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 #ifndef lint 17 static char rcsid[] = "$Id$"; 18 #endif 19 20 #include "math.h" 21 #include "math_private.h" 22 23 #ifdef __STDC__ 24 static const float 25 #else 26 static float 27 #endif 28 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 29 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 30 two25 = 3.355443200e+07, /* 0x4c000000 */ 31 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ 32 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ 33 Lp3 = 2.8571429849e-01, /* 3E924925 */ 34 Lp4 = 2.2222198546e-01, /* 3E638E29 */ 35 Lp5 = 1.8183572590e-01, /* 3E3A3325 */ 36 Lp6 = 1.5313838422e-01, /* 3E1CD04F */ 37 Lp7 = 1.4798198640e-01; /* 3E178897 */ 38 39 #ifdef __STDC__ 40 static const float zero = 0.0; 41 #else 42 static float zero = 0.0; 43 #endif 44 45 #ifdef __STDC__ 46 float log1pf(float x) 47 #else 48 float log1pf(x) 49 float x; 50 #endif 51 { 52 float hfsq,f,c,s,z,R,u; 53 int32_t k,hx,hu,ax; 54 55 GET_FLOAT_WORD(hx,x); 56 ax = hx&0x7fffffff; 57 58 k = 1; 59 if (hx < 0x3ed413d7) { /* x < 0.41422 */ 60 if(ax>=0x3f800000) { /* x <= -1.0 */ 61 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ 62 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 63 } 64 if(ax<0x31000000) { /* |x| < 2**-29 */ 65 if(two25+x>zero /* raise inexact */ 66 &&ax<0x24800000) /* |x| < 2**-54 */ 67 return x; 68 else 69 return x - x*x*(float)0.5; 70 } 71 if(hx>0||hx<=((int32_t)0xbe95f61f)) { 72 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ 73 } 74 if (hx >= 0x7f800000) return x+x; 75 if(k!=0) { 76 if(hx<0x5a000000) { 77 u = (float)1.0+x; 78 GET_FLOAT_WORD(hu,u); 79 k = (hu>>23)-127; 80 /* correction term */ 81 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 82 c /= u; 83 } else { 84 u = x; 85 GET_FLOAT_WORD(hu,u); 86 k = (hu>>23)-127; 87 c = 0; 88 } 89 hu &= 0x007fffff; 90 if(hu<0x3504f7) { 91 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 92 } else { 93 k += 1; 94 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 95 hu = (0x00800000-hu)>>2; 96 } 97 f = u-(float)1.0; 98 } 99 hfsq=(float)0.5*f*f; 100 if(hu==0) { /* |f| < 2**-20 */ 101 if(f==zero) if(k==0) return zero; 102 else {c += k*ln2_lo; return k*ln2_hi+c;} 103 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 104 if(k==0) return f-R; else 105 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 106 } 107 s = f/((float)2.0+f); 108 z = s*s; 109 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 110 if(k==0) return f-(hfsq-s*(hfsq+R)); else 111 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 112 } 113