1 /* @(#)e_log.c 1.3 95/01/18 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
16 #include "math_private.h"
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 */
29 static const double zero = 0.0;
34 double hfsq,f,s,z,R,w,t1,t2,dk;
38 EXTRACT_WORDS(hx,lx,x);
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 */
48 if (hx >= 0x7ff00000) return x+x;
51 i = (hx+0x95f64)&0x100000;
52 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
56 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
59 R = f*f*(0.5-0.33333333333333333*f);
60 return (dk-(R-f)/ln2);
67 t1= w*(Lg2+w*(Lg4+w*Lg6));
68 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
73 return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
75 return (dk-((s*(f-R))-f)/ln2);
78 #if LDBL_MANT_DIG == DBL_MANT_DIG
79 __strong_alias(log2l, log2);
80 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */