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, 342 insertions, 0 deletions

diff --git a/src/math/j1f.c b/src/math/j1f.c
new file mode 100644
index 00000000..0323ec78
--- /dev/null
+++ b/src/math/j1f.c
@@ -0,0 +1,342 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.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 float ponef(float), qonef(float);
+
+static const float
+huge      = 1e30,
+one       = 1.0,
+invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
+tpi       = 6.3661974669e-01, /* 0x3f22f983 */
+/* R0/S0 on [0,2] */
+r00 = -6.2500000000e-02, /* 0xbd800000 */
+r01 =  1.4070566976e-03, /* 0x3ab86cfd */
+r02 = -1.5995563444e-05, /* 0xb7862e36 */
+r03 =  4.9672799207e-08, /* 0x335557d2 */
+s01 =  1.9153760746e-02, /* 0x3c9ce859 */
+s02 =  1.8594678841e-04, /* 0x3942fab6 */
+s03 =  1.1771846857e-06, /* 0x359dffc2 */
+s04 =  5.0463624390e-09, /* 0x31ad6446 */
+s05 =  1.2354227016e-11; /* 0x2d59567e */
+
+static const float zero = 0.0;
+
+float j1f(float x)
+{
+	float z,s,c,ss,cc,r,u,v,y;
+	int32_t hx,ix;
+
+	GET_FLOAT_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+	if (ix >= 0x7f800000)
+		return one/x;
+	y = fabsf(x);
+	if (ix >= 0x40000000) {  /* |x| >= 2.0 */
+		s = sinf(y);
+		c = cosf(y);
+		ss = -s-c;
+		cc = s-c;
+		if (ix < 0x7f000000) {  /* make sure y+y not overflow */
+			z = cosf(y+y);
+			if (s*c > zero)
+				cc = z/ss;
+			else
+				ss = z/cc;
+		}
+		/*
+		 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
+		 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
+		 */
+		if (ix > 0x80000000)
+			z = (invsqrtpi*cc)/sqrtf(y);
+		else {
+			u = ponef(y);
+			v = qonef(y);
+			z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
+		}
+		if (hx < 0)
+			return -z;
+		return  z;
+	}
+	if (ix < 0x32000000) {  /* |x| < 2**-27 */
+		/* raise inexact if x!=0 */
+		if (huge+x > one)
+			return (float)0.5*x;
+	}
+	z = x*x;
+	r = z*(r00+z*(r01+z*(r02+z*r03)));
+	s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
+	r *= x;
+	return x*(float)0.5 + r/s;
+}
+
+static const float U0[5] = {
+ -1.9605709612e-01, /* 0xbe48c331 */
+  5.0443872809e-02, /* 0x3d4e9e3c */
+ -1.9125689287e-03, /* 0xbafaaf2a */
+  2.3525259166e-05, /* 0x37c5581c */
+ -9.1909917899e-08, /* 0xb3c56003 */
+};
+static const float V0[5] = {
+  1.9916731864e-02, /* 0x3ca3286a */
+  2.0255257550e-04, /* 0x3954644b */
+  1.3560879779e-06, /* 0x35b602d4 */
+  6.2274145840e-09, /* 0x31d5f8eb */
+  1.6655924903e-11, /* 0x2d9281cf */
+};
+
+float y1f(float x)
+{
+	float z,s,c,ss,cc,u,v;
+	int32_t hx,ix;
+
+	GET_FLOAT_WORD(hx, x);
+	ix = 0x7fffffff & hx;
+	/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
+	if (ix >= 0x7f800000)
+		return one/(x+x*x);
+	if (ix == 0)
+		return -one/zero;
+	if (hx < 0)
+		return zero/zero;
+	if (ix >= 0x40000000) {  /* |x| >= 2.0 */
+		s = sinf(x);
+		c = cosf(x);
+		ss = -s-c;
+		cc = s-c;
+		if (ix < 0x7f000000) {  /* make sure x+x not overflow */
+			z = cosf(x+x);
+			if (s*c > zero)
+				cc = z/ss;
+			else
+				ss = z/cc;
+		}
+		/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
+		 * where x0 = x-3pi/4
+		 *      Better formula:
+		 *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+		 *                      =  1/sqrt(2) * (sin(x) - cos(x))
+		 *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+		 *                      = -1/sqrt(2) * (cos(x) + sin(x))
+		 * To avoid cancellation, use
+		 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+		 * to compute the worse one.
