1/* s_log1pf.c -- float version of s_log1p.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5/* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16#include <sys/cdefs.h> 17#if defined(LIBM_SCCS) && !defined(lint) 18__RCSID("$NetBSD: s_log1pf.c,v 1.9 2024/07/16 14:52:50 riastradh Exp $"); 19#endif 20 21#include "namespace.h" 22 23#include "math.h" 24#include "math_private.h" 25 26static const float 27ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 28ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 29two25 = 3.355443200e+07, /* 0x4c000000 */ 30Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ 31Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ 32Lp3 = 2.8571429849e-01, /* 3E924925 */ 33Lp4 = 2.2222198546e-01, /* 3E638E29 */ 34Lp5 = 1.8183572590e-01, /* 3E3A3325 */ 35Lp6 = 1.5313838422e-01, /* 3E1CD04F */ 36Lp7 = 1.4798198640e-01; /* 3E178897 */ 37 38static const float zero = 0.0; 39 40__weak_alias(log1pf, _log1pf) 41float 42log1pf(float x) 43{ 44 float hfsq,f,c,s,z,R,u; 45 int32_t k,hx,hu,ax; 46 47 f = c = 0; 48 hu = 0; 49 GET_FLOAT_WORD(hx,x); 50 ax = hx&0x7fffffff; 51 52 k = 1; 53 if (hx < 0x3ed413d7) { /* x < 0.41422 */ 54 if(ax>=0x3f800000) { /* x <= -1.0 */ 55 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ 56 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 57 } 58 if(ax<0x31000000) { /* |x| < 2**-29 */ 59 if(two25+x>zero /* raise inexact */ 60 &&ax<0x24800000) /* |x| < 2**-54 */ 61 return x; 62 else 63 return x - x*x*(float)0.5; 64 } 65 if(hx>0||hx<=((int32_t)0xbe95f61f)) { 66 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ 67 } 68 if (hx >= 0x7f800000) return x+x; 69 if(k!=0) { 70 if(hx<0x5a000000) { 71 u = (float)1.0+x; 72 GET_FLOAT_WORD(hu,u); 73 k = (hu>>23)-127; 74 /* correction term */ 75 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 76 c /= u; 77 } else { 78 u = x; 79 GET_FLOAT_WORD(hu,u); 80 k = (hu>>23)-127; 81 c = 0; 82 } 83 hu &= 0x007fffff; 84 if(hu<0x3504f7) { 85 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 86 } else { 87 k += 1; 88 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 89 hu = (0x00800000-hu)>>2; 90 } 91 f = u-(float)1.0; 92 } 93 hfsq=(float)0.5*f*f; 94 if(hu==0) { /* |f| < 2**-20 */ 95 if(f==zero) { if(k==0) return zero; 96 else {c += k*ln2_lo; return k*ln2_hi+c;} 97 } 98 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 99 if(k==0) return f-R; else 100 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 101 } 102 s = f/((float)2.0+f); 103 z = s*s; 104 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 105 if(k==0) return f-(hfsq-s*(hfsq+R)); else 106 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 107} 108