pqc/external/flint-2.4.3/nmod_poly/xgcd_euclidean.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
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 "nmod_poly.h"
#include "mpn_extras.h"
slong _nmod_poly_xgcd_euclidean(mp_ptr G, mp_ptr S, mp_ptr T,
mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod)
{
flint_mpn_zero(G, lenB);
flint_mpn_zero(S, lenB - 1);
flint_mpn_zero(T, lenA - 1);
if (lenB == 1)
{
G[0] = B[0];
T[0] = 1;
return 1;
}
else
{
mp_ptr Q, R;
slong lenQ, lenR, lenG;
Q = _nmod_vec_init(2 * lenA);
R = Q + lenA;
_nmod_poly_divrem(Q, R, A, lenA, B, lenB, mod);
lenR = lenB - 1;
MPN_NORM(R, lenR);
if (lenR == 0)
{
_nmod_vec_set(G, B, lenB);
T[0] = 1;
lenG = lenB;
}
else
{
mp_ptr D, U, V1, V3, W;
slong lenD, lenU, lenV1, lenV3, lenW;
W = _nmod_vec_init(FLINT_MAX(5 * lenB, lenA + lenB));
D = W + lenB;
U = D + lenB;
V1 = U + lenB;
V3 = V1 + lenB;
lenU = 0;
_nmod_vec_set(D, B, lenB);
lenD = lenB;
V1[0] = 1;
lenV1 = 1;
lenV3 = 0;
MPN_SWAP(V3, lenV3, R, lenR);
do {
_nmod_poly_divrem(Q, R, D, lenD, V3, lenV3, mod);
lenQ = lenD - lenV3 + 1;
lenR = lenV3 - 1;
MPN_NORM(R, lenR);
if (lenV1 >= lenQ)
_nmod_poly_mul(W, V1, lenV1, Q, lenQ, mod);
else
_nmod_poly_mul(W, Q, lenQ, V1, lenV1, mod);
lenW = lenQ + lenV1 - 1;
_nmod_poly_sub(U, U, lenU, W, lenW, mod);
lenU = FLINT_MAX(lenU, lenW);
MPN_NORM(U, lenU);
MPN_SWAP(U, lenU, V1, lenV1);
{
mp_ptr __t;
slong __tn;
__t = D;
D = V3;
V3 = R;
R = __t;
__tn = lenD;
lenD = lenV3;
lenV3 = lenR;
lenR = __tn;
}
} while (lenV3 != 0);
_nmod_vec_set(G, D, lenD);
_nmod_vec_set(S, U, lenU);
{
lenQ = lenA + lenU - 1;
_nmod_poly_mul(Q, A, lenA, S, lenU, mod);
_nmod_vec_neg(Q, Q, lenQ, mod);
_nmod_poly_add(Q, G, lenD, Q, lenQ, mod);
_nmod_poly_divrem(T, W, Q, lenQ, B, lenB, mod);
}
_nmod_vec_clear(W);
lenG = lenD;
}
_nmod_vec_clear(Q);
return lenG;
}
}
void
nmod_poly_xgcd_euclidean(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B)
{
if (A->length < B->length)
{
nmod_poly_xgcd_euclidean(G, T, S, B, A);
}
else /* lenA >= lenB >= 0 */
{
const slong lenA = A->length, lenB = B->length;
mp_limb_t inv;
if (lenA == 0) /* lenA = lenB = 0 */
{
nmod_poly_zero(G);
nmod_poly_zero(S);
nmod_poly_zero(T);
}
else if (lenB == 0) /* lenA > lenB = 0 */
{
inv = n_invmod(A->coeffs[lenA - 1], A->mod.n);
nmod_poly_scalar_mul_nmod(G, A, inv);
nmod_poly_zero(T);
nmod_poly_set_coeff_ui(S, 0, inv);
S->length = 1;
}
else if (lenB == 1) /* lenA >= lenB = 1 */
{
nmod_poly_fit_length(T, 1);
T->length = 1;
T->coeffs[0] = n_invmod(B->coeffs[0], A->mod.n);
nmod_poly_one(G);
nmod_poly_zero(S);
}
else /* lenA >= lenB >= 2 */
{
mp_ptr g, s, t;
slong lenG;
if (G == A || G == B)
{
g = _nmod_vec_init(FLINT_MIN(lenA, lenB));
}
else
{
nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
g = G->coeffs;
}
if (S == A || S == B)
{
s = _nmod_vec_init(lenB - 1);
}
else
{
nmod_poly_fit_length(S, lenB - 1);
s = S->coeffs;
}
if (T == A || T == B)
{
t = _nmod_vec_init(lenA - 1);
}
else
{
nmod_poly_fit_length(T, lenA - 1);
t = T->coeffs;
}
if (lenA >= lenB)
lenG = _nmod_poly_xgcd_euclidean(g, s, t, A->coeffs, lenA,
B->coeffs, lenB, A->mod);
else
lenG = _nmod_poly_xgcd_euclidean(g, t, s, B->coeffs, lenB,
A->coeffs, lenA, A->mod);
if (G == A || G == B)
{
flint_free(G->coeffs);
G->coeffs = g;
G->alloc = FLINT_MIN(lenA, lenB);
}
if (S == A || S == B)
{
flint_free(S->coeffs);
S->coeffs = s;
S->alloc = lenB - 1;
}
if (T == A || T == B)
{
flint_free(T->coeffs);
T->coeffs = t;
T->alloc = lenA - 1;
}
G->length = lenG;
S->length = FLINT_MAX(lenB - lenG, 1);
T->length = FLINT_MAX(lenA - lenG, 1);
MPN_NORM(S->coeffs, S->length);
MPN_NORM(T->coeffs, T->length);
if (G->coeffs[lenG - 1] != 1)
{
inv = n_invmod(G->coeffs[lenG - 1], A->mod.n);
nmod_poly_scalar_mul_nmod(G, G, inv);
nmod_poly_scalar_mul_nmod(S, S, inv);
nmod_poly_scalar_mul_nmod(T, T, inv);
}
}
}
}