/* 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
tiny = 1e-30,
/* c = (subfloat)0.84506291151 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
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 */
float erff(float x)
{
int32_t hx,ix,i;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix >= 0x7f800000) {
/* erf(nan)=nan, erf(+-inf)=+-1 */
i = ((uint32_t)hx>>31)<<1;
return (float)(1-i)+1.0f/x;
}
if (ix < 0x3f580000) { /* |x| < 0.84375 */
if (ix < 0x31800000) { /* |x| < 2**-28 */
if (ix < 0x04000000)
/*avoid underflow */
return 0.125f*(8.0f*x + efx8*x);
return x + efx*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;
return x + x*y;
}
if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-1.0f;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = 1.0f+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if (hx >= 0)
return erx + P/Q;
return -erx - P/Q;
}
if (ix >= 0x40c00000) { /* inf > |x| >= 6 */
if (hx >= 0)
return 1.0f - tiny;
return tiny - 1.0f;
}
x = fabsf(x);
s = 1.0f/(x*x);
if (ix < 0x4036DB6E) { /* |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&0xfffff000);
r = expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S);
if (hx >= 0)
return 1.0f - r/x;
return r/x - 1.0f;
}
float erfcf(float x)
{
int32_t hx,ix;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix >= 0x7f800000) {
/* erfc(nan)=nan, erfc(+-inf)=0,2 */
return (float)(((uint32_t)hx>>31)<<1) + 1.0f/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 (hx < 0x3e800000) { /* x<1/4 */
return 1.0f - (x+x*y);
} else {
r = x*y;
r += (x-0.5f);
return 0.5f - r ;
}
}
if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-1.0f;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = 1.0f+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx >= 0) {
z = 1.0f - erx;
return z - P/Q;
} else {
z = erx + P/Q;
return 1.0f + z;
}
}
if (ix < 0x41e00000) { /* |x| < 28 */
x = fabsf(x);
s = 1.0f/(x*x);
if (ix < 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
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/.35 ~ 2.857143 */
if (hx < 0 && ix >= 0x40c00000) /* x < -6 */
return 2.0f-tiny;
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&0xfffff000);
r = expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S);
if (hx > 0)
return r/x;
return 2.0f - r/x;
}
if (hx > 0)
return tiny*tiny;
return 2.0f - tiny;
}
