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[] = "$FreeBSD$"; 18 #endif 19 20 #include "math.h" 21 #include "math_private.h" 22 23 static const float 24 tiny = 1e-30, 25 half= 5.0000000000e-01, /* 0x3F000000 */ 26 one = 1.0000000000e+00, /* 0x3F800000 */ 27 two = 2.0000000000e+00, /* 0x40000000 */ 28 /* c = (subfloat)0.84506291151 */ 29 erx = 8.4506291151e-01, /* 0x3f58560b */ 30 /* 31 * Coefficients for approximation to erf on [0,0.84375] 32 */ 33 efx = 1.2837916613e-01, /* 0x3e0375d4 */ 34 efx8= 1.0270333290e+00, /* 0x3f8375d4 */ 35 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ 36 pp1 = -3.2504209876e-01, /* 0xbea66beb */ 37 pp2 = -2.8481749818e-02, /* 0xbce9528f */ 38 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ 39 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ 40 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ 41 qq2 = 6.5022252500e-02, /* 0x3d852a63 */ 42 qq3 = 5.0813062117e-03, /* 0x3ba68116 */ 43 qq4 = 1.3249473704e-04, /* 0x390aee49 */ 44 qq5 = -3.9602282413e-06, /* 0xb684e21a */ 45 /* 46 * Coefficients for approximation to erf in [0.84375,1.25] 47 */ 48 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ 49 pa1 = 4.1485610604e-01, /* 0x3ed46805 */ 50 pa2 = -3.7220788002e-01, /* 0xbebe9208 */ 51 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ 52 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ 53 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ 54 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ 55 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ 56 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ 57 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ 58 qa4 = 1.2617121637e-01, /* 0x3e013307 */ 59 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ 60 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ 61 /* 62 * Coefficients for approximation to erfc in [1.25,1/0.35] 63 */ 64 ra0 = -9.8649440333e-03, /* 0xbc21a093 */ 65 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ 66 ra2 = -1.0558626175e+01, /* 0xc128f022 */ 67 ra3 = -6.2375331879e+01, /* 0xc2798057 */ 68 ra4 = -1.6239666748e+02, /* 0xc322658c */ 69 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ 70 ra6 = -8.1287437439e+01, /* 0xc2a2932b */ 71 ra7 = -9.8143291473e+00, /* 0xc11d077e */ 72 sa1 = 1.9651271820e+01, /* 0x419d35ce */ 73 sa2 = 1.3765776062e+02, /* 0x4309a863 */ 74 sa3 = 4.3456588745e+02, /* 0x43d9486f */ 75 sa4 = 6.4538726807e+02, /* 0x442158c9 */ 76 sa5 = 4.2900814819e+02, /* 0x43d6810b */ 77 sa6 = 1.0863500214e+02, /* 0x42d9451f */ 78 sa7 = 6.5702495575e+00, /* 0x40d23f7c */ 79 sa8 = -6.0424413532e-02, /* 0xbd777f97 */ 80 /* 81 * Coefficients for approximation to erfc in [1/.35,28] 82 */ 83 rb0 = -9.8649431020e-03, /* 0xbc21a092 */ 84 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ 85 rb2 = -1.7757955551e+01, /* 0xc18e104b */ 86 rb3 = -1.6063638306e+02, /* 0xc320a2ea */ 87 rb4 = -6.3756646729e+02, /* 0xc41f6441 */ 88 rb5 = -1.0250950928e+03, /* 0xc480230b */ 89 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ 90 sb1 = 3.0338060379e+01, /* 0x41f2b459 */ 91 sb2 = 3.2579251099e+02, /* 0x43a2e571 */ 92 sb3 = 1.5367296143e+03, /* 0x44c01759 */ 93 sb4 = 3.1998581543e+03, /* 0x4547fdbb */ 94 sb5 = 2.5530502930e+03, /* 0x451f90ce */ 95 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ 96 sb7 = -2.2440952301e+01; /* 0xc1b38712 */ 97 98 float 99 erff(float x) 100 { 101 int32_t hx,ix,i; 102 float