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/*
Copyright (C) 2011 William Hart
Copyright (C) 2011 Sebastian Pancratz
Copyright (C) 2013 Mike Hansen
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#ifdef T
#include "templates.h"
slong
_TEMPLATE(T, poly_gcd_euclidean_f) (TEMPLATE(T, t) f, TEMPLATE(T, struct) * G,
const TEMPLATE(T, struct) * A, slong lenA,
const TEMPLATE(T, struct) * B, slong lenB,
const TEMPLATE(T, ctx_t) ctx)
{
slong lenG = 0;
if (lenB == 1)
{
TEMPLATE(T, t) invB;
TEMPLATE(T, init) (invB, ctx);
TEMPLATE(T, gcdinv) (f, invB, B, ctx);
if (TEMPLATE(T, is_one) (f, ctx))
{
TEMPLATE(T, one) (G, ctx);
lenG = 1;
}
TEMPLATE(T, clear) (invB, ctx);
}
else /* lenA >= lenB > 1 */
{
const slong lenW = FLINT_MAX(lenA - lenB + 1, lenB) + lenA + 2 * lenB;
TEMPLATE(T, struct) * Q, *R1, *R2, *R3, *T, *W;
slong lenR2, lenR3;
W = _TEMPLATE(T, vec_init) (lenW, ctx);
Q = W;
R1 = W + FLINT_MAX(lenA - lenB + 1, lenB);
R2 = R1 + lenA;
R3 = R2 + lenB;
_TEMPLATE(T, poly_divrem_f) (f, Q, R1, A, lenA, B, lenB, ctx);
if (!TEMPLATE(T, is_one) (f, ctx))
goto exit;
lenR3 = lenB - 1;
TEMPLATE(CAP_T, VEC_NORM) (R1, lenR3, ctx);
if (lenR3 == 0)
{
_TEMPLATE(T, vec_set) (G, B, lenB, ctx);
lenG = lenB;
}
else
{
T = R3;
R3 = R1;
R1 = T;
_TEMPLATE(T, vec_set) (R2, B, lenB, ctx);
lenR2 = lenB;
do
{
_TEMPLATE(T, poly_divrem_f) (f, Q, R1, R2, lenR2, R3, lenR3,
ctx);
if (!TEMPLATE(T, is_one) (f, ctx))
goto exit;
lenR2 = lenR3--;
TEMPLATE(CAP_T, VEC_NORM) (R1, lenR3, ctx);
T = R2;
R2 = R3;
R3 = R1;
R1 = T;
}
while (lenR3 > 0);
_TEMPLATE(T, vec_set) (G, R2, lenR2, ctx);
lenG = lenR2;
}
exit:
_TEMPLATE(T, vec_clear) (W, lenW, ctx);
}
return lenG;
}
void
TEMPLATE(T, poly_gcd_euclidean_f) (TEMPLATE(T, t) f, TEMPLATE(T, poly_t) G,
const TEMPLATE(T, poly_t) A,
const TEMPLATE(T, poly_t) B,
const TEMPLATE(T, ctx_t) ctx)
{
if (A->length < B->length)
{
TEMPLATE(T, poly_gcd_euclidean_f) (f, G, B, A, ctx);
}
else /* lenA >= lenB >= 0 */
{
const slong lenA = A->length, lenB = B->length;
slong lenG;
TEMPLATE(T, struct) * g;
if (lenA == 0) /* lenA = lenB = 0 */
{
TEMPLATE(T, poly_zero) (G, ctx);
TEMPLATE(T, one) (f, ctx);
}
else if (lenB == 0) /* lenA > lenB = 0 */
{
TEMPLATE(T, t) invA;
TEMPLATE(T, init) (invA, ctx);
TEMPLATE(T, gcdinv) (f, invA, A->coeffs + lenA - 1, ctx);
if (TEMPLATE(T, is_one) (f, ctx))
TEMPLATE3(T, poly_scalar_mul, T) (G, A, invA, ctx);
else
TEMPLATE(T, poly_zero) (G, ctx);
TEMPLATE(T, clear) (invA, ctx);
}
else /* lenA >= lenB >= 1 */
{
if (G == A || G == B)
{
g = _TEMPLATE(T, vec_init) (FLINT_MIN(lenA, lenB), ctx);
}
else
{
TEMPLATE(T, poly_fit_length) (G, FLINT_MIN(lenA, lenB), ctx);
g = G->coeffs;
}
lenG = _TEMPLATE(T, poly_gcd_euclidean_f) (f, g, A->coeffs, lenA,
B->coeffs, lenB, ctx);
if (TEMPLATE(T, is_one) (f, ctx))
{
if (G == A || G == B)
{
_TEMPLATE(T, vec_clear) (G->coeffs, G->alloc, ctx);
G->coeffs = g;
G->alloc = FLINT_MIN(lenA, lenB);
G->length = FLINT_MIN(lenA, lenB);
}
_TEMPLATE(T, poly_set_length) (G, lenG, ctx);
if (lenG == 1)
TEMPLATE(T, one) (G->coeffs, ctx);
else
TEMPLATE(T, poly_make_monic) (G, G, ctx);
}
else /* Factor found, ensure G is normalised */
{
if (G == A || G == B)
_TEMPLATE(T, vec_clear) (g, FLINT_MIN(lenA, lenB), ctx);
else
{
_TEMPLATE(T, vec_zero) (G->coeffs, FLINT_MIN(lenA, lenB),
ctx);
_TEMPLATE(T, poly_set_length) (G, 0, ctx);
}
}
}
}
}
#endif