xref: /illumos-gate/usr/src/lib/libm/common/LD/tanl.c (revision ddc0e0b5)
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 #pragma weak __tanl = tanl
31 
32 /* INDENT OFF */
33 /* cosl(x)
34  * Table look-up algorithm by K.C. Ng, November, 1989.
35  *
36  * kernel function:
37  *	__k_tanl	... tangent function on [-pi/4,pi/4]
38  *	__rem_pio2l	... argument reduction routine
39  *
40  * Method.
41  *      Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
42  *      1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
43  *	   [-pi/2 , +pi/2], and let n = k mod 4.
44  *	2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
45  *
46  *          n        sin(x)      cos(x)        tan(x)
47  *     ----------------------------------------------------------
48  *	    0	       S	   C		 S/C
49  *	    1	       C	  -S		-C/S
50  *	    2	      -S	  -C		 S/C
51  *	    3	      -C	   S		-C/S
52  *     ----------------------------------------------------------
53  *
54  * Special cases:
55  *      Let trig be any of sin, cos, or tan.
56  *      trig(+-INF)  is NaN, with signals;
57  *      trig(NaN)    is that NaN;
58  *
59  * Accuracy:
60  *	computer TRIG(x) returns trig(x) nearly rounded.
61  */
62 /* INDENT ON */
63 
64 #include "libm.h"
65 #include "longdouble.h"
66 
67 #include <sys/isa_defs.h>
68 
69 long double
tanl(long double x)70 tanl(long double x) {
71 	long double y[2], z = 0.0L;
72 	int n, ix;
73 #if defined(__i386) || defined(__amd64)
74 	int *px = (int *) &x;
75 #endif
76 
77 	/* trig(Inf or NaN) is NaN */
78 	if (!finitel(x))
79 		return x - x;
80 
81 	/* High word of x. */
82 #if defined(__i386) || defined(__amd64)
83 	XTOI(px, ix);
84 #else
85 	ix = *(int *) &x;
86 #endif
87 
88 	/* |x| ~< pi/4 */
89 	ix &= 0x7fffffff;
90 	if (ix <= 0x3ffe9220)
91 		return __k_tanl(x, z, 0);
92 
93 	/* argument reduction needed */
94 	else {
95 		n = __rem_pio2l(x, y);
96 		return __k_tanl(y[0], y[1], n & 1);
97 	}
98 }
99