[352] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
|
---|
| 2 | /*
|
---|
| 3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
---|
| 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 "libm.h"
|
---|
| 17 |
|
---|
| 18 | static const float
|
---|
| 19 | erx = 8.4506291151e-01, /* 0x3f58560b */
|
---|
| 20 | /*
|
---|
| 21 | * Coefficients for approximation to erf on [0,0.84375]
|
---|
| 22 | */
|
---|
| 23 | efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
|
---|
| 24 | pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
|
---|
| 25 | pp1 = -3.2504209876e-01, /* 0xbea66beb */
|
---|
| 26 | pp2 = -2.8481749818e-02, /* 0xbce9528f */
|
---|
| 27 | pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
|
---|
| 28 | pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
|
---|
| 29 | qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
|
---|
| 30 | qq2 = 6.5022252500e-02, /* 0x3d852a63 */
|
---|
| 31 | qq3 = 5.0813062117e-03, /* 0x3ba68116 */
|
---|
| 32 | qq4 = 1.3249473704e-04, /* 0x390aee49 */
|
---|
| 33 | qq5 = -3.9602282413e-06, /* 0xb684e21a */
|
---|
| 34 | /*
|
---|
| 35 | * Coefficients for approximation to erf in [0.84375,1.25]
|
---|
| 36 | */
|
---|
| 37 | pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
|
---|
| 38 | pa1 = 4.1485610604e-01, /* 0x3ed46805 */
|
---|
| 39 | pa2 = -3.7220788002e-01, /* 0xbebe9208 */
|
---|
| 40 | pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
|
---|
| 41 | pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
|
---|
| 42 | pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
|
---|
| 43 | pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
|
---|
| 44 | qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
|
---|
| 45 | qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
|
---|
| 46 | qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
|
---|
| 47 | qa4 = 1.2617121637e-01, /* 0x3e013307 */
|
---|
| 48 | qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
|
---|
| 49 | qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
|
---|
| 50 | /*
|
---|
| 51 | * Coefficients for approximation to erfc in [1.25,1/0.35]
|
---|
| 52 | */
|
---|
| 53 | ra0 = -9.8649440333e-03, /* 0xbc21a093 */
|
---|
| 54 | ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
|
---|
| 55 | ra2 = -1.0558626175e+01, /* 0xc128f022 */
|
---|
| 56 | ra3 = -6.2375331879e+01, /* 0xc2798057 */
|
---|
| 57 | ra4 = -1.6239666748e+02, /* 0xc322658c */
|
---|
| 58 | ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
|
---|
| 59 | ra6 = -8.1287437439e+01, /* 0xc2a2932b */
|
---|
| 60 | ra7 = -9.8143291473e+00, /* 0xc11d077e */
|
---|
| 61 | sa1 = 1.9651271820e+01, /* 0x419d35ce */
|
---|
| 62 | sa2 = 1.3765776062e+02, /* 0x4309a863 */
|
---|
| 63 | sa3 = 4.3456588745e+02, /* 0x43d9486f */
|
---|
| 64 | sa4 = 6.4538726807e+02, /* 0x442158c9 */
|
---|
| 65 | sa5 = 4.2900814819e+02, /* 0x43d6810b */
|
---|
| 66 | sa6 = 1.0863500214e+02, /* 0x42d9451f */
|
---|
| 67 | sa7 = 6.5702495575e+00, /* 0x40d23f7c */
|
---|
| 68 | sa8 = -6.0424413532e-02, /* 0xbd777f97 */
|
---|
| 69 | /*
|
---|
| 70 | * Coefficients for approximation to erfc in [1/.35,28]
|
---|
| 71 | */
|
---|
| 72 | rb0 = -9.8649431020e-03, /* 0xbc21a092 */
|
---|
| 73 | rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
|
---|
| 74 | rb2 = -1.7757955551e+01, /* 0xc18e104b */
|
---|
| 75 | rb3 = -1.6063638306e+02, /* 0xc320a2ea */
|
---|
| 76 | rb4 = -6.3756646729e+02, /* 0xc41f6441 */
|
---|
| 77 | rb5 = -1.0250950928e+03, /* 0xc480230b */
|
---|
| 78 | rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
|
---|
| 79 | sb1 = 3.0338060379e+01, /* 0x41f2b459 */
|
---|
| 80 | sb2 = 3.2579251099e+02, /* 0x43a2e571 */
|
---|
| 81 | sb3 = 1.5367296143e+03, /* 0x44c01759 */
|
---|
| 82 | sb4 = 3.1998581543e+03, /* 0x4547fdbb */
