long _nmod_poly_xgcd(mp_ptr G, mp_ptr S, mp_ptr T,
mp_srcptr A, long lenA, mp_srcptr B, long lenB, nmod_t mod)
{
const long cutoff = FLINT_BIT_COUNT(mod.n) <= 8 ?
NMOD_POLY_SMALL_GCD_CUTOFF : NMOD_POLY_GCD_CUTOFF;
if (lenA < cutoff)
return _nmod_poly_xgcd_euclidean(G, S, T, A, lenA, B, lenB, mod);
else
return _nmod_poly_xgcd_hgcd(G, S, T, A, lenA, B, lenB, mod);
}
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);
}
}
}
}
