xref: /illumos-gate/usr/src/lib/libm/common/C/__cos.c (revision 25c28e83)
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_cos(double x; double y)
32  * kernel cos 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
__k_cos(double x,double y)93 __k_cos(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 (ONE);
104 		z = x * x;
105 		if (ix < 0x3f800000)	/* |x| < 0.008 */
106 			q = z * (QQ1 + z * QQ2);
107 		else
108 			q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
109 		return (ONE + q);
110 	} else {		/* 0.164062500 < |x| < ~pi/4 */
111 		n = ix >> 20;
112 		i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
113 		j = i - 10;
114 		if (hx < 0)
115 			v = -y - (_TBL_sincosx[j] + x);
116 		else
117 			v = y - (_TBL_sincosx[j] - x);
118 		s = v * v;
119 		j <<= 1;
120 		w = _TBL_sincos[j];
121 		z = _TBL_sincos[j+1];
122 		p = s * (PP1 + s * PP2);
123 		q = s * (QQ1 + s * QQ2);
124 		p = v + v * p;
125 		return (z - (w * p - z * q));
126 	}
127 }
128