1/* s_erff.c -- float version of s_erf.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_erff.c,v 1.6 1999/07/02 15:37:42 simonb Exp $"); 19#endif 20 21#include "math.h" 22#include "math_private.h" 23 24static const float 25tiny = 1e-30, 26half= 5.0000000000e-01, /* 0x3F000000 */ 27one = 1.0000000000e+00, /* 0x3F800000 */ 28two = 2.0000000000e+00, /* 0x40000000 */ 29 /* c = (subfloat)0.84506291151 */ 30erx = 8.4506291151e-01, /* 0x3f58560b */ 31/* 32 * Coefficients for approximation to erf on [0,0.84375] 33 */ 34efx = 1.2837916613e-01, /* 0x3e0375d4 */ 35efx8= 1.0270333290e+00, /* 0x3f8375d4 */ 36pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ 37pp1 = -3.2504209876e-01, /* 0xbea66beb */ 38pp2 = -2.8481749818e-02, /* 0xbce9528f */ 39pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ 40pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ 41qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ 42qq2 = 6.5022252500e-02, /* 0x3d852a63 */ 43qq3 = 5.0813062117e-03, /* 0x3ba68116 */ 44qq4 = 1.3249473704e-04, /* 0x390aee49 */ 45qq5 = -3.9602282413e-06, /* 0xb684e21a */ 46/* 47 * Coefficients for approximation to erf in [0.84375,1.25] 48 */ 49pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ 50pa1 = 4.1485610604e-01, /* 0x3ed46805 */ 51pa2 = -3.7220788002e-01, /* 0xbebe9208 */ 52pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ 53pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ 54pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ 55pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ 56qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ 57qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ 58qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ 59qa4 = 1.2617121637e-01, /* 0x3e013307 */ 60qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ 61qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ 62/* 63 * Coefficients for approximation to erfc in [1.25,1/0.35] 64 */ 65ra0 = -9.8649440333e-03, /* 0xbc21a093 */ 66ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ 67ra2 = -1.0558626175e+01, /* 0xc128f022 */ 68ra3 = -6.2375331879e+01, /* 0xc2798057 */ 69ra4 = -1.6239666748e+02, /* 0xc322658c */ 70ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ 71ra6 = -8.1287437439e+01, /* 0xc2a2932b */ 72ra7 = -9.8143291473e+00, /* 0xc11d077e */ 73sa1 = 1.9651271820e+01, /* 0x419d35ce */ 74sa2 = 1.3765776062e+02, /* 0x4309a863 */ 75sa3 = 4.3456588745e+02, /* 0x43d9486f */ 76sa4 = 6.4538726807e+02, /* 0x442158c9 */ 77sa5 = 4.2900814819e+02, /* 0x43d6810b */ 78sa6 = 1.0863500214e+02, /* 0x42d9451f */ 79sa7 = 6.5702495575e+00, /* 0x40d23f7c */ 80sa8 = -6.0424413532e-02, /* 0xbd777f97 */ 81/* 82 * Coefficients for approximation to erfc in [1/.35,28] 83 */ 84rb0 = -9.8649431020e-03, /* 0xbc21a092 */ 85rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ 86rb2 = -1.7757955551e+01, /* 0xc18e104b */ 87rb3 = -1.6063638306e+02, /* 0xc320a2ea */ 88rb4 = -6.3756646729e+02, /* 0xc41f6441 */ 89rb5 = -1.0250950928e+03, /* 0xc480230b */ 90rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ 91sb1 = 3.0338060379e+01, /* 0x41f2b459 */ 92sb2 = 3.2579251099e+02, /* 0x43a2e571 */ 93sb3 = 1.5367296143e+03, /* 0x44c01759 */ 94sb4 = 3.1998581543e+03, /* 0x4547fdbb */ 95sb5 = 2.5530502930e+03, /* 0x451f90ce */ 96sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ 97sb7 = -2.2440952301e+01; /* 0xc1b38712 */ 98 99float 100erff(float x) 101{ 102 int32_t hx,ix,i; 