693 Opensource replacement of sunwlibm

Reviewed by: Igor Kozhukhov ikozhukhov@gmail.com
Reviewed by: Keith M Wesolowski <keith.wesolowski@joyent.com>
Reviewed by: Richard Lowe <richlowe@richlowe.net>
Approved by: Dan McDonald <danmcd@omniti.com>

1 files changed, 195 insertions, 0 deletions

diff --git a/usr/src/lib/libm/common/Q/sincospil.c b/usr/src/lib/libm/common/Q/sincospil.c
new file mode 100644
index 0000000000..fda3d45490
--- /dev/null
+++ b/usr/src/lib/libm/common/Q/sincospil.c
@@ -0,0 +1,195 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak sincospil = __sincospil
+
+/*
+ * void sincospil(long double x, long double *s, long double *c)
+ * *s = sinl(pi*x); *c = cosl(pi*x);
+ *
+ * Algorithm, 10/17/2002, K.C. Ng
+ * ------------------------------
+ * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
+ *	1. If y == z, then x is a multiple of pi/4. Return the following values:
+ *             ---------------------------------------------------
+ *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
+ *             ---------------------------------------------------
+ *              000  0.00       +0 ___       +1 ___      +0
+ *              001  0.25       +\/0.5       +\/0.5      +1
+ *              010  0.50       +1 ___       +0 ___      +inf
+ *              011  0.75       +\/0.5       -\/0.5      -1
+ *              100  1.00       -0 ___       -1 ___      +0
+ *              101  1.25       -\/0.5       -\/0.5      +1
+ *              110  1.50       -1 ___       -0 ___      +inf
+ *              111  1.75       -\/0.5       +\/0.5      -1
+ *             ---------------------------------------------------
+ *      2. Otherwise,
+ *             ---------------------------------------------------
+ *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
+ *             ---------------------------------------------------
+ *              000  (y-z)/4	 sinpi(t)     cospi(t)    tanpi(t)
+ *              001  (z+1-y)/4   cospi(t)     sinpi(t)	  1/tanpi(t)
+ *              010  (y-z)/4	 cospi(t)    -sinpi(t)   -1/tanpi(t)
+ *              011  (z+1-y)/4	 sinpi(t)    -cospi(t)	 -tanpi(t)
+ *              100  (y-z)/4	-sinpi(t)    -cospi(t)    tanpi(t)
+ *              101  (z+1-y)/4	-cospi(t)    -sinpi(t)	  1/tanpi(t)
+ *              110  (y-z)/4	-cospi(t)     sinpi(t)	 -1/tanpi(t)
+ *              111  (z+1-y)/4	-sinpi(t)     cospi(t)	 -tanpi(t)
+ *             ---------------------------------------------------
+ *
+ * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
+ * This will return a result with error slightly more than one ulp (but less
+ * than 2 ulp). If one wants accurate result,  one may break up pi*t in
+ * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
+ * instead.
+ */
+
+#include "libm.h"
+#include "longdouble.h"
+
+#define	I(q, m)	((int *) &(q))[m]
+#define	U(q, m)	((unsigned *) &(q))[m]
+#if defined(__LITTLE_ENDIAN) || defined(__x86)
+#define	LDBL_MOST_SIGNIF_I(ld)	((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
+#define	LDBL_LEAST_SIGNIF_U(ld)	U(ld, 0)
+#define	PREC	64
+#define	PRECM1	63
+#define	PRECM2	62
+static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
+#else
+#define	LDBL_MOST_SIGNIF_I(ld)	I(ld, 0)
+#define	LDBL_LEAST_SIGNIF_U(ld)	U(ld, sizeof (long double) / sizeof (int) - 1)
+#define	PREC	113
+#define	PRECM1	112
+#define	PRECM2	111
+static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
+#endif
+
+static const long double
+zero	= 0.0L,
+quater	= 0.25L,
+one	= 1.0L,
+pi	= 3.141592653589793238462643383279502884197e+0000L,
+sqrth	= 0.707106781186547524400844362104849039284835937688474,
+tiny	= 1.0e-100;
+
+void
+sincospil(long double x, long double *s, long double *c) {
+	long double y, z, t;
+	int hx, n, k;
+	unsigned lx;
+
+	hx = LDBL_MOST_SIGNIF_I(x);
+	lx = LDBL_LEAST_SIGNIF_U(x);
+	k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
+	if (k >= PRECM2) {		/* |x| >= 2**(Prec-2) */
+		if (k >= 16384) {
+			*s = *c = x - x;
+		} else {
+			if (k >= PREC) {
+				*s = zero;
+				*c = one;
+			} else if (k == PRECM1) {
+				if ((lx & 1) == 0) {
+					*s = zero;
+					*c = one;
+				} else {
+					*s = -zero;
+					*c = -one;
+				}
+			} else {	/* k = Prec - 2 */
+				if ((lx & 1) == 0) {
+					*s = zero;
+					*c = one;
+				} else {
+					*s = one;
+					*c = zero;
+				}
+				if ((lx & 2) != 0) {
+					*s = -*s;
+					*c = -*c;
+				}
+			}
+		}
+	} else if (k < -2) 	/* |x| < 0.25 */
+		*s = __k_sincosl(pi * fabsl(x), zero, c);
+	else {
+		/* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
+		y = 4.0L * fabsl(x);
+		if (k < PRECM2) {
+			z = y + twoPRECM2;
+			n = LDBL_LEAST_SIGNIF_U(z) & 7;	/* 3 LSb of z */
+			t = z - twoPRECM2;
+			k = 0;
+			if (t == y)
+				k = 1;
+			else if (t > y) {
+				n -= 1;
+				t = quater + (y - t) * quater;
+			} else
+				t = (y - t) * quater;
+		} else { 	/* k = Prec-3 */
+			n = LDBL_LEAST_SIGNIF_U(y) & 7;	/* 3 LSb of z */
+			k = 1;
+		}
+		if (k) {	/* x = N/4 */
+			if ((n & 1) != 0)
+				*s = *c = sqrth + tiny;
+			else
+				if ((n & 2) == 0) {
+					*s = zero;
+					*c = one;
+				} else {
+					*s = one;
+					*c = zero;
+				}
+			if ((n & 4) != 0)
+				*s = -*s;
+			if (((n + 1) & 4) != 0)
+				*c = -*c;
+		} else {
+			if ((n & 1) != 0)
+				t = quater - t;
+			if (((n + (n & 1)) & 2) == 0)
+				*s = __k_sincosl(pi * t, zero, c);
+			else
+				*c = __k_sincosl(pi * t, zero, s);
+			if ((n & 4) != 0)
+				*s = -*s;
+			if (((n + 2) & 4) != 0)
+				*c = -*c;
+		}
+	}
+	if (hx < 0)
+		*s = -*s;
+}
+#undef U
+#undef LDBL_LEAST_SIGNIF_U
+#undef I
+#undef LDBL_MOST_SIGNIF_I