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
|
/*=============================================================================
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) 2011 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
/* Avoid computing every reciprocal */
#if FLINT64
#define PROD_TAKE4 UWORD(65535)
#define PROD_TAKE3 UWORD(2642245)
#define PROD_TAKE2 UWORD(4294967295)
#else
#define PROD_TAKE4 UWORD(255)
#define PROD_TAKE3 UWORD(1625)
#define PROD_TAKE2 UWORD(65535)
#endif
#define MUL3(xx,yy,zz) n_mulmod2_preinv(xx,\
n_mulmod2_preinv(yy,zz,mod.n,mod.ninv),mod.n,mod.ninv);
void _nmod_poly_integral(mp_ptr x_int, mp_srcptr x, slong len, nmod_t mod)
{
mp_limb_t r;
slong k = len - 1;
while (k > 0)
{
if (k > 3 && k < PROD_TAKE4)
{
r = n_invmod(k*(k-1)*(k-2)*(k-3), mod.n);
x_int[k] = MUL3(x[k-1], r, (k-1)*(k-2)*(k-3));
x_int[k-1] = MUL3(x[k-2], r, k*(k-2)*(k-3));
x_int[k-2] = MUL3(x[k-3], r, k*(k-1)*(k-3));
x_int[k-3] = MUL3(x[k-4], r, k*(k-1)*(k-2));
k -= 4;
}
else if (k > 2 && k < PROD_TAKE3)
{
r = n_invmod(k*(k-1)*(k-2), mod.n);
x_int[k] = MUL3(x[k-1], r, (k-1)*(k-2));
x_int[k-1] = MUL3(x[k-2], r, k*(k-2));
x_int[k-2] = MUL3(x[k-3], r, k*(k-1));
k -= 3;
}
else if (k > 1 && k < PROD_TAKE2)
{
r = n_invmod(k*(k-1), mod.n);
x_int[k] = MUL3(x[k-1], r, k-1);
x_int[k-1] = MUL3(x[k-2], r, k);
k -= 2;
}
else
{
r = n_invmod(k, mod.n);
x_int[k] = n_mulmod2_preinv(x[k-1], r, mod.n, mod.ninv);
k -= 1;
}
}
x_int[0] = UWORD(0);
}
void nmod_poly_integral(nmod_poly_t x_int, const nmod_poly_t x)
{
nmod_poly_fit_length(x_int, x->length + 1);
_nmod_poly_integral(x_int->coeffs, x->coeffs, x->length + 1, x->mod);
x_int->length = x->length + 1;
_nmod_poly_normalise(x_int);
}
|
