiny*tiny (raise underflow) if x > 0
+ * = 2 - tiny if x<0
+ *
+ * 7. Special case:
+ * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
+ * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ * erfc/erf(NaN) is NaN
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+tiny = 1e-300,
+half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
+ /* c = (float)0.84506291151 */
+erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
+efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
+pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
+pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
+pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
+pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
+pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
+qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
+qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
+qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
+qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
+qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
+pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
+pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
+pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
+pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
+pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
+pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
+qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
+qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
+qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
+qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
+qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
+qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
+ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
+ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
+ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
+ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
+ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
+ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
+ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
+sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
+sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
+sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
+sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
+sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
+sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
+sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
+sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
+rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
+rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
+rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
+rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
+rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
+rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
+sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
+sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
+sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
+sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
+sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
+sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
+sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
+
+#ifdef __STDC__
+ double erf(double x)
+#else
+ double erf(x)
+ double x;
+#endif
+{
+ int32_t hx,ix,i;
+ double R,S,P,Q,s,y,z,r;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7ff00000) { /* erf(nan)=nan */
+ i = ((u_int32_t)hx>>31)<<1;
+ return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */
+ }
+
+ if(ix < 0x3feb0000) { /* |x|<0.84375 */
+ if(ix < 0x3e300000) { /* |x|<2**-28 */
+ if (ix < 0x00800000)
+ return 0.125*(8.0*x+efx8*x); /*avoid underflow */
+ return x + efx*x;
+ }
+ z = x*x;
+ r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
+ s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+ y = r/s;
+ return x + x*y;
+ }
+ if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
+ s = fabs(x)-one;
+ P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
+ Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+ if(hx>=0) return erx + P/Q; else return -erx - P/Q;
+ }
+ if (ix >= 0x40180000) { /* inf>|x|>=6 */
+ if(hx>=0) return one-tiny; else return tiny-one;
+ }
+ x = fabs(x);
+ s = one/(x*x);
+ if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
+ R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
+ ra5+s*(ra6+s*ra7))))));
+ S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
+ sa5+s*(sa6+s*(sa7+s*sa8)))))));
+ } else { /* |x| >= 1/0.35 */
+ R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
+ rb5+s*rb6)))));
+ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
+ sb5+s*(sb6+s*sb7))))));
+ }
+ z = x;
+ SET_LOW_WORD(z,0);
+ r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S);
+ if(hx>=0) return one-r/x; else return r/x-one;
+}
+
+#ifdef __STDC__
+ double erfc(double x)
+#else
+ double erfc(x)
+ double x;
+#endif
+{
+ int32_t hx,ix;
+ double R,S,P,Q,s,y,z,r;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7ff00000) { /* erfc(nan)=nan */
+ /* erfc(+-inf)=0,2 */
+ return (double)(((u_int32_t)hx>>31)<<1)+one/x;
+ }
+
+ if(ix < 0x3feb0000) { /* |x|<0.84375 */
+ if(ix < 0x3c700000) /* |x|<2**-56 */
+ return one-x;
+ z = x*x;
+ r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
+ s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+ y = r/s;
+ if(hx < 0x3fd00000) { /* x<1/4 */
+ return one-(x+x*y);
+ } else {
+ r = x*y;
+ r += (x-half);
+ return half - r ;
+ }
+ }
+ if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
+ s = fabs(x)-one;
+ P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
+ Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+ if(hx>=0) {
+ z = one-erx; return z - P/Q;
+ } else {
+ z = erx+P/Q; return one+z;
+ }
+ }
+ if (ix < 0x403c0000) { /* |x|<28 */
+ x = fabs(x);
+ s = one/(x*x);
+ if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
+ R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
+ ra5+s*(ra6+s*ra7))))));
+ S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
+ sa5+s*(sa6+s*(sa7+s*sa8)))))));
+ } else { /* |x| >= 1/.35 ~ 2.857143 */
+ if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
+ R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
+ rb5+s*rb6)))));
+ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
+ sb5+s*(sb6+s*sb7))))));
+ }
+ z = x;
+ SET_LOW_WORD(z,0);
+ r = __ieee754_exp(-z*z-0.5625)*
+ __ieee754_exp((z-x)*(z+x)+R/S);
+ if(hx>0) return r/x; else return two-r/x;
+ } else {
+ if(hx>0) return tiny*tiny; else return two-tiny;
+ }
+}
--- /dev/null
+/* @(#)s_expm1.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
+#endif
+
+/* expm1(x)
+ * Returns exp(x)-1, the exponential of x minus 1.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
+ *
+ * Here a correction term c will be computed to compensate
+ * the error in r when rounded to a floating-point number.
+ *
+ * 2. Approximating expm1(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Since
+ * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
+ * we define R1(r*r) by
+ * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
+ * That is,
+ * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
+ * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
+ * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
+ * We use a special Reme algorithm on [0,0.347] to generate
+ * a polynomial of degree 5 in r*r to approximate R1. The
+ * maximum error of this polynomial approximation is bounded
+ * by 2**-61. In other words,
+ * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
+ * where Q1 = -1.6666666666666567384E-2,
+ * Q2 = 3.9682539681370365873E-4,
+ * Q3 = -9.9206344733435987357E-6,
+ * Q4 = 2.5051361420808517002E-7,
+ * Q5 = -6.2843505682382617102E-9;
+ * (where z=r*r, and the values of Q1 to Q5 are listed below)
+ * with error bounded by
+ * | 5 | -61
+ * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
+ * | |
+ *
+ * expm1(r) = exp(r)-1 is then computed by the following
+ * specific way which minimize the accumulation rounding error:
+ * 2 3
+ * r r [ 3 - (R1 + R1*r/2) ]
+ * expm1(r) = r + --- + --- * [--------------------]
+ * 2 2 [ 6 - r*(3 - R1*r/2) ]
+ *
+ * To compensate the error in the argument reduction, we use
+ * expm1(r+c) = expm1(r) + c + expm1(r)*c
+ * ~ expm1(r) + c + r*c
+ * Thus c+r*c will be added in as the correction terms for
+ * expm1(r+c). Now rearrange the term to avoid optimization
+ * screw up:
+ * ( 2 2 )
+ * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
+ * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
+ * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
+ * ( )
+ *
+ * = r - E
+ * 3. Scale back to obtain expm1(x):
+ * From step 1, we have
+ * expm1(x) = either 2^k*[expm1(r)+1] - 1
+ * = or 2^k*[expm1(r) + (1-2^-k)]
+ * 4. Implementation notes:
+ * (A). To save one multiplication, we scale the coefficient Qi
+ * to Qi*2^i, and replace z by (x^2)/2.
