xref: /illumos-gate/usr/src/lib/libm/common/LD/atanhl.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 #pragma weak __atanhl = atanhl
31 
32 #include "libm.h"
33 
34 #define GENERIC	long double
35 #define	ATANH 	atanhl
36 
37 /* ATANH(x)
38  *                  1              2x                          x
39  *	ATANH(x) = --- * LOG(1 + -------) = 0.5 * LOG1P(2 * --------)
40  *                  2             1 - x                      1 - x
41  * Note: to guarantee ATANH(-x) = -ATANH(x), we use
42  *                 sign(x)             |x|
43  *	ATANH(x) = ------- * LOG1P(2*-------).
44  *                    2              1 - |x|
45  *
46  * Special cases:
47  *	ATANH(x) is NaN if |x| > 1 with signal;
48  *	ATANH(NaN) is that NaN with no signal;
49  *	ATANH(+-1) is +-INF with signal.
50  *
51  */
52 
53 #define	FABS 	fabsl
54 #define	LOG1P 	log1pl
55 #define	COPYSIGN 	copysignl
56 
57 
58 extern GENERIC 	FABS(),LOG1P(),COPYSIGN();
59 
60 static GENERIC
61 zero	= (GENERIC) 0.0,
62 half 	= (GENERIC) 0.5,
63 one	= (GENERIC) 1.0;
64 
ATANH(x)65 GENERIC ATANH(x)
66 GENERIC x;
67 {
68 	GENERIC t;
69 	t = FABS(x);
70 	if (t == one) return x/zero;
71 	t = t/(one-t);
72 	return COPYSIGN(half,x)*LOG1P(t+t);
73 }
74