103 float R,S,P,Q,s,y,z,r; 104 GET_FLOAT_WORD(hx,x); 105 ix = hx&0x7fffffff; 106 if(ix>=0x7f800000) { /* erf(nan)=nan */ 107 i = ((u_int32_t)hx>>31)<<1; 108 return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ 109 } 110 111 if(ix < 0x3f580000) { /* |x|<0.84375 */ 112 if(ix < 0x31800000) { /* |x|<2**-28 */ 113 if (ix < 0x04000000) 114 /*avoid underflow */ 115 return (float)0.125*((float)8.0*x+efx8*x); 116 return x + efx*x; 117 } 118 z = x*x; 119 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 120 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 121 y = r/s; 122 return x + x*y; 123 } 124 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 125 s = fabsf(x)-one; 126 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 127 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 128 if(hx>=0) return erx + P/Q; else return -erx - P/Q; 129 } 130 if (ix >= 0x40c00000) { /* inf>|x|>=6 */ 131 if(hx>=0) return one-tiny; else return tiny-one; 132 } 133 x = fabsf(x); 134 s = one/(x*x); 135 if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ 136 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 137 ra5+s*(ra6+s*ra7)))))); 138 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 139 sa5+s*(sa6+s*(sa7+s*sa8))))))); 140 } else { /* |x| >= 1/0.35 */ 141 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 142 rb5+s*rb6))))); 143 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 144 sb5+s*(sb6+s*sb7)))))); 145 } 146 GET_FLOAT_WORD(ix,x); 147 SET_FLOAT_WORD(z,ix&0xfffff000); 148 r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); 149 if(hx>=0) return one-r/x; else return r/x-one; 150} 151 152float 153erfcf(float x) 154{ 155 int32_t hx,ix; 156 float R,S,P,Q,s,y,z,r; 157 GET_FLOAT_WORD(hx,x); 158 ix = hx&0x7fffffff; 159 if(ix>=0x7f800000) { /* erfc(nan)=nan */ 160 /* erfc(+-inf)=0,2 */ 161 return (float)(((u_int32_t)hx>>31)<<1)+one/x; 162 } 163 164 if(ix < 0x3f580000) { /* |x|<0.84375 */ 165 if(ix < 0x23800000) /* |x|<2**-56 */ 166 return one-x; 167 z = x*x; 168 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 169 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 170 y = r/s; 171 if(hx < 0x3e800000) { /* x<1/4 */ 172 return one-(x+x*y); 173 } else { 174 r = x*y; 175 r += (x-half); 176 return half - r ; 177 } 178 } 179 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 180 s = fabsf(x)-one; 181 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 182 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 183 if(hx>=0) { 184 z = one-erx; return z - P/Q; 185 } else { 186 z = erx+P/Q; return one+z; 187 } 188 } 189 if (ix < 0x41e00000) { /* |x|<28 */ 190 x = fabsf(x); 191 s = one/(x*x); 192 if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ 193 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 194 ra5+s*(ra6+s*ra7)))))); 195 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 196 sa5+s*(sa6+s*(sa7+s*sa8))))))); 197 } else { /* |x| >= 1/.35 ~ 2.857143 */ 198 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ 199 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 200 rb5+s*rb6))))); 201 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 202 sb5+s*(sb6+s*sb7)))))); 203 } 204 GET_FLOAT_WORD(ix,x); 205 SET_FLOAT_WORD(z,ix&0xfffff000); 206 r = __ieee754_expf(-z*z-(float)0.5625)* 207 __ieee754_expf((z-x)*(z+x)+R/S); 208 if(hx>0) return r/x; else return two-r/x; 209 } else { 210 if(hx>0) return tiny*tiny; else return two-tiny; 211 } 212} 213