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_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
17 #endif
18
19 #include "math.h"
20 #include "math_private.h"
21
22 static const double
23 ln2 = 0.6931471805599452862268,
24 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
25 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
26 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
27 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
28 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
29 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
30 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
31 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
32
33 static const double zero = 0.0;
34
35 double
__ieee754_log2(double x)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