|
sl@0
|
1 |
/* S_TANH.C
|
|
sl@0
|
2 |
*
|
|
sl@0
|
3 |
* Portions Copyright (c) 1993-1999 Nokia Corporation and/or its subsidiary(-ies).
|
|
sl@0
|
4 |
* All rights reserved.
|
|
sl@0
|
5 |
*/
|
|
sl@0
|
6 |
|
|
sl@0
|
7 |
|
|
sl@0
|
8 |
/* @(#)s_tanh.c 5.1 93/09/24 */
|
|
sl@0
|
9 |
/*
|
|
sl@0
|
10 |
* ====================================================
|
|
sl@0
|
11 |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
sl@0
|
12 |
*
|
|
sl@0
|
13 |
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
sl@0
|
14 |
* Permission to use, copy, modify, and distribute this
|
|
sl@0
|
15 |
* software is freely granted, provided that this notice
|
|
sl@0
|
16 |
* is preserved.
|
|
sl@0
|
17 |
* ====================================================
|
|
sl@0
|
18 |
*/
|
|
sl@0
|
19 |
|
|
sl@0
|
20 |
/*
|
|
sl@0
|
21 |
|
|
sl@0
|
22 |
FUNCTION
|
|
sl@0
|
23 |
<<tanh>>, <<tanhf>>---hyperbolic tangent
|
|
sl@0
|
24 |
|
|
sl@0
|
25 |
INDEX
|
|
sl@0
|
26 |
tanh
|
|
sl@0
|
27 |
INDEX
|
|
sl@0
|
28 |
tanhf
|
|
sl@0
|
29 |
|
|
sl@0
|
30 |
ANSI_SYNOPSIS
|
|
sl@0
|
31 |
#include <math.h>
|
|
sl@0
|
32 |
double tanh(double <[x]>);
|
|
sl@0
|
33 |
float tanhf(float <[x]>);
|
|
sl@0
|
34 |
|
|
sl@0
|
35 |
TRAD_SYNOPSIS
|
|
sl@0
|
36 |
#include <math.h>
|
|
sl@0
|
37 |
double tanh(<[x]>)
|
|
sl@0
|
38 |
double <[x]>;
|
|
sl@0
|
39 |
|
|
sl@0
|
40 |
float tanhf(<[x]>)
|
|
sl@0
|
41 |
float <[x]>;
|
|
sl@0
|
42 |
|
|
sl@0
|
43 |
|
|
sl@0
|
44 |
DESCRIPTION
|
|
sl@0
|
45 |
|
|
sl@0
|
46 |
<<tanh>> computes the hyperbolic tangent of
|
|
sl@0
|
47 |
the argument <[x]>. Angles are specified in radians.
|
|
sl@0
|
48 |
|
|
sl@0
|
49 |
<<tanh(<[x]>)>> is defined as
|
|
sl@0
|
50 |
. sinh(<[x]>)/cosh(<[x]>)
|
|
sl@0
|
51 |
|
|
sl@0
|
52 |
<<tanhf>> is identical, save that it takes and returns <<float>> values.
|
|
sl@0
|
53 |
|
|
sl@0
|
54 |
RETURNS
|
|
sl@0
|
55 |
The hyperbolic tangent of <[x]> is returned.
|
|
sl@0
|
56 |
|
|
sl@0
|
57 |
PORTABILITY
|
|
sl@0
|
58 |
<<tanh>> is ANSI C. <<tanhf>> is an extension.
|
|
sl@0
|
59 |
|
|
sl@0
|
60 |
*/
|
|
sl@0
|
61 |
|
|
sl@0
|
62 |
/* Tanh(x)
|
|
sl@0
|
63 |
* Return the Hyperbolic Tangent of x
|
|
sl@0
|
64 |
*
|
|
sl@0
|
65 |
* Method :
|
|
sl@0
|
66 |
* x -x
|
|
sl@0
|
67 |
* e - e
|
|
sl@0
|
68 |
* 0. tanh(x) is defined to be -----------
|
|
sl@0
|
69 |
* x -x
|
|
sl@0
|
70 |
* e + e
|
|
sl@0
|
71 |
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
|
sl@0
|
72 |
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
|
|
sl@0
|
73 |
* -t
|
|
sl@0
|
74 |
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
|
sl@0
|
75 |
* t + 2
|
|
sl@0
|
76 |
* 2
|
|
sl@0
|
77 |
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
|
sl@0
|
78 |
* t + 2
|
|
sl@0
|
79 |
* 22.0 < x <= INF : tanh(x) := 1.
|
|
sl@0
|
80 |
*
|
|
sl@0
|
81 |
* Special cases:
|
|
sl@0
|
82 |
* tanh(NaN) is NaN;
|
|
sl@0
|
83 |
* only tanh(0)=0 is exact for finite argument.
|
|
sl@0
|
84 |
*/
|
|
sl@0
|
85 |
|
|
sl@0
|
86 |
#include "FDLIBM.H"
|
|
sl@0
|
87 |
|
|
sl@0
|
88 |
static const double one=1.0, two=2.0, tiny = 1.0e-300;
|
|
sl@0
|
89 |
|
|
sl@0
|
90 |
/**
|
|
sl@0
|
91 |
Calculate hyperbolic tangent.
|
|
sl@0
|
92 |
@return hyperbolic tangent of x.
|
|
sl@0
|
93 |
@param x Angle expressed in radians (180 degrees = PI radians).
|
|
sl@0
|
94 |
*/
|
|
sl@0
|
95 |
EXPORT_C double tanh(double x) __SOFTFP
|
|
sl@0
|
96 |
{
|
|
sl@0
|
97 |
double t,z;
|
|
sl@0
|
98 |
__int32_t jx,ix;
|
|
sl@0
|
99 |
|
|
sl@0
|
100 |
/* High word of |x|. */
|
|
sl@0
|
101 |
GET_HIGH_WORD(jx,x);
|
|
sl@0
|
102 |
ix = jx&0x7fffffff;
|
|
sl@0
|
103 |
|
|
sl@0
|
104 |
/* x is INF or NaN */
|
|
sl@0
|
105 |
if(ix>=0x7ff00000) {
|
|
sl@0
|
106 |
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
|
sl@0
|
107 |
else return one/x-one; /* tanh(NaN) = NaN */
|
|
sl@0
|
108 |
}
|
|
sl@0
|
109 |
|
|
sl@0
|
110 |
/* |x| < 22 */
|
|
sl@0
|
111 |
if (ix < 0x40360000) { /* |x|<22 */
|
|
sl@0
|
112 |
if (ix<0x3c800000) /* |x|<2**-55 */
|
|
sl@0
|
113 |
return x*(one+x); /* tanh(small) = small */
|
|
sl@0
|
114 |
if (ix>=0x3ff00000) { /* |x|>=1 */
|
|
sl@0
|
115 |
t = expm1(two*fabs(x));
|
|
sl@0
|
116 |
z = one - two/(t+two);
|
|
sl@0
|
117 |
} else {
|
|
sl@0
|
118 |
t = expm1(-two*fabs(x));
|
|
sl@0
|
119 |
z= -t/(t+two);
|
|
sl@0
|
120 |
}
|
|
sl@0
|
121 |
/* |x| > 22, return +-1 */
|
|
sl@0
|
122 |
} else {
|
|
sl@0
|
123 |
z = one - tiny; /* raised inexact flag */
|
|
sl@0
|
124 |
}
|
|
sl@0
|
125 |
return (jx>=0)? z: -z;
|
|
sl@0
|
126 |
}
|