xref: /titanic_51/usr/src/lib/libm/common/C/sincospi.c (revision 7509ca605713ac7f244b0e812b1712dd25f04da1)
1 /*
2  * CDDL HEADER START
3  *
4  * The contents of this file are subject to the terms of the
5  * Common Development and Distribution License (the "License").
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
17  * information: Portions Copyright [yyyy] [name of copyright owner]
18  *
19  * CDDL HEADER END
20  */
21 
22 /*
23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24  */
25 /*
26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29 
30 /* INDENT OFF */
31 /*
32  * void sincospi(double x, double *s, double *c)
33  * *s = sin(pi*x); *c = cos(pi*x);
34  *
35  * Algorithm, 10/17/2002, K.C. Ng
36  * ------------------------------
37  * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
38  *	1. If y == z, then x is a multiple of pi/4. Return the following values:
39  *             ---------------------------------------------------
40  *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
41  *             ---------------------------------------------------
42  *              000  0.00       +0 ___       +1 ___      +0
43  *              001  0.25       +\/0.5       +\/0.5      +1
44  *              010  0.50       +1 ___       +0 ___      +inf
45  *              011  0.75       +\/0.5       -\/0.5      -1
46  *              100  1.00       -0 ___       -1 ___      +0
47  *              101  1.25       -\/0.5       -\/0.5      +1
48  *              110  1.50       -1 ___       -0 ___      +inf
49  *              111  1.75       -\/0.5       +\/0.5      -1
50  *             ---------------------------------------------------
51  *      2. Otherwise,
52  *             ---------------------------------------------------
53  *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
54  *             ---------------------------------------------------
55  *              000  (y-z)/4	 sinpi(t)     cospi(t)    tanpi(t)
56  *              001  (z+1-y)/4   cospi(t)     sinpi(t)	  1/tanpi(t)
57  *              010  (y-z)/4	 cospi(t)    -sinpi(t)   -1/tanpi(t)
58  *              011  (z+1-y)/4	 sinpi(t)    -cospi(t)	 -tanpi(t)
59  *              100  (y-z)/4	-sinpi(t)    -cospi(t)    tanpi(t)
60  *              101  (z+1-y)/4	-cospi(t)    -sinpi(t)	  1/tanpi(t)
61  *              110  (y-z)/4	-cospi(t)     sinpi(t)	 -1/tanpi(t)
62  *              111  (z+1-y)/4	-sinpi(t)     cospi(t)	 -tanpi(t)
63  *             ---------------------------------------------------
64  *
65  * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
66  * This will return a result with error slightly more than one ulp (but less
67  * than 2 ulp). If one wants accurate result,  one may break up pi*t in
68  * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
69  * instead.
70  */
71 
72 #include "libm.h"
73 #include "libm_protos.h"
74 #include "libm_macros.h"
75 #include <math.h>
76 #if defined(__SUNPRO_C)
77 #include <sunmath.h>
78 #endif
79 
80 static const double
81 	pi 	= 3.14159265358979323846,	/* 400921FB,54442D18 */
82 	sqrth_h = 0.70710678118654757273731092936941422522068023681640625,
83 	sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17;
84 /* INDENT ON */
85 
86 void
87 sincospi(double x, double *s, double *c) {
88 	double y, z, t;
89 	int n, ix, k;
90 	int hx = ((int *) &x)[HIWORD];
91 	unsigned h, lx = ((unsigned *) &x)[LOWORD];
92 
93 	ix = hx & ~0x80000000;
94 	n = (ix >> 20) - 0x3ff;
95 	if (n >= 51) {			/* |x| >= 2**51 */
96 		if (n >= 1024)
97 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
98 			*s = *c = ix >= 0x7ff80000 ? x : x - x;
99 			/* assumes sparc-like QNaN */
100 #else
101 			*s = *c = x - x;
102 #endif
103 		else {
104 			if (n >= 53)  {
105 				*s = 0.0;
106 				*c = 1.0;
107 			}
108 			else if (n == 52)  {
109 				if ((lx & 1) == 0) {
110 					*s = 0.0;
111 					*c = 1.0;
112 				}
113 				else {
114 					*s = -0.0;
115 					*c = -1.0;
116 				}
117 			}
118 			else {	/* n == 51 */
119 				if ((lx & 1) == 0) {
120 					*s = 0.0;
121 					*c = 1.0;
122 				}
123 				else {
124 					*s = 1.0;
125 					*c = 0.0;
126 				}
127 				if ((lx & 2) != 0) {
128 					*s = -*s;
129 					*c = -*c;
130 				}
131 			}
132 		}
133 	}
134 	else if (n < -2) 	/* |x| < 0.25 */
135 		*s = __k_sincos(pi * fabs(x), 0.0, c);
136 	else {
137 		/* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
138 		if (ix < 0x41C00000) {		/* |x| < 2**29 */
139 			y = 4.0 * fabs(x);
140 			n = (int) y;		/* exact */
141 			z = (double) n;
142 			k = z == y;
143 			t = (y - z) * 0.25;
144 		}
145 		else {				/* 2**29 <= |x| < 2**51 */
146 			y = fabs(x);
147 			k = 50 - n;
148 			n = lx >> k;
149 			h = n << k;
150 			((unsigned *) &z)[LOWORD] = h;
151 			((int *) &z)[HIWORD] = ix;
152 			k = h == lx;
153 			t = y - z;
154 		}
155 		if (k) {			/* x = N/4 */
156 			if ((n & 1) != 0)
157 				*s = *c = sqrth_h + sqrth_l;
158 			else
159 				if ((n & 2) == 0) {
160 					*s = 0.0;
161 					*c = 1.0;
162 				}
163 				else {
164 					*s = 1.0;
165 					*c = 0.0;
166 				}
167 				y = (n & 2) == 0 ? 0.0 : 1.0;
168 				if ((n & 4) != 0)
169 					*s = -*s;
170 				if (((n + 1) & 4) != 0)
171 					*c = -*c;
172 		}
173 		else {
174 			if ((n & 1) != 0)
175 				t = 0.25 - t;
176 			if (((n + (n & 1)) & 2) == 0)
177 				*s = __k_sincos(pi * t, 0.0, c);
178 			else
179 				*c = __k_sincos(pi * t, 0.0, s);
180 				if ((n & 4) != 0)
181 					*s = -*s;
182 				if (((n + 2) & 4) != 0)
183 					*c = -*c;
184 		}
185 	}
186 	if (hx < 0)
187 		*s = -*s;
188 }
189