first commit of the new libm!

thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).

based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.

various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.

1 files changed, 217 insertions, 0 deletions

diff --git a/src/math/erff.c b/src/math/erff.c
new file mode 100644
index 00000000..e4e353d7
--- /dev/null
+++ b/src/math/erff.c
@@ -0,0 +1,217 @@
+/* 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;
+}