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
151
|
/* mpfr_log10 -- logarithm in base 10.
Copyright 2001, 2002, 2003 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 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 <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of r=log10(a)
r=log10(a)=log(a)/log(10)
*/
int
mpfr_log10 (mpfr_ptr r, mpfr_srcptr a, mp_rnd_t rnd_mode)
{
int inexact = 0;
/* If a is NaN, the result is NaN */
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(a) ))
{
if (MPFR_IS_NAN(a))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
/* check for infinity before zero */
else if (MPFR_IS_INF(a))
{
if (MPFR_IS_NEG(a))
/* log10(-Inf) = NaN */
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
else /* log10(+Inf) = +Inf */
{
MPFR_SET_INF(r);
MPFR_SET_POS(r);
MPFR_RET(0); /* exact */
}
}
/* Now we can clear the flags without damage even if r == a */
else if (MPFR_IS_ZERO(a))
{
MPFR_SET_INF(r);
MPFR_SET_NEG(r);
MPFR_RET(0); /* log10(0) is an exact -infinity */
}
else
MPFR_ASSERTN(0);
}
/* If a is negative, the result is NaN */
if (MPFR_UNLIKELY( MPFR_IS_NEG(a) ))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
/* If a is 1, the result is 0 */
if (mpfr_cmp_ui (a, 1) == 0)
{
MPFR_SET_ZERO(r);
MPFR_SET_POS(r);
MPFR_RET(0); /* result is exact */
}
/* Useless due to mpfr_set
MPFR_CLEAR_FLAGS(r);*/
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, tt;
int ok;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(a); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(r); /* Precision of output 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 + 4+ __gmpfr_ceil_log2 (Nt);
/* initialise of intermediary variables */
mpfr_init (t);
mpfr_init (tt);
/* First computation of log10 */
do {
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (tt, Nt);
/* compute log10 */
mpfr_set_ui (t, 10, GMP_RNDN); /* 10 */
mpfr_log (t, t, GMP_RNDD); /* log(10) */
mpfr_log (tt, a, GMP_RNDN); /* log(a) */
mpfr_div (t, tt, t, GMP_RNDN); /* log(a)/log(10) */
/* estimation of the error */
err = Nt - 4;
ok = mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN));
/* log10(10^n) is exact */
if ((MPFR_SIGN(t) > 0) && mpfr_integer_p (t))
if (mpfr_ui_pow_ui (tt, 10, (unsigned long int) mpfr_get_d1 (t) + 0.5,
GMP_RNDN) == 0)
if (mpfr_cmp (a, tt) == 0)
ok = 1;
/* actualisation of the precision */
Nt += 10;
} while ((err < 0) || !ok);
inexact = mpfr_set (r, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (tt);
}
return inexact;
}
|
