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 1.8 2002/05/26 22:01:57 wiz Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float 25 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 26 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 27 two25 = 3.355443200e+07, /* 0x4c000000 */ 28 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ 29 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ 30 Lp3 = 2.8571429849e-01, /* 3E924925 */ 31 Lp4 = 2.2222198546e-01, /* 3E638E29 */ 32 Lp5 = 1.8183572590e-01, /* 3E3A3325 */ 33 Lp6 = 1.5313838422e-01, /* 3E1CD04F */ 34 Lp7 = 1.4798198640e-01; /* 3E178897 */ 35 36 static const float zero = 0.0; 37 38 float 39 log1pf(float x) 40 { 41 float hfsq,f,c,s,z,R,u; 42 int32_t k,hx,hu,ax; 43 44 f = c = 0; 45 hu = 0; 46 GET_FLOAT_WORD(hx,x); 47 ax = hx&0x7fffffff; 48 49 k = 1; 50 if (hx < 0x3ed413d7) { /* x < 0.41422 */ 51 if(ax>=0x3f800000) { /* x <= -1.0 */ 52 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ 53 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 54 } 55 if(ax<0x31000000) { /* |x| < 2**-29 */ 56 if(two25+x>zero /* raise inexact */ 57 &&ax<0x24800000) /* |x| < 2**-54 */ 58 return x; 59 else 60 return x - x*x*(float)0.5; 61 } 62 if(hx>0||hx<=((int32_t)0xbe95f61f)) { 63 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ 64 } 65 if (hx >= 0x7f800000) return x+x; 66 if(k!=0) { 67 if(hx<0x5a000000) { 68 u = (float)1.0+x; 69 GET_FLOAT_WORD(hu,u); 70 k = (hu>>23)-127; 71 /* correction term */ 72 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 73 c /= u; 74 } else { 75 u = x; 76 GET_FLOAT_WORD(hu,u); 77 k = (hu>>23)-127; 78 c = 0; 79 } 80 hu &= 0x007fffff; 81 if(hu<0x3504f7) { 82 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 83 } else { 84 k += 1; 85 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 86 hu = (0x00800000-hu)>>2; 87 } 88 f = u-(float)1.0; 89 } 90 hfsq=(float)0.5*f*f; 91 if(hu==0) { /* |f| < 2**-20 */ 92 if(f==zero) { if(k==0) return zero; 93 else {c += k*ln2_lo; return k*ln2_hi+c;} 94 } 95 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 96 if(k==0) return f-R; else 97 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 98 } 99 s = f/((float)2.0+f); 100 z = s*s; 101 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 102 if(k==0) return f-(hfsq-s*(hfsq+R)); else 103 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 104 } 105