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| Rev | Author | Line No. | Line |
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| 3362 | Serge | 1 | /* sf_erf.c -- float version of s_erf.c. |
| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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| 3 | */ |
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| 4 | |||
| 5 | /* |
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| 6 | * ==================================================== |
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 8 | * |
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 10 | * Permission to use, copy, modify, and distribute this |
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| 11 | * software is freely granted, provided that this notice |
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| 12 | * is preserved. |
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| 13 | * ==================================================== |
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| 14 | */ |
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| 15 | |||
| 16 | #include "fdlibm.h" |
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| 17 | |||
| 18 | #ifdef __v810__ |
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| 19 | #define const |
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| 20 | #endif |
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| 21 | |||
| 22 | #ifdef __STDC__ |
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| 23 | static const float |
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| 24 | #else |
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| 25 | static float |
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| 26 | #endif |
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| 27 | tiny = 1e-30, |
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| 28 | half= 5.0000000000e-01, /* 0x3F000000 */ |
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| 29 | one = 1.0000000000e+00, /* 0x3F800000 */ |
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| 30 | two = 2.0000000000e+00, /* 0x40000000 */ |
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| 31 | /* c = (subfloat)0.84506291151 */ |
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| 32 | erx = 8.4506291151e-01, /* 0x3f58560b */ |
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| 33 | /* |
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| 34 | * Coefficients for approximation to erf on [0,0.84375] |
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| 35 | */ |
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| 36 | efx = 1.2837916613e-01, /* 0x3e0375d4 */ |
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| 37 | efx8= 1.0270333290e+00, /* 0x3f8375d4 */ |
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| 38 | pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ |
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| 39 | pp1 = -3.2504209876e-01, /* 0xbea66beb */ |
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| 40 | pp2 = -2.8481749818e-02, /* 0xbce9528f */ |
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| 41 | pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ |
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| 42 | pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ |
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| 43 | qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ |
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| 44 | qq2 = 6.5022252500e-02, /* 0x3d852a63 */ |
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| 45 | qq3 = 5.0813062117e-03, /* 0x3ba68116 */ |
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| 46 | qq4 = 1.3249473704e-04, /* 0x390aee49 */ |
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| 47 | qq5 = -3.9602282413e-06, /* 0xb684e21a */ |
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| 48 | /* |
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| 49 | * Coefficients for approximation to erf in [0.84375,1.25] |
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| 50 | */ |
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| 51 | pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ |
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| 52 | pa1 = 4.1485610604e-01, /* 0x3ed46805 */ |
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| 53 | pa2 = -3.7220788002e-01, /* 0xbebe9208 */ |
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| 54 | pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ |
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| 55 | pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ |
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| 56 | pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ |
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| 57 | pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ |
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| 58 | qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ |
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| 59 | qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ |
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| 60 | qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ |
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| 61 | qa4 = 1.2617121637e-01, /* 0x3e013307 */ |
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| 62 | qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ |
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| 63 | qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ |
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| 64 | /* |
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| 65 | * Coefficients for approximation to erfc in [1.25,1/0.35] |
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| 66 | */ |
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| 67 | ra0 = -9.8649440333e-03, /* 0xbc21a093 */ |
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| 68 | ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ |
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| 69 | ra2 = -1.0558626175e+01, /* 0xc128f022 */ |
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| 70 | ra3 = -6.2375331879e+01, /* 0xc2798057 */ |
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| 71 | ra4 = -1.6239666748e+02, /* 0xc322658c */ |
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| 72 | ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ |
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| 73 | ra6 = -8.1287437439e+01, /* 0xc2a2932b */ |
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| 74 | ra7 = -9.8143291473e+00, /* 0xc11d077e */ |
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| 75 | sa1 = 1.9651271820e+01, /* 0x419d35ce */ |
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| 76 | sa2 = 1.3765776062e+02, /* 0x4309a863 */ |
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| 77 | sa3 = 4.3456588745e+02, /* 0x43d9486f */ |
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| 78 | sa4 = 6.4538726807e+02, /* 0x442158c9 */ |
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| 79 | sa5 = 4.2900814819e+02, /* 0x43d6810b */ |
