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 }