summaryrefslogtreecommitdiff
path: root/usr/src/libm/src/C/sincos.c
diff options
context:
space:
mode:
Diffstat (limited to 'usr/src/libm/src/C/sincos.c')
-rw-r--r--usr/src/libm/src/C/sincos.c367
1 files changed, 367 insertions, 0 deletions
diff --git a/usr/src/libm/src/C/sincos.c b/usr/src/libm/src/C/sincos.c
new file mode 100644
index 0000000..0143a54
--- /dev/null
+++ b/usr/src/libm/src/C/sincos.c
@@ -0,0 +1,367 @@
+/*
+ * 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 2005 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma ident "@(#)sincos.c 1.13 06/01/23 SMI"
+
+#pragma weak sincos = __sincos
+
+/* INDENT OFF */
+/*
+ * sincos(x,s,c)
+ * Accurate Table look-up algorithm by K.C. Ng, 2000.
+ *
+ * 1. Reduce x to x>0 by cos(-x)=cos(x), sin(-x)=-sin(x).
+ * 2. For 0<= x < 8, let i = (64*x chopped)-10. Let d = x - a[i], where
+ * a[i] is a double that is close to (i+10.5)/64 (and hence |d|< 10.5/64)
+ * and such that sin(a[i]) and cos(a[i]) is close to a double (with error
+ * less than 2**-8 ulp). Then
+ *
+ * cos(x) = cos(a[i]+d) = cos(a[i])cos(d) - sin(a[i])*sin(d)
+ * = TBL_cos_a[i]*(1+QQ1*d^2+QQ2*d^4) -
+ * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5)
+ * = TBL_cos_a[i] + (TBL_cos_a[i]*d^2*(QQ1+QQ2*d^2) -
+ * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5))
+ *
+ * sin(x) = sin(a[i]+d) = sin(a[i])cos(d) + cos(a[i])*sin(d)
+ * = TBL_sin_a[i]*(1+QQ1*d^2+QQ2*d^4) +
+ * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5)
+ * = TBL_sin_a[i] + (TBL_sin_a[i]*d^2*(QQ1+QQ2*d^2) +
+ * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5))
+ *
+ * Note: for x close to n*pi/2, special treatment is need for either
+ * sin or cos:
+ * i in [81, 100] ( pi/2 +-10.5/64 => tiny cos(x) = sin(pi/2-x)
+ * i in [181,200] ( pi +-10.5/64 => tiny sin(x) = sin(pi-x)
+ * i in [282,301] ( 3pi/2+-10.5/64 => tiny cos(x) = sin(x-3pi/2)
+ * i in [382,401] ( 2pi +-10.5/64 => tiny sin(x) = sin(x-2pi)
+ * i in [483,502] ( 5pi/2+-10.5/64 => tiny cos(x) = sin(5pi/2-x)
+ *
+ * 3. For x >= 8.0, use kernel function __rem_pio2 to perform argument
+ * reduction and call __k_sincos_ to compute sin and cos.
+ *
+ * kernel function:
+ * __rem_pio2 ... argument reduction routine
+ * __k_sincos_ ... sine and cosine function on [-pi/4,pi/4]
+ *
+ * Method.
+ * Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
+ * 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
+ * [-pi/2 , +pi/2], and let n = k mod 4.
