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
/*
Copyright (C) 2010 Fredrik Johansson
Copyright (C) 2020 William Hart
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
#include "mpn_extras.h"
#include "fmpz.h"
#include "fmpz_factor.h"
int
fmpz_factor_trial(fmpz_factor_t factor, const fmpz_t n, slong num_primes)
{
ulong exp;
ulong p;
mpz_t x;
nn_ptr xd;
slong xsize;
slong found;
int ret = 1;
slong * idx;
slong bits, i;
const ulong * primes;
if (num_primes > 3512 || num_primes < 0)
{
flint_throw(FLINT_ERROR, "(fmpz_factor_trial) Number of primes must be in 0..3512\n");
}
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 */
xsize = flint_mpn_remove_2exp(xd, xsize, &exp);
if (exp != 0)
_fmpz_factor_append_ui(factor, UWORD(2), exp);
bits = fmpz_sizeinbase(n, 2) - exp;
idx = (slong *) flint_malloc((5 + bits/4)*sizeof(slong));
found = flint_mpn_factor_trial_tree(idx, xd, xsize, num_primes);
if (found)
{
primes = n_primes_arr_readonly(3512);
for (i = 0; i < found; i++)
{
p = primes[idx[i]];
if (p == 2)
continue;
exp = 1;
mpn_divexact_1(xd, xd, xsize, p);
xsize -= (xd[xsize - 1] == 0);
/* Check if p^2 divides n */
if (flint_mpn_divisible_1_odd(xd, xsize, p))
{
/* TODO: when searching for squarefree numbers
(Moebius function, etc), we can abort here. */
mpn_divexact_1(xd, xd, xsize, p);
xsize -= (xd[xsize - 1] == 0);
exp = 2;
}
/* If we're up to cubes, then maybe there are higher powers */
if (exp == 2 && flint_mpn_divisible_1_odd(xd, xsize, p))
{
mpn_divexact_1(xd, xd, xsize, p);
xsize -= (xd[xsize - 1] == 0);
xsize = flint_mpn_remove_power_ascending(xd, xsize, &p, 1, &exp);
exp += 3;
}
_fmpz_factor_append_ui(factor, p, exp);
}
}
/* Any factor left? */
if (xsize > 1 || xd[0] != 1)
{
fmpz_t cofactor;
mpz_t mockx; /* do not free */
fmpz_init(cofactor);
mockx->_mp_d = xd;
mockx->_mp_size = xsize;
mockx->_mp_alloc = x->_mp_alloc;
fmpz_set_mpz(cofactor, mockx);
_fmpz_factor_append(factor, cofactor, 1);
fmpz_clear(cofactor);
ret = 0;
}
mpz_clear(x);
flint_free(idx);
return ret;
}