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	siliconforks	2	/* -- 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			}