1 /*
2  * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4  *
5  * This code is free software; you can redistribute it and/or modify it
6  * under the terms of the GNU General Public License version 2 only, as
7  * published by the Free Software Foundation.  Oracle designates this
8  * particular file as subject to the "Classpath" exception as provided
9  * by Oracle in the LICENSE file that accompanied this code.
10  *
11  * This code is distributed in the hope that it will be useful, but WITHOUT
12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
14  * version 2 for more details (a copy is included in the LICENSE file that
15  * accompanied this code).
16  *
17  * You should have received a copy of the GNU General Public License version
18  * 2 along with this work; if not, write to the Free Software Foundation,
19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20  *
21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22  * or visit www.oracle.com if you need additional information or have any
23  * questions.
24  */
25 
26 /* __ieee754_atanh(x)
27  * Method :
28  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
29  *    2.For x>=0.5
30  *                  1              2x                          x
31  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
32  *                  2             1 - x                      1 - x
33  *
34  *      For x<0.5
35  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
36  *
37  * Special cases:
38  *      atanh(x) is NaN if |x| > 1 with signal;
39  *      atanh(NaN) is that NaN with no signal;
40  *      atanh(+-1) is +-INF with signal.
41  *
42  */
43 
44 #include "fdlibm.h"
45 
46 #ifdef __STDC__
47 static const double one = 1.0, huge = 1e300;
48 #else
49 static double one = 1.0, huge = 1e300;
50 #endif
51 
52 static double zero = 0.0;
53 
54 #ifdef __STDC__
__ieee754_atanh(double x)55         double __ieee754_atanh(double x)
56 #else
57         double __ieee754_atanh(x)
58         double x;
59 #endif
60 {
61         double t;
62         int hx,ix;
63         unsigned lx;
64         hx = __HI(x);           /* high word */
65         lx = __LO(x);           /* low word */
66         ix = hx&0x7fffffff;
67         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
68             return (x-x)/(x-x);
69         if(ix==0x3ff00000)
70             return x/zero;
71         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
72         __HI(x) = ix;           /* x <- |x| */
73         if(ix<0x3fe00000) {             /* x < 0.5 */
74             t = x+x;
75             t = 0.5*log1p(t+t*x/(one-x));
76         } else
77             t = 0.5*log1p((x+x)/(one-x));
78         if(hx>=0) return t; else return -t;
79 }
80