xref: /illumos-gate/usr/src/lib/libm/common/Q/atanhl.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 #pragma weak atanhl = __atanhl
31 
32 #include "libm.h"
33 
34 /*
35  *                   1              2x                           x
36  *	atanhl(x) = --- * LOG(1 + -------) = 0.5 * log1pl(2 * --------)
37  *                   2             1 - x                       1 - x
38  * Note: to guarantee atanhl(-x) = -atanhl(x), we use
39  *                  sign(x)              |x|
40  *	atanhl(x) = ------- * log1pl(2*-------).
41  *                     2               1 - |x|
42  *
43  * Special cases:
44  *	atanhl(x) is NaN if |x| > 1 with signal;
45  *	atanhl(NaN) is that NaN with no signal;
46  *	atanhl(+-1) is +-INF with signal.
47  *
48  */
49 
50 static const long double zero = 0.0L, half = 0.5L, one = 1.0L;
51 
52 long double
53 atanhl(long double x) {
54 	long double t;
55 
56 	t = fabsl(x);
57 	if (t == one)
58 		return (x / zero);
59 	t = t / (one - t);
60 	return (copysignl(half, x) * log1pl(t + t));
61 }
62