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
142
143
144
145
146
147
148
149
150
|
/* mpfr_tanh -- hyperbolic tangent
Copyright (C) 2001 Free Software Foundation.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of cosh is done by
tanh= [e^(x)^2-1]/+[e^(x)^2+1]
*/
int
#if __STDC__
mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
#else
mpfr_tanh (y, xt, rnd_mode)
mpfr_ptr y;
mpfr_srcptr xt;
mp_rnd_t rnd_mode;
#endif
{
/****** Declaration ******/
mpfr_t x;
mp_prec_t Nxt = MPFR_PREC(xt);
int flag_neg=0, inexact=0;
/* Special value checking */
if (MPFR_IS_NAN(xt))
{
MPFR_SET_NAN(y);
return 1;
}
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(xt))
{
if(MPFR_SIGN(xt) > 0)
return mpfr_set_si(y,1,rnd_mode); /* tanh(inf) = 1 */
else
return mpfr_set_si(y,-1,rnd_mode); /* tanh(-inf) = -1 */
}
MPFR_CLEAR_INF(y);
/* tanh(0) = 0 */
if(!MPFR_NOTZERO(xt))
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN(y,xt);
return 0;
}
mpfr_init2(x,Nxt);
mpfr_set(x,xt,GMP_RNDN);
if(MPFR_SIGN(x)<0)
{
MPFR_CHANGE_SIGN(x);
flag_neg=1;
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te, ta,tb;
int d;
/* Declaration of the size variable */
mp_prec_t Nx = Nxt; /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt=MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt = Nt+_mpfr_ceil_log2(9)+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
mpfr_init(ta);
mpfr_init(tb);
/* First computation of cosh */
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ta,Nt);
mpfr_set_prec(tb,Nt);
/* compute tanh */
mpfr_mul_2exp(te,x,1,GMP_RNDN); /* 2x */
mpfr_exp(te,te,GMP_RNDN); /* exp(2x) */
mpfr_add_ui(ta,te,1,GMP_RNDD); /* exp(2x) + 1*/
mpfr_sub_ui(tb,te,1,GMP_RNDU); /* exp(2x) - 1*/
mpfr_div(t,tb,ta,GMP_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/
/* calculation of the error*/
d = MPFR_EXP(te)-MPFR_EXP(t);
/* estimation of the error */
/*err = Nt-(_mpfr_ceil_log2(7+pow(2,d+1)));*/
err = Nt-(MAX(d+1,3)+1);
/* actualisation of the precision */
Nt += 10;
} while ((err <0)||!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
if (flag_neg==1)
MPFR_CHANGE_SIGN(t);
inexact = mpfr_set(y,t,rnd_mode);
mpfr_clear(t);
mpfr_clear(te);
mpfr_clear(ta);
mpfr_clear(tb);
}
mpfr_clear(x);
return inexact;
}
|