+ * (B). To achieve maximum accuracy, we compute expm1(x) by
+ * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
+ * (ii) if k=0, return r-E
+ * (iii) if k=-1, return 0.5*(r-E)-0.5
+ * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
+ * else return 1.0+2.0*(r-E);
+ * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
+ * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
+ * (vii) return 2^k(1-((E+2^-k)-r))
+ *
+ * Special cases:
+ * expm1(INF) is INF, expm1(NaN) is NaN;
+ * expm1(-INF) is -1, and
+ * for finite argument, only expm1(0)=0 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 7.09782712893383973096e+02 then expm1(x) overflow
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.0,
+huge = 1.0e+300,
+tiny = 1.0e-300,
+o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
+ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
+ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
+invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
+ /* scaled coefficients related to expm1 */
+Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
+Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
+Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
+Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
+Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+#ifdef __STDC__
+ double expm1(double x)
+#else
+ double expm1(x)
+ double x;
+#endif
+{
+ double y,hi,lo,c,t,e,hxs,hfx,r1;
+ int32_t k,xsb;
+ u_int32_t hx;
+
+ GET_HIGH_WORD(hx,x);
+ xsb = hx&0x80000000; /* sign bit of x */
+ if(xsb==0) y=x; else y= -x; /* y = |x| */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out huge and non-finite argument */
+ if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ u_int32_t low;
+ GET_LOW_WORD(low,x);
+ if(((hx&0xfffff)|low)!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ }
+ if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
+ if(x+tiny<0.0) /* raise inexact */
+ return tiny-one; /* return -1 */
+ }
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ if(xsb==0)
+ {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
+ else
+ {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
+ } else {
+ k = invln2*x+((xsb==0)?0.5:-0.5);
+ t = k;
+ hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
+ lo = t*ln2_lo;
+ }
+ x = hi - lo;
+ c = (hi-x)-lo;
+ }
+ else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
+ t = huge+x; /* return x with inexact flags when x!=0 */
+ return x - (t-(huge+x));
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ hfx = 0.5*x;
+ hxs = x*hfx;
+ r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
+ t = 3.0-r1*hfx;
+ e = hxs*((r1-t)/(6.0 - x*t));
+ if(k==0) return x - (x*e-hxs); /* c is 0 */
+ else {
+ e = (x*(e-c)-c);
+ e -= hxs;
+ if(k== -1) return 0.5*(x-e)-0.5;
+ if(k==1)
+ if(x < -0.25) return -2.0*(e-(x+0.5));
+ else return one+2.0*(x-e);
+ if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
+ u_int32_t high;
+ y = one-(e-x);
+ GET_HIGH_WORD(high,y);
+ SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
+ return y-one;
+ }
+ t = one;
+ if(k<20) {
+ u_int32_t high;
+ SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
+ y = t-(e-x);
+ GET_HIGH_WORD(high,y);
+ SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
+ } else {
+ u_int32_t high;
+ SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */
+ y = x-(e+t);
+ y += one;
+ GET_HIGH_WORD(high,y);
+ SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
+ }
+ }
+ return y;
+}
--- /dev/null
+/* @(#)s_fabs.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $";
+#endif
+
+/*
+ * fabs(x) returns the absolute value of x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double fabs(double x)
+#else
+ double fabs(x)
+ double x;
+#endif
+{
+ u_int32_t high;
+ GET_HIGH_WORD(high,x);
+ SET_HIGH_WORD(x,high&0x7fffffff);
+ return x;
+}
--- /dev/null
+/* @(#)s_finite.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_finite.c,v 1.8 1995/05/10 20:47:17 jtc Exp $";
+#endif
+
+/*
+ * finite(x) returns 1 is x is finite, else 0;
+ * no branching!
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ int finite(double x)
+#else
+ int finite(x)
+ double x;
+#endif
+{
+ int32_t hx;
+ GET_HIGH_WORD(hx,x);
+ return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31);
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_floor.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_floor.c,v 1.8 1995/05/10 20:47:20 jtc Exp $";
+#endif
+
+/*
+ * floor(x)
+ * Return x rounded toward -inf to integral value
+ * Method:
+ * Bit twiddling.
+ * Exception:
+ * Inexact flag raised if x not equal to floor(x).
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double huge = 1.0e300;
+#else
+static double huge = 1.0e300;
+#endif
+
+#ifdef __STDC__
+ double floor(double x)
+#else
+ double floor(x)
+ double x;
+#endif
+{
+ int32_t i0,i1,j0;
+ u_int32_t i,j;
+ EXTRACT_WORDS(i0,i1,x);
+ j0 = ((i0>>20)&0x7ff)-0x3ff;
+ if(j0<20) {
+ if(j0<0) { /* raise inexact if x != 0 */
+ if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
+ if(i0>=0) {i0=i1=0;}
+ else if(((i0&0x7fffffff)|i1)!=0)
+ { i0=0xbff00000;i1=0;}
+ }
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0<0) i0 += (0x00100000)>>j0;
+ i0 &= (~i); i1=0;
+ }
+ }
+ } else if (j0>51) {
+ if(j0==0x400) return x+x; /* inf or NaN */
+ else return x; /* x is integral */
+ } else {
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0<0) {
+ if(j0==20) i0+=1;
+ else {
+ j = i1+(1<<(52-j0));
+ if(j<i1) i0 +=1 ; /* got a carry */
+ i1=j;
+ }
+ }
+ i1 &= (~i);
+ }
+ }
+ INSERT_WORDS(x,i0,i1);
+ return x;
+}
+#endif /* !__ppc__ */
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_frexp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_frexp.c,v 1.9 1995/05/10 20:47:24 jtc Exp $";
+#endif
+
+/*
+ * for non-zero x
+ * x = frexp(arg,&exp);
+ * return a double fp quantity x such that 0.5 <= |x| <1.0
+ * and the corresponding binary exponent "exp". That is
+ * arg = x*2^exp.
+ * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
+ * with *exp=0.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
+
+#ifdef __STDC__
+ double frexp(double x, int *eptr)
+#else
+ double frexp(x, eptr)
+ double x; int *eptr;
+#endif
+{
+ int32_t hx, ix, lx;
+ EXTRACT_WORDS(hx,lx,x);
+ ix = 0x7fffffff&hx;
+ *eptr = 0;
+ if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
+ if (ix<0x00100000) { /* subnormal */
+ x *= two54;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ *eptr = -54;
+ }
+ *eptr += (ix>>20)-1022;
+ hx = (hx&0x800fffff)|0x3fe00000;
+ SET_HIGH_WORD(x,hx);
+ return x;
+}
+#endif /* !__ppc__ */
--- /dev/null
+/* @(#)s_ilogb.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_ilogb.c,v 1.9 1995/05/10 20:47:28 jtc Exp $";
+#endif
+
+/* ilogb(double x)
+ * return the binary exponent of non-zero x
+ * ilogb(0) = 0x80000001
+ * ilogb(inf/NaN) = 0x7fffffff (no signal is raised)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ int ilogb(double x)
+#else
+ int ilogb(x)
+ double x;
+#endif
+{
+ int32_t hx,lx,ix;
+
+ GET_HIGH_WORD(hx,x);
+ hx &= 0x7fffffff;
+ if(hx<0x00100000) {
+ GET_LOW_WORD(lx,x);
+ if((hx|lx)==0)
+ return 0x80000001; /* ilogb(0) = 0x80000001 */
+ else /* subnormal x */
+ if(hx==0) {
+ for (ix = -1043; lx>0; lx<<=1) ix -=1;
+ } else {
+ for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
+ }
+ return ix;
+ }
+ else if (hx<0x7ff00000) return (hx>>20)-1023;
+ else return 0x7fffffff;
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_ldexp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_ldexp.c,v 1.6 1995/05/10 20:47:40 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+#include <errno.h>
+
+#ifdef __STDC__
+ double ldexp(double value, int exp)
+#else
+ double ldexp(value, exp)
+ double value; int exp;
+#endif
+{
+ if(!finite(value)||value==0.0) return value;
+ value = scalbn(value,exp);
+ if(!finite(value)||value==0.0) errno = ERANGE;
+ return value;
+}
+#endif /* !__ppc__ */
--- /dev/null
+/* @(#)s_lib_ver.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_lib_version.c,v 1.6 1995/05/10 20:47:44 jtc Exp $";
+#endif
+
+/*
+ * MACRO for standards
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/*
+ * define and initialize _LIB_VERSION
+ */
+#ifdef _POSIX_MODE
+_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_;
+#else
+#ifdef _XOPEN_MODE
+_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_;
+#else
+#ifdef _SVID3_MODE
+_LIB_VERSION_TYPE _LIB_VERSION = _SVID_;
+#else /* default _IEEE_MODE */
+_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_;
+#endif
+#endif
+#endif
--- /dev/null
+/* @(#)s_log1p.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $";
+#endif
+
+/* double log1p(double x)
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * 1+x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * Note. If k=0, then f=x is exact. However, if k!=0, then f
+ * may not be representable exactly. In that case, a correction
+ * term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+ * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+ * and add back the correction term c/u.
+ * (Note: when x > 2**53, one can simply return log(x))
+ *
+ * 2. Approximation of log1p(f).
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ * = 2s + s*R
+ * We use a special Reme algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * of this polynomial approximation is bounded by 2**-58.45. In
+ * other words,
+ * 2 4 6 8 10 12 14
+ * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
+ * (the values of Lp1 to Lp7 are listed in the program)
+ * and
+ * | 2 14 | -58.45
+ * | Lp1*s +...+Lp7*s - R(z) | <= 2
+ * | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ * In order to guarantee error in log below 1ulp, we compute log
+ * by
+ * log1p(f) = f - (hfsq - s*(hfsq+R)).
+ *
+ * 3. Finally, log1p(x) = k*ln2 + log1p(f).
+ * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ * Here ln2 is split into two floating point number:
+ * ln2_hi + ln2_lo,
+ * where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ * log1p(x) is NaN with signal if x < -1 (including -INF) ;
+ * log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+ * log1p(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ *
+ * Note: Assuming log() return accurate answer, the following
+ * algorithm can be used to compute log1p(x) to within a few ULP:
+ *
+ * u = 1+x;
+ * if(u==1.0) return x ; else
+ * return log(u)*(x/(u-1.0));
+ *
+ * See HP-15C Advanced Functions Handbook, p.193.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
+ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
+two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
+Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double log1p(double x)
+#else
+ double log1p(x)
+ double x;
+#endif
+{
+ double hfsq,f,c,s,z,R,u;
+ int32_t k,hx,hu,ax;
+
+ GET_HIGH_WORD(hx,x);
+ ax = hx&0x7fffffff;
+
+ k = 1;
+ if (hx < 0x3FDA827A) { /* x < 0.41422 */
+ if(ax>=0x3ff00000) { /* x <= -1.0 */
+ if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */
+ else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
+ }
+ if(ax<0x3e200000) { /* |x| < 2**-29 */
+ if(two54+x>zero /* raise inexact */
+ &&ax<0x3c900000) /* |x| < 2**-54 */
+ return x;
+ else
+ return x - x*x*0.5;
+ }
+ if(hx>0||hx<=((int32_t)0xbfd2bec3)) {
+ k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ if(k!=0) {
+ if(hx<0x43400000) {
+ u = 1.0+x;
+ GET_HIGH_WORD(hu,u);
+ k = (hu>>20)-1023;
+ c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
+ c /= u;
+ } else {
+ u = x;
+ GET_HIGH_WORD(hu,u);
+ k = (hu>>20)-1023;
+ c = 0;
+ }
+ hu &= 0x000fffff;
+ if(hu<0x6a09e) {
+ SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */
+ } else {
+ k += 1;
+ SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */
+ hu = (0x00100000-hu)>>2;
+ }
+ f = u-1.0;
+ }
+ hfsq=0.5*f*f;
+ if(hu==0) { /* |f| < 2**-20 */
+ if(f==zero) if(k==0) return zero;
+ else {c += k*ln2_lo; return k*ln2_hi+c;}
+ R = hfsq*(1.0-0.66666666666666666*f);
+ if(k==0) return f-R; else
+ return k*ln2_hi-((R-(k*ln2_lo+c))-f);
+ }
+ s = f/(2.0+f);
+ z = s*s;
+ R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
+ if(k==0) return f-(hfsq-s*(hfsq+R)); else
+ return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_logb.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_logb.c,v 1.8 1995/05/10 20:47:50 jtc Exp $";
+#endif
+
+/*
+ * double logb(x)
+ * IEEE 754 logb. Included to pass IEEE test suite. Not recommend.
+ * Use ilogb instead.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double logb(double x)
+#else
+ double logb(x)
+ double x;
+#endif
+{
+ int32_t lx,ix;
+ EXTRACT_WORDS(ix,lx,x);
+ ix &= 0x7fffffff; /* high |x| */
+ if((ix|lx)==0) return -1.0/fabs(x);
+ if(ix>=0x7ff00000) return x*x;
+ if((ix>>=20)==0) /* IEEE 754 logb */
+ return -1022.0;
+ else
+ return (double) (ix-1023);
+}
+#endif /* !__ppc__ */
--- /dev/null
+/* @(#)s_matherr.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_matherr.c,v 1.6 1995/05/10 20:47:53 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ int matherr(struct exception *x)
+#else
+ int matherr(x)
+ struct exception *x;
+#endif
+{
+ int n=0;
+ if(x->arg1!=x->arg1) return 0;
+ return n;
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_modf.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_modf.c,v 1.8 1995/05/10 20:47:55 jtc Exp $";
+#endif
+
+/*
+ * modf(double x, double *iptr)
+ * return fraction part of x, and return x's integral part in *iptr.
