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 /* BEGIN CSTYLED */
32 /*
33 * long double sinpil(long double x),
34 * return long double precision sinl(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 /* END CSTYLED */
73
74 #include "libm.h"
75 #include "longdouble.h"
76
77 #include <sys/isa_defs.h>
78
79 #define I(q, m) ((int *)&(q))[m]
80 #define U(q, m) ((unsigned *)&(q))[m]
81 #if defined(__i386) || defined(__amd64)
82 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, \
83 1) >> 15)))
84 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
85 #define PREC 64
86 #define PRECM1 63
87 #define PRECM2 62
88
89 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
90 #else
91 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
92 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof (long double) / \
93 sizeof (int) - 1)
94 #define PREC 113
95 #define PRECM1 112
96 #define PRECM2 111
97
98 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
99 #endif
100
101 static const long double zero = 0.0L,
102 quater = 0.25L,
103 one = 1.0L,
104 pi = 3.141592653589793238462643383279502884197e+0000L,
105 sqrth = 0.707106781186547524400844362104849039284835937688474,
106 tiny = 1.0e-100;
107
108 long double
109 sinpil(long double x)
110 {
111 long double y, z, t;
112 int hx, n, k;
113 unsigned lx;
114
115 hx = LDBL_MOST_SIGNIF_I(x);
116 lx = LDBL_LEAST_SIGNIF_U(x);
117 k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
118
119 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */
120 if (k >= 16384) {
121 y = x - x;
122 } else {
123 if (k >= PREC) {
124 y = zero;
125 } else if (k == PRECM1) {
126 y = (lx & 1) == 0 ? zero : -zero;
127 } else { /* k = Prec - 2 */
128 y = (lx & 1) == 0 ? zero : one;
129
130 if ((lx & 2) != 0)
131 y = -y;
132 }
133 }
134 } else if (k < -2) { /* |x| < 0.25 */
135 y = __k_sinl(pi * fabsl(x), zero);
136 } else {
137 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
138 y = 4.0L * fabsl(x);
139
140 if (k < PRECM2) {
141 z = y + twoPRECM2;
142 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
143 t = z - twoPRECM2;
144 k = 0;
145
146 if (t == y) {
147 k = 1;
148 } else if (t > y) {
149 n -= 1;
150 t = quater + (y - t) * quater;
151 } else {
152 t = (y - t) * quater;
153 }
154 } else { /* k = Prec-3 */
155 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
156 k = 1;
157 }
158
159 if (k) { /* x = N/4 */
160 if ((n & 1) != 0)
161 y = sqrth + tiny;
162 else
163 y = (n & 2) == 0 ? zero : one;
164
165 if ((n & 4) != 0)
166 y = -y;
167 } else {
168 if ((n & 1) != 0)
169 t = quater - t;
170
171 if (((n + (n & 1)) & 2) == 0)
172 y = __k_sinl(pi * t, zero);
173 else
174 y = __k_cosl(pi * t, zero);
175
176 if ((n & 4) != 0)
177 y = -y;
178 }
179 }
180
181 return (hx >= 0 ? y : -y);
182 }
183
184 #undef U
185 #undef LDBL_LEAST_SIGNIF_U
186 #undef I
187 #undef LDBL_MOST_SIGNIF_I