148 lines
3.9 KiB
C
148 lines
3.9 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 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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#include "fmpq_poly.h"
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#define FMPQ_POLY_INV_NEWTON_CUTOFF 32
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void
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_fmpq_poly_inv_series_newton(fmpz * Qinv, fmpz_t Qinvden,
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const fmpz * Q, const fmpz_t Qden, slong n)
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{
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if (n == 1)
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{
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if (fmpz_sgn(Q) > 0)
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{
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fmpz_set(Qinv, Qden);
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fmpz_set(Qinvden, Q);
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}
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else
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{
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fmpz_neg(Qinv, Qden);
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fmpz_neg(Qinvden, Q);
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}
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}
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else
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{
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const slong alloc = FLINT_MAX(n, 3 * FMPQ_POLY_INV_NEWTON_CUTOFF);
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slong *a, i, m;
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fmpz *W, *Wden;
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W = _fmpz_vec_init(alloc + 1);
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Wden = W + 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 >= FMPQ_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 *rev = W + 2 * FMPQ_POLY_INV_NEWTON_CUTOFF;
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_fmpz_poly_reverse(rev, 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_one(Wden);
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_fmpq_poly_div(Qinv, Qinvden, W, Wden, 2*n - 1, rev, Qden, n, NULL);
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_fmpq_poly_canonicalise(Qinv, Qinvden, 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_mul(Wden, Qden, Qinvden);
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_fmpz_poly_mullow(Qinv + m, Qinv, m, W + m, n - m, n - m);
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fmpz_mul(Qinvden, Qinvden, Wden);
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_fmpz_vec_scalar_mul_fmpz(Qinv, Qinv, m, Wden);
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_fmpz_vec_neg(Qinv + m, Qinv + m, n - m);
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_fmpq_poly_canonicalise(Qinv, Qinvden, n);
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}
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_fmpz_vec_clear(W, alloc + 1);
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flint_free(a);
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}
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}
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void fmpq_poly_inv_series_newton(fmpq_poly_t Qinv, const fmpq_poly_t Q, slong n)
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{
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fmpz *copy;
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int alloc;
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if (Q->length >= n)
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{
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copy = Q->coeffs;
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alloc = 0;
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}
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else
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{
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slong i;
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copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
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for (i = 0; i < Q->length; i++)
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copy[i] = Q->coeffs[i];
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for ( ; i < n; i++)
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copy[i] = 0;
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alloc = 1;
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}
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if (Qinv != Q)
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{
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fmpq_poly_fit_length(Qinv, n);
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_fmpq_poly_inv_series_newton(Qinv->coeffs, Qinv->den, copy, Q->den, n);
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}
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else
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{
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fmpq_poly_t t;
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fmpq_poly_init2(t, n);
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_fmpq_poly_inv_series_newton(t->coeffs, t->den, copy, Q->den, n);
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fmpq_poly_swap(Qinv, t);
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fmpq_poly_clear(t);
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}
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_fmpq_poly_set_length(Qinv, n);
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fmpq_poly_canonicalise(Qinv);
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if (alloc)
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flint_free(copy);
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}
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