+ * Method:
+ * Bit twiddling.
+ *
+ * Exception:
+ * No exception.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0;
+#else
+static double one = 1.0;
+#endif
+
+#ifdef __STDC__
+ double modf(double x, double *iptr)
+#else
+ double modf(x, iptr)
+ double x,*iptr;
+#endif
+{
+ int32_t i0,i1,j0;
+ u_int32_t i;
+ EXTRACT_WORDS(i0,i1,x);
+ j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */
+ if(j0<20) { /* integer part in high x */
+ if(j0<0) { /* |x|<1 */
+ INSERT_WORDS(*iptr,i0&0x80000000,0); /* *iptr = +-0 */
+ return x;
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) { /* x is integral */
+ u_int32_t high;
+ *iptr = x;
+ GET_HIGH_WORD(high,x);
+ INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */
+ return x;
+ } else {
+ INSERT_WORDS(*iptr,i0&(~i),0);
+ return x - *iptr;
+ }
+ }
+ } else if (j0>51) { /* no fraction part */
+ u_int32_t high;
+ *iptr = x*one;
+ GET_HIGH_WORD(high,x);
+ INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */
+ return x;
+ } else { /* fraction part in low x */
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) { /* x is integral */
+ u_int32_t high;
+ *iptr = x;
+ GET_HIGH_WORD(high,x);
+ INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */
+ return x;
+ } else {
+ INSERT_WORDS(*iptr,i0,i1&(~i));
+ return x - *iptr;
+ }
+ }
+}
+#endif /* !__ppc__ */
--- /dev/null
+/* @(#)s_nextafter.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_nextafter.c,v 1.8 1995/05/10 20:47:58 jtc Exp $";
+#endif
+
+/* IEEE functions
+ * nextafter(x,y)
+ * return the next machine floating-point number of x in the
+ * direction toward y.
+ * Special cases:
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double nextafter(double x, double y)
+#else
+ double nextafter(x,y)
+ double x,y;
+#endif
+{
+ int32_t hx,hy,ix,iy;
+ u_int32_t lx,ly;
+
+ EXTRACT_WORDS(hx,lx,x);
+ EXTRACT_WORDS(hy,ly,y);
+ ix = hx&0x7fffffff; /* |x| */
+ iy = hy&0x7fffffff; /* |y| */
+
+ if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
+ ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */
+ return x+y;
+ if(x==y) return x; /* x=y, return x */
+ if((ix|lx)==0) { /* x == 0 */
+ INSERT_WORDS(x,hy&0x80000000,1); /* return +-minsubnormal */
+ y = x*x;
+ if(y==x) return y; else return x; /* raise underflow flag */
+ }
+ if(hx>=0) { /* x > 0 */
+ if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */
+ if(lx==0) hx -= 1;
+ lx -= 1;
+ } else { /* x < y, x += ulp */
+ lx += 1;
+ if(lx==0) hx += 1;
+ }
+ } else { /* x < 0 */
+ if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */
+ if(lx==0) hx -= 1;
+ lx -= 1;
+ } else { /* x > y, x += ulp */
+ lx += 1;
+ if(lx==0) hx += 1;
+ }
+ }
+ hy = hx&0x7ff00000;
+ if(hy>=0x7ff00000) return x+x; /* overflow */
+ if(hy<0x00100000) { /* underflow */
+ y = x*x;
+ if(y!=x) { /* raise underflow flag */
+ INSERT_WORDS(y,hx,lx);
+ return y;
+ }
+ }
+ INSERT_WORDS(x,hx,lx);
+ return x;
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)s_rint.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $";
+#endif
+
+/*
+ * rint(x)
+ * Return x rounded to integral value according to the prevailing
+ * rounding mode.
+ * Method:
+ * Using floating addition.
+ * Exception:
+ * Inexact flag raised if x not equal to rint(x).
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+TWO52[2]={
+ 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
+ -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
+};
+
+#ifdef __STDC__
+ double rint(double x)
+#else
+ double rint(x)
+ double x;
+#endif
+{
+ int32_t i0,j0,sx;
+ u_int32_t i,i1;
+ double w,t;
+ EXTRACT_WORDS(i0,i1,x);
+ sx = (i0>>31)&1;
+ j0 = ((i0>>20)&0x7ff)-0x3ff;
+ if(j0<20) {
+ if(j0<0) {
+ if(((i0&0x7fffffff)|i1)==0) return x;
+ i1 |= (i0&0x0fffff);
+ i0 &= 0xfffe0000;
+ i0 |= ((i1|-i1)>>12)&0x80000;
+ SET_HIGH_WORD(x,i0);
+ w = TWO52[sx]+x;
+ t = w-TWO52[sx];
+ GET_HIGH_WORD(i0,t);
+ SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31));
+ return t;
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) return x; /* x is integral */
+ i>>=1;
+ if(((i0&i)|i1)!=0) {
+ if(j0==19) i1 = 0x40000000; else
+ i0 = (i0&(~i))|((0x20000)>>j0);
+ }
+ }
+ } else if (j0>51) {
+ if(j0==0x400) return x+x; /* inf or NaN */
+ else return x; /* x is integral */
+ } else {
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) return x; /* x is integral */
+ i>>=1;
+ if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
+ }
+ INSERT_WORDS(x,i0,i1);
+ w = TWO52[sx]+x;
+ return w-TWO52[sx];
+}
+#endif /* !__ppc__ */
--- /dev/null
+/* @(#)s_scalbn.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $";
+#endif
+
+/*
+ * scalbn (double x, int n)
+ * scalbn(x,n) returns x* 2**n computed by exponent
+ * manipulation rather than by actually performing an
+ * exponentiation or a multiplication.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
+huge = 1.0e+300,
+tiny = 1.0e-300;
+
+#ifdef __STDC__
+ double scalbn (double x, int n)
+#else
+ double scalbn (x,n)
+ double x; int n;
+#endif
+{
+ int32_t k,hx,lx;
+ EXTRACT_WORDS(hx,lx,x);
+ k = (hx&0x7ff00000)>>20; /* extract exponent */
+ if (k==0) { /* 0 or subnormal x */
+ if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
+ x *= two54;
+ GET_HIGH_WORD(hx,x);
+ k = ((hx&0x7ff00000)>>20) - 54;
+ if (n< -50000) return tiny*x; /*underflow*/
+ }
+ if (k==0x7ff) return x+x; /* NaN or Inf */
+ k = k+n;
+ if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
+ if (k > 0) /* normal result */
+ {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
+ if (k <= -54)
+ if (n > 50000) /* in case integer overflow in n+k */
+ return huge*copysign(huge,x); /*overflow*/
+ else return tiny*copysign(tiny,x); /*underflow*/
+ k += 54; /* subnormal result */
+ SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
+ return x*twom54;
+}
--- /dev/null
+#include "math.h"
+#include "math_private.h"
+int signgam = 0;
--- /dev/null
+/* @(#)s_signif.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_significand.c,v 1.6 1995/05/10 20:48:11 jtc Exp $";
+#endif
+
+/*
+ * significand(x) computes just
+ * scalb(x, (double) -ilogb(x)),
+ * for exercising the fraction-part(F) IEEE 754-1985 test vector.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double significand(double x)
+#else
+ double significand(x)
+ double x;
+#endif
+{
+ return __ieee754_scalb(x,(double) -ilogb(x));
+}
--- /dev/null
+/* @(#)s_sin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $";
+#endif
+
+/* sin(x)
+ * Return sine function of x.
