pqc/external/flint-2.4.3/fmpz_mod_poly/xgcd_euclidean.c
2014-05-24 23:16:06 +02:00

244 lines
7.2 KiB
C

/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 William Hart
Copyright (C) 2012 Sebastian Pancratz
******************************************************************************/
#include <stdlib.h>
#include "fmpz_vec.h"
#include "fmpz_mod_poly.h"
slong _fmpz_mod_poly_xgcd_euclidean(fmpz *G, fmpz *S, fmpz *T,
const fmpz *A, slong lenA,
const fmpz *B, slong lenB,
const fmpz_t invB, const fmpz_t p)
{
_fmpz_vec_zero(G, lenB);
_fmpz_vec_zero(S, lenB - 1);
_fmpz_vec_zero(T, lenA - 1);
if (lenB == 1)
{
fmpz_set(G + 0, B + 0);
fmpz_one(T + 0);
return 1;
}
else
{
fmpz *Q, *R;
slong lenQ, lenR;
Q = _fmpz_vec_init(2 * lenA);
R = Q + lenA;
_fmpz_mod_poly_divrem(Q, R, A, lenA, B, lenB, invB, p);
lenR = lenB - 1;
FMPZ_VEC_NORM(R, lenR);
if (lenR == 0)
{
_fmpz_vec_set(G, B, lenB);
fmpz_one(T + 0);
_fmpz_vec_clear(Q, 2 * lenA);
return lenB;
}
else
{
fmpz_t inv;
fmpz *D, *U, *V1, *V3, *W;
slong lenD, lenU, lenV1, lenV3, lenW;
fmpz_init(inv);
W = _fmpz_vec_init(FLINT_MAX(5 * lenB, lenA + lenB));
D = W + lenB;
U = D + lenB;
V1 = U + lenB;
V3 = V1 + lenB;
lenU = 0;
_fmpz_vec_set(D, B, lenB);
lenD = lenB;
fmpz_one(V1 + 0);
lenV1 = 1;
lenV3 = 0;
FMPZ_VEC_SWAP(V3, lenV3, R, lenR);
do {
fmpz_invmod(inv, V3 + (lenV3 - 1), p);
_fmpz_mod_poly_divrem(Q, R, D, lenD, V3, lenV3, inv, p);
lenQ = lenD - lenV3 + 1;
lenR = lenV3 - 1;
FMPZ_VEC_NORM(R, lenR);
if (lenV1 >= lenQ)
_fmpz_mod_poly_mul(W, V1, lenV1, Q, lenQ, p);
else
_fmpz_mod_poly_mul(W, Q, lenQ, V1, lenV1, p);
lenW = lenQ + lenV1 - 1;
_fmpz_mod_poly_sub(U, U, lenU, W, lenW, p);
lenU = FLINT_MAX(lenU, lenW);
FMPZ_VEC_NORM(U, lenU);
FMPZ_VEC_SWAP(U, lenU, V1, lenV1);
{
fmpz *__t;
slong __tn;
__t = D;
D = V3;
V3 = R;
R = __t;
__tn = lenD;
lenD = lenV3;
lenV3 = lenR;
lenR = __tn;
}
} while (lenV3 != 0);
_fmpz_vec_set(G, D, lenD);
_fmpz_vec_set(S, U, lenU);
{
lenQ = lenA + lenU - 1;
_fmpz_mod_poly_mul(Q, A, lenA, S, lenU, p);
_fmpz_mod_poly_neg(Q, Q, lenQ, p);
_fmpz_mod_poly_add(Q, G, lenD, Q, lenQ, p);
_fmpz_mod_poly_divrem(T, W, Q, lenQ, B, lenB, invB, p);
}
_fmpz_vec_clear(W, FLINT_MAX(5 * lenB, lenA + lenB));
_fmpz_vec_clear(Q, 2 * lenA);
fmpz_clear(inv);
return lenD;
}
}
}
void
fmpz_mod_poly_xgcd_euclidean(fmpz_mod_poly_t G,
fmpz_mod_poly_t S, fmpz_mod_poly_t T,
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
{
if (A->length < B->length)
{
fmpz_mod_poly_xgcd_euclidean(G, T, S, B, A);
}
else /* lenA >= lenB >= 0 */
{
const slong lenA = A->length, lenB = B->length;
fmpz_t inv;
fmpz_init(inv);
if (lenA == 0) /* lenA = lenB = 0 */
{
fmpz_mod_poly_zero(G);
fmpz_mod_poly_zero(S);
fmpz_mod_poly_zero(T);
}
else if (lenB == 0) /* lenA > lenB = 0 */
{
fmpz_invmod(inv, fmpz_mod_poly_lead(A), &A->p);
fmpz_mod_poly_scalar_mul_fmpz(G, A, inv);
fmpz_mod_poly_zero(T);
fmpz_mod_poly_set_fmpz(S, inv);
}
else /* lenA >= lenB >= 2 */
{
fmpz *g, *s, *t;
slong lenG;
if (G == A || G == B)
{
g = _fmpz_vec_init(FLINT_MIN(lenA, lenB));
}
else
{
fmpz_mod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
g = G->coeffs;
}
if (S == A || S == B)
{
s = _fmpz_vec_init(lenB);
}
else
{
fmpz_mod_poly_fit_length(S, lenB);
s = S->coeffs;
}
if (T == A || T == B)
{
t = _fmpz_vec_init(lenA);
}
else
{
fmpz_mod_poly_fit_length(T, lenA);
t = T->coeffs;
}
fmpz_invmod(inv, fmpz_mod_poly_lead(B), &B->p);
lenG = _fmpz_mod_poly_xgcd_euclidean(g, s, t,
A->coeffs, lenA, B->coeffs, lenB, inv, &B->p);
if (G == A || G == B)
{
_fmpz_vec_clear(G->coeffs, G->alloc);
G->coeffs = g;
G->alloc = FLINT_MIN(lenA, lenB);
}
if (S == A || S == B)
{
_fmpz_vec_clear(S->coeffs, S->alloc);
S->coeffs = s;
S->alloc = lenB;
}
if (T == A || T == B)
{
_fmpz_vec_clear(T->coeffs, T->alloc);
T->coeffs = t;
T->alloc = lenA;
}
_fmpz_mod_poly_set_length(G, lenG);
_fmpz_mod_poly_set_length(S, FLINT_MAX(lenB - lenG, 1));
_fmpz_mod_poly_set_length(T, FLINT_MAX(lenA - lenG, 1));
_fmpz_mod_poly_normalise(S);
_fmpz_mod_poly_normalise(T);
if (!fmpz_is_one(fmpz_mod_poly_lead(G)))
{
fmpz_invmod(inv, fmpz_mod_poly_lead(G), &A->p);
fmpz_mod_poly_scalar_mul_fmpz(G, G, inv);
fmpz_mod_poly_scalar_mul_fmpz(S, S, inv);
fmpz_mod_poly_scalar_mul_fmpz(T, T, inv);
}
}
fmpz_clear(inv);
}
}