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| 80 | sa6 = 1.0863500214e+02, /* 0x42d9451f */ |
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| 81 | sa7 = 6.5702495575e+00, /* 0x40d23f7c */ |
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| 82 | sa8 = -6.0424413532e-02, /* 0xbd777f97 */ |
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| 83 | /* |
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| 84 | * Coefficients for approximation to erfc in [1/.35,28] |
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| 85 | */ |
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| 86 | rb0 = -9.8649431020e-03, /* 0xbc21a092 */ |
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| 87 | rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ |
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| 88 | rb2 = -1.7757955551e+01, /* 0xc18e104b */ |
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| 89 | rb3 = -1.6063638306e+02, /* 0xc320a2ea */ |
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| 90 | rb4 = -6.3756646729e+02, /* 0xc41f6441 */ |
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| 91 | rb5 = -1.0250950928e+03, /* 0xc480230b */ |
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| 92 | rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ |
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| 93 | sb1 = 3.0338060379e+01, /* 0x41f2b459 */ |
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| 94 | sb2 = 3.2579251099e+02, /* 0x43a2e571 */ |
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| 95 | sb3 = 1.5367296143e+03, /* 0x44c01759 */ |
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| 96 | sb4 = 3.1998581543e+03, /* 0x4547fdbb */ |
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| 97 | sb5 = 2.5530502930e+03, /* 0x451f90ce */ |
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| 98 | sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ |
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| 99 | sb7 = -2.2440952301e+01; /* 0xc1b38712 */ |
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| 100 | |||
| 101 | #ifdef __STDC__ |
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| 102 | float erff(float x) |
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| 103 | #else |
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| 104 | float erff(x) |
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| 105 | float x; |
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| 106 | #endif |
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| 107 | { |
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| 108 | __int32_t hx,ix,i; |
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| 109 | float R,S,P,Q,s,y,z,r; |
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| 110 | GET_FLOAT_WORD(hx,x); |
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| 111 | ix = hx&0x7fffffff; |
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| 112 | if(!FLT_UWORD_IS_FINITE(ix)) { /* erf(nan)=nan */ |
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| 113 | i = ((__uint32_t)hx>>31)<<1; |
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| 114 | return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ |
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| 115 | } |
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| 116 | |||
| 117 | if(ix < 0x3f580000) { /* |x|<0.84375 */ |
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| 118 | if(ix < 0x31800000) { /* |x|<2**-28 */ |
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| 119 | if (ix < 0x04000000) |
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| 120 | /*avoid underflow */ |
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| 121 | return (float)0.125*((float)8.0*x+efx8*x); |
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| 122 | return x + efx*x; |
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| 123 | } |
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| 124 | z = x*x; |
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| 125 | r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); |
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| 126 | s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); |
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| 127 | y = r/s; |
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| 128 | return x + x*y; |
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| 129 | } |
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| 130 | if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ |
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| 131 | s = fabsf(x)-one; |
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| 132 | P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); |
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| 133 | Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); |
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| 134 | if(hx>=0) return erx + P/Q; else return -erx - P/Q; |
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| 135 | } |
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| 136 | if (ix >= 0x40c00000) { /* inf>|x|>=6 */ |
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| 137 | if(hx>=0) return one-tiny; else return tiny-one; |
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| 138 | } |
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| 139 | x = fabsf(x); |
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| 140 | s = one/(x*x); |
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| 141 | if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ |
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| 142 | R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( |
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| 143 | ra5+s*(ra6+s*ra7)))))); |
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| 144 | S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( |
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| 145 | sa5+s*(sa6+s*(sa7+s*sa8))))))); |
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| 146 | } else { /* |x| >= 1/0.35 */ |
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| 147 | R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( |
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| 148 | rb5+s*rb6))))); |
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| 149 | S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( |
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| 150 | sb5+s*(sb6+s*sb7)))))); |
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| 151 | } |
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| 152 | GET_FLOAT_WORD(ix,x); |
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| 153 | SET_FLOAT_WORD(z,ix&0xfffff000); |
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| 154 | r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); |
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| 155 | if(hx>=0) return one-r/x; else return r/x-one; |
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| 156 | } |
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| 157 | |||
| 158 | #ifdef __STDC__ |