+ *
+ * kernel function:
+ * __kernel_sin ... sine function on [-pi/4,pi/4]
+ * __kernel_cos ... cose function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double sin(double x)
+#else
+ double sin(x)
+ double x;
+#endif
+{
+ double y[2],z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix,x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
+
+ /* sin(Inf or NaN) is NaN */
+ else if (ix>=0x7ff00000) return x-x;
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2(x,y);
+ switch(n&3) {
+ case 0: return __kernel_sin(y[0],y[1],1);
+ case 1: return __kernel_cos(y[0],y[1]);
+ case 2: return -__kernel_sin(y[0],y[1],1);
+ default:
+ return -__kernel_cos(y[0],y[1]);
+ }
+ }
+}
--- /dev/null
+/* @(#)s_tan.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $";
+#endif
+
+/* tan(x)
+ * Return tangent function of x.
+ *
+ * kernel function:
+ * __kernel_tan ... tangent function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double tan(double x)
+#else
+ double tan(x)
+ double x;
+#endif
+{
+ double y[2],z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix,x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
+
+ /* tan(Inf or NaN) is NaN */
+ else if (ix>=0x7ff00000) return x-x; /* NaN */
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2(x,y);
+ return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
+ -1 -- n odd */
+ }
+}
--- /dev/null
+/* @(#)s_tanh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
+#endif
+
+/* Tanh(x)
+ * Return the Hyperbolic Tangent of x
+ *
+ * Method :
+ * x -x
+ * e - e
+ * 0. tanh(x) is defined to be -----------
+ * x -x
+ * e + e
+ * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
+ * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
+ * -t
+ * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
+ * t + 2
+ * 2
+ * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
+ * t + 2
+ * 22.0 < x <= INF : tanh(x) := 1.
+ *
+ * Special cases:
+ * tanh(NaN) is NaN;
+ * only tanh(0)=0 is exact for finite argument.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one=1.0, two=2.0, tiny = 1.0e-300;
+#else
+static double one=1.0, two=2.0, tiny = 1.0e-300;
+#endif
+
+#ifdef __STDC__
+ double tanh(double x)
+#else
+ double tanh(x)
+ double x;
+#endif
+{
+ double t,z;
+ int32_t jx,ix;
+
+ /* High word of |x|. */
+ GET_HIGH_WORD(jx,x);
+ ix = jx&0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) {
+ if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
+ else return one/x-one; /* tanh(NaN) = NaN */
+ }
+
+ /* |x| < 22 */
+ if (ix < 0x40360000) { /* |x|<22 */
+ if (ix<0x3c800000) /* |x|<2**-55 */
+ return x*(one+x); /* tanh(small) = small */
+ if (ix>=0x3ff00000) { /* |x|>=1 */
+ t = expm1(two*fabs(x));
+ z = one - two/(t+two);
+ } else {
+ t = expm1(-two*fabs(x));
+ z= -t/(t+two);
+ }
+ /* |x| > 22, return +-1 */
+ } else {
+ z = one - tiny; /* raised inexact flag */
+ }
+ return (jx>=0)? z: -z;
+}
--- /dev/null
+#if defined(__ppc__)
+/***********************************************************************
+** File: scalb.c
+**
+** Contains: C source code for implementations of floating-point
+** scalb functions defined in header <fp.h>. In
+** particular, this file contains implementations of
+** functions scalb and scalbl for double and long double
+** formats on PowerPC platforms.
+**
+** Written by: Jon Okada, SANEitation Engineer, ext. 4-4838
+**
+** Copyright: © 1992 by Apple Computer, Inc., all rights reserved
+**
+** Change History ( most recent first ):
+**
+** 28 May 97 ali made an speed improvement for large n,
+** removed scalbl.
+** 12 Dec 92 JPO First created.
+**
+***********************************************************************/
+
+typedef union
+ {
+ struct {
+#if defined(__BIG_ENDIAN__)
+ unsigned long int hi;
+ unsigned long int lo;
+#else
+ unsigned long int lo;
+ unsigned long int hi;
+#endif
+ } words;
+ double dbl;
+ } DblInHex;
+
+static const double twoTo1023 = 8.988465674311579539e307; // 0x1p1023
+static const double twoToM1022 = 2.225073858507201383e-308; // 0x1p-1022
+
+
+/***********************************************************************
+ double scalb( double x, long int n ) returns its argument x scaled
+ by the factor 2^m. NaNs, signed zeros, and infinities are propagated
+ by this function regardless of the value of n.
+
+ Exceptions: OVERFLOW/INEXACT or UNDERFLOW inexact may occur;
+ INVALID for signaling NaN inputs ( quiet NaN returned ).
+
+ Calls: none.
