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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak __sin = sin
30
31 /* INDENT OFF */
32 /*
33 * sin(x)
34 * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
35 *
36 * Algorithm: see sincos.c
37 */
38
39 #include "libm.h"
40
41 static const double sc[] = {
42 /* ONE = */ 1.0,
43 /* NONE = */ -1.0,
44 /*
45 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
46 */
47 /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
48 /* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
49 /*
50 * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
51 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
52 * | x |
53 */
54 /* P1 = */ -1.666666666666629669805215138920301589656e-0001,
55 /* P2 = */ 8.333333332390951295683993455280336376663e-0003,
56 /* P3 = */ -1.984126237997976692791551778230098403960e-0004,
57 /* P4 = */ 2.753403624854277237649987622848330351110e-0006,
58 /*
59 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
60 */
61 /* QQ1 = */ -0.4999999999975492381842911981948418542742729,
62 /* QQ2 = */ 0.041666542904352059294545209158357640398771740,
63 /* PI_H = */ 3.1415926535897931159979634685,
64 /* PI_L = */ 1.22464679914735317722606593227425e-16,
65 /* PI_L0 = */ 1.22464679914558443311283879205095e-16,
66 /* PI_L1 = */ 1.768744113227140223300005233735517376e-28,
67 /* PI2_H = */ 6.2831853071795862319959269370,
68 /* PI2_L = */ 2.44929359829470635445213186454850e-16,
69 /* PI2_L0 = */ 2.44929359829116886622567758410190e-16,
70 /* PI2_L1 = */ 3.537488226454280446600010467471034752e-28,
71 };
72 /* INDENT ON */
73
74 #define ONEA sc
75 #define ONE sc[0]
76 #define NONE sc[1]
77 #define PP1 sc[2]
78 #define PP2 sc[3]
79 #define P1 sc[4]
80 #define P2 sc[5]
81 #define P3 sc[6]
82 #define P4 sc[7]
83 #define QQ1 sc[8]
84 #define QQ2 sc[9]
85 #define PI_H sc[10]
86 #define PI_L sc[11]
87 #define PI_L0 sc[12]
88 #define PI_L1 sc[13]
89 #define PI2_H sc[14]
90 #define PI2_L sc[15]
91 #define PI2_L0 sc[16]
92 #define PI2_L1 sc[17]
93
94 extern const double _TBL_sincos[], _TBL_sincosx[];
95
96 double
97 sin(double x) {
98 double z, y[2], w, s, v, p, q;
99 int i, j, n, hx, ix, lx;
100
101 hx = ((int *)&x)[HIWORD];
102 lx = ((int *)&x)[LOWORD];
103 ix = hx & ~0x80000000;
104
105 if (ix <= 0x3fc50000) { /* |x| < .1640625 */
106 if (ix < 0x3e400000) /* |x| < 2**-27 */
107 if ((int)x == 0)
108 return (x);
109 z = x * x;
110 if (ix < 0x3f800000) /* |x| < 2**-8 */
111 w = (z * x) * (PP1 + z * PP2);
112 else
113 w = (x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4));
114 return (x + w);
115 }
116
117 /* for .1640625 < x < M, */
118 n = ix >> 20;
119 if (n < 0x402) { /* x < 8 */
120 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
121 j = i - 10;
122 x = fabs(x);
123 v = x - _TBL_sincosx[j];
124 if (((j - 181) ^ (j - 201)) < 0) {
125 /* near pi, sin(x) = sin(pi-x) */
126 p = PI_H - x;
127 i = ix - 0x400921fb;
128 x = p + PI_L;
129 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
130 /* very close to pi */
131 x = p + PI_L0;
132 return ((hx >= 0)? x + PI_L1 : -(x + PI_L1));
133 }
134 z = x * x;
135 if (((ix - 0x40092000) >> 11) == 0) {
136 /* |pi-x|<2**-8 */
137 w = PI_L + (z * x) * (PP1 + z * PP2);
138 } else {
139 w = PI_L + (z * x) * ((P1 + z * P2) +
140 (z * z) * (P3 + z * P4));
141 }
142 return ((hx >= 0)? p + w : -p - w);
143 }
144 s = v * v;
145 if (((j - 382) ^ (j - 402)) < 0) {
146 /* near 2pi, sin(x) = sin(x-2pi) */
147 p = x - PI2_H;
148 i = ix - 0x401921fb;
149 x = p - PI2_L;
150 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
151 /* very close to 2pi */
152 x = p - PI2_L0;
153 return ((hx >= 0)? x - PI2_L1 : -(x - PI2_L1));
154 }
155 z = x * x;
156 if (((ix - 0x40192000) >> 10) == 0) {
157 /* |x-2pi|<2**-8 */
158 w = (z * x) * (PP1 + z * PP2) - PI2_L;
159 } else {
160 w = (z * x) * ((P1 + z * P2) +
161 (z * z) * (P3 + z * P4)) - PI2_L;
162 }
163 return ((hx >= 0)? p + w : -p - w);
164 }
165 j <<= 1;
166 w = _TBL_sincos[j+1];
167 z = _TBL_sincos[j];
168 p = v + (v * s) * (PP1 + s * PP2);
169 q = s * (QQ1 + s * QQ2);
170 v = w * p + z * q;
171 return ((hx >= 0)? z + v : -z - v);
172 }
173
174 if (ix >= 0x7ff00000) /* sin(Inf or NaN) is NaN */
175 return (x / x);
176
177 /* argument reduction needed */
178 n = __rem_pio2(x, y);
179 switch (n & 3) {
180 case 0:
181 return (__k_sin(y[0], y[1]));
182 case 1:
183 return (__k_cos(y[0], y[1]));
184 case 2:
185 return (-__k_sin(y[0], y[1]));
186 default:
187 return (-__k_cos(y[0], y[1]));
188 }
189 }