1 /* @(#)e_log.c 1.3 95/01/18 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #include <float.h>
14 #include <math.h>
15
16 #include "math_private.h"
17
18 static const double
19 ln2 = 0.6931471805599452862268,
20 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
21 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
22 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
23 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
24 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
25 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
26 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
27 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
28
29 static const double zero = 0.0;
30
31 double
log2(double x)32 log2(double x)
33 {
34 double hfsq,f,s,z,R,w,t1,t2,dk;
35 int32_t k,hx,i,j;
36 u_int32_t lx;
37
38 EXTRACT_WORDS(hx,lx,x);
39
40 k=0;
41 if (hx < 0x00100000) { /* x < 2**-1022 */
42 if (((hx&0x7fffffff)|lx)==0)
43 return -two54/zero; /* log(+-0)=-inf */
44 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
45 k -= 54; x *= two54; /* subnormal number, scale up x */
46 GET_HIGH_WORD(hx,x);
47 }
48 if (hx >= 0x7ff00000) return x+x;
49 k += (hx>>20)-1023;
50 hx &= 0x000fffff;
51 i = (hx+0x95f64)&0x100000;
52 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
53 k += (i>>20);
54 f = x-1.0;
55 dk = (double)k;
56 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
57 if (f==zero)
58 return (dk);
59 R = f*f*(0.5-0.33333333333333333*f);
60 return (dk-(R-f)/ln2);
61 }
62 s = f/(2.0+f);
63 z = s*s;
64 i = hx-0x6147a;
65 w = z*z;
66 j = 0x6b851-hx;
67 t1= w*(Lg2+w*(Lg4+w*Lg6));
68 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
69 i |= j;
70 R = t2+t1;
71 if(i>0) {
72 hfsq=0.5*f*f;
73 return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
74 } else
75 return (dk-((s*(f-R))-f)/ln2);
76 }
77 DEF_STD(log2);
78 LDBL_MAYBE_UNUSED_CLONE(log2);
79