-/* @(#)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
+ * 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),
+ * 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
+ * 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
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
- * | Lg1*s +...+Lg7*s - R(z) | <= 2
+ * | 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).
+ *
+ * 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:
+ * 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(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.
*
* 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
+ * 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 */
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 __ieee754_log(double x)
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int32_t k,hx,i,j;
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
- if (((hx&0x7fffffff)|lx)==0)
+ 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;
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
- s = f/(2.0+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)));
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
+
+/*
+ * wrapper log(x)
+ */
+#ifndef _IEEE_LIBM
+double log(double x)
+{
+ double 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) */
+ return __kernel_standard(x, x, 17); /* log(x<0) */
+}
+#else
+strong_alias(__ieee754_log, log)
+#endif
+libm_hidden_def(log)
OSDN Git Service
