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 /* INDENT OFF */
30 /*
31 * __k_sin( double x; double y )
32 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.785398164
33 * Input x is assumed to be bounded by ~pi/4 in magnitude.
34 * Input y is the tail of x.
35 *
36 * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
37 *
38 * Algorithm: see __sincos.c
39 */
40
41 #include "libm.h"
42
43 static const double sc[] = {
44 /* ONE = */ 1.0,
45 /* NONE = */ -1.0,
46 /*
47 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
48 */
49 /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
50 /* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
51 /*
52 * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
53 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
54 * | x |
55 */
56 /* P1 = */ -1.666666666666629669805215138920301589656e-0001,
57 /* P2 = */ 8.333333332390951295683993455280336376663e-0003,
58 /* P3 = */ -1.984126237997976692791551778230098403960e-0004,
59 /* P4 = */ 2.753403624854277237649987622848330351110e-0006,
60 /*
61 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
62 */
63 /* QQ1 = */ -0.4999999999975492381842911981948418542742729,
64 /* QQ2 = */ 0.041666542904352059294545209158357640398771740,
65 /*
66 * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
67 */
68 /* Q1 = */ -0.5,
69 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
70 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
71 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
72 };
73 /* INDENT ON */
74
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 Q1 sc[10]
86 #define Q2 sc[11]
87 #define Q3 sc[12]
88 #define Q4 sc[13]
89
90 extern const double _TBL_sincos[], _TBL_sincosx[];
91
92 double
93 __k_sin(double x, double y) {
94 double z, w, s, v, p, q;
95 int i, j, n, hx, ix;
96
97 hx = ((int *)&x)[HIWORD];
98 ix = hx & ~0x80000000;
99
100 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
101 if (ix < 0x3e400000) /* |x| < 2**-27 */
102 if ((int)x == 0)
103 return (x + y);
104 z = x * x;
105 if (ix < 0x3f800000) /* |x| < 0.008 */
106 p = (x * z) * (PP1 + z * PP2) + y;
107 else
108 p = (x * z) * ((P1 + z * P2) + (z * z) * (P3 +
109 z * P4)) + y;
110 return (x + p);
111 } else { /* 0.164062500 < |x| < ~pi/4 */
112 n = ix >> 20;
113 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
114 j = i - 10;
115 if (hx < 0)
116 v = -y - (_TBL_sincosx[j] + x);
117 else
118 v = y - (_TBL_sincosx[j] - x);
119 s = v * v;
120 j <<= 1;
121 w = _TBL_sincos[j];
122 z = _TBL_sincos[j+1];
123 p = s * (PP1 + s * PP2);
124 q = s * (QQ1 + s * QQ2);
125 p = v + v * p;
126 s = w * q + z * p;
127 return ((hx >= 0)? w + s : -(w + s));
128 }
129 }