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 sincospil(long double x, long double *s, long double *c)
33 * *s = sinl(pi*x); *c = cosl(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 "longdouble.h"
74
75 #include <sys/isa_defs.h>
76
77 #define I(q, m) ((int *)&(q))[m]
78 #define U(q, m) ((unsigned *)&(q))[m]
79 #if defined(__i386) || defined(__amd64)
80 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, \
81 1) >> 15)))
82 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
83 #define PREC 64
84 #define PRECM1 63
85 #define PRECM2 62
86
87 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
88 #else
89 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
90 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof (long double) / \
91 sizeof (int) - 1)
92 #define PREC 113
93 #define PRECM1 112
94 #define PRECM2 111
95
96 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
97 #endif
98
99 static const long double zero = 0.0L,
100 quater = 0.25L,
101 one = 1.0L,
102 pi = 3.141592653589793238462643383279502884197e+0000L,
103 sqrth = 0.707106781186547524400844362104849039284835937688474,
104 tiny = 1.0e-100;
105
106 void
107 sincospil(long double x, long double *s, long double *c)
108 {
109 long double y, z, t;
110 int hx, n, k;
111 unsigned lx;
112
113 hx = LDBL_MOST_SIGNIF_I(x);
114 lx = LDBL_LEAST_SIGNIF_U(x);
115 k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
116
117 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */
118 if (k >= 16384) {
119 *s = *c = x - x;
120 } else {
121 if (k >= PREC) {
122 *s = zero;
123 *c = one;
124 } else if (k == PRECM1) {
125 if ((lx & 1) == 0) {
126 *s = zero;
127 *c = one;
128 } else {
129 *s = -zero;
130 *c = -one;
131 }
132 } else { /* k = Prec - 2 */
133 if ((lx & 1) == 0) {
134 *s = zero;
135 *c = one;
136 } else {
137 *s = one;
138 *c = zero;
139 }
140
141 if ((lx & 2) != 0) {
142 *s = -*s;
143 *c = -*c;
144 }
145 }
146 }
147 } else if (k < -2) { /* |x| < 0.25 */
148 *s = __k_sincosl(pi * fabsl(x), zero, c);
149 } else {
150 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
151 y = 4.0L * fabsl(x);
152
153 if (k < PRECM2) {
154 z = y + twoPRECM2;
155 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
156 t = z - twoPRECM2;
157 k = 0;
158
159 if (t == y) {
160 k = 1;
161 } else if (t > y) {
162 n -= 1;
163 t = quater + (y - t) * quater;
164 } else {
165 t = (y - t) * quater;
166 }
167 } else { /* k = Prec-3 */
168 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
169 k = 1;
170 }
171
172 if (k) { /* x = N/4 */
173 if ((n & 1) != 0) {
174 *s = *c = sqrth + tiny;
175 } else if ((n & 2) == 0) {
176 *s = zero;
177 *c = one;
178 } else {
179 *s = one;
180 *c = zero;
181 }
182
183 if ((n & 4) != 0)
184 *s = -*s;
185
186 if (((n + 1) & 4) != 0)
187 *c = -*c;
188 } else {
189 if ((n & 1) != 0)
190 t = quater - t;
191
192 if (((n + (n & 1)) & 2) == 0)
193 *s = __k_sincosl(pi * t, zero, c);
194 else
195 *c = __k_sincosl(pi * t, zero, s);
196
197 if ((n & 4) != 0)
198 *s = -*s;
199
200 if (((n + 2) & 4) != 0)
201 *c = -*c;
202 }
203 }
204
205 if (hx < 0)
206 *s = -*s;
207 }
208
209 #undef U
210 #undef LDBL_LEAST_SIGNIF_U
211 #undef I
212 #undef LDBL_MOST_SIGNIF_I