1 /* sf_erf.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 "fdlibm.h" 17 18 #ifdef __v810__ 19 #define const 20 #endif 21 22 #ifdef __STDC__ 23 static const float 24 #else 25 static float 26 #endif 27 tiny = 1e-30, 28 half= 5.0000000000e-01, /* 0x3F000000 */ 29 one = 1.0000000000e+00, /* 0x3F800000 */ 30 two = 2.0000000000e+00, /* 0x40000000 */ 31 /* c = (subfloat)0.84506291151 */ 32 erx = 8.4506291151e-01, /* 0x3f58560b */ 33 /* 34 * Coefficients for approximation to erf on [0,0.84375] 35 */ 36 efx = 1.2837916613e-01, /* 0x3e0375d4 */ 37 efx8= 1.0270333290e+00, /* 0x3f8375d4 */ 38 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ 39 pp1 = -3.2504209876e-01, /* 0xbea66beb */ 40 pp2 = -2.8481749818e-02, /* 0xbce9528f */ 41 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ 42 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ 43 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ 44 qq2 = 6.5022252500e-02, /* 0x3d852a63 */ 45 qq3 = 5.0813062117e-03, /* 0x3ba68116 */ 46 qq4 = 1.3249473704e-04, /* 0x390aee49 */ 47 qq5 = -3.9602282413e-06, /* 0xb684e21a */ 48 /* 49 * Coefficients for approximation to erf in [0.84375,1.25] 50 */ 51 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ 52 pa1 = 4.1485610604e-01, /* 0x3ed46805 */ 53 pa2 = -3.7220788002e-01, /* 0xbebe9208 */ 54 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ 55 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ 56 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ 57 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ 58 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ 59 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ 60 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ 61 qa4 = 1.2617121637e-01, /* 0x3e013307 */ 62 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ 63 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ 64 /* 65 * Coefficients for approximation to erfc in [1.25,1/0.35] 66 */ 67 ra0 = -9.8649440333e-03, /* 0xbc21a093 */ 68 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ 69 ra2 = -1.0558626175e+01, /* 0xc128f022 */ 70 ra3 = -6.2375331879e+01, /* 0xc2798057 */ 71 ra4 = -1.6239666748e+02, /* 0xc322658c */ 72 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ 73 ra6 = -8.1287437439e+01, /* 0xc2a2932b */ 74 ra7 = -9.8143291473e+00, /* 0xc11d077e */ 75 sa1 = 1.9651271820e+01, /* 0x419d35ce */ 76 sa2 = 1.3765776062e+02, /* 0x4309a863 */ 77 sa3 = 4.3456588745e+02, /* 0x43d9486f */ 78 sa4 = 6.4538726807e+02, /* 0x442158c9 */ 79 sa5 = 4.2900814819e+02, /* 0x43d6810b */ 80 sa6 = 1.0863500214e+02, /* 0x42d9451f */ 81 sa7 = 6.5702495575e+00, /* 0x40d23f7c */ 82 sa8 = -6.0424413532e-02, /* 0xbd777f97 */ 83 /* 84 * Coefficients for approximation to erfc in [1/.35,28] 85 */ 86 rb0 = -9.8649431020e-03, /* 0xbc21a092 */ 87 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ 88 rb2 = -1.7757955551e+01, /* 0xc18e104b */ 89 rb3 = -1.6063638306e+02, /* 0xc320a2ea */ 90 rb4 = -6.3756646729e+02, /* 0xc41f6441 */ 91 rb5 = -1.0250950928e+03, /* 0xc480230b */ 92 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ 93 sb1 = 3.0338060379e+01, /* 0x41f2b459 */ 94 sb2 = 3.2579251099e+02, /* 0x43a2e571 */ 95 sb3 = 1.5367296143e+03, /* 0x44c01759 */ 96 sb4 = 3.1998581543e+03, /* 0x4547fdbb */ 97 sb5 = 2.5530502930e+03, /* 0x451f90ce */ 98 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ 99 sb7 = -2.2440952301e+01; /* 0xc1b38712 */ 100 101 #ifdef __STDC__ erff(float x)102 float erff(float x) 103 #else 104 float erff(x) 105 float x; 106 #endif 107 { 108 __int32_t hx,ix,i; 109 float R,S,P,Q,s,y,z,r; 110 GET_FLOAT_WORD(hx,x); 111 ix = hx&0x7fffffff; 112 if(!FLT_UWORD_IS_FINITE(ix)) { /* erf(nan)=nan */ 113 i = ((__uint32_t)hx>>31)<<1; 114 return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ 