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
|
/* mpfr_pow_si -- power function x^y with y an unsigned int
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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of y=pow(x,z) is done by
y=pow_ui(x,z) if z>0
else
y=1/pow_ui(x,z) if z<0
*/
int
mpfr_pow_si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd_mode)
{
if (n > 0)
return mpfr_pow_ui (y, x, n, rnd_mode);
else
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
if (n == 0)
return mpfr_set_ui (y, 1, GMP_RNDN);
if (MPFR_IS_INF(x))
{
MPFR_SET_ZERO(y);
if (MPFR_SIGN(x) > 0 || ((unsigned) n & 1) == 0)
MPFR_SET_POS(y);
else
MPFR_SET_NEG(y);
MPFR_RET(0);
}
if (MPFR_IS_ZERO(x))
{
MPFR_SET_INF(y);
if (MPFR_SIGN(x) > 0 || ((unsigned) n & 1) == 0)
MPFR_SET_POS(y);
else
MPFR_SET_NEG(y);
MPFR_RET(0);
}
MPFR_CLEAR_INF(y);
/* detect exact powers: x^(-n) is exact iff x is a power of 2 */
if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0)
{
mpfr_set_si (y, (n % 2) ? MPFR_SIGN(x) : 1, rnd_mode);
MPFR_EXP(y) += n * (MPFR_EXP(x) - 1);
return 0;
}
n = -n;
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, 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 */
long int err; /* Precision of error */
int inexact;
/* compute the precision of intermediary variable */
Nt = MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + 3 + __gmpfr_ceil_log2 (Nt);
mpfr_save_emin_emax ();
/* initialise of intermediary variable */
mpfr_init (t);
mpfr_init (ti);
do
{
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (ti, Nt);
/* compute 1/(x^n) n>0*/
mpfr_pow_ui (ti, x, (unsigned long int) n, GMP_RNDN);
mpfr_ui_div (t, 1, ti, GMP_RNDN);
/* error estimate -- see pow function in algorithms.ps */
err = Nt - 3;
/* actualisation of the precision */
Nt += 10;
}
while (err < 0 || !mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN)));
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_restore_emin_emax ();
return mpfr_check_range (y, inexact, rnd_mode);
}
}
}
|
