249 lines
6.9 KiB
C
249 lines
6.9 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 Sebastian Pancratz
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******************************************************************************/
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#include <stdlib.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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void _fmpq_poly_xgcd(fmpz *G, fmpz_t denG,
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fmpz *S, fmpz_t denS, fmpz *T, fmpz_t denT,
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const fmpz *A, const fmpz_t denA, slong lenA,
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const fmpz *B, const fmpz_t denB, slong lenB)
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{
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int alloc = 0;
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fmpz *primA, *primB, *C, *D;
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fmpz_t cA, cB;
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slong lenG, lenC, lenD;
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fmpz_init(cA);
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fmpz_init(cB);
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_fmpz_vec_content(cA, A, lenA);
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_fmpz_vec_content(cB, B, lenB);
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if (fmpz_is_one(cA))
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{
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if (fmpz_is_one(cB))
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{
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primA = (fmpz *) A;
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primB = (fmpz *) B;
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}
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else
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{
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alloc |= 1;
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primA = (fmpz *) A;
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primB = _fmpz_vec_init(lenB);
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_fmpz_vec_scalar_divexact_fmpz(primB, B, lenB, cB);
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}
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}
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else
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{
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if (fmpz_is_one(cA))
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{
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alloc |= 2;
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primA = _fmpz_vec_init(lenA);
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primB = (fmpz *) B;
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_fmpz_vec_scalar_divexact_fmpz(primA, A, lenA, cA);
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}
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else
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{
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alloc |= 3;
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primA = _fmpz_vec_init(lenA + lenB);
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primB = primA + lenA;
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_fmpz_vec_scalar_divexact_fmpz(primA, A, lenA, cA);
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_fmpz_vec_scalar_divexact_fmpz(primB, B, lenB, cB);
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}
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}
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_fmpz_poly_gcd(G, primA, lenA, primB, lenB);
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for (lenG = lenB - 1; !G[lenG]; lenG--) ;
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lenG++;
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if (lenG > 1)
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{
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alloc |= 4;
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lenC = lenA - lenG + 1;
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lenD = lenB - lenG + 1;
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C = _fmpz_vec_init(lenC + lenD);
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D = C + lenC;
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_fmpz_poly_div(C, primA, lenA, G, lenG);
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_fmpz_poly_div(D, primB, lenB, G, lenG);
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}
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else
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{
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lenC = lenA;
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lenD = lenB;
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C = primA;
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D = primB;
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}
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_fmpz_poly_xgcd(denG, S, T, C, lenC, D, lenD);
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if (!fmpz_is_one(denA))
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_fmpz_vec_scalar_mul_fmpz(S, S, lenD, denA);
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fmpz_mul(cA, cA, denG);
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fmpz_mul(denS, cA, G + (lenG - 1));
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if (!fmpz_is_one(denB))
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_fmpz_vec_scalar_mul_fmpz(T, T, lenC, denB);
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fmpz_mul(cB, cB, denG);
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fmpz_mul(denT, cB, G + (lenG - 1));
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_fmpz_vec_zero(S + lenD, lenB - lenD);
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_fmpz_vec_zero(T + lenC, lenA - lenC);
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_fmpq_poly_canonicalise(S, denS, lenD);
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_fmpq_poly_canonicalise(T, denT, lenC);
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fmpz_set(denG, G + (lenG - 1));
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if ((alloc & 3) == 1)
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_fmpz_vec_clear(primB, lenB);
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else if ((alloc & 3) == 2)
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_fmpz_vec_clear(primA, lenA);
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else if ((alloc & 3) == 3)
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_fmpz_vec_clear(primA, lenA + lenB);
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if ((alloc & 4))
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_fmpz_vec_clear(C, lenC + lenD);
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fmpz_clear(cA);
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fmpz_clear(cB);
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}
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void fmpq_poly_xgcd(fmpq_poly_t G, fmpq_poly_t S, fmpq_poly_t T,
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const fmpq_poly_t A, const fmpq_poly_t B)
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{
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if (G == S || G == T || S == T)
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{
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flint_printf("Exception (fmpq_poly_xgcd). Output arguments aliased.\n");
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abort();
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}
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if (A->length < B->length)
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{
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fmpq_poly_xgcd(G, T, S, B, A);
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} else
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{
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slong lenA = A->length, lenB = B->length, lenG = lenB;
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if (lenA == 0) /* lenA = lenB = 0 */
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{
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fmpq_poly_zero(G);
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fmpq_poly_zero(S);
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fmpq_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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fmpq_poly_make_monic(G, A);
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fmpq_poly_zero(T);
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fmpq_poly_fit_length(S, 1);
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_fmpq_poly_set_length(S, 1);
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if (fmpz_sgn(A->coeffs + (lenA - 1)) > 0)
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{
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fmpz_set(S->coeffs, A->den);
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fmpz_set(S->den, A->coeffs + (lenA - 1));
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}
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else
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{
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fmpz_neg(S->coeffs, A->den);
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fmpz_neg(S->den, A->coeffs + (lenA - 1));
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}
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fmpq_poly_canonicalise(S);
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}
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else if (lenB == 1) /* lenA >= lenB = 1 */
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{
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fmpq_poly_set_ui(G, 1);
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fmpq_poly_zero(S);
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fmpq_poly_fit_length(T, 1);
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_fmpq_poly_set_length(T, 1);
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if (fmpz_sgn(B->coeffs) > 0)
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{
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fmpz_set(T->coeffs, B->den);
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fmpz_set(T->den, B->coeffs);
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}
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else
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{
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fmpz_neg(T->coeffs, B->den);
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fmpz_neg(T->den, B->coeffs);
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}
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}
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else /* lenA >= lenB >= 2 */
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{
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/* Aliasing */
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if (G == A || G == B)
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{
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fmpq_poly_t tG;
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fmpq_poly_init2(tG, lenG);
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fmpq_poly_xgcd(tG, S, T, A, B);
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fmpq_poly_swap(tG, G);
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fmpq_poly_clear(tG);
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}
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else if (S == A || S == B)
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{
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fmpq_poly_t tS;
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fmpq_poly_init2(tS, lenB);
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fmpq_poly_xgcd(G, tS, T, A, B);
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fmpq_poly_swap(tS, S);
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fmpq_poly_clear(tS);
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}
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else if (T == A || T == B)
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{
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fmpq_poly_t tT;
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fmpq_poly_init2(tT, lenA);
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fmpq_poly_xgcd(G, S, tT, A, B);
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fmpq_poly_swap(tT, T);
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fmpq_poly_clear(tT);
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}
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else /* no aliasing */
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{
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fmpq_poly_fit_length(G, lenG);
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fmpq_poly_fit_length(S, lenB);
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fmpq_poly_fit_length(T, lenA);
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_fmpq_poly_xgcd(G->coeffs, G->den, S->coeffs, S->den, T->coeffs, T->den,
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A->coeffs, A->den, lenA, B->coeffs, B->den, lenB);
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_fmpq_poly_set_length(G, lenG);
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_fmpq_poly_set_length(S, lenB);
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_fmpq_poly_set_length(T, lenA);
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_fmpq_poly_normalise(G);
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_fmpq_poly_normalise(S);
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_fmpq_poly_normalise(T);
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}
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}
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}
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}
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