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
|
/* mpfr_acosh -- Inverse Hyperbolic Cosine of Unsigned Integer Number
Copyright (C) 1999, 2001 Free Software Foundation, Inc.
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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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 <limits.h>
#include <math.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of acosh is done by
acosh= ln(x+sqrt(x-1)*sqrt(x+1))
*/
int
mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
{
int inexact =0;
int comp;
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
return 1;
}
comp=mpfr_cmp_ui(x,1);
if(comp < 0)
{
MPFR_SET_NAN(y);
return(1);
}
MPFR_CLEAR_NAN(y);
if(comp == 0)
{
MPFR_SET_ZERO(y); /* acosh(1) = 0 */
return(0);
}
if (MPFR_IS_INF(x))
{
MPFR_SET_INF(y);
if (MPFR_SIGN(y) < 0)
MPFR_CHANGE_SIGN(y);
return 1;
}
MPFR_CLEAR_INF(y);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te,ti;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
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+4+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
mpfr_init(ti);
/* First computation of cosh */
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ti,Nt);
/* compute acosh */
mpfr_mul(te,x,x,GMP_RNDD); /* (x^2) */
mpfr_sub_ui(ti,te,1,GMP_RNDD); /* (x^2-1) */
mpfr_sqrt(t,ti,GMP_RNDN); /* sqrt(x^2-1) */
mpfr_add(t,t,x,GMP_RNDN); /* sqrt(x^2-1)+x */
mpfr_log(t,t,GMP_RNDN); /* ln(sqrt(x^2-1)+x)*/
/* estimation of the error see- algorithms.ps*/
err=Nt-_mpfr_ceil_log2(0.5+pow(2,2-MPFR_EXP(t))+pow(2,1+MPFR_EXP(te)-MPFR_EXP(ti)-MPFR_EXP(t)));
/* actualisation of the precision */
Nt += 10;
} while ((err<0) ||!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
inexact = mpfr_set(y,t,rnd_mode);
mpfr_clear(t);
mpfr_clear(ti);
mpfr_clear(te);
}
return inexact;
}
|
