106 lines
3.3 KiB
C
106 lines
3.3 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 "nmod_poly.h"
|
||
|
|
#include "arith.h"
|
||
|
|
|
||
|
|
#define CRT_MAX_RESOLUTION 16
|
||
|
|
|
||
|
|
void
|
||
|
|
arith_bell_number_vec_multi_mod(fmpz * res, slong n)
|
||
|
|
{
|
||
|
|
fmpz_comb_t comb[CRT_MAX_RESOLUTION];
|
||
|
|
fmpz_comb_temp_t temp[CRT_MAX_RESOLUTION];
|
||
|
|
mp_ptr primes, residues;
|
||
|
|
mp_ptr * polys;
|
||
|
|
nmod_t mod;
|
||
|
|
slong i, j, k, num_primes, num_primes_k, resolution;
|
||
|
|
mp_bitcnt_t size, prime_bits;
|
||
|
|
|
||
|
|
if (n < 1)
|
||
|
|
return;
|
||
|
|
|
||
|
|
resolution = FLINT_MAX(1, FLINT_MIN(CRT_MAX_RESOLUTION, n / 16));
|
||
|
|
|
||
|
|
size = arith_bell_number_size(n);
|
||
|
|
prime_bits = FLINT_BITS - 1;
|
||
|
|
num_primes = (size + prime_bits - 1) / prime_bits;
|
||
|
|
|
||
|
|
primes = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||
|
|
residues = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||
|
|
polys = flint_malloc(num_primes * sizeof(mp_ptr));
|
||
|
|
|
||
|
|
/* Compute Bell numbers mod p */
|
||
|
|
primes[0] = n_nextprime(UWORD(1)<<prime_bits, 0);
|
||
|
|
for (k = 1; k < num_primes; k++)
|
||
|
|
primes[k] = n_nextprime(primes[k-1], 0);
|
||
|
|
|
||
|
|
for (k = 0; k < num_primes; k++)
|
||
|
|
{
|
||
|
|
/* flint_printf("prime %wd of %wd\n", k, num_primes); */
|
||
|
|
polys[k] = _nmod_vec_init(n);
|
||
|
|
nmod_init(&mod, primes[k]);
|
||
|
|
arith_bell_number_nmod_vec(polys[k], n, mod);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Init CRT comb */
|
||
|
|
for (i = 0; i < resolution; i++)
|
||
|
|
{
|
||
|
|
fmpz_comb_init(comb[i], primes, num_primes * (i + 1) / resolution);
|
||
|
|
fmpz_comb_temp_init(temp[i], comb[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Reconstruction */
|
||
|
|
for (k = 0; k < n; k++)
|
||
|
|
{
|
||
|
|
size = arith_bell_number_size(k);
|
||
|
|
/* Use only as large a comb as needed */
|
||
|
|
num_primes_k = (size + prime_bits - 1) / prime_bits;
|
||
|
|
for (i = 0; i < resolution; i++)
|
||
|
|
{
|
||
|
|
if (comb[i]->num_primes >= num_primes_k)
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
num_primes_k = comb[i]->num_primes;
|
||
|
|
for (j = 0; j < num_primes_k; j++)
|
||
|
|
residues[j] = polys[j][k];
|
||
|
|
fmpz_multi_CRT_ui(res + k, residues, comb[i], temp[i], 0);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Cleanup */
|
||
|
|
for (k = 0; k < num_primes; k++)
|
||
|
|
_nmod_vec_clear(polys[k]);
|
||
|
|
|
||
|
|
for (i = 0; i < resolution; i++)
|
||
|
|
{
|
||
|
|
fmpz_comb_temp_clear(temp[i]);
|
||
|
|
fmpz_comb_clear(comb[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
flint_free(primes);
|
||
|
|
flint_free(residues);
|
||
|
|
flint_free(polys);
|
||
|
|
}
|