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| 159 | float erfcf(float x) |
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| 160 | #else |
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| 161 | float erfcf(x) |
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| 162 | float x; |
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| 163 | #endif |
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| 164 | { |
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| 165 | __int32_t hx,ix; |
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| 166 | float R,S,P,Q,s,y,z,r; |
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| 167 | GET_FLOAT_WORD(hx,x); |
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| 168 | ix = hx&0x7fffffff; |
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| 169 | if(!FLT_UWORD_IS_FINITE(ix)) { /* erfc(nan)=nan */ |
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| 170 | /* erfc(+-inf)=0,2 */ |
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| 171 | return (float)(((__uint32_t)hx>>31)<<1)+one/x; |
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| 172 | } |
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| 173 | |||
| 174 | if(ix < 0x3f580000) { /* |x|<0.84375 */ |
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| 175 | if(ix < 0x23800000) /* |x|<2**-56 */ |
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| 176 | return one-x; |
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| 177 | z = x*x; |
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| 178 | r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); |
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| 179 | s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); |
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| 180 | y = r/s; |
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| 181 | if(hx < 0x3e800000) { /* x<1/4 */ |
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| 182 | return one-(x+x*y); |
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| 183 | } else { |
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| 184 | r = x*y; |
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| 185 | r += (x-half); |
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| 186 | return half - r ; |
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| 187 | } |
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| 188 | } |
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| 189 | if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ |
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| 190 | s = fabsf(x)-one; |
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| 191 | P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); |
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| 192 | Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); |
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| 193 | if(hx>=0) { |
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| 194 | z = one-erx; return z - P/Q; |
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| 195 | } else { |
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| 196 | z = erx+P/Q; return one+z; |
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| 197 | } |
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| 198 | } |
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| 199 | if (ix < 0x41e00000) { /* |x|<28 */ |
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| 200 | x = fabsf(x); |
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| 201 | s = one/(x*x); |
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| 202 | if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ |
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| 203 | R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( |
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| 204 | ra5+s*(ra6+s*ra7)))))); |
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| 205 | S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( |
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| 206 | sa5+s*(sa6+s*(sa7+s*sa8))))))); |
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| 207 | } else { /* |x| >= 1/.35 ~ 2.857143 */ |
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| 208 | if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ |
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| 209 | R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( |
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| 210 | rb5+s*rb6))))); |
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| 211 | S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( |
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| 212 | sb5+s*(sb6+s*sb7)))))); |
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| 213 | } |
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| 214 | GET_FLOAT_WORD(ix,x); |
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| 215 | SET_FLOAT_WORD(z,ix&0xfffff000); |
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| 216 | r = __ieee754_expf(-z*z-(float)0.5625)* |
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| 217 | __ieee754_expf((z-x)*(z+x)+R/S); |
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| 218 | if(hx>0) return r/x; else return two-r/x; |
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| 219 | } else { |
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| 220 | if(hx>0) return tiny*tiny; else return two-tiny; |
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| 221 | } |
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| 222 | } |
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| 223 | |||
| 224 | #ifdef _DOUBLE_IS_32BITS |
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| 225 | |||
| 226 | #ifdef __STDC__ |
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| 227 | double erf(double x) |
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| 228 | #else |
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| 229 | double erf(x) |
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| 230 | double x; |
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| 231 | #endif |
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| 232 | { |
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| 233 | return (double) erff((float) x); |
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| 234 | } |
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| 235 | |||
| 236 | #ifdef __STDC__ |
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| 237 | double erfc(double x) |
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| 238 | #else |
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| 239 | double erfc(x) |
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| 240 | double x; |
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| 241 | #endif |
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| 242 | { |
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| 243 | return (double) erfcf((float) x); |
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| 244 | } |
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| 245 | |||
| 246 | #endif /* defined(_DOUBLE_IS_32BITS) */ |