81 lines
2.1 KiB
C
81 lines
2.1 KiB
C
|
|
||
|
|
/* @(#)e_log.c 1.3 95/01/18 */
|
||
|
|
/*
|
||
|
|
* ====================================================
|
||
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||
|
|
*
|
||
|
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||
|
|
* Permission to use, copy, modify, and distribute this
|
||
|
|
* software is freely granted, provided that this notice
|
||
|
|
* is preserved.
|
||
|
|
* ====================================================
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include <sys/cdefs.h>
|
||
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
||
|
|
__RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#include "math.h"
|
||
|
|
#include "math_private.h"
|
||
|
|
|
||
|
|
static const double
|
||
|
|
ln2 = 0.6931471805599452862268,
|
||
|
|
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 */
|
||
|
|
|
||
|
|
static const double zero = 0.0;
|
||
|
|
|
||
|
|
double
|
||
|
|
__ieee754_log2(double x)
|
||
|
|
{
|
||
|
|
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;
|
||
|
|
dk = (double)k;
|
||
|
|
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
|
||
|
|
if (f==zero)
|
||
|
|
return (dk);
|
||
|
|
R = f*f*(0.5-0.33333333333333333*f);
|
||
|
|
return (dk-(R-f)/ln2);
|
||
|
|
}
|
||
|
|
s = f/(2.0+f);
|
||
|
|
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;
|
||
|
|
return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
|
||
|
|
} else
|
||
|
|
return (dk-((s*(f-R))-f)/ln2);
|
||
|
|
}
|