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;
+}