xref: /titanic_41/usr/src/lib/libm/common/Q/tanl.c (revision bb6fd8f9750a0c1d46a75c5bcc91952d3709334b)
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  * tanl(x)
32  * Table look-up algorithm by K.C. Ng, November, 1989.
33  *
34  * kernel function:
35  *	__k_tanl	... tangent function on [-pi/4,pi/4]
36  *	__rem_pio2l	... argument reduction routine
37  *
38  * Method.
39  *      Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
40  *      1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
41  *	   [-pi/2 , +pi/2], and let n = k mod 4.
42  *	2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
43  *
44  *          n        sin(x)      cos(x)        tan(x)
45  *     ----------------------------------------------------------
46  *	    0	       S	   C		 S/C
47  *	    1	       C	  -S		-C/S
48  *	    2	      -S	  -C		 S/C
49  *	    3	      -C	   S		-C/S
50  *     ----------------------------------------------------------
51  *
52  * Special cases:
53  *      Let trig be any of sin, cos, or tan.
54  *      trig(+-INF)  is NaN, with signals;
55  *      trig(NaN)    is that NaN;
56  *
57  * Accuracy:
58  *	computer TRIG(x) returns trig(x) nearly rounded.
59  */
60 
61 #pragma weak __tanl = tanl
62 
63 #include "libm.h"
64 #include "longdouble.h"
65 
66 long double
67 tanl(long double x) {
68 	long double y[2], z = 0.0L;
69 	int n, ix;
70 
71 	ix = *(int *) &x;		/* High word of x */
72 	ix &= 0x7fffffff;
73 	if (ix <= 0x3ffe9220)		/* |x| ~< pi/4 */
74 		return (__k_tanl(x, z, 0));
75 	else if (ix >= 0x7fff0000)	/* trig(Inf or NaN) is NaN */
76 		return (x - x);
77 	else {				/* argument reduction needed */
78 		n = __rem_pio2l(x, y);
79 		return (__k_tanl(y[0], y[1], (n & 1)));
80 	}
81 }
82