+***********************************************************************/
+
+double scalb ( double x, int n )
+ {
+ DblInHex xInHex;
+
+ xInHex.words.lo = 0UL; // init. low half of xInHex
+
+ if ( n > 1023 )
+ { // large positive scaling
+ if ( n > 2097 ) // huge scaling
+ return ( ( x * twoTo1023 ) * twoTo1023 ) * twoTo1023;
+ while ( n > 1023 )
+ { // scale reduction loop
+ x *= twoTo1023; // scale x by 2^1023
+ n -= 1023; // reduce n by 1023
+ }
+ }
+
+ else if ( n < -1022 )
+ { // large negative scaling
+ if ( n < -2098 ) // huge negative scaling
+ return ( ( x * twoToM1022 ) * twoToM1022 ) * twoToM1022;
+ while ( n < -1022 )
+ { // scale reduction loop
+ x *= twoToM1022; // scale x by 2^( -1022 )
+ n += 1022; // incr n by 1022
+ }
+ }
+
+/*******************************************************************************
+* -1022 <= n <= 1023; convert n to double scale factor. *
+*******************************************************************************/
+
+ xInHex.words.hi = ( ( unsigned long ) ( n + 1023 ) ) << 20;
+ return ( x * xInHex.dbl );
+ }
+#endif /* __ppc__ */
--- /dev/null
+#if defined(__ppc__)
+/*******************************************************************************
+* *
+* File sign.c, *
+* Functions copysign and __signbitd. *
+* For PowerPC based machines. *
+* *
+* Copyright © 1991, 2001 Apple Computer, Inc. All rights reserved. *
+* *
+* Written by Ali Sazegari, started on June 1991. *
+* *
+* August 26 1991: no CFront Version 1.1d17 warnings. *
+* September 06 1991: passes the test suite with invalid raised on *
+* signaling nans. sane rom code behaves the same. *
+* September 24 1992: took the Ò#include support.hÓ out. *
+* Dcember 02 1992: PowerPC port. *
+* July 20 1994: __fabs added *
+* July 21 1994: deleted unnecessary functions: neg, COPYSIGNnew, *
+* and SIGNNUMnew. *
+* April 11 2001: first port to os x using gcc. *
+* removed fabs and deffered to gcc for direct *
+* instruction generation. *
+* *
+*******************************************************************************/
+
+#include "fp_private.h"
+
+/*******************************************************************************
+* *
+* Function copysign. *
+* Implementation of copysign for the PowerPC. *
+* *
+********************************************************************************
+* Note: The order of the operands in this function is reversed from that *
+* suggested in the IEEE standard 754. *
+*******************************************************************************/
+
+double copysign ( double arg2, double arg1 )
+ {
+ union
+ {
+ dHexParts hex;
+ double dbl;
+ } x, y;
+
+/*******************************************************************************
+* No need to flush NaNs out. *
+*******************************************************************************/
+
+ x.dbl = arg1;
+ y.dbl = arg2;
+
+ y.hex.high = y.hex.high & 0x7FFFFFFF;
+ y.hex.high = ( y.hex.high | ( x.hex.high & dSgnMask ) );
+
+ return y.dbl;
+ }
+#endif /* __ppc__ */
--- /dev/null
+/* @(#)w_acos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_acos.c,v 1.6 1995/05/10 20:48:26 jtc Exp $";
+#endif
+
+/*
+ * wrap_acos(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double acos(double x) /* wrapper acos */
+#else
+ double acos(x) /* wrapper acos */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_acos(x);
+#else
+ double z;
+ z = __ieee754_acos(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>1.0) {
+ return __kernel_standard(x,x,1); /* acos(|x|>1) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_acosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_acosh.c,v 1.6 1995/05/10 20:48:31 jtc Exp $";
+#endif
+
+/*
+ * wrapper acosh(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double acosh(double x) /* wrapper acosh */
+#else
+ double acosh(x) /* wrapper acosh */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_acosh(x);
+#else
+ double z;
+ z = __ieee754_acosh(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(x<1.0) {
+ return __kernel_standard(x,x,29); /* acosh(x<1) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_asin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_asin.c,v 1.6 1995/05/10 20:48:35 jtc Exp $";
+#endif
+
+/*
+ * wrapper asin(x)
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double asin(double x) /* wrapper asin */
+#else
+ double asin(x) /* wrapper asin */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_asin(x);
+#else
+ double z;
+ z = __ieee754_asin(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>1.0) {
+ return __kernel_standard(x,x,2); /* asin(|x|>1) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_atan2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_atan2.c,v 1.6 1995/05/10 20:48:39 jtc Exp $";
+#endif
+
+/*
+ * wrapper atan2(y,x)
+ */
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double atan2(double y, double x) /* wrapper atan2 */
+#else
+ double atan2(y,x) /* wrapper atan2 */
+ double y,x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_atan2(y,x);
+#else
+ double z;
+ z = __ieee754_atan2(y,x);
+ if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z;
+ if(x==0.0&&y==0.0) {
+ return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_atanh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_atanh.c,v 1.6 1995/05/10 20:48:43 jtc Exp $";
+#endif
+
+/*
+ * wrapper atanh(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double atanh(double x) /* wrapper atanh */
+#else
+ double atanh(x) /* wrapper atanh */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_atanh(x);
+#else
+ double z,y;
+ z = __ieee754_atanh(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ y = fabs(x);
+ if(y>=1.0) {
+ if(y>1.0)
+ return __kernel_standard(x,x,30); /* atanh(|x|>1) */
+ else
+ return __kernel_standard(x,x,31); /* atanh(|x|==1) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/*
+ * cabs() wrapper for hypot().
+ *
+ * Written by J.T. Conklin, <jtc@wimsey.com>
+ * Placed into the Public Domain, 1994.
+ */
+
+#include <math.h>
+
+struct complex {
+ double x;
+ double y;
+};
+
+double
+cabs(z)
+ struct complex z;
+{
+ return hypot(z.x, z.y);
+}
--- /dev/null
+/* @(#)w_cosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_cosh.c,v 1.6 1995/05/10 20:48:47 jtc Exp $";
+#endif
+
+/*
+ * wrapper cosh(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double cosh(double x) /* wrapper cosh */
+#else
+ double cosh(x) /* wrapper cosh */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_cosh(x);
+#else
+ double z;
+ z = __ieee754_cosh(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>7.10475860073943863426e+02) {
+ return __kernel_standard(x,x,5); /* cosh overflow */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/*
+ * drem() wrapper for remainder().
+ *
+ * Written by J.T. Conklin, <jtc@wimsey.com>
+ * Placed into the Public Domain, 1994.
