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

362 lines
12 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) 2011 Sebastian Pancratz
******************************************************************************/
#include <stdlib.h>
#include <gmp.h>
#include "flint.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "nmod_poly_mat.h"
#include "mpn_extras.h"
/*
We define a whole bunch of macros here which essentially provide
the nmod_poly functionality as far as the setting of coefficient
data and lengths is concerned, but which do not do any separate
memory allocation. None of these macros support aliasing.
*/
#define __set(B, lenB, A, lenA) \
do { \
_nmod_vec_set((B), (A), (lenA)); \
(lenB) = (lenA); \
} while (0)
#define __add(C, lenC, A, lenA, B, lenB) \
do { \
_nmod_poly_add((C), (A), (lenA), (B), (lenB), mod); \
(lenC) = FLINT_MAX((lenA), (lenB)); \
MPN_NORM((C), (lenC)); \
} while (0)
#define __sub(C, lenC, A, lenA, B, lenB) \
do { \
_nmod_poly_sub((C), (A), (lenA), (B), (lenB), mod); \
(lenC) = FLINT_MAX((lenA), (lenB)); \
MPN_NORM((C), (lenC)); \
} while (0)
#define __mul(C, lenC, A, lenA, B, lenB) \
do { \
if ((lenA) != 0 && (lenB) != 0) \
{ \
if ((lenA) >= (lenB)) \
_nmod_poly_mul((C), (A), (lenA), (B), (lenB), mod); \
else \
_nmod_poly_mul((C), (B), (lenB), (A), (lenA), mod); \
(lenC) = (lenA) + (lenB) - 1; \
} \
else \
{ \
(lenC) = 0; \
} \
} while (0)
#define __divrem(Q, lenQ, R, lenR, A, lenA, B, lenB) \
do { \
if ((lenA) >= (lenB)) \
{ \
_nmod_poly_divrem((Q), (R), (A), (lenA), (B), (lenB), mod); \
(lenQ) = (lenA) - (lenB) + 1; \
(lenR) = (lenB) - 1; \
MPN_NORM((R), (lenR)); \
} \
else \
{ \
_nmod_vec_set((R), (A), (lenA)); \
(lenQ) = 0; \
(lenR) = (lenA); \
} \
} while (0)
#define __div(Q, lenQ, A, lenA, B, lenB) \
do { \
if ((lenA) >= (lenB)) \
{ \
_nmod_poly_div((Q), (A), (lenA), (B), (lenB), mod); \
(lenQ) = (lenA) - (lenB) + 1; \
} \
else \
{ \
(lenQ) = 0; \
} \
} while (0)
slong _nmod_poly_xgcd_hgcd(mp_ptr G, mp_ptr S, mp_ptr T,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB,
nmod_t mod)
{
const slong cutoff = FLINT_BIT_COUNT(mod.n) <= 8 ?
