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-rw-r--r--src/math/erff.c217
1 files changed, 217 insertions, 0 deletions
diff --git a/src/math/erff.c b/src/math/erff.c
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--- /dev/null
+++ b/src/math/erff.c
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+/* 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,
+half =  5.0000000000e-01, /* 0x3F000000 */
+one  =  1.0000000000e+00, /* 0x3F800000 */
+two  =  2.0000000000e+00, /* 0x40000000 */
+/* 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)+one/x;
+	}
+	if (ix < 0x3f580000) {  /* |x| < 0.84375 */
+		if (ix < 0x31800000) {  /* |x| < 2**-28 */
+			if (ix < 0x04000000)
+				/*avoid underflow */
+				return (float)0.125*((float)8.0*x+efx8*x);
+			return x + efx*x;
+		}
+		z = x*x;
+		r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
+		s = one+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)-one;
+		P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
+		Q = one+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 one - tiny;
+		return tiny - one;
+	}
+	x = fabsf(x);
+	s = one/(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 = one+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 = one+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 - (float)0.5625) * expf((z-x)*(z+x) + R/S);
+	if (hx >= 0)
+		return one - r/x;
+	return  r/x - one;
+}
+
+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) + one/x;
+	}
+
+	if (ix < 0x3f580000) {  /* |x| < 0.84375 */
+		if (ix < 0x23800000)  /* |x| < 2**-56 */
+			return one - x;
+		z = x*x;
+		r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
+		s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+		y = r/s;
+		if (hx < 0x3e800000) {  /* x<1/4 */
+			return one - (x+x*y);
+		} else {
+			r = x*y;
+			r += (x-half);
+			return half - r ;
+		}
+	}
+	if (ix < 0x3fa00000) {  /* 0.84375 <= |x| < 1.25 */
+		s = fabsf(x)-one;
+		P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
+		Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+		if(hx >= 0) {
+			z = one - erx;
+			return z - P/Q;
+		} else {
+			z = erx + P/Q;
+			return one + z;
+		}
+	}
+	if (ix < 0x41e00000) {  /* |x| < 28 */
+		x = fabsf(x);
+		s = one/(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 = one+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 two-tiny;
+			R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
+			     rb5+s*rb6)))));
+			S = one+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 - (float)0.5625) * expf((z-x)*(z+x) + R/S);
+		if (hx > 0)
+			return r/x;
+		return two - r/x;
+	}
+	if (hx > 0)
+		return tiny*tiny;
+	return two - tiny;
+}
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