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