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 * long double sinpil(long double x),
33 * return long double precision sinl(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 #define I(q, m) ((int *)&(q))[m]
76 #define U(q, m) ((unsigned *)&(q))[m]
77 #if defined(__LITTLE_ENDIAN) || defined(__x86)
78 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, \
79 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
85 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
86 #else
87 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
88 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof (long double) / \
89 sizeof (int) - 1)
90 #define PREC 113
91 #define PRECM1 112
92 #define PRECM2 111
93
94 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
95 #endif
96
97 static const long double zero = 0.0L,
98 quater = 0.25L,
99 one = 1.0L,
100 pi = 3.141592653589793238462643383279502884197e+0000L,
101 sqrth = 0.707106781186547524400844362104849039284835937688474,
102 tiny = 1.0e-100;
103
104 long double
105 sinpil(long double x)
106 {
107 long double y, z, t;
108 int hx, n, k;
109 unsigned lx;
110
111 hx = LDBL_MOST_SIGNIF_I(x);
112 lx = LDBL_LEAST_SIGNIF_U(x);
113 k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
114
115 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */
116 if (k >= 16384) {
117 y = x - x;
118 } else {
119 if (k >= PREC) {
120 y = zero;
121 } else if (k == PRECM1) {
122 y = (lx & 1) == 0 ? zero : -zero;
123 } else { /* k = Prec - 2 */
124 y = (lx & 1) == 0 ? zero : one;
125
126 if ((lx & 2) != 0)
127 y = -y;
128 }
129 }
130 } else if (k < -2) { /* |x| < 0.25 */
131 y = __k_sinl(pi * fabsl(x), zero);
132 } else {
133 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
134 y = 4.0L * fabsl(x);
135
136 if (k < PRECM2) {
137 z = y + twoPRECM2;
138 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
139 t = z - twoPRECM2;
140 k = 0;
141
142 if (t == y) {
143 k = 1;
144 } else if (t > y) {
145 n -= 1;
146 t = quater + (y - t) * quater;
147 } else {
148 t = (y - t) * quater;
149 }
150 } else { /* k = Prec-3 */
151 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
152 k = 1;
153 }
154
155 if (k) { /* x = N/4 */
156 if ((n & 1) != 0)
157 y = sqrth + tiny;
158 else
159 y = (n & 2) == 0 ? zero : one;
160
161 if ((n & 4) != 0)
162 y = -y;
163 } else {
164 if ((n & 1) != 0)
165 t = quater - t;
166
167 if (((n + (n & 1)) & 2) == 0)
168 y = __k_sinl(pi * t, zero);
169 else
170 y = __k_cosl(pi * t, zero);
171
172 if ((n & 4) != 0)
173 y = -y;
174 }
175 }
176
177 return (hx >= 0 ? y : -y);
178 }
179
180 #undef U
181 #undef LDBL_LEAST_SIGNIF_U
182 #undef I
183 #undef LDBL_MOST_SIGNIF_I