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/*=============================================================================
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 <math.h>
#include "arith.h"
/* Computes length-m vector containing |E_{2k}| */
static void
__euler_number_vec_mod_p(mp_ptr res, mp_ptr tmp, slong m, nmod_t mod)
{
mp_limb_t fac, c;
slong k;
/* Divide by factorials */
fac = n_factorial_mod2_preinv(2*(m-1), mod.n, mod.ninv);
c = n_invmod(fac, mod.n);
for (k = m - 1; k >= 0; k--)
{
tmp[k] = c;
c = n_mulmod2_preinv(c, (2*k)*(2*k-1), mod.n, mod.ninv);
}
_nmod_poly_inv_series(res, tmp, m, mod);
/* Multiply by factorials */
c = UWORD(1);
for (k = 0; k < m; k++)
{
res[k] = n_mulmod2_preinv(res[k], c, mod.n, mod.ninv);
c = n_mulmod2_preinv(c, (2*k+1)*(2*k+2), mod.n, mod.ninv);
c = n_negmod(c, mod.n);
}
}
#define CRT_MAX_RESOLUTION 16
void __euler_number_vec_multi_mod(fmpz * res, slong n)
{
fmpz_comb_t comb[CRT_MAX_RESOLUTION];
fmpz_comb_temp_t temp[CRT_MAX_RESOLUTION];
mp_limb_t * primes;
mp_limb_t * residues;
mp_ptr * polys;
mp_ptr temppoly;
nmod_t mod;
slong i, j, k, m, num_primes, num_primes_k, resolution;
mp_bitcnt_t size, prime_bits;
if (n < 1)
return;
/* Number of nonzero entries */
m = (n + 1) / 2;
resolution = FLINT_MAX(1, FLINT_MIN(CRT_MAX_RESOLUTION, m / 16));
size = arith_euler_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 Euler 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);
temppoly = _nmod_vec_init(m);
for (k = 0; k < num_primes; k++)
{
polys[k] = _nmod_vec_init(m);
nmod_init(&mod, primes[k]);
__euler_number_vec_mod_p(polys[k], temppoly, m, 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]);
}
/* Trivial entries */
for (k = 1; k < n; k += 2)
fmpz_zero(res + k);
/* Reconstruction */
for (k = 0; k < n; k += 2)
{
size = arith_euler_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 / 2];
fmpz_multi_CRT_ui(res + k, residues, comb[i], temp[i], 0);
if (k % 4)
fmpz_neg(res + k, res + k);
}
/* Cleanup */
for (k = 0; k < num_primes; k++)
_nmod_vec_clear(polys[k]);
_nmod_vec_clear(temppoly);
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);
}
void arith_euler_number_vec(fmpz * res, slong n)
{
__euler_number_vec_multi_mod(res, n);
}
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