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/* @(#)s_tanh.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
 
/*
 
FUNCTION
        <<tanh>>, <<tanhf>>---hyperbolic tangent
 
INDEX
tanh
INDEX
tanhf
 
ANSI_SYNOPSIS
        #include <math.h>
        double tanh(double <[x]>);
        float tanhf(float <[x]>);
 
TRAD_SYNOPSIS
        #include <math.h>
        double tanh(<[x]>)
        double <[x]>;
 
        float tanhf(<[x]>)
        float <[x]>;
 
 
DESCRIPTION
 
<<tanh>> computes the hyperbolic tangent of
the argument <[x]>.  Angles are specified in radians.
 
<<tanh(<[x]>)>> is defined as
. sinh(<[x]>)/cosh(<[x]>)
 
<<tanhf>> is identical, save that it takes and returns <<float>> values.
 
RETURNS
The hyperbolic tangent of <[x]> is returned.
 
PORTABILITY
<<tanh>> is ANSI C.  <<tanhf>> is an extension.
 
*/
 
/* Tanh(x)
 * Return the Hyperbolic Tangent of x
 *
 * Method :
 *                                     x    -x
 *                                    e  - e
 *      0. tanh(x) is defined to be -----------
 *                                     x    -x
 *                                    e  + e
 *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
 *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
 *                                              -t
 *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
 *                                             t + 2
 *                                                   2
 *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
 *                                                 t + 2
 *          22.0   <  x <= INF    : tanh(x) := 1.
 *
 * Special cases:
 *      tanh(NaN) is NaN;
 *      only tanh(0)=0 is exact for finite argument.
 */
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one=1.0, two=2.0, tiny = 1.0e-300;
#else
static double one=1.0, two=2.0, tiny = 1.0e-300;
#endif
 
#ifdef __STDC__
        double tanh(double x)
#else
        double tanh(x)
        double x;
#endif
{
        double t,z;
        __int32_t jx,ix;
 
    /* High word of |x|. */
        GET_HIGH_WORD(jx,x);
        ix = jx&0x7fffffff;
 
    /* x is INF or NaN */
        if(ix>=0x7ff00000) {
            if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
            else       return one/x-one;    /* tanh(NaN) = NaN */
        }
 
    /* |x| < 22 */
        if (ix < 0x40360000) {          /* |x|<22 */
            if (ix<0x3c800000)          /* |x|<2**-55 */
                return x*(one+x);       /* tanh(small) = small */
            if (ix>=0x3ff00000) {       /* |x|>=1  */
                t = expm1(two*fabs(x));
                z = one - two/(t+two);
            } else {
                t = expm1(-two*fabs(x));
                z= -t/(t+two);
            }
    /* |x| > 22, return +-1 */
        } else {
            z = one - tiny;             /* raised inexact flag */
        }
        return (jx>=0)? z: -z;
}
 
#endif /* _DOUBLE_IS_32BITS */

Line No.	Rev	Author	Line
1	39	lampret
2			`/* @(#)s_tanh.c 5.1 93/09/24 */`
3			`/*`
4			`* ====================================================`
5			`* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
6			`*`
7			`* Developed at SunPro, a Sun Microsystems, Inc. business.`
8			`* Permission to use, copy, modify, and distribute this`
9			`* software is freely granted, provided that this notice`
10			`* is preserved.`
11			`* ====================================================`
12			`*/`
13
14			`/*`
15
16			`FUNCTION`
17			`<<tanh>>, <<tanhf>>---hyperbolic tangent`
18
19			`INDEX`
20			`tanh`
21			`INDEX`
22			`tanhf`
23
24			`ANSI_SYNOPSIS`
25			`#include <math.h>`
26			`double tanh(double <[x]>);`
27			`float tanhf(float <[x]>);`
28
29			`TRAD_SYNOPSIS`
30			`#include <math.h>`
31			`double tanh(<[x]>)`
32			`double <[x]>;`
33
34			`float tanhf(<[x]>)`
35			`float <[x]>;`
36
37
38			`DESCRIPTION`
39
40			`<<tanh>> computes the hyperbolic tangent of`
41			`the argument <[x]>. Angles are specified in radians.`
42
43			`<<tanh(<[x]>)>> is defined as`
44			`. sinh(<[x]>)/cosh(<[x]>)`
45
46			`<<tanhf>> is identical, save that it takes and returns <<float>> values.`
47
48			`RETURNS`
49			`The hyperbolic tangent of <[x]> is returned.`
50
51			`PORTABILITY`
52			`<<tanh>> is ANSI C. <<tanhf>> is an extension.`
53
54			`*/`
55
56			`/* Tanh(x)`
57			`* Return the Hyperbolic Tangent of x`
58			`*`
59			`* Method :`
60			`* x -x`
61			`* e - e`
62			`* 0. tanh(x) is defined to be -----------`
63			`* x -x`
64			`* e + e`
65			`* 1. reduce x to non-negative by tanh(-x) = -tanh(x).`
66			`* 2. 0 <= x <= 2*-55 : tanh(x) := x(one+x)`
67			`* -t`
68			`* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)`
69			`* t + 2`
70			`* 2`
71			`* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)`
72			`* t + 2`
73			`* 22.0 < x <= INF : tanh(x) := 1.`
74			`*`
75			`* Special cases:`
76			`* tanh(NaN) is NaN;`
77			`* only tanh(0)=0 is exact for finite argument.`
78			`*/`
79
80			`#include "fdlibm.h"`
81
82			`#ifndef _DOUBLE_IS_32BITS`
83
84			`#ifdef __STDC__`
85			`static const double one=1.0, two=2.0, tiny = 1.0e-300;`
86			`#else`
87			`static double one=1.0, two=2.0, tiny = 1.0e-300;`
88			`#endif`
89
90			`#ifdef __STDC__`
91			`double tanh(double x)`
92			`#else`
93			`double tanh(x)`
94			`double x;`
95			`#endif`
96			`{`
97			`double t,z;`
98			`__int32_t jx,ix;`
99
100			`/* High word of \|x\|. */`
101			`GET_HIGH_WORD(jx,x);`
102			`ix = jx&0x7fffffff;`
103
104			`/* x is INF or NaN */`
105			`if(ix>=0x7ff00000) {`
106			`if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */`
107			`else return one/x-one; /* tanh(NaN) = NaN */`
108			`}`
109
110			`/* \|x\| < 22 */`
111			`if (ix < 0x40360000) { /* \|x\|<22 */`
112			`if (ix<0x3c800000) /* \|x\|<2*-55 /`
113			`return x(one+x); / tanh(small) = small */`
114			`if (ix>=0x3ff00000) { /* \|x\|>=1 */`
115			`t = expm1(two*fabs(x));`
116			`z = one - two/(t+two);`
117			`} else {`
118			`t = expm1(-two*fabs(x));`
119			`z= -t/(t+two);`
120			`}`
121			`/* \|x\| > 22, return +-1 */`
122			`} else {`
123			`z = one - tiny; /* raised inexact flag */`
124			`}`
125			`return (jx>=0)? z: -z;`
126			`}`
127
128			`#endif /* _DOUBLE_IS_32BITS */`

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