+ * 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C S/C
+ * 1 C -S -C/S
+ * 2 -S -C S/C
+ * 3 -C S -C/S
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded (less than 1 ulp)
+ */
+
+#include "libm.h"
+
+static const double sc[] = {
+/* ONE = */ 1.0,
+/* NONE = */ -1.0,
+/*
+ * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
+ */
+/* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
+/* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
+/*
+ * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
+ * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
+ * | x |
+ */
+/* P1 = */ -1.666666666666629669805215138920301589656e-0001,
+/* P2 = */ 8.333333332390951295683993455280336376663e-0003,
+/* P3 = */ -1.984126237997976692791551778230098403960e-0004,
+/* P4 = */ 2.753403624854277237649987622848330351110e-0006,
+/*
+ * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
+ */
+/* QQ1 = */ -0.4999999999975492381842911981948418542742729,
+/* QQ2 = */ 0.041666542904352059294545209158357640398771740,
+/* Q1 = */ -0.5,
+/* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
+/* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
+/* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
+/* PIO2_H = */ 1.570796326794896557999,
+/* PIO2_L = */ 6.123233995736765886130e-17,
+/* PIO2_L0 = */ 6.123233995727922165564e-17,
+/* PIO2_L1 = */ 8.843720566135701120255e-29,
+/* PI_H = */ 3.1415926535897931159979634685,
+/* PI_L = */ 1.22464679914735317722606593227425e-16,
+/* PI_L0 = */ 1.22464679914558443311283879205095e-16,
+/* PI_L1 = */ 1.768744113227140223300005233735517376e-28,
+/* PI3O2_H = */ 4.712388980384689673997,
+/* PI3O2_L = */ 1.836970198721029765839e-16,
+/* PI3O2_L0 = */ 1.836970198720396133587e-16,
+/* PI3O2_L1 = */ 6.336322524749201142226e-29,
+/* PI2_H = */ 6.2831853071795862319959269370,
+/* PI2_L = */ 2.44929359829470635445213186454850e-16,
+/* PI2_L0 = */ 2.44929359829116886622567758410190e-16,
+/* PI2_L1 = */ 3.537488226454280446600010467471034752e-28,
+/* PI5O2_H = */ 7.853981633974482789995,
+/* PI5O2_L = */ 3.061616997868382943065e-16,
+/* PI5O2_L0 = */ 3.061616997861941598865e-16,
+/* PI5O2_L1 = */ 6.441344200433640781982e-28,
+};
+/* INDENT ON */
+
+#define ONE sc[0]
+#define PP1 sc[2]
+#define PP2 sc[3]
+#define P1 sc[4]
+#define P2 sc[5]
+#define P3 sc[6]
+#define P4 sc[7]
+#define QQ1 sc[8]
+#define QQ2 sc[9]
+#define Q1 sc[10]
+#define Q2 sc[11]
+#define Q3 sc[12]
+#define Q4 sc[13]
+#define PIO2_H sc[14]
+#define PIO2_L sc[15]
+#define PIO2_L0 sc[16]
+#define PIO2_L1 sc[17]
+#define PI_H sc[18]
+#define PI_L sc[19]
+#define PI_L0 sc[20]
+#define PI_L1 sc[21]
+#define PI3O2_H sc[22]
+#define PI3O2_L sc[23]
+#define PI3O2_L0 sc[24]
+#define PI3O2_L1 sc[25]
+#define PI2_H sc[26]
+#define PI2_L sc[27]
+#define PI2_L0 sc[28]
+#define PI2_L1 sc[29]
+#define PI5O2_H sc[30]
+#define PI5O2_L sc[31]
+#define PI5O2_L0 sc[32]
+#define PI5O2_L1 sc[33]
+#define PoS(x, z) ((x * z) * (PP1 + z * PP2))
+#define PoL(x, z) ((x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)))
+
+extern const double _TBL_sincos[], _TBL_sincosx[];
+
+void
+sincos(double x, double *s, double *c) {
+ double z, y[2], w, t, v, p, q;
+ int i, j, n, hx, ix, lx;
+
+ hx = ((int *)&x)[HIWORD];
+ lx = ((int *)&x)[LOWORD];
+ ix = hx & ~0x80000000;
+
+ if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
+ if (ix < 0x3e400000) { /* |x| < 2**-27 */
+ if ((int)x == 0)
+ *c = ONE;
+ *s = x;
+ } else {
+ z = x * x;
+ if (ix < 0x3f800000) { /* |x| < 0.008 */
