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/*
Copyright (C) 2011 William Hart
Copyright (C) 2012 Sebastian Pancratz
Copyright (C) 2013 Mike Hansen
Copyright (C) 2023 Fredrik Johansson
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/>.
*/
#include "gr.h"
#include "gr_vec.h"
#include "gr_poly.h"
#define GR_VEC_NORM(R, lenR) \
(status) |= _gr_vec_normalise(&(lenR), (R), (lenR), (ctx))
#define __set(B, lenB, A, lenA) \
do { \
status |= _gr_vec_set((B), (A), (lenA), ctx); \
(lenB) = (lenA); \
} while (0)
#define __add(C, lenC, A, lenA, B, lenB) \
do { \
status |= _gr_poly_add((C), (A), (lenA), (B), (lenB), ctx); \
(lenC) = FLINT_MAX((lenA), (lenB)); \
GR_VEC_NORM((C), (lenC)); \
} while (0)
#define __sub(C, lenC, A, lenA, B, lenB) \
do { \
status |= _gr_poly_sub((C), (A), (lenA), (B), (lenB), ctx); \
(lenC) = FLINT_MAX((lenA), (lenB)); \
GR_VEC_NORM((C), (lenC)); \
} while (0)
#define __mul(C, lenC, A, lenA, B, lenB) \
do { \
if ((lenA) != 0 && (lenB) != 0) \
{ \
if ((lenA) >= (lenB)) \
status |= _gr_poly_mul((C), (A), (lenA), (B), (lenB), ctx); \
else \
status |= _gr_poly_mul((C), (B), (lenB), (A), (lenA), ctx); \
(lenC) = (lenA) + (lenB) - 1; \
} \
else \
{ \
(lenC) = 0; \
} \
} while (0)
#define __divrem(Q, lenQ, R, lenR, A, lenA, B, lenB) \
do { \
if ((lenA) >= (lenB)) \
{ \
status |= _gr_poly_divrem((Q), (R), (A), (lenA), (B), (lenB), ctx); \
(lenQ) = (lenA) - (lenB) + 1; \
(lenR) = (lenB) - 1; \
GR_VEC_NORM((R), (lenR)); \
} \
else \
{ \
status |= _gr_vec_set((R), (A), (lenA), ctx); \
(lenQ) = 0; \
(lenR) = (lenA); \
} \
} while (0)
/* todo: add _gr_poly_div */
#define __div(Q, lenQ, A, lenA, B, lenB) \
do { \
if ((lenA) >= (lenB)) \
{ \
status |= _gr_poly_div_newton((Q), (A), (lenA), (B), (lenB), ctx); \
(lenQ) = (lenA) - (lenB) + 1; \
} \
else \
{ \
(lenQ) = 0; \
} \
} while (0)
int _gr_poly_xgcd_hgcd(slong * Glen, gr_ptr G, gr_ptr S, gr_ptr T,
gr_srcptr A, slong lenA, gr_srcptr B, slong lenB,
slong hgcd_cutoff,
slong cutoff,
gr_ctx_t ctx)
{
int status = GR_SUCCESS;
slong sz = ctx->sizeof_elem;
slong lenG, lenS, lenT;
if (lenB == 1)
{
status |= gr_set(G, B, ctx);
status |= gr_one(T, ctx);
lenG = 1;
lenS = 0;
lenT = 1;
}
else
{
slong lenq, lenr, len1 = lenA + lenB;
gr_ptr q, r, invB;
GR_TMP_INIT_VEC(q, len1, ctx);
r = GR_ENTRY(q, lenA, sz);
GR_TMP_INIT(invB, ctx);
__divrem(q, lenq, r, lenr, A, lenA, B, lenB);
if (lenr == 0)
{
__set(G, lenG, B, lenB);
status |= gr_one(T, ctx);
