130 lines
3.5 KiB
C
130 lines
3.5 KiB
C
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/*=============================================================================
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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 "nmod_vec.h"
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#include "nmod_poly.h"
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#include "ulong_extras.h"
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#define FLINT_REVERSE_NEWTON_CUTOFF 15
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void
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_nmod_poly_revert_series_newton(mp_ptr Qinv, mp_srcptr Q, slong n, nmod_t mod)
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{
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slong *a, i, k;
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mp_ptr T, U, V;
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if (n >= 1) Qinv[0] = UWORD(0);
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if (n >= 2) Qinv[1] = n_invmod(Q[1], mod.n);
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if (n <= 2)
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return;
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T = _nmod_vec_init(n);
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U = _nmod_vec_init(n);
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V = _nmod_vec_init(n);
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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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_nmod_poly_revert_series_lagrange(Qinv, Q, k, mod);
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_nmod_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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_nmod_poly_compose_series(T, Q, k, Qinv, k, k, mod);
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_nmod_poly_derivative(U, T, k, mod); U[k - 1] = UWORD(0);
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T[1] = UWORD(0);
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_nmod_poly_div_series(V, T, U, k, mod);
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_nmod_poly_derivative(T, Qinv, k, mod);
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_nmod_poly_mullow(U, V, k, T, k, k, mod);
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_nmod_vec_sub(Qinv, Qinv, U, k, mod);
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}
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flint_free(a);
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_nmod_vec_clear(T);
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_nmod_vec_clear(U);
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_nmod_vec_clear(V);
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}
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void
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nmod_poly_revert_series_newton(nmod_poly_t Qinv,
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const nmod_poly_t Q, slong n)
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{
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mp_ptr Qinv_coeffs, Q_coeffs;
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nmod_poly_t t1;
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slong Qlen;
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Qlen = Q->length;
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if (Qlen < 2 || Q->coeffs[0] != 0 || Q->coeffs[1] == 0)
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{
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flint_printf("Exception (nmod_poly_revert_series_newton). Input must have \n"
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"zero constant and an invertible coefficient of x^1.\n");
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abort();
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}
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if (Qlen < n)
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{
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Q_coeffs = _nmod_vec_init(n);
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flint_mpn_copyi(Q_coeffs, Q->coeffs, Qlen);
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flint_mpn_zero(Q_coeffs + Qlen, n - Qlen);
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}
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else
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Q_coeffs = Q->coeffs;
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if (Q == Qinv && Qlen >= n)
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{
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nmod_poly_init2(t1, Q->mod.n, n);
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Qinv_coeffs = t1->coeffs;
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}
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else
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{
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nmod_poly_fit_length(Qinv, n);
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Qinv_coeffs = Qinv->coeffs;
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}
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_nmod_poly_revert_series_newton(Qinv_coeffs, Q_coeffs, n, Q->mod);
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if (Q == Qinv && Qlen >= n)
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{
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nmod_poly_swap(Qinv, t1);
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nmod_poly_clear(t1);
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}
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Qinv->length = n;
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if (Qlen < n)
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_nmod_vec_clear(Q_coeffs);
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_nmod_poly_normalise(Qinv);
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}
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