| Index: fusl/src/math/erff.c
|
| diff --git a/fusl/src/math/erff.c b/fusl/src/math/erff.c
|
| new file mode 100644
|
| index 0000000000000000000000000000000000000000..ed5f3975741595057cbc981d13fd6c43ce11270a
|
| --- /dev/null
|
| +++ b/fusl/src/math/erff.c
|
| @@ -0,0 +1,183 @@
|
| +/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
|
| +/*
|
| + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
| + */
|
| +/*
|
| + * ====================================================
|
| + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
| + *
|
| + * Developed at SunPro, a Sun Microsystems, Inc. business.
|
| + * Permission to use, copy, modify, and distribute this
|
| + * software is freely granted, provided that this notice
|
| + * is preserved.
|
| + * ====================================================
|
| + */
|
| +
|
| +#include "libm.h"
|
| +
|
| +static const float
|
| +erx = 8.4506291151e-01, /* 0x3f58560b */
|
| +/*
|
| + * Coefficients for approximation to erf on [0,0.84375]
|
| + */
|
| +efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
|
| +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
|
| +pp1 = -3.2504209876e-01, /* 0xbea66beb */
|
| +pp2 = -2.8481749818e-02, /* 0xbce9528f */
|
| +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
|
| +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
|
| +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
|
| +qq2 = 6.5022252500e-02, /* 0x3d852a63 */
|
| +qq3 = 5.0813062117e-03, /* 0x3ba68116 */
|
| +qq4 = 1.3249473704e-04, /* 0x390aee49 */
|
| +qq5 = -3.9602282413e-06, /* 0xb684e21a */
|
| +/*
|
| + * Coefficients for approximation to erf in [0.84375,1.25]
|
| + */
|
| +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
|
| +pa1 = 4.1485610604e-01, /* 0x3ed46805 */
|
| +pa2 = -3.7220788002e-01, /* 0xbebe9208 */
|
| +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
|
| +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
|
| +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
|
| +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
|
| +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
|
| +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
|
| +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
|
| +qa4 = 1.2617121637e-01, /* 0x3e013307 */
|
| +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
|
| +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
|
| +/*
|
| + * Coefficients for approximation to erfc in [1.25,1/0.35]
|
| + */
|
| +ra0 = -9.8649440333e-03, /* 0xbc21a093 */
|
| +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
|
| +ra2 = -1.0558626175e+01, /* 0xc128f022 */
|
| +ra3 = -6.2375331879e+01, /* 0xc2798057 */
|
| +ra4 = -1.6239666748e+02, /* 0xc322658c */
|
| +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
|
| +ra6 = -8.1287437439e+01, /* 0xc2a2932b */
|
| +ra7 = -9.8143291473e+00, /* 0xc11d077e */
|
| +sa1 = 1.9651271820e+01, /* 0x419d35ce */
|
| +sa2 = 1.3765776062e+02, /* 0x4309a863 */
|
| +sa3 = 4.3456588745e+02, /* 0x43d9486f */
|
| +sa4 = 6.4538726807e+02, /* 0x442158c9 */
|
| +sa5 = 4.2900814819e+02, /* 0x43d6810b */
|
| +sa6 = 1.0863500214e+02, /* 0x42d9451f */
|
| +sa7 = 6.5702495575e+00, /* 0x40d23f7c */
|
| +sa8 = -6.0424413532e-02, /* 0xbd777f97 */
|
| +/*
|
| + * Coefficients for approximation to erfc in [1/.35,28]
|
| + */
|
| +rb0 = -9.8649431020e-03, /* 0xbc21a092 */