115 } 116 117 if(ix < 0x3f580000) { /* |x|<0.84375 */ 118 if(ix < 0x31800000) { /* |x|<2**-28 */ 119 if (ix < 0x04000000) 120 /*avoid underflow */ 121 return (float)0.125*((float)8.0*x+efx8*x); 122 return x + efx*x; 123 } 124 z = x*x; 125 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 126 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 127 y = r/s; 128 return x + x*y; 129 } 130 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 131 s = fabsf(x)-one; 132 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 133 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 134 if(hx>=0) return erx + P/Q; else return -erx - P/Q; 135 } 136 if (ix >= 0x40c00000) { /* inf>|x|>=6 */ 137 if(hx>=0) return one-tiny; else return tiny-one; 138 } 139 x = fabsf(x); 140 s = one/(x*x); 141 if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ 142 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 143 ra5+s*(ra6+s*ra7)))))); 144 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 145 sa5+s*(sa6+s*(sa7+s*sa8))))))); 146 } else { /* |x| >= 1/0.35 */ 147 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 148 rb5+s*rb6))))); 149 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 150 sb5+s*(sb6+s*sb7)))))); 151 } 152 GET_FLOAT_WORD(ix,x); 153 SET_FLOAT_WORD(z,ix&0xfffff000); 154 r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); 155 if(hx>=0) return one-r/x; else return r/x-one; 156 } 157 158 #ifdef __STDC__ erfcf(float x)159 float erfcf(float x) 160 #else 161 float erfcf(x) 162 float x; 163 #endif 164 { 165 __int32_t hx,ix; 166 float R,S,P,Q,s,y,z,r; 167 GET_FLOAT_WORD(hx,x); 168 ix = hx&0x7fffffff; 169 if(!FLT_UWORD_IS_FINITE(ix)) { /* erfc(nan)=nan */ 170 /* erfc(+-inf)=0,2 */ 171 return (float)(((__uint32_t)hx>>31)<<1)+one/x; 172 } 173 174 if(ix < 0x3f580000) { /* |x|<0.84375 */ 175 if(ix < 0x23800000) /* |x|<2**-56 */ 176 return one-x; 177 z = x*x; 178 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 179 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 180 y = r/s; 181 if(hx < 0x3e800000) { /* x<1/4 */ 182 return one-(x+x*y); 183 } else { 184 r = x*y; 185 r += (x-half); 186 return half - r ; 187 } 188 } 189 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 190 s = fabsf(x)-one; 191 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 192 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 193 if(hx>=0) { 194 z = one-erx; return z - P/Q; 195 } else { 196 z = erx+P/Q; return one+z; 197 } 198 } 199 if (ix < 0x41e00000) { /* |x|<28 */ 200 x = fabsf(x); 201 s = one/(x*x); 202 if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ 203 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 204 ra5+s*(ra6+s*ra7)))))); 205 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 206 sa5+s*(sa6+s*(sa7+s*sa8))))))); 207 } else { /* |x| >= 1/.35 ~ 2.857143 */ 208 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ 209 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 210 rb5+s*rb6))))); 211 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 212 sb5+s*(sb6+s*sb7)))))); 213 } 214 GET_FLOAT_WORD(ix,x); 215 SET_FLOAT_WORD(z,ix&0xfffff000); 216 r = __ieee754_expf(-z*z-(float)0.5625)* 217 __ieee754_expf((z-x)*(z+x)+R/S); 218 if(hx>0) return r/x; else return two-r/x; 219 } else { 220 if(hx>0) return tiny*tiny; else return two-tiny; 221 } 222 } 223 224 #ifdef _DOUBLE_IS_32BITS 225 226 #ifdef __STDC__ erf(double x)227 double erf(double x) 228 #else 229 double erf(x) 230 double x; 231 #endif 232 { 233 return (double) erff((float) x); 234 } 235 236 #ifdef __STDC__ erfc(double x)237 double erfc(double x) 238 #else 239 double erfc(x) 240 double x; 241 #endif 242 { 243 return (double) erfcf((float) x); 244 } 245 246 #endif /* defined(_DOUBLE_IS_32BITS) */ 247