third_party/musl/src/math/erff.c

/* 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;
}