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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
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 /* BEGIN CSTYLEd */
81 static const double pi = 3.14159265358979323846, /* 400921FB,54442D18 */
82 sqrth_h = 0.70710678118654757273731092936941422522068023681640625,
83 sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17;
84 /* END CSTYLED */
85
86 void
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
97 if (n >= 51) { /* |x| >= 2**51 */
98 if (n >= 1024) {
99 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
100 *s = *c = ix >= 0x7ff80000 ? x : x - x;
101 /* assumes sparc-like QNaN */
102 #else
103 *s = *c = x - x;
104 #endif
105 } else {
106 if (n >= 53) {
107 *s = 0.0;
108 *c = 1.0;
109 } else if (n == 52) {
110 if ((lx & 1) == 0) {
111 *s = 0.0;
112 *c = 1.0;
113 } else {
114 *s = -0.0;
115 *c = -1.0;
116 }
117 } else { /* n == 51 */
118 if ((lx & 1) == 0) {
119 *s = 0.0;
120 *c = 1.0;
121 } else {
122 *s = 1.0;
123 *c = 0.0;
124 }
125
126 if ((lx & 2) != 0) {
127 *s = -*s;
128 *c = -*c;
129 }
130 }
131 }
132 } else if (n < -2) { /* |x| < 0.25 */
133 *s = __k_sincos(pi * fabs(x), 0.0, c);
134 } else {
135 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
136 if (ix < 0x41C00000) { /* |x| < 2**29 */
137 y = 4.0 * fabs(x);
138 n = (int)y; /* exact */
139 z = (double)n;
140 k = z == y;
141 t = (y - z) * 0.25;
142 } else { /* 2**29 <= |x| < 2**51 */
143 y = fabs(x);
144 k = 50 - n;
145 n = lx >> k;
146 h = n << k;
147 ((unsigned *)&z)[LOWORD] = h;
148 ((int *)&z)[HIWORD] = ix;
149 k = h == lx;
150 t = y - z;
151 }
152
153 if (k) { /* x = N/4 */
154 if ((n & 1) != 0) {
155 *s = *c = sqrth_h + sqrth_l;
156 } else {
157 if ((n & 2) == 0) {
158 *s = 0.0;
159 *c = 1.0;
160 } else {
161 *s = 1.0;
162 *c = 0.0;
163 }
164 }
165
166 if ((n & 4) != 0)
167 *s = -*s;
168
169 if (((n + 1) & 4) != 0)
170 *c = -*c;
171 } else {
172 if ((n & 1) != 0)
173 t = 0.25 - t;
174
175 if (((n + (n & 1)) & 2) == 0)
176 *s = __k_sincos(pi * t, 0.0, c);
177 else
178 *c = __k_sincos(pi * t, 0.0, s);
179
180 if ((n & 4) != 0)
181 *s = -*s;
182
183 if (((n + 2) & 4) != 0)
184 *c = -*c;
185 }
186 }
187
188 if (hx < 0)
189 *s = -*s;
190 }