1*2fe8fb19SBen Gras
2*2fe8fb19SBen Gras /* @(#)e_log.c 1.3 95/01/18 */
3*2fe8fb19SBen Gras /*
4*2fe8fb19SBen Gras * ====================================================
5*2fe8fb19SBen Gras * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6*2fe8fb19SBen Gras *
7*2fe8fb19SBen Gras * Developed at SunSoft, a Sun Microsystems, Inc. business.
8*2fe8fb19SBen Gras * Permission to use, copy, modify, and distribute this
9*2fe8fb19SBen Gras * software is freely granted, provided that this notice
10*2fe8fb19SBen Gras * is preserved.
11*2fe8fb19SBen Gras * ====================================================
12*2fe8fb19SBen Gras */
13*2fe8fb19SBen Gras
14*2fe8fb19SBen Gras #include <sys/cdefs.h>
15*2fe8fb19SBen Gras #if defined(LIBM_SCCS) && !defined(lint)
16*2fe8fb19SBen Gras __RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
17*2fe8fb19SBen Gras #endif
18*2fe8fb19SBen Gras
19*2fe8fb19SBen Gras #include "math.h"
20*2fe8fb19SBen Gras #include "math_private.h"
21*2fe8fb19SBen Gras
22*2fe8fb19SBen Gras static const double
23*2fe8fb19SBen Gras ln2 = 0.6931471805599452862268,
24*2fe8fb19SBen Gras two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
25*2fe8fb19SBen Gras Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
26*2fe8fb19SBen Gras Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
27*2fe8fb19SBen Gras Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
28*2fe8fb19SBen Gras Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
29*2fe8fb19SBen Gras Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
30*2fe8fb19SBen Gras Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
31*2fe8fb19SBen Gras Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
32*2fe8fb19SBen Gras
33*2fe8fb19SBen Gras static const double zero = 0.0;
34*2fe8fb19SBen Gras
35*2fe8fb19SBen Gras double
__ieee754_log2(double x)36*2fe8fb19SBen Gras __ieee754_log2(double x)
37*2fe8fb19SBen Gras {
38*2fe8fb19SBen Gras double hfsq,f,s,z,R,w,t1,t2,dk;
39*2fe8fb19SBen Gras int32_t k,hx,i,j;
40*2fe8fb19SBen Gras u_int32_t lx;
41*2fe8fb19SBen Gras
42*2fe8fb19SBen Gras EXTRACT_WORDS(hx,lx,x);
43*2fe8fb19SBen Gras
44*2fe8fb19SBen Gras k=0;
45*2fe8fb19SBen Gras if (hx < 0x00100000) { /* x < 2**-1022 */
46*2fe8fb19SBen Gras if (((hx&0x7fffffff)|lx)==0)
47*2fe8fb19SBen Gras return -two54/zero; /* log(+-0)=-inf */
48*2fe8fb19SBen Gras if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
49*2fe8fb19SBen Gras k -= 54; x *= two54; /* subnormal number, scale up x */
50*2fe8fb19SBen Gras GET_HIGH_WORD(hx,x);
51*2fe8fb19SBen Gras }
52*2fe8fb19SBen Gras if (hx >= 0x7ff00000) return x+x;
53*2fe8fb19SBen Gras k += (hx>>20)-1023;
54*2fe8fb19SBen Gras hx &= 0x000fffff;
55*2fe8fb19SBen Gras i = (hx+0x95f64)&0x100000;
56*2fe8fb19SBen Gras SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
57*2fe8fb19SBen Gras k += (i>>20);
58*2fe8fb19SBen Gras f = x-1.0;
59*2fe8fb19SBen Gras dk = (double)k;
60*2fe8fb19SBen Gras if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
61*2fe8fb19SBen Gras if (f==zero)
62*2fe8fb19SBen Gras return (dk);
63*2fe8fb19SBen Gras R = f*f*(0.5-0.33333333333333333*f);
64*2fe8fb19SBen Gras return (dk-(R-f)/ln2);
65*2fe8fb19SBen Gras }
66*2fe8fb19SBen Gras s = f/(2.0+f);
67*2fe8fb19SBen Gras z = s*s;
68*2fe8fb19SBen Gras i = hx-0x6147a;
69*2fe8fb19SBen Gras w = z*z;
70*2fe8fb19SBen Gras j = 0x6b851-hx;
71*2fe8fb19SBen Gras t1= w*(Lg2+w*(Lg4+w*Lg6));
72*2fe8fb19SBen Gras t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
73*2fe8fb19SBen Gras i |= j;
74*2fe8fb19SBen Gras R = t2+t1;
75*2fe8fb19SBen Gras if(i>0) {
76*2fe8fb19SBen Gras hfsq=0.5*f*f;
77*2fe8fb19SBen Gras return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
78*2fe8fb19SBen Gras } else
79*2fe8fb19SBen Gras return (dk-((s*(f-R))-f)/ln2);
80*2fe8fb19SBen Gras }
81