xref: /illumos-gate/usr/src/lib/libm/common/C/sincospi.c (revision 709db5a3)
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
sincospi(double x,double * s,double * c)87 sincospi(double x, double *s, double *c)
88 {
89 	double y, z, t;
90 	int n, ix, k;
91 	int hx = ((int *)&x)[HIWORD];
92 	unsigned h, lx = ((unsigned *)&x)[LOWORD];
93 
94 	ix = hx & ~0x80000000;
95 	n = (ix >> 20) - 0x3ff;
96 	if (n >= 51) {			/* |x| >= 2**51 */
97 		if (n >= 1024) {
98 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
99 			*s = *c = ix >= 0x7ff80000 ? x : x - x;
100 			/* assumes sparc-like QNaN */
101 #else
102 			*s = *c = x - x;
103 #endif
104 		} else {
105 			if (n >= 53) {
106 				*s = 0.0;
107 				*c = 1.0;
108 			} else if (n == 52) {
109 				if ((lx & 1) == 0) {
110 					*s = 0.0;
111 					*c = 1.0;
112 				} else {
113 					*s = -0.0;
114 					*c = -1.0;
115 				}
116 			} else {	/* n == 51 */
117 				if ((lx & 1) == 0) {
118 					*s = 0.0;
119 					*c = 1.0;
120 				} else {
121 					*s = 1.0;
122 					*c = 0.0;
123 				}
124 				if ((lx & 2) != 0) {
125 					*s = -*s;
126 					*c = -*c;
127 				}
128 			}
129 		}
130 	} else if (n < -2)	/* |x| < 0.25 */
131 		*s = __k_sincos(pi * fabs(x), 0.0, c);
132 	else {
133 		/* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
134 		if (ix < 0x41C00000) {		/* |x| < 2**29 */
135 			y = 4.0 * fabs(x);
136 			n = (int)y;		/* exact */
137 			z = (double)n;
138 			k = z == y;
139 			t = (y - z) * 0.25;
140 		} else {			/* 2**29 <= |x| < 2**51 */
141 			y = fabs(x);
142 			k = 50 - n;
143 			n = lx >> k;
144 			h = n << k;
145 			((unsigned *)&z)[LOWORD] = h;
146 			((int *)&z)[HIWORD] = ix;
147 			k = h == lx;
148 			t = y - z;
149 		}
150 		if (k) {			/* x = N/4 */
151 			if ((n & 1) != 0) {
152 				*s = *c = sqrth_h + sqrth_l;
153 			} else {
154 				if ((n & 2) == 0) {
155 					*s = 0.0;
156 					*c = 1.0;
157 				} else {
158 					*s = 1.0;
159 					*c = 0.0;
160 				}
161 			}
162 			if ((n & 4) != 0)
163 				*s = -*s;
164 			if (((n + 1) & 4) != 0)
165 				*c = -*c;
166 		} else {
167 			if ((n & 1) != 0)
168 				t = 0.25 - t;
169 			if (((n + (n & 1)) & 2) == 0)
170 				*s = __k_sincos(pi * t, 0.0, c);
171 			else
172 				*c = __k_sincos(pi * t, 0.0, s);
173 			if ((n & 4) != 0)
174 				*s = -*s;
175 			if (((n + 2) & 4) != 0)
176 				*c = -*c;
177 		}
178 	}
179 	if (hx < 0)
180 		*s = -*s;
181 }
182