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 #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 tiny = 1e-30, 29 half= 5.0000000000e-01, /* 0x3F000000 */ 30 one = 1.0000000000e+00, /* 0x3F800000 */ 31 two = 2.0000000000e+00, /* 0x40000000 */ 32 /* c = (subfloat)0.84506291151 */ 33 erx = 8.4506291151e-01, /* 0x3f58560b */ 34 /* 35 * Coefficients for approximation to erf on [0,0.84375] 36 */ 37 efx = 1.2837916613e-01, /* 0x3e0375d4 */ 38 efx8= 1.0270333290e+00, /* 0x3f8375d4 */ 39 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ 40 pp1 = -3.2504209876e-01, /* 0xbea66beb */ 41 pp2 = -2.8481749818e-02, /* 0xbce9528f */ 42 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ 43 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ 44 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ 45 qq2 = 6.5022252500e-02, /* 0x3d852a63 */ 46 qq3 = 5.0813062117e-03, /* 0x3ba68116 */ 47 qq4 = 1.3249473704e-04, /* 0x390aee49 */ 48 qq5 = -3.9602282413e-06, /* 0xb684e21a */ 49 /* 50 * Coefficients for approximation to erf in [0.84375,1.25] 51 */ 52 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ 53 pa1 = 4.1485610604e-01, /* 0x3ed46805 */ 54 pa2 = -3.7220788002e-01, /* 0xbebe9208 */ 55 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ 56 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ 57 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ 58 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ 59 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ 60 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ 61 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ 62 qa4 = 1.2617121637e-01, /* 0x3e013307 */ 63 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ 64 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ 65 /* 66 * Coefficients for approximation to erfc in [1.25,1/0.35] 67 */ 68 ra0 = -9.8649440333e-03, /* 0xbc21a093 */ 69 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ 70 ra2 = -1.0558626175e+01, /* 0xc128f022 */ 71 ra3 = -6.2375331879e+01, /* 0xc2798057 */ 72 ra4 = -1.6239666748e+02, /* 0xc322658c */ 73 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ 74 ra6 = -8.1287437439e+01, /* 0xc2a2932b */ 75 ra7 = -9.8143291473e+00, /* 0xc11d077e */ 76 sa1 = 1.9651271820e+01, /* 0x419d35ce */ 77 sa2 = 1.3765776062e+02, /* 0x4309a863 */ 78 sa3 = 4.3456588745e+02, /* 0x43d9486f */ 79 sa4 = 6.4538726807e+02, /* 0x442158c9 */ 80 sa5 = 4.2900814819e+02, /* 0x43d6810b */ 81 sa6 = 1.0863500214e+02, /* 0x42d9451f */ 82 sa7 = 6.5702495575e+00, /* 0x40d23f7c */ 83 sa8 = -6.0424413532e-02, /* 0xbd777f97 */ 84 /* 85 * Coefficients for approximation to erfc in [1/.35,28] 86 */ 87 rb0 = -9.8649431020e-03, /* 0xbc21a092 */ 88 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ 89 rb2 = -1.7757955551e+01, /* 0xc18e104b */ 90 rb3 = -1.6063638306e+02, /* 0xc320a2ea */ 91 rb4 = -6.3756646729e+02, /* 0xc41f6441 */ 92 rb5 = -1.0250950928e+03, /* 0xc480230b */ 93 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ 94 sb1 = 3.0338060379e+01, /* 0x41f2b459 */ 95 sb2 = 3.2579251099e+02, /* 0x43a2e571 */ 96 sb3 = 1.5367296143e+03, /* 0x44c01759 */ 97 sb4 = 3.1998581543e+03, /* 0x4547fdbb */ 98 sb5 = 2.5530502930e+03, /* 0x451f90ce */ 99 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ 100 sb7 = -2.2440952301e+01; /* 0xc1b38712 */ 101 102 #ifdef __STDC__ 103 float erff(float x) 104 #else 105 float erff(x) 106 float x; 107 #endif 108 { 109 int32_t hx,ix,i; 110 float R,S,P,Q,s,y,z,r; 111 