lenS = 0;
lenT = 1;
}
else
{
gr_ptr h, j, v, w, R[4], X;
slong lenh, lenj, lenv, lenw, lenR[4], len2;
slong sgnR;
lenh = lenj = lenB;
lenv = lenw = lenA + lenB - 2;
lenR[0] = lenR[1] = lenR[2] = lenR[3] = (lenB + 1) / 2;
len2 = 2 * lenh + 2 * lenv + 4 * lenR[0];
GR_TMP_INIT_VEC(X, len2, ctx);
h = X;
j = GR_ENTRY(h, lenh, sz);
v = GR_ENTRY(j, lenj, sz);
w = GR_ENTRY(v, lenv, sz);
R[0] = GR_ENTRY(w, lenw, sz);
R[1] = GR_ENTRY(R[0], lenR[0], sz);
R[2] = GR_ENTRY(R[1], lenR[1], sz);
R[3] = GR_ENTRY(R[2], lenR[2], sz);
status |= _gr_poly_hgcd(NULL, &sgnR, R, lenR, h, &lenh, j, &lenj, B, lenB, r, lenr, hgcd_cutoff, ctx);
if (sgnR > 0)
{
status |= _gr_vec_neg(S, R[1], lenR[1], ctx);
status |= _gr_vec_set(T, R[0], lenR[0], ctx);
}
else
{
status |= _gr_vec_set(S, R[1], lenR[1], ctx);
status |= _gr_vec_neg(T, R[0], lenR[0], ctx);
}
lenS = lenR[1];
lenT = lenR[0];
while (lenj != 0 && status == GR_SUCCESS)
{
__divrem(q, lenq, r, lenr, h, lenh, j, lenj);
__mul(v, lenv, q, lenq, T, lenT);
{
slong l;
_gr_vec_swap(S, T, FLINT_MAX(lenS, lenT), ctx);
l = lenS; lenS = lenT; lenT = l;
}
if (lenr != 0) /* prevent overflow of T on last iteration */
__sub(T, lenT, T, lenT, v, lenv);
else /* lenr == 0 */
{
__set(G, lenG, j, lenj);
goto cofactor;
}
if (lenj < cutoff)
{
gr_ptr u0 = R[0], u1 = R[1];
slong lenu0 = lenr - 1, lenu1 = lenj - 1;
status |= _gr_poly_xgcd_euclidean(&lenG, G, u0, u1, j, lenj, r, lenr, ctx);
GR_VEC_NORM(u0, lenu0);
GR_VEC_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;
}
status |= _gr_poly_hgcd(NULL, &sgnR, R, lenR, h, &lenh, j, &lenj, j,lenj, r, lenr, hgcd_cutoff, ctx);
__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 > 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);
GR_TMP_CLEAR_VEC(X, len2, ctx);
}
GR_TMP_CLEAR_VEC(q, len1, ctx);
GR_TMP_CLEAR(invB, ctx);
}
status |= _gr_vec_zero(GR_ENTRY(S, lenS, sz), lenB - 1 - lenS, ctx);
status |= _gr_vec_zero(GR_ENTRY(T, lenT, sz), lenA - 1 - lenT, ctx);
*Glen = lenG;
return status;
}
int
gr_poly_xgcd_hgcd(gr_poly_t G, gr_poly_t S, gr_poly_t T, const gr_poly_t A, const gr_poly_t B, slong hgcd_cutoff, slong cutoff, gr_ctx_t ctx)
{
if (A->length < B->length)
{
return gr_poly_xgcd_hgcd(G, T, S, B, A, hgcd_cutoff, cutoff, ctx);
}
else /* lenA >= lenB >= 0 */
{
const slong lenA = A->length, lenB = B->length;
int status = GR_SUCCESS;
slong sz = ctx->sizeof_elem;
gr_ptr t;
if (lenA == 0) /* lenA = lenB = 0 */
