xref: /illumos-gate/usr/src/lib/libm/common/Q/sinl.c (revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af)
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  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29 
30 /*
31  * sinl(x)
32  * Table look-up algorithm by K.C. Ng, November, 1989.
33  *
34  * kernel function:
35  *	__k_sinl		... sin function on [-pi/4,pi/4]
36  *	__k_cosl		... cos function on [-pi/4,pi/4]
37  *	__rem_pio2l	... argument reduction routine
38  *
39  * Method.
40  *      Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
41  *      1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
42  *	   [-pi/2 , +pi/2], and let n = k mod 4.
43  *	2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
44  *
45  *          n        sin(x)      cos(x)        tan(x)
46  *     ----------------------------------------------------------
47  *	    0	       S	   C		 S/C
48  *	    1	       C	  -S		-C/S
49  *	    2	      -S	  -C		 S/C
50  *	    3	      -C	   S		-C/S
51  *     ----------------------------------------------------------
52  *
53  * Special cases:
54  *      Let trig be any of sin, cos, or tan.
55  *      trig(+-INF)  is NaN, with signals;
56  *      trig(NaN)    is that NaN;
57  *
58  * Accuracy:
59  *	computer TRIG(x) returns trig(x) nearly rounded.
60  */
61 
62 #pragma weak __sinl = sinl
63 
64 #include "libm.h"
65 #include "longdouble.h"
66 
67 long double
sinl(long double x)68 sinl(long double x) {
69 	long double y[2], z = 0.0L;
70 	int n, ix;
71 
72 	ix = *(int *) &x;		/* High word of x */
73 	ix &= 0x7fffffff;
74 	if (ix <= 0x3ffe9220)		/* |x| ~< pi/4 */
75 		return (__k_sinl(x, z));
76 	else if (ix >= 0x7fff0000)	/* sin(Inf or NaN) is NaN */
77 		return (x - x);
78 	else {				/* argument reduction needed */
79 		n = __rem_pio2l(x, y);
80 		switch (n & 3) {
81 			case 0:
82 				return (__k_sinl(y[0], y[1]));
83 			case 1:
84 				return (__k_cosl(y[0], y[1]));
85 			case 2:
86 				return (-__k_sinl(y[0], y[1]));
87 			case 3:
88 				return (-__k_cosl(y[0], y[1]));
89 		}
90 	}
91 	/* NOTREACHED */
92     return 0.0L;
93 }
94