+ */
+
+#include <math.h>
+
+double
+drem(x, y)
+ double x, y;
+{
+ return remainder(x, y);
+}
--- /dev/null
+/* @(#)w_exp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_exp.c,v 1.6 1995/05/10 20:48:51 jtc Exp $";
+#endif
+
+/*
+ * wrapper exp(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
+
+#ifdef __STDC__
+ double exp(double x) /* wrapper exp */
+#else
+ double exp(x) /* wrapper exp */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_exp(x);
+#else
+ double z;
+ z = __ieee754_exp(x);
+ if(_LIB_VERSION == _IEEE_) return z;
+ if(finite(x)) {
+ if(x>o_threshold)
+ return __kernel_standard(x,x,6); /* exp overflow */
+ else if(x<u_threshold)
+ return __kernel_standard(x,x,7); /* exp underflow */
+ }
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_fmod.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_fmod.c,v 1.6 1995/05/10 20:48:55 jtc Exp $";
+#endif
+
+/*
+ * wrapper fmod(x,y)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double fmod(double x, double y) /* wrapper fmod */
+#else
+ double fmod(x,y) /* wrapper fmod */
+ double x,y;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_fmod(x,y);
+#else
+ double z;
+ z = __ieee754_fmod(x,y);
+ if(_LIB_VERSION == _IEEE_ ||isnan(y)||isnan(x)) return z;
+ if(y==0.0) {
+ return __kernel_standard(x,y,27); /* fmod(x,0) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_gamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_gamma.c,v 1.7 1995/11/20 22:06:43 jtc Exp $";
+#endif
+
+/* double gamma(double x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call gamma_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+ double gamma(double x)
+#else
+ double gamma(x)
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_lgamma_r(x,&signgam);
+#else
+ double y;
+ y = __ieee754_lgamma_r(x,&signgam);
+ if(_LIB_VERSION == _IEEE_) return y;
+ if(!finite(y)&&finite(x)) {
+ if(floor(x)==x&&x<=0.0)
+ return __kernel_standard(x,x,41); /* gamma pole */
+ else
+ return __kernel_standard(x,x,40); /* gamma overflow */
+ } else
+ return y;
+#endif
+}
--- /dev/null
+/* @(#)wr_gamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_gamma_r.c,v 1.7 1995/11/20 22:06:45 jtc Exp $";
+#endif
+
+/*
+ * wrapper double gamma_r(double x, int *signgamp)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double gamma_r(double x, int *signgamp) /* wrapper lgamma_r */
+#else
+ double gamma_r(x,signgamp) /* wrapper lgamma_r */
+ double x; int *signgamp;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_lgamma_r(x,signgamp);
+#else
+ double y;
+ y = __ieee754_lgamma_r(x,signgamp);
+ if(_LIB_VERSION == _IEEE_) return y;
+ if(!finite(y)&&finite(x)) {
+ if(floor(x)==x&&x<=0.0)
+ return __kernel_standard(x,x,41); /* gamma pole */
+ else
+ return __kernel_standard(x,x,40); /* gamma overflow */
+ } else
+ return y;
+#endif
+}
--- /dev/null
+/* @(#)w_hypot.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_hypot.c,v 1.6 1995/05/10 20:49:07 jtc Exp $";
+#endif
+
+/*
+ * wrapper hypot(x,y)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double hypot(double x, double y)/* wrapper hypot */
+#else
+ double hypot(x,y) /* wrapper hypot */
+ double x,y;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_hypot(x,y);
+#else
+ double z;
+ z = __ieee754_hypot(x,y);
+ if(_LIB_VERSION == _IEEE_) return z;
+ if((!finite(z))&&finite(x)&&finite(y))
+ return __kernel_standard(x,y,4); /* hypot overflow */
+ else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_j0.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_j0.c,v 1.6 1995/05/10 20:49:11 jtc Exp $";
+#endif
+
+/*
+ * wrapper j0(double x), y0(double x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double j0(double x) /* wrapper j0 */
+#else
+ double j0(x) /* wrapper j0 */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_j0(x);
+#else
+ double z = __ieee754_j0(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>X_TLOSS) {
+ return __kernel_standard(x,x,34); /* j0(|x|>X_TLOSS) */
+ } else
+ return z;
+#endif
+}
+
+#ifdef __STDC__
+ double y0(double x) /* wrapper y0 */
+#else
+ double y0(x) /* wrapper y0 */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_y0(x);
+#else
+ double z;
+ z = __ieee754_y0(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
+ if(x <= 0.0){
+ if(x==0.0)
+ /* d= -one/(x-x); */
+ return __kernel_standard(x,x,8);
+ else
+ /* d = zero/(x-x); */
+ return __kernel_standard(x,x,9);
+ }
+ if(x>X_TLOSS) {
+ return __kernel_standard(x,x,35); /* y0(x>X_TLOSS) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_j1.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_j1.c,v 1.6 1995/05/10 20:49:15 jtc Exp $";
+#endif
+
+/*
+ * wrapper of j1,y1
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double j1(double x) /* wrapper j1 */
+#else
+ double j1(x) /* wrapper j1 */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_j1(x);
+#else
+ double z;
+ z = __ieee754_j1(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
+ if(fabs(x)>X_TLOSS) {
+ return __kernel_standard(x,x,36); /* j1(|x|>X_TLOSS) */
+ } else
+ return z;
+#endif
+}
+
+#ifdef __STDC__
+ double y1(double x) /* wrapper y1 */
+#else
+ double y1(x) /* wrapper y1 */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_y1(x);
+#else
+ double z;
+ z = __ieee754_y1(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
+ if(x <= 0.0){
+ if(x==0.0)
+ /* d= -one/(x-x); */
+ return __kernel_standard(x,x,10);
+ else
+ /* d = zero/(x-x); */
+ return __kernel_standard(x,x,11);
+ }
+ if(x>X_TLOSS) {
+ return __kernel_standard(x,x,37); /* y1(x>X_TLOSS) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_jn.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_jn.c,v 1.6 1995/05/10 20:49:19 jtc Exp $";
+#endif
+
+/*
+ * wrapper jn(int n, double x), yn(int n, double x)
+ * floating point Bessel's function of the 1st and 2nd kind
+ * of order n
+ *
+ * Special cases:
+ * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
+ * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
+ * Note 2. About jn(n,x), yn(n,x)
+ * For n=0, j0(x) is called,
+ * for n=1, j1(x) is called,
+ * for n<x, forward recursion us used starting
+ * from values of j0(x) and j1(x).
+ * for n>x, a continued fraction approximation to
+ * j(n,x)/j(n-1,x) is evaluated and then backward
+ * recursion is used starting from a supposed value
+ * for j(n,x). The resulting value of j(0,x) is
+ * compared with the actual value to correct the
+ * supposed value of j(n,x).
+ *
+ * yn(n,x) is similar in all respects, except
+ * that forward recursion is used for all
+ * values of n>1.
