106 lines
3.3 KiB
C
106 lines
3.3 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include "nmod_poly.h"
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#include "arith.h"
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#define CRT_MAX_RESOLUTION 16
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void
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arith_bell_number_vec_multi_mod(fmpz * res, slong n)
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{
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fmpz_comb_t comb[CRT_MAX_RESOLUTION];
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fmpz_comb_temp_t temp[CRT_MAX_RESOLUTION];
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mp_ptr primes, residues;
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mp_ptr * polys;
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nmod_t mod;
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slong i, j, k, num_primes, num_primes_k, resolution;
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mp_bitcnt_t size, prime_bits;
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if (n < 1)
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return;
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resolution = FLINT_MAX(1, FLINT_MIN(CRT_MAX_RESOLUTION, n / 16));
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size = arith_bell_number_size(n);
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prime_bits = FLINT_BITS - 1;
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num_primes = (size + prime_bits - 1) / prime_bits;
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primes = flint_malloc(num_primes * sizeof(mp_limb_t));
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residues = flint_malloc(num_primes * sizeof(mp_limb_t));
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polys = flint_malloc(num_primes * sizeof(mp_ptr));
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/* Compute Bell numbers mod p */
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primes[0] = n_nextprime(UWORD(1)<<prime_bits, 0);
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for (k = 1; k < num_primes; k++)
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primes[k] = n_nextprime(primes[k-1], 0);
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for (k = 0; k < num_primes; k++)
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{
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/* flint_printf("prime %wd of %wd\n", k, num_primes); */
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polys[k] = _nmod_vec_init(n);
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nmod_init(&mod, primes[k]);
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arith_bell_number_nmod_vec(polys[k], n, mod);
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}
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/* Init CRT comb */
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for (i = 0; i < resolution; i++)
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{
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fmpz_comb_init(comb[i], primes, num_primes * (i + 1) / resolution);
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fmpz_comb_temp_init(temp[i], comb[i]);
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}
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/* Reconstruction */
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for (k = 0; k < n; k++)
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{
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size = arith_bell_number_size(k);
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/* Use only as large a comb as needed */
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num_primes_k = (size + prime_bits - 1) / prime_bits;
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for (i = 0; i < resolution; i++)
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{
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if (comb[i]->num_primes >= num_primes_k)
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break;
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}
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num_primes_k = comb[i]->num_primes;
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for (j = 0; j < num_primes_k; j++)
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residues[j] = polys[j][k];
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fmpz_multi_CRT_ui(res + k, residues, comb[i], temp[i], 0);
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}
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/* Cleanup */
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for (k = 0; k < num_primes; k++)
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_nmod_vec_clear(polys[k]);
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for (i = 0; i < resolution; i++)
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{
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fmpz_comb_temp_clear(temp[i]);
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fmpz_comb_clear(comb[i]);
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}
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flint_free(primes);
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flint_free(residues);
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flint_free(polys);
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}
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