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
|
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2010 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "mpn_extras.h"
#include "ulong_extras.h"
int
fmpz_factor_trial_range(fmpz_factor_t factor, const fmpz_t n, ulong start, ulong num_primes)
{
ulong exp;
mp_limb_t p;
mpz_t x;
mp_ptr xd;
mp_size_t xsize;
slong found;
slong trial_start, trial_stop;
int ret = 1;
if (!COEFF_IS_MPZ(*n))
{
fmpz_factor_si(factor, *n);
return ret;
}
_fmpz_factor_set_length(factor, 0);
/* Make an mpz_t copy whose limbs will be mutated */
mpz_init(x);
fmpz_get_mpz(x, n);
if (x->_mp_size < 0)
{
x->_mp_size = -(x->_mp_size);
factor->sign = -1;
}
else
{
factor->sign = 1;
}
xd = x->_mp_d;
xsize = x->_mp_size;
/* Factor out powers of two */
if (start == 0)
{
xsize = flint_mpn_remove_2exp(xd, xsize, &exp);
if (exp != 0)
_fmpz_factor_append_ui(factor, UWORD(2), exp);
}
trial_start = FLINT_MAX(1, start);
trial_stop = FLINT_MIN(start + 1000, start + num_primes);
do
{
found = flint_mpn_factor_trial(xd, xsize, trial_start, trial_stop);
if (found)
{
p = n_primes_arr_readonly(found+1)[found];
exp = 1;
xsize = flint_mpn_divexact_1(xd, xsize, p);
/* Check if p^2 divides n */
if (flint_mpn_divisible_1_p(xd, xsize, p))
{
/* TODO: when searching for squarefree numbers
(Moebius function, etc), we can abort here. */
xsize = flint_mpn_divexact_1(xd, xsize, p);
exp = 2;
}
/* If we're up to cubes, then maybe there are higher powers */
if (exp == 2 && flint_mpn_divisible_1_p(xd, xsize, p))
{
xsize = flint_mpn_divexact_1(xd, xsize, p);
xsize = flint_mpn_remove_power_ascending(xd, xsize, &p, 1, &exp);
exp += 3;
}
_fmpz_factor_append_ui(factor, p, exp);
/* flint_printf("added %wu %wu\n", p, exp); */
/* Continue using only trial division whilst it is successful.
This allows quickly factoring huge highly composite numbers
such as factorials, which can arise in some applications. */
trial_start = found + 1;
trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
continue;
}
else
{
/* Insert primality test, perfect power test, other factoring
algorithms here... */
trial_start = trial_stop;
trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
}
} while ((xsize > 1 || xd[0] != 1) && trial_start != trial_stop);
/* Any factor left? */
if (xsize > 1 || xd[0] != 1)
ret = 0;
mpz_clear(x);
return ret;
}
|
