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 sincospil = __sincospil
31
32 /*
33 * void sincospil(long double x, long double *s, long double *c)
34 * *s = sinl(pi*x); *c = cosl(pi*x);
35 *
36 * Algorithm, 10/17/2002, K.C. Ng
37 * ------------------------------
38 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
39 * 1. If y==z, then x is a multiple of pi/4. Return the following values:
40 * ---------------------------------------------------
41 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi)
42 * ---------------------------------------------------
43 * 000 0.00 +0 ___ +1 ___ +0
44 * 001 0.25 +\/0.5 +\/0.5 +1
45 * 010 0.50 +1 ___ +0 ___ +inf
46 * 011 0.75 +\/0.5 -\/0.5 -1
47 * 100 1.00 -0 ___ -1 ___ +0
48 * 101 1.25 -\/0.5 -\/0.5 +1
49 * 110 1.50 -1 ___ -0 ___ +inf
50 * 111 1.75 -\/0.5 +\/0.5 -1
51 * ---------------------------------------------------
52 * 2. Otherwise,
53 * ---------------------------------------------------
54 * n t sin(x*pi) cos(x*pi) tan(x*pi)
55 * ---------------------------------------------------
56 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t)
57 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t)
58 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t)
59 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t)
60 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t)
61 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t)
62 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t)
63 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t)
64 * ---------------------------------------------------
65 *
66 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
67 * This will return a result with error slightly more than one ulp (but less
68 * than 2 ulp). If one wants accurate result, one may break up pi*t in
69 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
70 * instead.
71 */
72
73 #include "libm.h"
74 #include "longdouble.h"
75
76 #define I(q, m) ((int *) &(q))[m]
77 #define U(q, m) ((unsigned *) &(q))[m]
78 #if defined(__LITTLE_ENDIAN) || defined(__x86)
79 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
80 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
81 #define PREC 64
82 #define PRECM1 63
83 #define PRECM2 62
84 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
85 #else
86 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
87 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof (long double) / sizeof (int) - 1)
88 #define PREC 113
89 #define PRECM1 112
90 #define PRECM2 111
91 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
92 #endif
93
94 static const long double
95 zero = 0.0L,
96 quater = 0.25L,
97 one = 1.0L,
98 pi = 3.141592653589793238462643383279502884197e+0000L,
99 sqrth = 0.707106781186547524400844362104849039284835937688474,
100 tiny = 1.0e-100;
101
102 void
103 sincospil(long double x, long double *s, long double *c) {
104 long double y, z, t;
105 int hx, n, k;
106 unsigned lx;
107
108 hx = LDBL_MOST_SIGNIF_I(x);
109 lx = LDBL_LEAST_SIGNIF_U(x);
110 k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
111 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */
112 if (k >= 16384) {
113 *s = *c = x - x;
114 } else {
115 if (k >= PREC) {
116 *s = zero;
117 *c = one;
118 } else if (k == PRECM1) {
119 if ((lx & 1) == 0) {
120 *s = zero;
121 *c = one;
122 } else {
123 *s = -zero;
124 *c = -one;
125 }
126 } else { /* k = Prec - 2 */
127 if ((lx & 1) == 0) {
128 *s = zero;
129 *c = one;
130 } else {
131 *s = one;
132 *c = zero;
133 }
134 if ((lx & 2) != 0) {
135 *s = -*s;
136 *c = -*c;
137 }
138 }
139 }
140 } else if (k < -2) /* |x| < 0.25 */
141 *s = __k_sincosl(pi * fabsl(x), zero, c);
142 else {
143 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
144 y = 4.0L * fabsl(x);
145 if (k < PRECM2) {
146 z = y + twoPRECM2;
147 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
148 t = z - twoPRECM2;
149 k = 0;
150 if (t == y)
151 k = 1;
152 else if (t > y) {
153 n -= 1;
154 t = quater + (y - t) * quater;
155 } else
156 t = (y - t) * quater;
157 } else { /* k = Prec-3 */
158 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
159 k = 1;
160 }
161 if (k) { /* x = N/4 */
162 if ((n & 1) != 0)
163 *s = *c = sqrth + tiny;
164 else
165 if ((n & 2) == 0) {
166 *s = zero;
167 *c = one;
168 } else {
169 *s = one;
170 *c = zero;
171 }
172 if ((n & 4) != 0)
173 *s = -*s;
174 if (((n + 1) & 4) != 0)
175 *c = -*c;
176 } else {
177 if ((n & 1) != 0)
178 t = quater - t;
179 if (((n + (n & 1)) & 2) == 0)
180 *s = __k_sincosl(pi * t, zero, c);
181 else
182 *c = __k_sincosl(pi * t, zero, 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 }
192 #undef U
193 #undef LDBL_LEAST_SIGNIF_U
194 #undef I
195 #undef LDBL_MOST_SIGNIF_I