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
|
/* mpfr_pow_ui, mpfr_ui_pow_ui -- compute the power of a floating-point
number or machine integer
Copyright (C) 1999 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 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 <math.h>
#include <stdio.h>
#include "gmp.h"
#include "mpfr.h"
/* sets x to y^n, and returns ceil(log2(max ulp error)) */
int
#if __STDC__
mpfr_pow_ui (mpfr_ptr x, mpfr_srcptr y, unsigned long int n, mp_rnd_t rnd)
#else
mpfr_pow_ui (x, y, n, rnd)
mpfr_ptr x;
mpfr_srcptr y;
unsigned long int n;
mp_rnd_t rnd;
#endif
{
long int i; double err;
if (MPFR_IS_INF(y))
{
if (n == 0) { MPFR_SET_NAN(x); return; }
else if ((MPFR_SIGN(y) < 0 && (MPFR_SIGN(x) > 0 || n % 2 == 0)) ||
MPFR_SIGN(y) > 0 && (MPFR_SIGN(x) < 0 && n % 2 == 1))
MPFR_CHANGE_SIGN(x);
MPFR_SET_INF(x); return;
}
if (n==0) { mpfr_set_ui(x, 1, rnd); return 0; }
mpfr_set(x, y, rnd); err = 1.0;
for (i=0;(1<<i)<=n;i++);
/* now 2^(i-1) <= n < 2^i */
for (i-=2; i>=0; i--) {
mpfr_mul(x, x, x, rnd); err = 2.0*err+1.0;
if (n & (1<<i)) { mpfr_mul(x, x, y, rnd); err += 1.0; }
}
return (int) ceil(log(err)/LOG2);
}
/* sets x to y^n, and returns ceil(log2(max ulp error)) */
/* TODO: gerer l'infini en cas de debordement ? Fait mecaniquement si fait
dans mul ? */
int
#if __STDC__
mpfr_ui_pow_ui (mpfr_ptr x, unsigned long int y, unsigned long int n,
mp_rnd_t rnd)
#else
mpfr_ui_pow_ui (x, y, n, rnd)
mpfr_ptr x;
unsigned long int y;
unsigned long int n;
mp_rnd_t rnd;
#endif
{
long int i; double err;
if (n==0) { mpfr_set_ui(x, 1, rnd); return 0; }
mpfr_set_ui(x, y, rnd);
err = 1.0;
for (i=0;(1<<i)<=n;i++);
/* now 2^(i-1) <= n < 2^i */
for (i-=2; i>=0; i--) {
mpfr_mul(x, x, x, rnd); err = 2.0 * err + 1.0;
if (n & (1<<i)) {
mpfr_mul_ui(x, x, y, rnd);
err = err + 1.0;
}
}
return (int) ceil(log(err)/LOG2);
}
|
