163 lines
4.4 KiB
C
163 lines
4.4 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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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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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_poly.h"
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#include "fmpq_poly.h"
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#define FLINT_REVERSE_NEWTON_CUTOFF 4
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void
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_fmpq_poly_revert_series_newton(fmpz * Qinv, fmpz_t den,
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const fmpz * Q, const fmpz_t Qden, slong n)
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{
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if (fmpz_is_one(Qden) && (n > 1) && fmpz_is_pm1(Q + 1))
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{
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_fmpz_poly_revert_series(Qinv, Q, n);
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fmpz_one(den);
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}
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else if (n <= 2)
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{
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fmpz_zero(Qinv);
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if (n == 2)
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{
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fmpz_set(Qinv + 1, Qden);
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fmpz_set(den, Q + 1);
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_fmpq_poly_canonicalise(Qinv, den, 2);
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}
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}
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else
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{
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slong *a, i, k;
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fmpz *T, *U, *V;
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fmpz_t Tden, Uden, Vden;
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T = _fmpz_vec_init(n);
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U = _fmpz_vec_init(n);
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V = _fmpz_vec_init(n);
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fmpz_init(Tden);
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fmpz_init(Uden);
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fmpz_init(Vden);
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k = n;
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for (i = 1; (WORD(1) << i) < k; i++);
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a = (slong *) flint_malloc(i * sizeof(slong));
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a[i = 0] = k;
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while (k >= FLINT_REVERSE_NEWTON_CUTOFF)
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a[++i] = (k = (k + 1) / 2);
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_fmpq_poly_revert_series_lagrange(Qinv, den, Q, Qden, k);
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_fmpz_vec_zero(Qinv + k, n - k);
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for (i--; i >= 0; i--)
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{
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k = a[i];
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_fmpq_poly_compose_series(T, Tden, Q, Qden, k, Qinv, den, k, k);
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_fmpq_poly_derivative(U, Uden, T, Tden, k); fmpz_zero(U + k - 1);
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fmpz_zero(T + 1);
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_fmpq_poly_div_series(V, Vden, T, Tden, U, Uden, k);
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_fmpq_poly_canonicalise(V, Vden, k);
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_fmpq_poly_derivative(T, Tden, Qinv, den, k);
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_fmpq_poly_mullow(U, Uden, V, Vden, k, T, Tden, k, k);
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_fmpq_poly_sub(Qinv, den, Qinv, den, k, U, Uden, k);
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}
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_fmpq_poly_canonicalise(Qinv, den, n);
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flint_free(a);
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_fmpz_vec_clear(T, n);
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_fmpz_vec_clear(U, n);
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_fmpz_vec_clear(V, n);
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fmpz_clear(Tden);
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fmpz_clear(Uden);
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fmpz_clear(Vden);
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}
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}
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void
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fmpq_poly_revert_series_newton(fmpq_poly_t res,
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const fmpq_poly_t poly, slong n)
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{
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fmpz *copy;
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int alloc;
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if (poly->length < 2 || !fmpz_is_zero(poly->coeffs)
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|| fmpz_is_zero(poly->coeffs + 1))
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{
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flint_printf("Exception (fmpq_poly_revert_series_newton). Input must have \n"
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"zero constant term and nonzero coefficient of x^1.\n");
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abort();
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}
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if (n < 2)
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{
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fmpq_poly_zero(res);
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return;
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}
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if (poly->length >= n)
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{
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copy = poly->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 < poly->length; i++)
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copy[i] = poly->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 (res != poly)
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{
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fmpq_poly_fit_length(res, n);
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_fmpq_poly_revert_series_newton(res->coeffs,
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res->den, copy, poly->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_revert_series_newton(t->coeffs,
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t->den, copy, poly->den, n);
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fmpq_poly_swap(res, t);
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fmpq_poly_clear(t);
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}
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_fmpq_poly_set_length(res, n);
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_fmpq_poly_normalise(res);
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if (alloc)
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flint_free(copy);
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}
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