s_log1pf.c revision 177711
1230557Sjimharris/* s_log1pf.c -- float version of s_log1p.c. 2230557Sjimharris * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3230557Sjimharris */ 4230557Sjimharris 5230557Sjimharris/* 6230557Sjimharris * ==================================================== 7230557Sjimharris * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8230557Sjimharris * 9230557Sjimharris * Developed at SunPro, a Sun Microsystems, Inc. business. 10230557Sjimharris * Permission to use, copy, modify, and distribute this 11230557Sjimharris * software is freely granted, provided that this notice 12230557Sjimharris * is preserved. 13230557Sjimharris * ==================================================== 14230557Sjimharris */ 15230557Sjimharris 16230557Sjimharris#include <sys/cdefs.h> 17230557Sjimharris__FBSDID("$FreeBSD: head/lib/msun/src/s_log1pf.c 177711 2008-03-29 16:37:59Z das $"); 18230557Sjimharris 19230557Sjimharris#include <float.h> 20230557Sjimharris 21230557Sjimharris#include "math.h" 22230557Sjimharris#include "math_private.h" 23230557Sjimharris 24230557Sjimharrisstatic const float 25230557Sjimharrisln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 26230557Sjimharrisln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 27230557Sjimharristwo25 = 3.355443200e+07, /* 0x4c000000 */ 28230557SjimharrisLp1 = 6.6666668653e-01, /* 3F2AAAAB */ 29230557SjimharrisLp2 = 4.0000000596e-01, /* 3ECCCCCD */ 30230557SjimharrisLp3 = 2.8571429849e-01, /* 3E924925 */ 31230557SjimharrisLp4 = 2.2222198546e-01, /* 3E638E29 */ 32230557SjimharrisLp5 = 1.8183572590e-01, /* 3E3A3325 */ 33230557SjimharrisLp6 = 1.5313838422e-01, /* 3E1CD04F */ 34230557SjimharrisLp7 = 1.4798198640e-01; /* 3E178897 */ 35230557Sjimharris 36230557Sjimharrisstatic const float zero = 0.0; 37230557Sjimharris 38230557Sjimharrisfloat 39230557Sjimharrislog1pf(float x) 40230557Sjimharris{ 41230557Sjimharris float hfsq,f,c,s,z,R,u; 42230557Sjimharris int32_t k,hx,hu,ax; 43230557Sjimharris 44230557Sjimharris GET_FLOAT_WORD(hx,x); 45230557Sjimharris ax = hx&0x7fffffff; 46230557Sjimharris 47230557Sjimharris k = 1; 48230557Sjimharris if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ 49230557Sjimharris if(ax>=0x3f800000) { /* x <= -1.0 */ 50230557Sjimharris if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ 51230557Sjimharris else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 52230557Sjimharris } 53230557Sjimharris if(ax<0x38000000) { /* |x| < 2**-15 */ 54230557Sjimharris if(two25+x>zero /* raise inexact */ 55230557Sjimharris &&ax<0x33800000) /* |x| < 2**-24 */ 56230557Sjimharris return x; 57230557Sjimharris else 58230557Sjimharris return x - x*x*(float)0.5; 59230557Sjimharris } 60230557Sjimharris if(hx>0||hx<=((int32_t)0xbe95f619)) { 61230557Sjimharris k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ 62230557Sjimharris } 63230557Sjimharris if (hx >= 0x7f800000) return x+x; 64230557Sjimharris if(k!=0) { 65230557Sjimharris if(hx<0x5a000000) { 66230557Sjimharris STRICT_ASSIGN(float,u,(float)1.0+x); 67230557Sjimharris GET_FLOAT_WORD(hu,u); 68230557Sjimharris k = (hu>>23)-127; 69230557Sjimharris /* correction term */ 70230557Sjimharris c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 71230557Sjimharris c /= u; 72230557Sjimharris } else { 73230557Sjimharris u = x; 74230557Sjimharris GET_FLOAT_WORD(hu,u); 75230557Sjimharris k = (hu>>23)-127; 76230557Sjimharris c = 0; 77230557Sjimharris } 78230557Sjimharris hu &= 0x007fffff; 79230557Sjimharris /* 80230557Sjimharris * The approximation to sqrt(2) used in thresholds is not 81230557Sjimharris * critical. However, the ones used above must give less 82230557Sjimharris * strict bounds than the one here so that the k==0 case is 83230557Sjimharris * never reached from here, since here we have committed to 84230557Sjimharris * using the correction term but don't use it if k==0. 85230557Sjimharris */ 86230557Sjimharris if(hu<0x3504f4) { /* u < sqrt(2) */ 87230557Sjimharris SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 88230557Sjimharris } else { 89230557Sjimharris k += 1; 90298955Spfg SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 91230557Sjimharris hu = (0x00800000-hu)>>2; 92230557Sjimharris } 93230557Sjimharris f = u-(float)1.0; 94230557Sjimharris } 95230557Sjimharris hfsq=(float)0.5*f*f; 96230557Sjimharris if(hu==0) { /* |f| < 2**-20 */ 97230557Sjimharris if(f==zero) { 98230557Sjimharris if(k==0) { 99230557Sjimharris return zero; 100230557Sjimharris } else { 101230557Sjimharris c += k*ln2_lo; 102230557Sjimharris return k*ln2_hi+c; 103230557Sjimharris } 104230557Sjimharris } 105230557Sjimharris R = hfsq*((float)1.0-(float)0.66666666666666666*f); 106230557Sjimharris if(k==0) return f-R; else 107230557Sjimharris return k*ln2_hi-((R-(k*ln2_lo+c))-f); 108230557Sjimharris } 109230557Sjimharris s = f/((float)2.0+f); 110230557Sjimharris z = s*s; 111230557Sjimharris R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 112230557Sjimharris if(k==0) return f-(hfsq-s*(hfsq+R)); else 113230557Sjimharris return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 114230557Sjimharris} 115230557Sjimharris