248 lines
7.1 KiB
C
248 lines
7.1 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) 2011 William Hart
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Copyright (C) 2012 Sebastian Pancratz
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******************************************************************************/
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#include <stdlib.h>
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#include "nmod_poly.h"
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#include "mpn_extras.h"
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slong _nmod_poly_xgcd_euclidean(mp_ptr G, mp_ptr S, mp_ptr T,
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mp_srcptr A, slong lenA,
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mp_srcptr B, slong lenB, nmod_t mod)
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{
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flint_mpn_zero(G, lenB);
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flint_mpn_zero(S, lenB - 1);
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flint_mpn_zero(T, lenA - 1);
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if (lenB == 1)
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{
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G[0] = B[0];
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T[0] = 1;
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return 1;
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}
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else
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{
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mp_ptr Q, R;
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slong lenQ, lenR, lenG;
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Q = _nmod_vec_init(2 * lenA);
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R = Q + lenA;
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_nmod_poly_divrem(Q, R, A, lenA, B, lenB, mod);
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lenR = lenB - 1;
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MPN_NORM(R, lenR);
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if (lenR == 0)
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{
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_nmod_vec_set(G, B, lenB);
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T[0] = 1;
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lenG = lenB;
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}
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else
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{
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mp_ptr D, U, V1, V3, W;
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slong lenD, lenU, lenV1, lenV3, lenW;
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W = _nmod_vec_init(FLINT_MAX(5 * lenB, lenA + lenB));
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D = W + lenB;
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U = D + lenB;
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V1 = U + lenB;
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V3 = V1 + lenB;
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lenU = 0;
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_nmod_vec_set(D, B, lenB);
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lenD = lenB;
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V1[0] = 1;
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lenV1 = 1;
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lenV3 = 0;
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MPN_SWAP(V3, lenV3, R, lenR);
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do {
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_nmod_poly_divrem(Q, R, D, lenD, V3, lenV3, mod);
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lenQ = lenD - lenV3 + 1;
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lenR = lenV3 - 1;
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MPN_NORM(R, lenR);
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if (lenV1 >= lenQ)
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_nmod_poly_mul(W, V1, lenV1, Q, lenQ, mod);
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else
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_nmod_poly_mul(W, Q, lenQ, V1, lenV1, mod);
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lenW = lenQ + lenV1 - 1;
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_nmod_poly_sub(U, U, lenU, W, lenW, mod);
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lenU = FLINT_MAX(lenU, lenW);
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MPN_NORM(U, lenU);
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MPN_SWAP(U, lenU, V1, lenV1);
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{
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mp_ptr __t;
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slong __tn;
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__t = D;
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D = V3;
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V3 = R;
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R = __t;
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__tn = lenD;
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lenD = lenV3;
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lenV3 = lenR;
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lenR = __tn;
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}
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} while (lenV3 != 0);
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_nmod_vec_set(G, D, lenD);
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_nmod_vec_set(S, U, lenU);
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{
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lenQ = lenA + lenU - 1;
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_nmod_poly_mul(Q, A, lenA, S, lenU, mod);
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_nmod_vec_neg(Q, Q, lenQ, mod);
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_nmod_poly_add(Q, G, lenD, Q, lenQ, mod);
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_nmod_poly_divrem(T, W, Q, lenQ, B, lenB, mod);
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}
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_nmod_vec_clear(W);
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lenG = lenD;
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}
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_nmod_vec_clear(Q);
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return lenG;
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}
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}
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void
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nmod_poly_xgcd_euclidean(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
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const nmod_poly_t A, const nmod_poly_t B)
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{
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if (A->length < B->length)
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{
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nmod_poly_xgcd_euclidean(G, T, S, B, A);
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}
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else /* lenA >= lenB >= 0 */
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{
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const slong lenA = A->length, lenB = B->length;
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mp_limb_t inv;
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if (lenA == 0) /* lenA = lenB = 0 */
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{
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nmod_poly_zero(G);
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nmod_poly_zero(S);
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nmod_poly_zero(T);
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}
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else if (lenB == 0) /* lenA > lenB = 0 */
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{
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inv = n_invmod(A->coeffs[lenA - 1], A->mod.n);
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nmod_poly_scalar_mul_nmod(G, A, inv);
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nmod_poly_zero(T);
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nmod_poly_set_coeff_ui(S, 0, inv);
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S->length = 1;
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}
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else if (lenB == 1) /* lenA >= lenB = 1 */
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{
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nmod_poly_fit_length(T, 1);
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T->length = 1;
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T->coeffs[0] = n_invmod(B->coeffs[0], A->mod.n);
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nmod_poly_one(G);
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nmod_poly_zero(S);
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}
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else /* lenA >= lenB >= 2 */
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{
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mp_ptr g, s, t;
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slong lenG;
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if (G == A || G == B)
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{
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g = _nmod_vec_init(FLINT_MIN(lenA, lenB));
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}
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else
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{
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nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
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g = G->coeffs;
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}
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if (S == A || S == B)
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{
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s = _nmod_vec_init(lenB - 1);
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}
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else
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{
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nmod_poly_fit_length(S, lenB - 1);
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s = S->coeffs;
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}
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if (T == A || T == B)
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{
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t = _nmod_vec_init(lenA - 1);
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}
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else
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{
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nmod_poly_fit_length(T, lenA - 1);
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t = T->coeffs;
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}
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if (lenA >= lenB)
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lenG = _nmod_poly_xgcd_euclidean(g, s, t, A->coeffs, lenA,
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B->coeffs, lenB, A->mod);
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else
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lenG = _nmod_poly_xgcd_euclidean(g, t, s, B->coeffs, lenB,
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A->coeffs, lenA, A->mod);
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if (G == A || G == B)
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{
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flint_free(G->coeffs);
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G->coeffs = g;
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G->alloc = FLINT_MIN(lenA, lenB);
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}
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if (S == A || S == B)
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{
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flint_free(S->coeffs);
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S->coeffs = s;
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S->alloc = lenB - 1;
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}
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if (T == A || T == B)
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{
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flint_free(T->coeffs);
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T->coeffs = t;
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T->alloc = lenA - 1;
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}
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G->length = lenG;
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S->length = FLINT_MAX(lenB - lenG, 1);
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T->length = FLINT_MAX(lenA - lenG, 1);
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MPN_NORM(S->coeffs, S->length);
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MPN_NORM(T->coeffs, T->length);
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if (G->coeffs[lenG - 1] != 1)
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{
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inv = n_invmod(G->coeffs[lenG - 1], A->mod.n);
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nmod_poly_scalar_mul_nmod(G, G, inv);
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nmod_poly_scalar_mul_nmod(S, S, inv);
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nmod_poly_scalar_mul_nmod(T, T, inv);
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}
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}
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}
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}
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