Add kernel functions for 128-bit long doubles. These could be improved

a bit, but access to a freebsd/sparc64 machine is needed.

Submitted by:	bde and Steve Kargl <sgk@apl.washington.edu> (earlier version)

3 files changed, 239 insertions, 0 deletions

diff --git a/lib/msun/ld128/k_cosl.c b/lib/msun/ld128/k_cosl.c
new file mode 100644
index 0000000..fe57773
--- /dev/null
+++ b/lib/msun/ld128/k_cosl.c
@@ -0,0 +1,61 @@
+/* From: @(#)k_cos.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * ld128 version of k_cos.c.  See ../src/k_cos.c for most comments.
+ */
+
+#include "math_private.h"
+
+/*
+ * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
+ * |cos(x) - c(x))| < 2**-122.0
+ *
+ * 113-bit precision requires more care than 64-bit precision, since
+ * simple methods give a minimax polynomial with coefficient for x^2
+ * that is 1 ulp below 0.5, but we want it to be precisely 0.5.  See
+ * ../ld80/k_cosl.c for more details.
+ */
+static const double
+one = 1.0;
+
+static const long double
+C1 =  0.04166666666666666666666666666666658424671L,
+C2 = -0.001388888888888888888888888888863490893732L,
+C3 =  0.00002480158730158730158730158600795304914210L,
+C4 = -0.2755731922398589065255474947078934284324e-6L,
+C5 =  0.2087675698786809897659225313136400793948e-8L,
+C6 = -0.1147074559772972315817149986812031204775e-10L,
+C7 =  0.4779477332386808976875457937252120293400e-13L;
+
+static const double
+C8 = -0.1561920696721507929516718307820958119868e-15,
+C9 =  0.4110317413744594971475941557607804508039e-18,
+C10 = -0.8896592467191938803288521958313920156409e-21,
+C11 =  0.1601061435794535138244346256065192782581e-23;
+
+long double
+__kernel_cosl(long double x, long double y)
+{
+	long double hz,z,r,w;
+
+	z  = x*x;
+	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
+	    z*(C8+z*(C9+z*(C10+z*C11))))))))));
+	hz = 0.5*z;
+	w  = one-hz;
+	return w + (((one-w)-hz) + (z*r-x*y));
+}
diff --git a/lib/msun/ld128/k_sinl.c b/lib/msun/ld128/k_sinl.c
new file mode 100644
index 0000000..09472d6
--- /dev/null
+++ b/lib/msun/ld128/k_sinl.c
@@ -0,0 +1,59 @@
+/* From: @(#)k_sin.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * ld128 version of k_sin.c.  See ../src/k_sin.c for most comments.
+ */
+
+#include "math_private.h"
+
+static const double
+half =  0.5;
+
+/*
+ * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37]
+ * |sin(x)/x - s(x)| < 2**-122.1
+ *
+ * See ../ld80/k_cosl.c for more details about the polynomial.
+ */
+static const long double
+S1 = -0.16666666666666666666666666666666666606732416116558L,
+S2 =  0.0083333333333333333333333333333331135404851288270047L,
+S3 = -0.00019841269841269841269841269839935785325638310428717L,
+S4 =  0.27557319223985890652557316053039946268333231205686e-5L,
+S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
+S6 =  0.16059043836821614596571832194524392581082444805729e-9L,
+S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
+S8 =  0.28114572543451292625024967174638477283187397621303e-14L;
+
+static const double
+S9  = -0.82206352458348947812512122163446202498005154296863e-17,
+S10 =  0.19572940011906109418080609928334380560135358385256e-19,
+S11 = -0.38680813379701966970673724299207480965452616911420e-22,
+S12 =  0.64038150078671872796678569586315881020659912139412e-25;
+
+long double
+__kernel_sinl(long double x, long double y, int iy)
+{
+	long double z,r,v;
+
+	z	=  x*x;
+	v	=  z*x;
+	r	=  S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+
+	    z*(S9+z*(S10+z*(S11+z*S12)))))))));
+	if(iy==0) return x+v*(S1+z*r);
+	else      return x-((z*(half*y-v*r)-y)-v*S1);
+}
diff --git a/lib/msun/ld128/k_tanl.c b/lib/msun/ld128/k_tanl.c
new file mode 100644
index 0000000..d7ec0b9
