| /* 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; |
| } |