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 /* Tanh(x)
27  * Return the Hyperbolic Tangent of x
28  *
29  * Method :
30  *                                     x    -x
31  *                                    e  - e
32  *      0. tanh(x) is defined to be -----------
33  *                                     x    -x
34  *                                    e  + e
35  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
36  *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
37  *                                              -t
38  *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
39  *                                             t + 2
40  *                                                   2
41  *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
42  *                                                 t + 2
43  *          22.0   <  x <= INF    : tanh(x) := 1.
44  *
45  * Special cases:
46  *      tanh(NaN) is NaN;
47  *      only tanh(0)=0 is exact for finite argument.
48  */
49 
50 #include "fdlibm.h"
51 
52 #ifdef __STDC__
53 static const double one=1.0, two=2.0, tiny = 1.0e-300;
54 #else
55 static double one=1.0, two=2.0, tiny = 1.0e-300;
56 #endif
57 
58 #ifdef __STDC__
tanh(double x)59         double tanh(double x)
60 #else
61         double tanh(x)
62         double x;
63 #endif
64 {
65         double t,z;
66         int jx,ix;
67 
68     /* High word of |x|. */
69         jx = __HI(x);
70         ix = jx&0x7fffffff;
71 
72     /* x is INF or NaN */
73         if(ix>=0x7ff00000) {
74             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
75             else       return one/x-one;    /* tanh(NaN) = NaN */
76         }
77 
78     /* |x| < 22 */
79         if (ix < 0x40360000) {          /* |x|<22 */
80             if (ix<0x3c800000)          /* |x|<2**-55 */
81                 return x*(one+x);       /* tanh(small) = small */
82             if (ix>=0x3ff00000) {       /* |x|>=1  */
83                 t = expm1(two*fabs(x));
84                 z = one - two/(t+two);
85             } else {
86                 t = expm1(-two*fabs(x));
87                 z= -t/(t+two);
88             }
89     /* |x| > 22, return +-1 */
90         } else {
91             z = one - tiny;             /* raised inexact flag */
92         }
93         return (jx>=0)? z: -z;
94 }
95