122 lines
3.3 KiB
C
122 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) 2010, 2011 Sebastian Pancratz
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******************************************************************************/
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#include <stdlib.h>
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "fmpz_poly.h"
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void
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_fmpz_poly_inv_series_newton(fmpz * Qinv, const fmpz * Q, slong n)
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{
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if (n == 1) /* Q is +-1 */
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{
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fmpz_set(Qinv, Q);
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}
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else
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{
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const slong alloc = FLINT_MAX(n, 3 * FMPZ_POLY_INV_NEWTON_CUTOFF);
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slong *a, i, m;
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fmpz *W;
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W = _fmpz_vec_init(alloc);
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for (i = 1; (WORD(1) << i) < n; i++) ;
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a = (slong *) flint_malloc(i * sizeof(slong));
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a[i = 0] = n;
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while (n >= FMPZ_POLY_INV_NEWTON_CUTOFF)
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a[++i] = (n = (n + 1) / 2);
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/* Base case */
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{
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fmpz *Qrev = W + 2 * FMPZ_POLY_INV_NEWTON_CUTOFF;
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_fmpz_poly_reverse(Qrev, Q, n, n);
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_fmpz_vec_zero(W, 2*n - 2);
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fmpz_one(W + (2*n - 2));
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_fmpz_poly_div_basecase(Qinv, W, W, 2*n - 1, Qrev, n);
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_fmpz_poly_reverse(Qinv, Qinv, n, n);
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}
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for (i--; i >= 0; i--)
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{
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m = n;
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n = a[i];
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_fmpz_poly_mullow(W, Q, n, Qinv, m, n);
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_fmpz_poly_mullow(Qinv + m, Qinv, m, W + m, n - m, n - m);
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_fmpz_vec_neg(Qinv + m, Qinv + m, n - m);
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}
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_fmpz_vec_clear(W, alloc);
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flint_free(a);
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}
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}
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void fmpz_poly_inv_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n)
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{
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fmpz *Qcopy;
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int Qalloc;
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if (Q->length >= n)
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{
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Qcopy = Q->coeffs;
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Qalloc = 0;
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}
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else
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{
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slong i;
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Qcopy = (fmpz *) flint_malloc(n * sizeof(fmpz));
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for (i = 0; i < Q->length; i++)
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Qcopy[i] = Q->coeffs[i];
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flint_mpn_zero((mp_ptr) Qcopy + i, n - i);
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Qalloc = 1;
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}
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if (Qinv != Q)
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{
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fmpz_poly_fit_length(Qinv, n);
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_fmpz_poly_inv_series_newton(Qinv->coeffs, Qcopy, n);
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}
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else
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{
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fmpz_poly_t t;
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fmpz_poly_init2(t, n);
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_fmpz_poly_inv_series_newton(t->coeffs, Qcopy, n);
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fmpz_poly_swap(Qinv, t);
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fmpz_poly_clear(t);
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}
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_fmpz_poly_set_length(Qinv, n);
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_fmpz_poly_normalise(Qinv);
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if (Qalloc)
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flint_free(Qcopy);
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}
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