+ *
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double jn(int n, double x) /* wrapper jn */
+#else
+ double jn(n,x) /* wrapper jn */
+ double x; int n;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_jn(n,x);
+#else
+ double z;
+ z = __ieee754_jn(n,x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
+ if(fabs(x)>X_TLOSS) {
+ return __kernel_standard((double)n,x,38); /* jn(|x|>X_TLOSS,n) */
+ } else
+ return z;
+#endif
+}
+
+#ifdef __STDC__
+ double yn(int n, double x) /* wrapper yn */
+#else
+ double yn(n,x) /* wrapper yn */
+ double x; int n;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_yn(n,x);
+#else
+ double z;
+ z = __ieee754_yn(n,x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
+ if(x <= 0.0){
+ if(x==0.0)
+ /* d= -one/(x-x); */
+ return __kernel_standard((double)n,x,12);
+ else
+ /* d = zero/(x-x); */
+ return __kernel_standard((double)n,x,13);
+ }
+ if(x>X_TLOSS) {
+ return __kernel_standard((double)n,x,39); /* yn(x>X_TLOSS,n) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_lgamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_lgamma.c,v 1.6 1995/05/10 20:49:24 jtc Exp $";
+#endif
+
+/* double lgamma(double x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_lgamma_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+ double lgamma(double x)
+#else
+ double lgamma(x)
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_lgamma_r(x,&signgam);
+#else
+ double y;
+ y = __ieee754_lgamma_r(x,&signgam);
+ if(_LIB_VERSION == _IEEE_) return y;
+ if(!finite(y)&&finite(x)) {
+ if(floor(x)==x&&x<=0.0)
+ return __kernel_standard(x,x,15); /* lgamma pole */
+ else
+ return __kernel_standard(x,x,14); /* lgamma overflow */
+ } else
+ return y;
+#endif
+}
--- /dev/null
+/* @(#)wr_lgamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_lgamma_r.c,v 1.6 1995/05/10 20:49:27 jtc Exp $";
+#endif
+
+/*
+ * wrapper double lgamma_r(double x, int *signgamp)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */
+#else
+ double lgamma_r(x,signgamp) /* wrapper lgamma_r */
+ double x; int *signgamp;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_lgamma_r(x,signgamp);
+#else
+ double y;
+ y = __ieee754_lgamma_r(x,signgamp);
+ if(_LIB_VERSION == _IEEE_) return y;
+ if(!finite(y)&&finite(x)) {
+ if(floor(x)==x&&x<=0.0)
+ return __kernel_standard(x,x,15); /* lgamma pole */
+ else
+ return __kernel_standard(x,x,14); /* lgamma overflow */
+ } else
+ return y;
+#endif
+}
--- /dev/null
+/* @(#)w_log.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_log.c,v 1.6 1995/05/10 20:49:33 jtc Exp $";
+#endif
+
+/*
+ * wrapper log(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double log(double x) /* wrapper log */
+#else
+ double log(x) /* wrapper log */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_log(x);
+#else
+ double z;
+ z = __ieee754_log(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z;
+ if(x==0.0)
+ return __kernel_standard(x,x,16); /* log(0) */
+ else
+ return __kernel_standard(x,x,17); /* log(x<0) */
+#endif
+}
--- /dev/null
+/* @(#)w_log10.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_log10.c,v 1.6 1995/05/10 20:49:35 jtc Exp $";
+#endif
+
+/*
+ * wrapper log10(X)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double log10(double x) /* wrapper log10 */
+#else
+ double log10(x) /* wrapper log10 */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_log10(x);
+#else
+ double z;
+ z = __ieee754_log10(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(x<=0.0) {
+ if(x==0.0)
+ return __kernel_standard(x,x,18); /* log10(0) */
+ else
+ return __kernel_standard(x,x,19); /* log10(x<0) */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+
+
+/* @(#)w_pow.c 5.2 93/10/01 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/*
+ * wrapper pow(x,y) return x**y
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+#ifdef __STDC__
+ double pow(double x, double y) /* wrapper pow */
+#else
+ double pow(x,y) /* wrapper pow */
+ double x,y;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_pow(x,y);
+#else
+ double z;
+ z=__ieee754_pow(x,y);
+ if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
+ if(isnan(x)) {
+ if(y==0.0)
+ return __kernel_standard(x,y,42); /* pow(NaN,0.0) */
+ else
+ return z;
+ }
+ if(x==0.0){
+ if(y==0.0)
+ return __kernel_standard(x,y,20); /* pow(0.0,0.0) */
+ if(finite(y)&&y<0.0)
+ return __kernel_standard(x,y,23); /* pow(0.0,negative) */
+ return z;
+ }
+ if(!finite(z)) {
+ if(finite(x)&&finite(y)) {
+ if(isnan(z))
+ return __kernel_standard(x,y,24); /* pow neg**non-int */
+ else
+ return __kernel_standard(x,y,21); /* pow overflow */
+ }
+ }
+ if(z==0.0&&finite(x)&&finite(y))
+ return __kernel_standard(x,y,22); /* pow underflow */
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_remainder.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_remainder.c,v 1.6 1995/05/10 20:49:44 jtc Exp $";
+#endif
+
+/*
+ * wrapper remainder(x,p)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double remainder(double x, double y) /* wrapper remainder */
+#else
+ double remainder(x,y) /* wrapper remainder */
+ double x,y;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_remainder(x,y);
+#else
+ double z;
+ z = __ieee754_remainder(x,y);
+ if(_LIB_VERSION == _IEEE_ || isnan(y)) return z;
+ if(y==0.0)
+ return __kernel_standard(x,y,28); /* remainder(x,0) */
+ else
+ return z;
+#endif
+}
--- /dev/null
+#if !defined(__ppc__)
+/* @(#)w_scalb.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_scalb.c,v 1.6 1995/05/10 20:49:48 jtc Exp $";
+#endif
+
+/*
+ * wrapper scalb(double x, double fn) is provide for
+ * passing various standard test suite. One
+ * should use scalbn() instead.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#include <errno.h>
+
+#ifdef __STDC__
+#ifdef _SCALB_INT
+ double scalb(double x, int fn) /* wrapper scalb */
+#else
+ double scalb(double x, double fn) /* wrapper scalb */
+#endif
+#else
+ double scalb(x,fn) /* wrapper scalb */
+#ifdef _SCALB_INT
+ double x; int fn;
+#else
+ double x,fn;
+#endif
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_scalb(x,fn);
+#else
+ double z;
+ z = __ieee754_scalb(x,fn);
+ if(_LIB_VERSION == _IEEE_) return z;
+ if(!(finite(z)||isnan(z))&&finite(x)) {
+ return __kernel_standard(x,(double)fn,32); /* scalb overflow */
+ }
+ if(z==0.0&&z!=x) {
+ return __kernel_standard(x,(double)fn,33); /* scalb underflow */
+ }
+#ifndef _SCALB_INT
+ if(!finite(fn)) errno = ERANGE;
+#endif
+ return z;
+#endif
+}
+#endif /* !__ppc__ */
--- /dev/null
+/* @(#)w_sinh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_sinh.c,v 1.6 1995/05/10 20:49:51 jtc Exp $";
+#endif
+
+/*
+ * wrapper sinh(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double sinh(double x) /* wrapper sinh */
+#else
+ double sinh(x) /* wrapper sinh */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_sinh(x);
+#else
+ double z;
+ z = __ieee754_sinh(x);
+ if(_LIB_VERSION == _IEEE_) return z;
+ if(!finite(z)&&finite(x)) {
+ return __kernel_standard(x,x,25); /* sinh overflow */
+ } else
+ return z;
+#endif
+}
--- /dev/null
+/* @(#)w_sqrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: w_sqrt.c,v 1.6 1995/05/10 20:49:55 jtc Exp $";
+#endif
+
+/*
+ * wrapper sqrt(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+ double sqrt(double x) /* wrapper sqrt */
+#else
+ double sqrt(x) /* wrapper sqrt */
+ double x;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_sqrt(x);
+#else
+ double z;
+ z = __ieee754_sqrt(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(x<0.0) {
+ return __kernel_standard(x,x,26); /* sqrt(negative) */
+ } else
+ return z;
+#endif
+}
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