--- /dev/null
+++ b/lib/msun/ld128/k_tanl.c
@@ -0,0 +1,119 @@
+/* From: @(#)k_tan.c 1.5 04/04/22 SMI */
+
+/*
+ * ====================================================
+ * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * ld128 version of k_tan.c.  See ../src/k_tan.c for most comments.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/*
+ * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
+ * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
+ *
+ * See ../ld80/k_cosl.c for more details about the polynomial.
+ */
+static const long double
+T3 = 0x1.5555555555555555555555555553p-2L,
+T5 = 0x1.1111111111111111111111111eb5p-3L,
+T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
+T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
+T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
+T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
+T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
+T17 = 0x1.355824803674477dfcf726649efep-11L,
+T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
+T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
+T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
+T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
+T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
+T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
+T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
+T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
+T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
+T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
+pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
+pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
+
+static const double
+T39 =  0.000000028443389121318352,	/*  0x1e8a7592977938.0p-78 */
+T41 =  0.000000011981013102001973,	/*  0x19baa1b1223219.0p-79 */
+T43 =  0.0000000038303578044958070,	/*  0x107385dfb24529.0p-80 */
+T45 =  0.0000000034664378216909893,	/*  0x1dc6c702a05262.0p-81 */
+T47 = -0.0000000015090641701997785,	/* -0x19ecef3569ebb6.0p-82 */
+T49 =  0.0000000029449552300483952,	/*  0x194c0668da786a.0p-81 */
+T51 = -0.0000000022006995706097711,	/* -0x12e763b8845268.0p-81 */
+T53 =  0.0000000015468200913196612,	/*  0x1a92fc98c29554.0p-82 */
+T55 = -0.00000000061311613386849674,	/* -0x151106cbc779a9.0p-83 */
+T57 =  1.4912469681508012e-10;		/*  0x147edbdba6f43a.0p-85 */
+
+long double
+__kernel_tanl(long double x, long double y, int iy) {
+	long double z, r, v, w, s;
+	long double osign;
+	int i;
+
+	iy = (iy == 1 ? -1 : 1);	/* XXX recover original interface */
+	osign = (x >= 0 ? 1.0 : -1.0);	/* XXX slow, probably wrong for -0 */
+	if (fabsl(x) >= 0.67434) {
+		if (x < 0) {
+			x = -x;
+			y = -y;
+		}
+		z = pio4 - x;
+		w = pio4lo - y;
+		x = z + w;
+		y = 0.0;
+		i = 1;
+	} else
+		i = 0;
+	z = x * x;
+	w = z * z;
+	r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
+	    w * (T25 + w * (T29 + w * (T33 +
+	    w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 +
+	    w * T57))))))))))));
+	v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
+	    w * (T27 + w * (T31 + w * (T35 +
+	    w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))));
+	s = z * x;
+	r = y + z * (s * (r + v) + y);
+	r += T3 * s;
+	w = x + r;
+	if (i == 1) {
+		v = (long double) iy;
+		return osign *
+			(v - 2.0 * (x - (w * w / (w + v) - r)));
+	}
+	if (iy == 1)
+		return w;
+	else {
+		/*
+		 * if allow error up to 2 ulp, simply return
+		 * -1.0 / (x+r) here
+		 */
+		/* compute -1.0 / (x+r) accurately */
+		long double a, t;
+		z = w;
+		z = z + 0x1p32 - 0x1p32;
+		v = r - (z - x);	/* z+v = r+x */
+		t = a = -1.0 / w;	/* a = -1.0/w */
+		t = t + 0x1p32 - 0x1p32;
+		s = 1.0 + t * z;
+		return t + a * (s + t * v);
+	}
+}