NMOD_POLY_SMALL_GCD_CUTOFF : NMOD_POLY_GCD_CUTOFF;
slong lenG, lenS, lenT;
if (lenB == 1)
{
G[0] = B[0];
T[0] = 1;
lenG = 1;
lenS = 0;
lenT = 1;
}
else
{
mp_ptr q = _nmod_vec_init(lenA + lenB);
mp_ptr r = q + lenA;
slong lenq, lenr;
__divrem(q, lenq, r, lenr, A, lenA, B, lenB);
if (lenr == 0)
{
__set(G, lenG, B, lenB);
T[0] = 1;
lenS = 0;
lenT = 1;
}
else
{
mp_ptr h, j, v, w, R[4], X;
slong lenh, lenj, lenv, lenw, lenR[4];
int sgnR;
lenh = lenj = lenB;
lenv = lenw = lenA + lenB - 2;
lenR[0] = lenR[1] = lenR[2] = lenR[3] = (lenB + 1) / 2;
X = _nmod_vec_init(2 * lenh + 2 * lenv + 4 * lenR[0]);
h = X;
j = h + lenh;
v = j + lenj;
w = v + lenv;
R[0] = w + lenw;
R[1] = R[0] + lenR[0];
R[2] = R[1] + lenR[1];
R[3] = R[2] + lenR[2];
sgnR = _nmod_poly_hgcd(R, lenR, h, &lenh, j, &lenj, B, lenB, r, lenr, mod);
if (sgnR > 0)
{
_nmod_vec_neg(S, R[1], lenR[1], mod);
_nmod_vec_set(T, R[0], lenR[0]);
}
else
{
_nmod_vec_set(S, R[1], lenR[1]);
_nmod_vec_neg(T, R[0], lenR[0], mod);
}
lenS = lenR[1];
lenT = lenR[0];
while (lenj != 0)
{
__divrem(q, lenq, r, lenr, h, lenh, j, lenj);
__mul(v, lenv, q, lenq, T, lenT);
{
slong l;
_nmod_vec_swap(S, T, FLINT_MAX(lenS, lenT));
l = lenS; lenS = lenT; lenT = l;
}
__sub(T, lenT, T, lenT, v, lenv);
if (lenr == 0)
{
__set(G, lenG, j, lenj);
goto cofactor;
}
if (lenj < cutoff)
{
mp_ptr u0 = R[0], u1 = R[1];
slong lenu0 = lenr - 1, lenu1 = lenj - 1;
lenG = _nmod_poly_xgcd_euclidean(G, u0, u1, j, lenj, r, lenr, mod);
MPN_NORM(u0, lenu0);
MPN_NORM(u1, lenu1);
__mul(v, lenv, S, lenS, u0, lenu0);
__mul(w, lenw, T, lenT, u1, lenu1);
__add(S, lenS, v, lenv, w, lenw);
goto cofactor;
}
sgnR = _nmod_poly_hgcd(R, lenR, h, &lenh, j, &lenj, j,lenj, r, lenr, mod);
__mul(v, lenv, R[1], lenR[1], T, lenT);
__mul(w, lenw, R[2], lenR[2], S, lenS);
__mul(q, lenq, S, lenS, R[3], lenR[3]);
if (sgnR > 0)
__sub(S, lenS, q, lenq, v, lenv);
else
__sub(S, lenS, v, lenv, q, lenq);
__mul(q, lenq, T, lenT, R[0], lenR[0]);
if (sgnR > WORD(0))
__sub(T, lenT, q, lenq, w, lenw);
else
__sub(T, lenT, w, lenw, q, lenq);
}
__set(G, lenG, h, lenh);
cofactor:
__mul(v, lenv, S, lenS, A, lenA);
__sub(w, lenw, G, lenG, v, lenv);
__div(T, lenT, w, lenw, B, lenB);
_nmod_vec_clear(X);
}
_nmod_vec_clear(q);
}
flint_mpn_zero(S + lenS, lenB - 1 - lenS);
flint_mpn_zero(T + lenT, lenA - 1 - lenT);
return lenG;
}
void
nmod_poly_xgcd_hgcd(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_hgcd(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(FLINT_MAX(lenB - 1, 2));
}
else
{
nmod_poly_fit_length(S, FLINT_MAX(lenB - 1, 2));
s = S->coeffs;
}
if (T == A || T == B)
{
t = _nmod_vec_init(FLINT_MAX(lenA - 1, 2));
}
else
{
nmod_poly_fit_length(T, FLINT_MAX(lenA - 1, 2));
t = T->coeffs;
}
if (lenA >= lenB)
lenG = _nmod_poly_xgcd_hgcd(g, s, t, A->coeffs, lenA,
B->coeffs, lenB, A->mod);
else
lenG = _nmod_poly_xgcd_hgcd(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 = FLINT_MAX(lenB - 1, 2);
}
if (T == A || T == B)
{
flint_free(T->coeffs);
T->coeffs = t;
T->alloc = FLINT_MAX(lenA - 1, 2);
}
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);
}
}
}
}
#undef __set
#undef __add
#undef __sub
#undef __mul
#undef __divrem
#undef __div