src/fdlibm/e_atanh.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)e_atanh.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 *
 */

/* __ieee754_atanh(x)
 * Method :
 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
 *    2.For x>=0.5
 *                  1              2x                          x
 *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
 *                  2             1 - x                      1 - x
 *      
 *      For x<0.5
 *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
 *
 * Special cases:
 *      atanh(x) is NaN if |x| > 1 with signal;
 *      atanh(NaN) is that NaN with no signal;
 *      atanh(+-1) is +-INF with signal.
 *
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double one = 1.0, really_big = 1e300;
#else
static double one = 1.0, really_big = 1e300;
#endif

static double zero = 0.0;

#ifdef __STDC__
        double __ieee754_atanh(double x)
#else
        double __ieee754_atanh(x)
        double x;
#endif
{
        double t;
        int hx,ix;
        unsigned lx;
        fd_twoints u;
        u.d = x;
        hx = __HI(u);           /* high word */
        lx = __LO(u);           /* low word */
        ix = hx&0x7fffffff;
        if ((ix|((lx|(-(int)lx))>>31))>0x3ff00000) /* |x|>1 */
            return (x-x)/(x-x);
        if(ix==0x3ff00000) 
            return x/zero;
        if(ix<0x3e300000&&(really_big+x)>zero) return x;        /* x<2**-28 */
        u.d = x;
        __HI(u) = ix;           /* x <- |x| */
        x = u.d;
        if(ix<0x3fe00000) {             /* x < 0.5 */
            t = x+x;
            t = 0.5*fd_log1p(t+t*x/(one-x));
        } else 
            t = 0.5*fd_log1p((x+x)/(one-x));
        if(hx>=0) return t; else return -t;
}
1	/* -- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 --
2	*
3	* *** BEGIN LICENSE BLOCK ***
4	* Version: MPL 1.1/GPL 2.0/LGPL 2.1
5	*
6	* The contents of this file are subject to the Mozilla Public License Version
7	* 1.1 (the "License"); you may not use this file except in compliance with
8	* the License. You may obtain a copy of the License at
9	* http://www.mozilla.org/MPL/
10	*
11	* Software distributed under the License is distributed on an "AS IS" basis,
12	* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13	* for the specific language governing rights and limitations under the
14	* License.
15	*
16	* The Original Code is Mozilla Communicator client code, released
17	* March 31, 1998.
18	*
19	* The Initial Developer of the Original Code is
20	* Sun Microsystems, Inc.
21	* Portions created by the Initial Developer are Copyright (C) 1998
22	* the Initial Developer. All Rights Reserved.
23	*
24	* Contributor(s):
25	*
26	* Alternatively, the contents of this file may be used under the terms of
27	* either of the GNU General Public License Version 2 or later (the "GPL"),
28	* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29	* in which case the provisions of the GPL or the LGPL are applicable instead
30	* of those above. If you wish to allow use of your version of this file only
31	* under the terms of either the GPL or the LGPL, and not to allow others to
32	* use your version of this file under the terms of the MPL, indicate your
33	* decision by deleting the provisions above and replace them with the notice
34	* and other provisions required by the GPL or the LGPL. If you do not delete
35	* the provisions above, a recipient may use your version of this file under
36	* the terms of any one of the MPL, the GPL or the LGPL.
37	*
38	* *** END LICENSE BLOCK *** */
39
40	/* @(#)e_atanh.c 1.3 95/01/18 */
41	/*
42	* ====================================================
43	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44	*
45	* Developed at SunSoft, a Sun Microsystems, Inc. business.
46	* Permission to use, copy, modify, and distribute this
47	* software is freely granted, provided that this notice
48	* is preserved.
49	* ====================================================
50	*
51	*/
52
53	/* __ieee754_atanh(x)
54	* Method :
55	* 1.Reduced x to positive by atanh(-x) = -atanh(x)
56	* 2.For x>=0.5
57	* 1 2x x
58	* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
59	* 2 1 - x 1 - x
60	*
61	* For x<0.5
62	* atanh(x) = 0.5log1p(2x+2xx/(1-x))
63	*
64	* Special cases:
65	* atanh(x) is NaN if \|x\| > 1 with signal;
66	* atanh(NaN) is that NaN with no signal;
67	* atanh(+-1) is +-INF with signal.
68	*
69	*/
70
71	#include "fdlibm.h"
72
73	#ifdef __STDC__
74	static const double one = 1.0, really_big = 1e300;
75	#else
76	static double one = 1.0, really_big = 1e300;
77	#endif
78
79	static double zero = 0.0;
80
81	#ifdef __STDC__
82	double __ieee754_atanh(double x)
83	#else
84	double __ieee754_atanh(x)
85	double x;
86	#endif
87	{
88	double t;
89	int hx,ix;
90	unsigned lx;
91	fd_twoints u;
92	u.d = x;
93	hx = __HI(u); /* high word */
94	lx = __LO(u); /* low word */
95	ix = hx&0x7fffffff;
96	if ((ix\|((lx\|(-(int)lx))>>31))>0x3ff00000) /* \|x\|>1 */
97	return (x-x)/(x-x);
98	if(ix==0x3ff00000)
99	return x/zero;
100	if(ix<0x3e300000&&(really_big+x)>zero) return x; /* x<2*-28 /
101	u.d = x;
102	__HI(u) = ix; /* x <- \|x\| */
103	x = u.d;
104	if(ix<0x3fe00000) { /* x < 0.5 */
105	t = x+x;
106	t = 0.5fd_log1p(t+tx/(one-x));
107	} else
108	t = 0.5*fd_log1p((x+x)/(one-x));
109	if(hx>=0) return t; else return -t;
110	}