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 2005 Sun Microsystems, Inc. All rights reserved.
23 * Use is subject to license terms.
24 */
25
26
27 /* INDENT OFF */
28 /*
29 * __k_cos(double x; double y)
30 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
31 * Input x is assumed to be bounded by ~pi/4 in magnitude.
32 * Input y is the tail of x.
33 *
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 /*
64 * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
65 */
66 /* Q1 = */ -0.5,
67 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
68 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
69 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
70 };
71 /* INDENT ON */
72
73 #define ONE sc[0]
74 #define NONE sc[1]
75 #define PP1 sc[2]
76 #define PP2 sc[3]
77 #define P1 sc[4]
78 #define P2 sc[5]
79 #define P3 sc[6]
80 #define P4 sc[7]
81 #define QQ1 sc[8]
82 #define QQ2 sc[9]
83 #define Q1 sc[10]
84 #define Q2 sc[11]
85 #define Q3 sc[12]
86 #define Q4 sc[13]
87
88 extern const double _TBL_sincos[], _TBL_sincosx[];
89
90 double
__k_cos(double x,double y)91 __k_cos(double x, double y) {
92 double z, w, s, v, p, q;
93 int i, j, n, hx, ix;
94
95 hx = ((int *)&x)[HIWORD];
96 ix = hx & ~0x80000000;
97
98 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
99 if (ix < 0x3e400000) /* |x| < 2**-27 */
100 if ((int)x == 0)
101 return (ONE);
102 z = x * x;
103 if (ix < 0x3f800000) /* |x| < 0.008 */
104 q = z * (QQ1 + z * QQ2);
105 else
106 q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
107 return (ONE + q);
108 } else { /* 0.164062500 < |x| < ~pi/4 */
109 n = ix >> 20;
110 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
111 j = i - 10;
112 if (hx < 0)
113 v = -y - (_TBL_sincosx[j] + x);
114 else
115 v = y - (_TBL_sincosx[j] - x);
116 s = v * v;
117 j <<= 1;
118 w = _TBL_sincos[j];
119 z = _TBL_sincos[j+1];
120 p = s * (PP1 + s * PP2);
121 q = s * (QQ1 + s * QQ2);
122 p = v + v * p;
123 return (z - (w * p - z * q));
124 }
125 }
126