1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
|
/* @(#)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 */
|
