1
2/* @(#)e_log.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14#include <sys/cdefs.h>
15#if defined(LIBM_SCCS) && !defined(lint)
16__RCSID("$NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
17#endif
18
19#include "math.h"
20#include "math_private.h"
21
22static const double
23ln2 = 0.6931471805599452862268,
24two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
25Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
26Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
27Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
28Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
29Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
30Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
31Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
32
33static const double zero   =  0.0;
34
35double
36__ieee754_log2(double x)
37{
38	double hfsq,f,s,z,R,w,t1,t2,dk;
39	int32_t k,hx,i,j;
40	u_int32_t lx;
41
42	EXTRACT_WORDS(hx,lx,x);
43
44	k=0;
45	if (hx < 0x00100000) {			/* x < 2**-1022  */
46	    if (((hx&0x7fffffff)|lx)==0)
47		return -two54/zero;		/* log(+-0)=-inf */
48	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
49	    k -= 54; x *= two54; /* subnormal number, scale up x */
50	    GET_HIGH_WORD(hx,x);
51	}
52	if (hx >= 0x7ff00000) return x+x;
53	k += (hx>>20)-1023;
54	hx &= 0x000fffff;
55	i = (hx+0x95f64)&0x100000;
56	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
57	k += (i>>20);
58	f = x-1.0;
59	dk = (double)k;
60	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
61	    if (f==zero)
62		    return (dk);
63	    R = f*f*(0.5-0.33333333333333333*f);
64	    return (dk-(R-f)/ln2);
65	}
66 	s = f/(2.0+f);
67	z = s*s;
68	i = hx-0x6147a;
69	w = z*z;
70	j = 0x6b851-hx;
71	t1= w*(Lg2+w*(Lg4+w*Lg6));
72	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
73	i |= j;
74	R = t2+t1;
75	if(i>0) {
76	    hfsq=0.5*f*f;
77	    return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
78	} else
79		return (dk-((s*(f-R))-f)/ln2);
80}
81