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 /*
31 * void sincospil(long double x, long double *s, long double *c)
32 * *s = sinl(pi*x); *c = cosl(pi*x);
33 *
34 * Algorithm, 10/17/2002, K.C. Ng
35 * ------------------------------
36 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
37 * 1. If y == z, then x is a multiple of pi/4. Return the following values:
38 * ---------------------------------------------------
39 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi)
40 * ---------------------------------------------------
41 * 000 0.00 +0 ___ +1 ___ +0
42 * 001 0.25 +\/0.5 +\/0.5 +1
43 * 010 0.50 +1 ___ +0 ___ +inf
44 * 011 0.75 +\/0.5 -\/0.5 -1
45 * 100 1.00 -0 ___ -1 ___ +0
46 * 101 1.25 -\/0.5 -\/0.5 +1
47 * 110 1.50 -1 ___ -0 ___ +inf
48 * 111 1.75 -\/0.5 +\/0.5 -1
49 * ---------------------------------------------------
50 * 2. Otherwise,
51 * ---------------------------------------------------
52 * n t sin(x*pi) cos(x*pi) tan(x*pi)
53 * ---------------------------------------------------
54 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t)
55 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t)
56 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t)
57 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t)
58 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t)
59 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t)
60 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t)
61 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t)
62 * ---------------------------------------------------
63 *
64 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
65 * This will return a result with error slightly more than one ulp (but less
66 * than 2 ulp). If one wants accurate result, one may break up pi*t in
67 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
68 * instead.
69 */
70
71 #include "libm.h"
72 #include "longdouble.h"
73
74 #define I(q, m) ((int *) &(q))[m]
75 #define U(q, m) ((unsigned *) &(q))[m]
76 #if defined(__LITTLE_ENDIAN) || defined(__x86)
77 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
78 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
79 #define PREC 64
80 #define PRECM1 63
81 #define PRECM2 62
82 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
83 #else
84 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
85 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof (long double) / sizeof (int) - 1)
86 #define PREC 113
87 #define PRECM1 112
88 #define PRECM2 111
89 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
90 #endif
91
92 static const long double
93 zero = 0.0L,
94 quater = 0.25L,
95 one = 1.0L,
96 pi = 3.141592653589793238462643383279502884197e+0000L,
97 sqrth = 0.707106781186547524400844362104849039284835937688474,
98 tiny = 1.0e-100;
99
100 void
101 sincospil(long double x, long double *s, long double *c) {
102 long double y, z, t;
103 int hx, n, k;
104 unsigned lx;
105
106 hx = LDBL_MOST_SIGNIF_I(x);
107 lx = LDBL_LEAST_SIGNIF_U(x);
108 k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
109 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */
110 if (k >= 16384) {
111 *s = *c = x - x;
112 } else {
113 if (k >= PREC) {
114 *s = zero;
115 *c = one;
116 } else if (k == PRECM1) {
117 if ((lx & 1) == 0) {
118 *s = zero;
119 *c = one;
120 } else {
121 *s = -zero;
122 *c = -one;
123 }
124 } else { /* k = Prec - 2 */
125 if ((lx & 1) == 0) {
126 *s = zero;
127 *c = one;
128 } else {
129 *s = one;
130 *c = zero;
131 }
132 if ((lx & 2) != 0) {
133 *s = -*s;
134 *c = -*c;
135 }
136 }
137 }
138 } else if (k < -2) /* |x| < 0.25 */
139 *s = __k_sincosl(pi * fabsl(x), zero, c);
140 else {
141 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
142 y = 4.0L * fabsl(x);
143 if (k < PRECM2) {
144 z = y + twoPRECM2;
145 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
146 t = z - twoPRECM2;
147 k = 0;
148 if (t == y)
149 k = 1;
150 else if (t > y) {
151 n -= 1;
152 t = quater + (y - t) * quater;
153 } else
154 t = (y - t) * quater;
155 } else { /* k = Prec-3 */
156 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
157 k = 1;
158 }
159 if (k) { /* x = N/4 */
160 if ((n & 1) != 0)
161 *s = *c = sqrth + tiny;
162 else
163 if ((n & 2) == 0) {
164 *s = zero;
165 *c = one;
166 } else {
167 *s = one;
168 *c = zero;
169 }
170 if ((n & 4) != 0)
171 *s = -*s;
172 if (((n + 1) & 4) != 0)
173 *c = -*c;
174 } else {
175 if ((n & 1) != 0)
176 t = quater - t;
177 if (((n + (n & 1)) & 2) == 0)
178 *s = __k_sincosl(pi * t, zero, c);
179 else
180 *c = __k_sincosl(pi * t, zero, s);
181 if ((n & 4) != 0)
182 *s = -*s;
183 if (((n + 2) & 4) != 0)
184 *c = -*c;
185 }
186 }
187 if (hx < 0)
188 *s = -*s;
189 }
190 #undef U
191 #undef LDBL_LEAST_SIGNIF_U
192 #undef I
193 #undef LDBL_MOST_SIGNIF_I