+		 */
+		if (ix > 0x48000000)
+			z = (invsqrtpi*ss)/sqrtf(x);
+		else {
+			u = ponef(x);
+			v = qonef(x);
+			z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
+		}
+		return z;
+	}
+	if (ix <= 0x24800000)  /* x < 2**-54 */
+		return -tpi/x;
+	z = x*x;
+	u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
+	v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
+	return x*(u/v) + tpi*(j1f(x)*logf(x)-one/x);
+}
+
+/* For x >= 8, the asymptotic expansions of pone is
+ *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
+ * We approximate pone by
+ *      pone(x) = 1 + (R/S)
+ * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ *        S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
+ */
+
+static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+  0.0000000000e+00, /* 0x00000000 */
+  1.1718750000e-01, /* 0x3df00000 */
+  1.3239480972e+01, /* 0x4153d4ea */
+  4.1205184937e+02, /* 0x43ce06a3 */
+  3.8747453613e+03, /* 0x45722bed */
+  7.9144794922e+03, /* 0x45f753d6 */
+};
+static const float ps8[5] = {
+  1.1420736694e+02, /* 0x42e46a2c */
+  3.6509309082e+03, /* 0x45642ee5 */
+  3.6956207031e+04, /* 0x47105c35 */
+  9.7602796875e+04, /* 0x47bea166 */
+  3.0804271484e+04, /* 0x46f0a88b */
+};
+
+static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+  1.3199052094e-11, /* 0x2d68333f */
+  1.1718749255e-01, /* 0x3defffff */
+  6.8027510643e+00, /* 0x40d9b023 */
+  1.0830818176e+02, /* 0x42d89dca */
+  5.1763616943e+02, /* 0x440168b7 */
+  5.2871520996e+02, /* 0x44042dc6 */
+};
+static const float ps5[5] = {
+  5.9280597687e+01, /* 0x426d1f55 */
+  9.9140142822e+02, /* 0x4477d9b1 */
+  5.3532670898e+03, /* 0x45a74a23 */
+  7.8446904297e+03, /* 0x45f52586 */
+  1.5040468750e+03, /* 0x44bc0180 */
+};
+
+static const float pr3[6] = {
+  3.0250391081e-09, /* 0x314fe10d */
+  1.1718686670e-01, /* 0x3defffab */
+  3.9329774380e+00, /* 0x407bb5e7 */
+  3.5119403839e+01, /* 0x420c7a45 */
+  9.1055007935e+01, /* 0x42b61c2a */
+  4.8559066772e+01, /* 0x42423c7c */
+};
+static const float ps3[5] = {
+  3.4791309357e+01, /* 0x420b2a4d */
+  3.3676245117e+02, /* 0x43a86198 */
+  1.0468714600e+03, /* 0x4482dbe3 */
+  8.9081134033e+02, /* 0x445eb3ed */
+  1.0378793335e+02, /* 0x42cf936c */
+};
+
+static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+  1.0771083225e-07, /* 0x33e74ea8 */
+  1.1717621982e-01, /* 0x3deffa16 */
+  2.3685150146e+00, /* 0x401795c0 */
+  1.2242610931e+01, /* 0x4143e1bc */
+  1.7693971634e+01, /* 0x418d8d41 */
+  5.0735230446e+00, /* 0x40a25a4d */
+};
+static const float ps2[5] = {
+  2.1436485291e+01, /* 0x41ab7dec */
+  1.2529022980e+02, /* 0x42fa9499 */
+  2.3227647400e+02, /* 0x436846c7 */
+  1.1767937469e+02, /* 0x42eb5bd7 */
+  8.3646392822e+00, /* 0x4105d590 */
+};
+
+static float ponef(float x)
+{
+	const float *p,*q;
+	float z,r,s;
+	int32_t ix;
+
+	GET_FLOAT_WORD(ix, x);
+	ix &= 0x7fffffff;
+	if      (ix >= 0x41000000){p = pr8; q = ps8;}
+	else if (ix >= 0x40f71c58){p = pr5; q = ps5;}
+	else if (ix >= 0x4036db68){p = pr3; q = ps3;}