+ q = z * (QQ1 + z * QQ2);
+ p = PoS(x, z);
+ } else {
+ q = z * ((Q1 + z * Q2) + (z * z) *
+ (Q3 + z * Q4));
+ p = PoL(x, z);
+ }
+ *c = ONE + q;
+ *s = x + p;
+ }
+ return;
+ }
+
+ n = ix >> 20;
+ i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
+ j = i - 10;
+ if (n < 0x402) { /* |x| < 8 */
+ x = fabs(x);
+ v = x - _TBL_sincosx[j];
+ t = v * v;
+ w = _TBL_sincos[(j<<1)];
+ z = _TBL_sincos[(j<<1)+1];
+ p = v + PoS(v, t);
+ q = t * (QQ1 + t * QQ2);
+ if ((((j - 81) ^ (j - 101)) |
+ ((j - 282) ^ (j - 302)) |
+ ((j - 483) ^ (j - 503)) |
+ ((j - 181) ^ (j - 201)) |
+ ((j - 382) ^ (j - 402))) < 0) {
+ if (j <= 101) {
+ /* near pi/2, cos(x) = sin(pi/2-x) */
+ t = w * q + z * p;
+ *s = (hx >= 0)? w + t : -w - t;
+ p = PIO2_H - x;
+ i = ix - 0x3ff921fb;
+ x = p + PIO2_L;
+ if ((i | ((lx - 0x54442D00) &
+ 0xffffff00)) == 0) {
+ /* very close to pi/2 */
+ x = p + PIO2_L0;
+ *c = x + PIO2_L1;
+ } else {
+ z = x * x;
+ if (((ix - 0x3ff92000) >> 12) == 0) {
+ /* |pi/2-x|<2**-8 */
+ w = PIO2_L + PoS(x, z);
+ } else {
+ w = PIO2_L + PoL(x, z);
+ }
+ *c = p + w;
+ }
+ } else if (j <= 201) {
+ /* near pi, sin(x) = sin(pi-x) */
+ *c = z - (w * p - z * q);
+ p = PI_H - x;
+ i = ix - 0x400921fb;
+ x = p + PI_L;
+ if ((i | ((lx - 0x54442D00) &
+ 0xffffff00)) == 0) {
+ /* very close to pi */
+ x = p + PI_L0;
+ *s = (hx >= 0)? x + PI_L1 :
+ -(x + PI_L1);
+ } else {
+ z = x * x;
+ if (((ix - 0x40092000) >> 11) == 0) {
+ /* |pi-x|<2**-8 */
+ w = PI_L + PoS(x, z);
+ } else {
+ w = PI_L + PoL(x, z);
+ }
+ *s = (hx >= 0)? p + w : -p - w;
+ }
+ } else if (j <= 302) {
+ /* near 3/2pi, cos(x)=sin(x-3/2pi) */
+ t = w * q + z * p;
+ *s = (hx >= 0)? w + t : -w - t;
+ p = x - PI3O2_H;
+ i = ix - 0x4012D97C;
+ x = p - PI3O2_L;
+ if ((i | ((lx - 0x7f332100) &
+ 0xffffff00)) == 0) {
+ /* very close to 3/2pi */
+ x = p - PI3O2_L0;
+ *c = x - PI3O2_L1;
+ } else {
+ z = x * x;
+ if (((ix - 0x4012D800) >> 9) == 0) {
+ /* |3/2pi-x|<2**-8 */
+ w = PoS(x, z) - PI3O2_L;
+ } else {
+ w = PoL(x, z) - PI3O2_L;
+ }
+ *c = p + w;
+ }
+ } else if (j <= 402) {
+ /* near 2pi, sin(x)=sin(x-2pi) */
+ *c = z - (w * p - z * q);
+ p = x - PI2_H;
+ i = ix - 0x401921fb;
+ x = p - PI2_L;
+ if ((i | ((lx - 0x54442D00) &
+ 0xffffff00)) == 0) {
+ /* very close to 2pi */
+ x = p - PI2_L0;
+ *s = (hx >= 0)? x - PI2_L1 :
+ -(x - PI2_L1);
+ } else {
+ z = x * x;
+ if (((ix - 0x40192000) >> 10) == 0) {
+ /* |x-2pi|<2**-8 */
+ w = PoS(x, z) - PI2_L;
+ } else {
+ w = PoL(x, z) - PI2_L;
+ }
+ *s = (hx >= 0)? p + w : -p - w;
+ }
+ } else {
+ /* near 5pi/2, cos(x) = sin(5pi/2-x) */
+ t = w * q + z * p;
+ *s = (hx >= 0)? w + t : -w - t;
+ p = PI5O2_H - x;
+ i = ix - 0x401F6A7A;
+ x = p + PI5O2_L;
+ if ((i | ((lx - 0x29553800) &
+ 0xffffff00)) == 0) {
+ /* very close to pi/2 */
+ x = p + PI5O2_L0;
+ *c = x + PI5O2_L1;
+ } else {
+ z = x * x;
+ if (((ix - 0x401F6A7A) >> 7) == 0) {
+ /* |5pi/2-x|<2**-8 */
+ w = PI5O2_L + PoS(x, z);
+ } else {
+ w = PI5O2_L + PoL(x, z);
+ }
+ *c = p + w;
+ }
+ }
+ } else {
+ *c = z - (w * p - z * q);
+ t = w * q + z * p;
+ *s = (hx >= 0)? w + t : -w - t;
+ }
+ return;
+ }
+
+ if (ix >= 0x7ff00000) {
+ *s = *c = x / x;
+ return;
+ }
+
+ /* argument reduction needed */
+ n = __rem_pio2(x, y);
+ switch (n & 3) {
+ case 0:
+ *s = __k_sincos(y[0], y[1], c);
+ break;
+ case 1:
+ *c = -__k_sincos(y[0], y[1], s);
+ break;
+ case 2:
+ *s = -__k_sincos(y[0], y[1], c);
+ *c = -*c;
+ break;
+ default:
+ *c = __k_sincos(y[0], y[1], s);
+ *s = -*s;
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-18 21:11:46 +0000