-/* @(#)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
+ * 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),
+ * 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
* 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 Lp1 to Lp7 are listed in the program)
* and
* | 2 14 | -58.45
- * | Lp1*s +...+Lp7*s - R(z) | <= 2
+ * | 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).
+ *
+ * 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:
+ * 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(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.
*
* 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.
*
* 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));
#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 */
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 log1p(double x)
{
- double hfsq,f,c,s,z,R,u;
- int32_t k,hx,hu,ax;
+ double hfsq,f=0,c=0,s,z,R,u;
+ int32_t k,hx,hu=0,ax;
GET_HIGH_WORD(hx,x);
ax = hx&0x7fffffff;
}
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;
+ 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 */
if(hu<0x6a09e) {
SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */
} else {
- k += 1;
+ k += 1;
SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */
hu = (0x00100000-hu)>>2;
}
}
hfsq=0.5*f*f;
if(hu==0) { /* |f| < 2**-20 */
- if(f==zero) if(k==0) return zero;
+ 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);
+ 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);
}
+libm_hidden_def(log1p)
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