+	else if (ix >= 0x40000000){p = pr2; q = ps2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+	return one + r/s;
+}
+
+/* For x >= 8, the asymptotic expansions of qone is
+ *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ *      qone(x) = s*(0.375 + (R/S))
+ * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ *        S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
+ */
+
+static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+  0.0000000000e+00, /* 0x00000000 */
+ -1.0253906250e-01, /* 0xbdd20000 */
+ -1.6271753311e+01, /* 0xc1822c8d */
+ -7.5960174561e+02, /* 0xc43de683 */
+ -1.1849806641e+04, /* 0xc639273a */
+ -4.8438511719e+04, /* 0xc73d3683 */
+};
+static const float qs8[6] = {
+  1.6139537048e+02, /* 0x43216537 */
+  7.8253862305e+03, /* 0x45f48b17 */
+  1.3387534375e+05, /* 0x4802bcd6 */
+  7.1965775000e+05, /* 0x492fb29c */
+  6.6660125000e+05, /* 0x4922be94 */
+ -2.9449025000e+05, /* 0xc88fcb48 */
+};
+
+static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ -2.0897993405e-11, /* 0xadb7d219 */
+ -1.0253904760e-01, /* 0xbdd1fffe */
+ -8.0564479828e+00, /* 0xc100e736 */
+ -1.8366960144e+02, /* 0xc337ab6b */
+ -1.3731937256e+03, /* 0xc4aba633 */
+ -2.6124443359e+03, /* 0xc523471c */
+};
+static const float qs5[6] = {
+  8.1276550293e+01, /* 0x42a28d98 */
+  1.9917987061e+03, /* 0x44f8f98f */
+  1.7468484375e+04, /* 0x468878f8 */
+  4.9851425781e+04, /* 0x4742bb6d */
+  2.7948074219e+04, /* 0x46da5826 */
+ -4.7191835938e+03, /* 0xc5937978 */
+};
+
+static const float qr3[6] = {
+ -5.0783124372e-09, /* 0xb1ae7d4f */
+ -1.0253783315e-01, /* 0xbdd1ff5b */
+ -4.6101160049e+00, /* 0xc0938612 */
+ -5.7847221375e+01, /* 0xc267638e */
+ -2.2824453735e+02, /* 0xc3643e9a */
+ -2.1921012878e+02, /* 0xc35b35cb */
+};
+static const float qs3[6] = {
+  4.7665153503e+01, /* 0x423ea91e */
+  6.7386511230e+02, /* 0x4428775e */
+  3.3801528320e+03, /* 0x45534272 */
+  5.5477290039e+03, /* 0x45ad5dd5 */
+  1.9031191406e+03, /* 0x44ede3d0 */
+ -1.3520118713e+02, /* 0xc3073381 */
+};
+
+static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+ -1.7838172539e-07, /* 0xb43f8932 */
+ -1.0251704603e-01, /* 0xbdd1f475 */
+ -2.7522056103e+00, /* 0xc0302423 */
+ -1.9663616180e+01, /* 0xc19d4f16 */
+ -4.2325313568e+01, /* 0xc2294d1f */
+ -2.1371921539e+01, /* 0xc1aaf9b2 */
+};
+static const float qs2[6] = {
+  2.9533363342e+01, /* 0x41ec4454 */
+  2.5298155212e+02, /* 0x437cfb47 */
+  7.5750280762e+02, /* 0x443d602e */
+  7.3939318848e+02, /* 0x4438d92a */
+  1.5594900513e+02, /* 0x431bf2f2 */
+ -4.9594988823e+00, /* 0xc09eb437 */
+};
+
+static float qonef(float x)
+{
+	const float *p,*q;
+	float s,r,z;
+	int32_t ix;
+
+	GET_FLOAT_WORD(ix, x);
+	ix &= 0x7fffffff;
+	if      (ix >= 0x40200000){p = qr8; q = qs8;}
+	else if (ix >= 0x40f71c58){p = qr5; q = qs5;}
+	else if (ix >= 0x4036db68){p = qr3; q = qs3;}
+	else if (ix >= 0x40000000){p = qr2; q = qs2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+	return ((float).375 + r/s)/x;
+}