|
---|
| 83 | sb5 = 2.5530502930e+03, /* 0x451f90ce */
|
---|
| 84 | sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
|
---|
| 85 | sb7 = -2.2440952301e+01; /* 0xc1b38712 */
|
---|
| 86 |
|
---|
| 87 | static float erfc1(float x)
|
---|
| 88 | {
|
---|
| 89 | float_t s,P,Q;
|
---|
| 90 |
|
---|
| 91 | s = fabsf(x) - 1;
|
---|
| 92 | P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
---|
| 93 | Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
---|
| 94 | return 1 - erx - P/Q;
|
---|
| 95 | }
|
---|
| 96 |
|
---|
| 97 | static float erfc2(uint32_t ix, float x)
|
---|
| 98 | {
|
---|
| 99 | float_t s,R,S;
|
---|
| 100 | float z;
|
---|
| 101 |
|
---|
| 102 | if (ix < 0x3fa00000) /* |x| < 1.25 */
|
---|
| 103 | return erfc1(x);
|
---|
| 104 |
|
---|
| 105 | x = fabsf(x);
|
---|
| 106 | s = 1/(x*x);
|
---|
| 107 | if (ix < 0x4036db6d) { /* |x| < 1/0.35 */
|
---|
| 108 | R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
---|
| 109 | ra5+s*(ra6+s*ra7))))));
|
---|
| 110 | S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
---|
| 111 | sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
---|
| 112 | } else { /* |x| >= 1/0.35 */
|
---|
| 113 | R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
---|
| 114 | rb5+s*rb6)))));
|
---|
| 115 | S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
---|
| 116 | sb5+s*(sb6+s*sb7))))));
|
---|
| 117 | }
|
---|
| 118 | GET_FLOAT_WORD(ix, x);
|
---|
| 119 | SET_FLOAT_WORD(z, ix&0xffffe000);
|
---|
| 120 | return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x;
|
---|
| 121 | }
|
---|
| 122 |
|
---|
| 123 | float erff(float x)
|
---|
| 124 | {
|
---|
| 125 | float r,s,z,y;
|
---|
| 126 | uint32_t ix;
|
---|
| 127 | int sign;
|
---|
| 128 |
|
---|
| 129 | GET_FLOAT_WORD(ix, x);
|
---|
| 130 | sign = ix>>31;
|
---|
| 131 | ix &= 0x7fffffff;
|
---|
| 132 | if (ix >= 0x7f800000) {
|
---|
| 133 | /* erf(nan)=nan, erf(+-inf)=+-1 */
|
---|
| 134 | return 1-2*sign + 1/x;
|
---|
| 135 | }
|
---|
| 136 | if (ix < 0x3f580000) { /* |x| < 0.84375 */
|
---|
| 137 | if (ix < 0x31800000) { /* |x| < 2**-28 */
|
---|
| 138 | /*avoid underflow */
|
---|
| 139 | return 0.125f*(8*x + efx8*x);
|
---|
| 140 | }
|
---|
| 141 | z = x*x;
|
---|
| 142 | r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
---|
| 143 | s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
---|
| 144 | y = r/s;
|
---|
| 145 | return x + x*y;
|
---|
| 146 | }
|
---|
| 147 | if (ix < 0x40c00000) /* |x| < 6 */
|
---|
| 148 | y = 1 - erfc2(ix,x);
|
---|
| 149 | else
|
---|
| 150 | y = 1 - 0x1p-120f;
|
---|
| 151 | return sign ? -y : y;
|
---|
| 152 | }
|
---|
| 153 |
|
---|
| 154 | float erfcf(float x)
|
---|
| 155 | {
|
---|
| 156 | float r,s,z,y;
|
---|
| 157 | uint32_t ix;
|
---|
| 158 | int sign;
|
---|
| 159 |
|
---|
| 160 | GET_FLOAT_WORD(ix, x);
|
---|
| 161 | sign = ix>>31;
|
---|
| 162 | ix &= 0x7fffffff;
|
---|
| 163 | if (ix >= 0x7f800000) {
|
---|
| 164 | /* erfc(nan)=nan, erfc(+-inf)=0,2 */
|
---|
| 165 | return 2*sign + 1/x;
|
---|
| 166 | }
|
---|
| 167 |
|
---|
| 168 | if (ix < 0x3f580000) { /* |x| < 0.84375 */
|
---|
| 169 | if (ix < 0x23800000) /* |x| < 2**-56 */
|
---|
| 170 | return 1.0f - x;
|
---|
| 171 | z = x*x;
|
---|
| 172 | r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
---|
| 173 | s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
---|
| 174 | y = r/s;
|
---|
| 175 | if (sign || ix < 0x3e800000) /* x < 1/4 */
|
---|
| 176 | return 1.0f - (x+x*y);
|
---|
| 177 | return 0.5f - (x - 0.5f + x*y);
|
---|
| 178 | }
|
---|
| 179 | if (ix < 0x41e00000) { /* |x| < 28 */
|
---|
| 180 | return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
|
---|
| 181 | }
|
---|
| 182 | return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f;
|
---|
| 183 | }
|
---|