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 #pragma weak sincospi = __sincospi
31
32 /* INDENT OFF */
33 /*
34 * void sincospi(double x, double *s, double *c)
35 * *s = sin(pi*x); *c = cos(pi*x);
36 *
37 * Algorithm, 10/17/2002, K.C. Ng
38 * ------------------------------
39 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
40 * 1. If y==z, then x is a multiple of pi/4. Return the following values:
41 * ---------------------------------------------------
42 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi)
43 * ---------------------------------------------------
44 * 000 0.00 +0 ___ +1 ___ +0
45 * 001 0.25 +\/0.5 +\/0.5 +1
46 * 010 0.50 +1 ___ +0 ___ +inf
47 * 011 0.75 +\/0.5 -\/0.5 -1
48 * 100 1.00 -0 ___ -1 ___ +0
49 * 101 1.25 -\/0.5 -\/0.5 +1
50 * 110 1.50 -1 ___ -0 ___ +inf
51 * 111 1.75 -\/0.5 +\/0.5 -1
52 * ---------------------------------------------------
53 * 2. Otherwise,
54 * ---------------------------------------------------
55 * n t sin(x*pi) cos(x*pi) tan(x*pi)
56 * ---------------------------------------------------
57 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t)
58 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t)
59 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t)
60 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t)
61 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t)
62 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t)
63 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t)
64 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t)
65 * ---------------------------------------------------
66 *
67 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
68 * This will return a result with error slightly more than one ulp (but less
69 * than 2 ulp). If one wants accurate result, one may break up pi*t in
70 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
71 * instead.
72 */
73
74 #include "libm.h"
75 #include "libm_synonyms.h"
76 #include "libm_protos.h"
77 #include "libm_macros.h"
78 #include <math.h>
79 #if defined(__SUNPRO_C)
80 #include <sunmath.h>
81 #endif
82
83 static const double
84 pi = 3.14159265358979323846, /* 400921FB,54442D18 */
85 sqrth_h = 0.70710678118654757273731092936941422522068023681640625,
86 sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17;
87 /* INDENT ON */
88
89 void
90 sincospi(double x, double *s, double *c) {
91 double y, z, t;
92 int n, ix, k;
93 int hx = ((int *) &x)[HIWORD];
94 unsigned h, lx = ((unsigned *) &x)[LOWORD];
95
96 ix = hx & ~0x80000000;
97 n = (ix >> 20) - 0x3ff;
98 if (n >= 51) { /* |x| >= 2**51 */
99 if (n >= 1024)
100 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
101 *s = *c = ix >= 0x7ff80000 ? x : x - x;
102 /* assumes sparc-like QNaN */
103 #else
104 *s = *c = x - x;
105 #endif
106 else {
107 if (n >= 53) {
108 *s = 0.0;
109 *c = 1.0;
110 }
111 else if (n == 52) {
112 if ((lx & 1) == 0) {
113 *s = 0.0;
114 *c = 1.0;
115 }
116 else {
117 *s = -0.0;
118 *c = -1.0;
119 }
120 }
121 else { /* n == 51 */
122 if ((lx & 1) == 0) {
123 *s = 0.0;
124 *c = 1.0;
125 }
126 else {
127 *s = 1.0;
128 *c = 0.0;
129 }
130 if ((lx & 2) != 0) {
131 *s = -*s;
132 *c = -*c;
133 }
134 }
135 }
136 }
137 else if (n < -2) /* |x| < 0.25 */
138 *s = __k_sincos(pi * fabs(x), 0.0, c);
139 else {
140 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
141 if (ix < 0x41C00000) { /* |x| < 2**29 */
142 y = 4.0 * fabs(x);
143 n = (int) y; /* exact */
144 z = (double) n;
145 k = z == y;
146 t = (y - z) * 0.25;
147 }
148 else { /* 2**29 <= |x| < 2**51 */
149 y = fabs(x);
150 k = 50 - n;
151 n = lx >> k;
152 h = n << k;
153 ((unsigned *) &z)[LOWORD] = h;
154 ((int *) &z)[HIWORD] = ix;
155 k = h == lx;
156 t = y - z;
157 }
158 if (k) { /* x = N/4 */
159 if ((n & 1) != 0)
160 *s = *c = sqrth_h + sqrth_l;
161 else
162 if ((n & 2) == 0) {
163 *s = 0.0;
164 *c = 1.0;
165 }
166 else {
167 *s = 1.0;
168 *c = 0.0;
169 }
170 y = (n & 2) == 0 ? 0.0 : 1.0;
171 if ((n & 4) != 0)
172 *s = -*s;
173 if (((n + 1) & 4) != 0)
174 *c = -*c;
175 }
176 else {
177 if ((n & 1) != 0)
178 t = 0.25 - t;
179 if (((n + (n & 1)) & 2) == 0)
180 *s = __k_sincos(pi * t, 0.0, c);
181 else
182 *c = __k_sincos(pi * t, 0.0, s);
183 if ((n & 4) != 0)
184 *s = -*s;
185 if (((n + 2) & 4) != 0)
186 *c = -*c;
187 }
188 }
189 if (hx < 0)
190 *s = -*s;
191 }