{
status |= gr_poly_zero(G, ctx);
status |= gr_poly_zero(S, ctx);
status |= gr_poly_zero(T, ctx);
}
else if (lenB == 0) /* lenA > lenB = 0 */
{
GR_TMP_INIT(t, ctx);
status |= gr_inv(t, GR_ENTRY(A->coeffs, lenA - 1, sz), ctx);
status |= gr_poly_mul_scalar(G, A, t, ctx);
status |= gr_poly_zero(T, ctx);
status |= gr_poly_set_scalar(S, t, ctx);
GR_TMP_CLEAR(t, ctx);
}
else if (gr_is_zero(GR_ENTRY(A->coeffs, A->length - 1, sz), ctx) != T_FALSE ||
gr_is_zero(GR_ENTRY(B->coeffs, B->length - 1, sz), ctx) != T_FALSE)
{
status |= GR_UNABLE;
}
else if (lenB == 1) /* lenA >= lenB = 1 */
{
GR_TMP_INIT(t, ctx);
status |= gr_inv(t, B->coeffs, ctx);
status |= gr_poly_set_scalar(T, t, ctx);
status |= gr_poly_one(G, ctx);
status |= gr_poly_zero(S, ctx);
GR_TMP_CLEAR(t, ctx);
}
else /* lenA >= lenB >= 2 */
{
gr_ptr g, *s, *t;
slong lenG;
if (G == A || G == B)
{
g = flint_malloc(sz * FLINT_MIN(lenA, lenB));
_gr_vec_init(g, FLINT_MIN(lenA, lenB), ctx);
}
else
{
gr_poly_fit_length(G, FLINT_MIN(lenA, lenB), ctx);
g = G->coeffs;
}
if (S == A || S == B)
{
s = flint_malloc(sz * lenB);
_gr_vec_init(s, lenB, ctx);
}
else
{
gr_poly_fit_length(S, lenB, ctx);
s = S->coeffs;
}
if (T == A || T == B)
{
t = flint_malloc(sz * lenA);
_gr_vec_init(t, lenA, ctx);
}
else
{
gr_poly_fit_length(T, lenA, ctx);
t = T->coeffs;
}
status |= _gr_poly_xgcd_hgcd(&lenG, g, s, t, A->coeffs, lenA, B->coeffs, lenB, hgcd_cutoff, cutoff, ctx);
if (G == A || G == B)
{
_gr_vec_clear(G->coeffs, G->alloc, ctx);
flint_free(G->coeffs);
G->coeffs = g;
G->alloc = FLINT_MIN(lenA, lenB);
G->length = G->alloc;
}
if (S == A || S == B)
{
_gr_vec_clear(S->coeffs, S->alloc, ctx);
flint_free(S->coeffs);
S->coeffs = s;
S->alloc = lenB;
S->length = S->alloc;
}
if (T == A || T == B)
{
_gr_vec_clear(T->coeffs, T->alloc, ctx);
flint_free(T->coeffs);
T->coeffs = t;
T->alloc = lenA;
T->length = T->alloc;
}
_gr_poly_set_length(G, lenG, ctx);
_gr_poly_set_length(S, FLINT_MAX(lenB - lenG, 1), ctx);
_gr_poly_set_length(T, FLINT_MAX(lenA - lenG, 1), ctx);
_gr_poly_normalise(S, ctx);
_gr_poly_normalise(T, ctx);
if (status == GR_SUCCESS && gr_is_one(GR_ENTRY(G->coeffs, G->length - 1, sz), ctx) != T_TRUE)
{
GR_TMP_INIT(t, ctx);
status |= gr_inv(t, GR_ENTRY(G->coeffs, G->length - 1, sz), ctx);
status |= gr_poly_mul_scalar(G, G, t, ctx);
status |= gr_poly_mul_scalar(S, S, t, ctx);
status |= gr_poly_mul_scalar(T, T, t, ctx);
GR_TMP_CLEAR(t, ctx);
}
}
return status;
}
}