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