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
129
130
131
132
133
134
135
136
137
138
139
140
141
|
/* tanh.c
*
* Hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* double x, y, tanh();
*
* y = tanh( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic tangent of argument in the range MINLOG to
* MAXLOG.
*
* A rational function is used for |x| < 0.625. The form
* x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
* Otherwise,
* tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -2,2 50000 3.3e-17 6.4e-18
* IEEE -2,2 30000 2.5e-16 5.8e-17
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include <math.h>
#ifdef UNK
static double P[] = {
-9.64399179425052238628E-1,
-9.92877231001918586564E1,
-1.61468768441708447952E3
};
static double Q[] = {
/* 1.00000000000000000000E0,*/
1.12811678491632931402E2,
2.23548839060100448583E3,
4.84406305325125486048E3
};
#endif
#ifdef DEC
static unsigned short P[] = {
0140166,0161335,0053753,0075126,
0141706,0111520,0070463,0040552,
0142711,0153001,0101300,0025430
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041741,0117624,0051300,0156060,
0043013,0133720,0071251,0127717,
0043227,0060201,0021020,0020136
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x6f4b,0xaafd,0xdc5b,0xbfee,
0x682d,0x0e26,0xd26a,0xc058,
0x0563,0x3058,0x3ac0,0xc099
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x1b86,0x8a58,0x33f2,0x405c,
0x35fa,0x0e55,0x76fa,0x40a1,
0x040c,0x2442,0xec10,0x40b2
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xbfee,0xdc5b,0xaafd,0x6f4b,
0xc058,0xd26a,0x0e26,0x682d,
0xc099,0x3ac0,0x3058,0x0563
};
static unsigned short Q[] = {
0x405c,0x33f2,0x8a58,0x1b86,
0x40a1,0x76fa,0x0e55,0x35fa,
0x40b2,0xec10,0x2442,0x040c
};
#endif
#ifdef ANSIPROT
extern double fabs ( double );
extern double exp ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
#else
double fabs(), exp(), polevl(), p1evl();
#endif
extern double MAXLOG;
double tanh(x)
double x;
{
double s, z;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
z = fabs(x);
if( z > 0.5 * MAXLOG )
{
if( x > 0 )
return( 1.0 );
else
return( -1.0 );
}
if( z >= 0.625 )
{
s = exp(2.0*z);
z = 1.0 - 2.0/(s + 1.0);
if( x < 0 )
z = -z;
}
else
{
if( x == 0.0 )
return(x);
s = x * x;
z = polevl( s, P, 2 )/p1evl(s, Q, 3);
z = x * s * z;
z = x + z;
}
return( z );
}
|
