/* 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" // for GET_FLOAT_WORD, SET_FLOAT_WORD

#include <math.h>   // for float_t, expf, fabsf, erfcf, erff
#include <stdint.h> // for uint32_t

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;
}