pqc/external/flint-2.4.3/ulong_extras/factorial_fast_mod2_preinv.c
2014-05-24 23:16:06 +02:00

79 lines
2.1 KiB
C

/*=============================================================================
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) 2012 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
mp_limb_t
n_factorial_fast_mod2_preinv(ulong n, mp_limb_t p, mp_limb_t pinv)
{
slong i, m;
nmod_t mod;
mp_ptr t, u, v;
mp_limb_t r, s;
if (p == UWORD(1) || n >= p)
return UWORD(0);
if (n <= 1)
return UWORD(1);
nmod_init(&mod, p);
m = n_sqrt(n);
t = _nmod_vec_init(m + 1);
u = _nmod_vec_init(m + 1);
v = _nmod_vec_init(m + 1);
t[0] = UWORD(0);
for (i = 1; i < m; i++)
t[i] = n_submod(t[i-1], UWORD(1), p);
_nmod_poly_product_roots_nmod_vec(u, t, m, mod);
for (i = 0; i < m; i++)
t[i] = n_mod2_preinv(i * m + 1, p, pinv);
_nmod_poly_evaluate_nmod_vec_fast(v, u, m + 1, t, m, mod);
r = 1;
for (i = 0; i < m; i++)
r = n_mulmod2_preinv(r, v[i], mod.n, mod.ninv);
for (s = m * m + 1; s <= n; s++)
r = n_mulmod2_preinv(r, s, mod.n, mod.ninv);
_nmod_vec_clear(t);
_nmod_vec_clear(u);
_nmod_vec_clear(v);
return r;
}