xref: /illumos-gate/usr/src/lib/libm/common/Q/tanhl.c (revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8)
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 #if defined(ELFOBJ)
31 #pragma weak tanhl = __tanhl
32 #endif
33 
34 /*
35  * tanhl(x) returns the hyperbolic tangent of x
36  *
37  * Method :
38  *	1. reduce x to non-negative:  tanhl(-x) = - tanhl(x).
39  *	2.
40  *	  0      <  x <=  small    :  tanhl(x) := x
41  *					          -expm1l(-2x)
42  *	  small  <  x <=  1        :  tanhl(x) := --------------
43  *					         expm1l(-2x) + 2
44  *							  2
45  *	  1      <= x <= threshold :  tanhl(x) := 1 -  ---------------
46  *						      expm1l(2x) + 2
47  *     threshold <  x <= INF       :  tanhl(x) := 1.
48  *
49  * where
50  *	single : 	small = 1.e-5		threshold = 11.0
51  *	double : 	small = 1.e-10		threshold = 22.0
52  *	quad   : 	small = 1.e-20		threshold = 45.0
53  *
54  * Note: threshold was chosen so that
55  *		fl(1.0+2/(expm1(2*threshold)+2)) == 1.
56  *
57  * Special cases:
58  *	tanhl(NaN) is NaN;
59  *	only tanhl(0.0)=0.0 is exact for finite argument.
60  */
61 
62 #include "libm.h"
63 #include "longdouble.h"
64 
65 static const long double small = 1.0e-20L, one = 1.0, two = 2.0,
66 #ifndef lint
67 	big = 1.0e+20L,
68 #endif
69 	threshold = 45.0L;
70 
71 long double
72 tanhl(long double x) {
73 	long double t, y, z;
74 	int signx;
75 	volatile long double dummy;
76 
77 	if (isnanl(x))
78 		return (x + x);		/* x is NaN */
79 	signx = signbitl(x);
80 	t = fabsl(x);
81 	z = one;
82 	if (t <= threshold) {
83 		if (t > one)
84 			z = one - two / (expm1l(t + t) + two);
85 		else if (t > small) {
86 			y = expm1l(-t - t);
87 			z = -y / (y + two);
88 		} else {
89 #ifndef lint
90 			dummy = t + big;
91 							/* inexact if t != 0 */
92 #endif
93 			return (x);
94 		}
95 	} else if (!finitel(t))
96 		return (copysignl(one, x));
97 	else
98 		return (signx ? -z + small * small : z - small * small);
99 	return (signx ? -z : z);
100 }
101