|
| +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
|
| +rb2 = -1.7757955551e+01, /* 0xc18e104b */
|
| +rb3 = -1.6063638306e+02, /* 0xc320a2ea */
|
| +rb4 = -6.3756646729e+02, /* 0xc41f6441 */
|
| +rb5 = -1.0250950928e+03, /* 0xc480230b */
|
| +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
|
| +sb1 = 3.0338060379e+01, /* 0x41f2b459 */
|
| +sb2 = 3.2579251099e+02, /* 0x43a2e571 */
|
| +sb3 = 1.5367296143e+03, /* 0x44c01759 */
|
| +sb4 = 3.1998581543e+03, /* 0x4547fdbb */
|
| +sb5 = 2.5530502930e+03, /* 0x451f90ce */
|
| +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
|
| +sb7 = -2.2440952301e+01; /* 0xc1b38712 */
|
| +
|
| +static float erfc1(float x)
|
| +{
|
| + float_t s,P,Q;
|
| +
|
| + s = fabsf(x) - 1;
|
| + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
| + Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
| + return 1 - erx - P/Q;
|
| +}
|
| +
|
| +static float erfc2(uint32_t ix, float x)
|
| +{
|
| + float_t s,R,S;
|
| + float z;
|
| +
|
| + if (ix < 0x3fa00000) /* |x| < 1.25 */
|
| + return erfc1(x);
|
| +
|
| + x = fabsf(x);
|
| + s = 1/(x*x);
|
| + if (ix < 0x4036db6d) { /* |x| < 1/0.35 */
|
| + R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
| + ra5+s*(ra6+s*ra7))))));
|
| + S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
| + sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
| + } else { /* |x| >= 1/0.35 */
|
| + R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
| + rb5+s*rb6)))));
|
| + S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
| + sb5+s*(sb6+s*sb7))))));
|
| + }
|
| + GET_FLOAT_WORD(ix, x);
|
| + SET_FLOAT_WORD(z, ix&0xffffe000);
|
| + return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x;
|
| +}
|
| +
|
| +float erff(float x)
|
| +{
|
| + float r,s,z,y;
|
| + uint32_t ix;
|
| + int sign;
|
| +
|
| + GET_FLOAT_WORD(ix, x);
|
| + sign = ix>>31;
|
| + ix &= 0x7fffffff;
|
| + if (ix >= 0x7f800000) {
|
| + /* erf(nan)=nan, erf(+-inf)=+-1 */
|
| + return 1-2*sign + 1/x;
|
| + }
|
| + if (ix < 0x3f580000) { /* |x| < 0.84375 */
|
| + if (ix < 0x31800000) { /* |x| < 2**-28 */
|
| + /*avoid underflow */
|
| + return 0.125f*(8*x + efx8*x);
|
| + }
|
| + z = x*x;
|
| + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
| + s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
| + y = r/s;
|
| + return x + x*y;
|
| + }
|
| + if (ix < 0x40c00000) /* |x| < 6 */
|
| + y = 1 - erfc2(ix,x);
|
| + else
|
| + y = 1 - 0x1p-120f;
|
| + return sign ? -y : y;
|
| +}
|
| +
|
| +float erfcf(float x)
|
| +{
|
| + float r,s,z,y;
|
| + uint32_t ix;
|
| + int sign;
|
| +
|
| + GET_FLOAT_WORD(ix, x);
|
| + sign = ix>>31;
|
| + ix &= 0x7fffffff;
|
| + if (ix >= 0x7f800000) {
|
| + /* erfc(nan)=nan, erfc(+-inf)=0,2 */
|
| + return 2*sign + 1/x;
|
| + }
|
| +
|
| + if (ix < 0x3f580000) { /* |x| < 0.84375 */
|
| + if (ix < 0x23800000) /* |x| < 2**-56 */
|
| + return 1.0f - x;
|
| + z = x*x;
|
| + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
| + s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
| + y = r/s;
|
| + if (sign || ix < 0x3e800000) /* x < 1/4 */
|
| + return 1.0f - (x+x*y);
|
| + return 0.5f - (x - 0.5f + x*y);
|
| + }
|
| + if (ix < 0x41e00000) { /* |x| < 28 */
|
| + return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
|
| + }
|
| + return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f;
|
| +}
|
|
|