12116Sjkh/* e_logf.c -- float version of e_log.c. 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 32116Sjkh */ 42116Sjkh 52116Sjkh/* 62116Sjkh * ==================================================== 72116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 82116Sjkh * 92116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 102116Sjkh * Permission to use, copy, modify, and distribute this 118870Srgrimes * software is freely granted, provided that this notice 122116Sjkh * is preserved. 132116Sjkh * ==================================================== 142116Sjkh */ 152116Sjkh 16176451Sdas#include <sys/cdefs.h> 17176451Sdas__FBSDID("$FreeBSD$"); 182116Sjkh 192116Sjkh#include "math.h" 202116Sjkh#include "math_private.h" 212116Sjkh 222116Sjkhstatic const float 232116Sjkhln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 242116Sjkhln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 252116Sjkhtwo25 = 3.355443200e+07, /* 0x4c000000 */ 26152335Sbde/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ 27152335SbdeLg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ 28152335SbdeLg2 = 0xccce13.0p-25, /* 0.40000972152 */ 29152335SbdeLg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ 30152335SbdeLg4 = 0xf89e26.0p-26; /* 0.24279078841 */ 312116Sjkh 322116Sjkhstatic const float zero = 0.0; 332116Sjkh 3497413Salfredfloat 3597413Salfred__ieee754_logf(float x) 362116Sjkh{ 372116Sjkh float hfsq,f,s,z,R,w,t1,t2,dk; 382116Sjkh int32_t k,ix,i,j; 392116Sjkh 402116Sjkh GET_FLOAT_WORD(ix,x); 412116Sjkh 422116Sjkh k=0; 432116Sjkh if (ix < 0x00800000) { /* x < 2**-126 */ 448870Srgrimes if ((ix&0x7fffffff)==0) 452116Sjkh return -two25/zero; /* log(+-0)=-inf */ 462116Sjkh if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ 472116Sjkh k -= 25; x *= two25; /* subnormal number, scale up x */ 482116Sjkh GET_FLOAT_WORD(ix,x); 498870Srgrimes } 502116Sjkh if (ix >= 0x7f800000) return x+x; 512116Sjkh k += (ix>>23)-127; 522116Sjkh ix &= 0x007fffff; 532116Sjkh i = (ix+(0x95f64<<3))&0x800000; 542116Sjkh SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ 552116Sjkh k += (i>>23); 562116Sjkh f = x-(float)1.0; 57160151Sbde if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */ 58177711Sdas if(f==zero) { 59177711Sdas if(k==0) { 60177711Sdas return zero; 61177711Sdas } else { 62177711Sdas dk=(float)k; 63177711Sdas return dk*ln2_hi+dk*ln2_lo; 64177711Sdas } 65177711Sdas } 662116Sjkh R = f*f*((float)0.5-(float)0.33333333333333333*f); 672116Sjkh if(k==0) return f-R; else {dk=(float)k; 682116Sjkh return dk*ln2_hi-((R-dk*ln2_lo)-f);} 692116Sjkh } 708870Srgrimes s = f/((float)2.0+f); 712116Sjkh dk = (float)k; 722116Sjkh z = s*s; 732116Sjkh i = ix-(0x6147a<<3); 742116Sjkh w = z*z; 752116Sjkh j = (0x6b851<<3)-ix; 76152335Sbde t1= w*(Lg2+w*Lg4); 77152335Sbde t2= z*(Lg1+w*Lg3); 782116Sjkh i |= j; 792116Sjkh R = t2+t1; 802116Sjkh if(i>0) { 812116Sjkh hfsq=(float)0.5*f*f; 822116Sjkh if(k==0) return f-(hfsq-s*(hfsq+R)); else 832116Sjkh return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); 842116Sjkh } else { 852116Sjkh if(k==0) return f-s*(f-R); else 862116Sjkh return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); 872116Sjkh } 882116Sjkh} 89