R,S,P,Q,s,y,z,r; 103 GET_FLOAT_WORD(hx,x); 104 ix = hx&0x7fffffff; 105 if(ix>=0x7f800000) { /* erf(nan)=nan */ 106 i = ((u_int32_t)hx>>31)<<1; 107 return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ 108 } 109 110 if(ix < 0x3f580000) { /* |x|<0.84375 */ 111 if(ix < 0x31800000) { /* |x|<2**-28 */ 112 if (ix < 0x04000000) 113 /*avoid underflow */ 114 return (float)0.125*((float)8.0*x+efx8*x); 115 return x + efx*x; 116 } 117 z = x*x; 118 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 119 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 120 y = r/s; 121 return x + x*y; 122 } 123 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 124 s = fabsf(x)-one; 125 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 126 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 127 if(hx>=0) return erx + P/Q; else return -erx - P/Q; 128 } 129 if (ix >= 0x40c00000) { /* inf>|x|>=6 */ 130 if(hx>=0) return one-tiny; else return tiny-one; 131 } 132 x = fabsf(x); 133 s = one/(x*x); 134 if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ 135 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 136 ra5+s*(ra6+s*ra7)))))); 137 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 138 sa5+s*(sa6+s*(sa7+s*sa8))))))); 139 } else { /* |x| >= 1/0.35 */ 140 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 141 rb5+s*rb6))))); 142 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 143 sb5+s*(sb6+s*sb7)))))); 144 } 145 GET_FLOAT_WORD(ix,x); 146 SET_FLOAT_WORD(z,ix&0xfffff000); 147 r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); 148 if(hx>=0) return one-r/x; else return r/x-one; 149 } 150 151 float 152 erfcf(float x) 153 { 154 int32_t hx,ix; 155 float R,S,P,Q,s,y,z,r; 156 GET_FLOAT_WORD(hx,x); 157 ix = hx&0x7fffffff; 158 if(ix>=0x7f800000) { /* erfc(nan)=nan */ 159 /* erfc(+-inf)=0,2 */ 160 return (float)(((u_int32_t)hx>>31)<<1)+one/x; 161 } 162 163 if(ix < 0x3f580000) { /* |x|<0.84375 */ 164 if(ix < 0x23800000) /* |x|<2**-56 */ 165 return one-x; 166 z = x*x; 167 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 168 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 169 y = r/s; 170 if(hx < 0x3e800000) { /* x<1/4 */ 171 return one-(x+x*y); 172 } else { 173 r = x*y; 174 r += (x-half); 175 return half - r ; 176 } 177 } 178 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 179 s = fabsf(x)-one; 180 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 181 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 182 if(hx>=0) { 183 z = one-erx; return z - P/Q; 184 } else { 185 z = erx+P/Q; return one+z; 186 } 187 } 188 if (ix < 0x41e00000) { /* |x|<28 */ 189 x = fabsf(x); 190 s = one/(x*x); 191 if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ 192 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 193 ra5+s*(ra6+s*ra7)))))); 194 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 195 sa5+s*(sa6+s*(sa7+s*sa8))))))); 196 } else { /* |x| >= 1/.35 ~ 2.857143 */ 197 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ 198 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 199 rb5+s*rb6))))); 200 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 201 sb5+s*(sb6+s*sb7)))))); 202 } 203 GET_FLOAT_WORD(ix,x); 204 SET_FLOAT_WORD(z,ix&0xfffff000); 205 r = __ieee754_expf(-z*z-(float)0.5625)* 206 __ieee754_expf((z-x)*(z+x)+R/S); 207 if(hx>0) return r/x; else return two-r/x; 208 } else { 209 if(hx>0) return tiny*tiny; else return two-tiny; 210 } 211 } 212