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

111 lines
3.6 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) 2011 Fredrik Johansson
******************************************************************************/
#include "arith.h"
const mp_limb_t bell_number_tab[] =
{
UWORD(1), UWORD(1), UWORD(2), UWORD(5), UWORD(15), UWORD(52), UWORD(203), UWORD(877), UWORD(4140), UWORD(21147), UWORD(115975),
UWORD(678570), UWORD(4213597), UWORD(27644437), UWORD(190899322), UWORD(1382958545),
#if FLINT64
UWORD(10480142147), UWORD(82864869804), UWORD(682076806159), UWORD(5832742205057),
UWORD(51724158235372), UWORD(474869816156751), UWORD(4506715738447323),
UWORD(44152005855084346), UWORD(445958869294805289),
UWORD(4638590332229999353),
#endif
};
static const char bell_mod_2[3] = {1, 1, 0};
static const char bell_mod_3[13] = {1, 1, 2, 2, 0, 1, 2, 1, 0, 0, 1, 0, 1};
mp_limb_t
arith_bell_number_nmod(ulong n, nmod_t mod)
{
mp_limb_t s, t, u;
mp_ptr facs, pows;
slong i, j;
if (n < BELL_NUMBER_TAB_SIZE)
return n_mod2_preinv(bell_number_tab[n], mod.n, mod.ninv);
if (mod.n == 2) return bell_mod_2[n % 3];
if (mod.n == 3) return bell_mod_3[n % 13];
if (mod.n <= n)
{
mp_ptr bvec = flint_malloc(sizeof(mp_limb_t) * (n + 1));
arith_bell_number_nmod_vec_recursive(bvec, n + 1, mod);
s = bvec[n];
flint_free(bvec);
return s;
}
/* Compute inverse factorials */
/* We actually compute (n! / i!) and divide out (n!)^2 at the end */
facs = flint_malloc(sizeof(mp_limb_t) * (n + 1));
facs[n] = 1;
for (i = n - 1; i >= 0; i--)
facs[i] = n_mulmod2_preinv(facs[i + 1], i + 1, mod.n, mod.ninv);
/* Compute powers */
pows = flint_calloc(n + 1, sizeof(mp_limb_t));
pows[0] = n_powmod2_ui_preinv(0, n, mod.n, mod.ninv);
pows[1] = n_powmod2_ui_preinv(1, n, mod.n, mod.ninv);
for (i = 2; i <= n; i++)
{
if (pows[i] == 0)
pows[i] = n_powmod2_ui_preinv(i, n, mod.n, mod.ninv);
for (j = 2; j <= i && i * j <= n; j++)
if (pows[i * j] == 0)
pows[i * j] = n_mulmod2_preinv(pows[i],
pows[j], mod.n, mod.ninv);
}
for (s = t = i = 0; i <= n; i++)
{
if (i % 2 == 0)
t = n_addmod(t, facs[i], mod.n);
else
t = n_submod(t, facs[i], mod.n);
u = pows[n - i];
u = n_mulmod2_preinv(u, facs[n - i], mod.n, mod.ninv);
u = n_mulmod2_preinv(u, t, mod.n, mod.ninv);
s = n_addmod(s, u, mod.n);
}
/* Remove (n!)^2 */
u = n_invmod(facs[0], mod.n);
u = n_mulmod2_preinv(u, u, mod.n, mod.ninv);
s = n_mulmod2_preinv(s, u, mod.n, mod.ninv);
flint_free(facs);
flint_free(pows);
return s;
}