GET_FLOAT_WORD(hx,x); 112 ix = hx&0x7fffffff; 113 if(ix>=0x7f800000) { /* erf(nan)=nan */ 114 i = ((u_int32_t)hx>>31)<<1; 115 return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ 116 } 117 118 if(ix < 0x3f580000) { /* |x|<0.84375 */ 119 if(ix < 0x31800000) { /* |x|<2**-28 */ 120 if (ix < 0x04000000) 121 /*avoid underflow */ 122 return (float)0.125*((float)8.0*x+efx8*x); 123 return x + efx*x; 124 } 125 z = x*x; 126 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 127 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 128 y = r/s; 129 return x + x*y; 130 } 131 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 132 s = fabsf(x)-one; 133 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 134 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 135 if(hx>=0) return erx + P/Q; else return -erx - P/Q; 136 } 137 if (ix >= 0x40c00000) { /* inf>|x|>=6 */ 138 if(hx>=0) return one-tiny; else return tiny-one; 139 } 140 x = fabsf(x); 141 s = one/(x*x); 142 if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ 143 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 144 ra5+s*(ra6+s*ra7)))))); 145 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 146 sa5+s*(sa6+s*(sa7+s*sa8))))))); 147 } else { /* |x| >= 1/0.35 */ 148 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 149 rb5+s*rb6))))); 150 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 151 sb5+s*(sb6+s*sb7)))))); 152 } 153 GET_FLOAT_WORD(ix,x); 154 SET_FLOAT_WORD(z,ix&0xfffff000); 155 r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); 156 if(hx>=0) return one-r/x; else return r/x-one; 157 } 158 159 #ifdef __STDC__ 160 float erfcf(float x) 161 #else 162 float erfcf(x) 163 float x; 164 #endif 165 { 166 int32_t hx,ix; 167 float R,S,P,Q,s,y,z,r; 168 GET_FLOAT_WORD(hx,x); 169 ix = hx&0x7fffffff; 170 if(ix>=0x7f800000) { /* erfc(nan)=nan */ 171 /* erfc(+-inf)=0,2 */ 172 return (float)(((u_int32_t)hx>>31)<<1)+one/x; 173 } 174 175 if(ix < 0x3f580000) { /* |x|<0.84375 */ 176 if(ix < 0x23800000) /* |x|<2**-56 */ 177 return one-x; 178 z = x*x; 179 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 180 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 181 y = r/s; 182 if(hx < 0x3e800000) { /* x<1/4 */ 183 return one-(x+x*y); 184 } else { 185 r = x*y; 186 r += (x-half); 187 return half - r ; 188 } 189 } 190 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 191 s = fabsf(x)-one; 192 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 193 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 194 if(hx>=0) { 195 z = one-erx; return z - P/Q; 196 } else { 197 z = erx+P/Q; return one+z; 198 } 199 } 200 if (ix < 0x41e00000) { /* |x|<28 */ 201 x = fabsf(x); 202 s = one/(x*x); 203 if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ 204 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 205 ra5+s*(ra6+s*ra7)))))); 206 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 207 sa5+s*(sa6+s*(sa7+s*sa8))))))); 208 } else { /* |x| >= 1/.35 ~ 2.857143 */ 209 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ 210 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 211 rb5+s*rb6))))); 212 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 213 sb5+s*(sb6+s*sb7)))))); 214 } 215 GET_FLOAT_WORD(ix,x); 216 SET_FLOAT_WORD(z,ix&0xfffff000); 217 r = __ieee754_expf(-z*z-(float)0.5625)* 218 __ieee754_expf((z-x)*(z+x)+R/S); 219 if(hx>0) return r/x; else return two-r/x; 220 } else { 221 if(hx>0) return tiny*tiny; else return two-tiny; 222 } 223 } 224