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pqc/external/flint-2.4.3/fq_poly_factor_templates/factor_distinct_deg.c

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/*=============================================================================
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) 2012 Lina Kulakova
Copyright (C) 2013 Martin Lee
Copyright (C) 2013 Mike Hansen
******************************************************************************/
#ifdef T
#include "templates.h"
#include <math.h>
void
TEMPLATE(T, poly_factor_distinct_deg) (TEMPLATE(T, poly_factor_t) res,
const TEMPLATE(T, poly_t) poly,
slong * const *degs,
const TEMPLATE(T, ctx_t) ctx)
{
TEMPLATE(T, poly_t) f, g, s, reducedH0, v, vinv, tmp;
TEMPLATE(T, poly_t) * h, *H, *I;
fmpz_t q;
slong i, j, l, m, n, index, d;
double beta;
TEMPLATE(T, mat_t) HH, HHH;
TEMPLATE(T, poly_init) (v, ctx);
TEMPLATE(T, poly_make_monic) (v, poly, ctx);
n = TEMPLATE(T, poly_degree) (poly, ctx);
if (n == 1)
{
TEMPLATE(T, poly_factor_insert) (res, poly, 1, ctx);
(*degs)[0] = 1;
TEMPLATE(T, poly_clear) (v, ctx);
return;
}
beta = 0.5 * (1. - (log(2) / log(n)));
l = ceil(pow(n, beta));
m = ceil(0.5 * n / l);
fmpz_init(q);
TEMPLATE(T, ctx_order) (q, ctx);
TEMPLATE(T, poly_init) (f, ctx);
TEMPLATE(T, poly_init) (g, ctx);
TEMPLATE(T, poly_init) (s, ctx);
TEMPLATE(T, poly_init) (reducedH0, ctx);
TEMPLATE(T, poly_init) (vinv, ctx);
TEMPLATE(T, poly_init) (tmp, ctx);
if (!
(h = flint_malloc((2 * m + l + 1) * sizeof(TEMPLATE(T, poly_struct)))))
{
TEMPLATE_PRINTF("Exception (%s_poly_factor_distinct_deg):\n", T);
flint_printf("Not enough memory.\n");
abort();
}
H = h + (l + 1);
I = H + m;
for (i = 0; i < l + 1; i++)
TEMPLATE(T, poly_init) (h[i], ctx);
for (i = 0; i < m; i++)
{
TEMPLATE(T, poly_init) (H[i], ctx);
TEMPLATE(T, poly_init) (I[i], ctx);
}
TEMPLATE(T, poly_make_monic) (v, poly, ctx);
TEMPLATE(T, poly_reverse) (vinv, v, v->length, ctx);
TEMPLATE(T, poly_inv_series_newton) (vinv, vinv, v->length, ctx);
/* compute baby steps: h[i]=x^{q^i}mod v */
/* h[0] = x */
TEMPLATE(T, poly_iterated_frobenius_preinv) (h, l + 1, v, vinv, ctx);
/* compute coarse distinct-degree factorisation */
index = 0;
TEMPLATE(T, poly_set) (s, v, ctx);
TEMPLATE(T, poly_set) (H[0], h[l], ctx);
TEMPLATE(T, poly_set) (reducedH0, H[0], ctx);
TEMPLATE(T, mat_init) (HH, n_sqrt(v->length - 1) + 1, v->length - 1, ctx);
TEMPLATE(T, poly_precompute_matrix) (HH, reducedH0, s, vinv, ctx);
d = 1;
for (j = 0; j < m; j++)
{
/* compute giant steps: H[j]=x^{q^(lj)}mod s */
if (j > 0)
{
if (I[j - 1]->length > 1)
{
_TEMPLATE(T, poly_reduce_matrix_mod_poly) (HHH, HH, s, ctx);
TEMPLATE(T, mat_clear) (HH, ctx);
TEMPLATE(T, mat_init_set) (HH, HHH, ctx);
TEMPLATE(T, mat_clear) (HHH, ctx);
TEMPLATE(T, poly_rem) (reducedH0, reducedH0, s, ctx);
TEMPLATE(T, poly_rem) (tmp, H[j - 1], s, ctx);
TEMPLATE(T, poly_compose_mod_brent_kung_precomp_preinv)
(H[j], tmp, HH, s, vinv, ctx);
}
else
{
TEMPLATE(T, poly_compose_mod_brent_kung_precomp_preinv)
(H[j], H[j - 1], HH, s, vinv, ctx);
}
}
/* compute interval polynomials */
TEMPLATE(T, poly_one) (I[j], ctx);
for (i = l - 1; (i >= 0) && (2 * d <= s->length - 1); i--, d++)
{
TEMPLATE(T, poly_rem) (tmp, h[i], s, ctx);
TEMPLATE(T, poly_sub) (tmp, H[j], tmp, ctx);
TEMPLATE(T, poly_mulmod_preinv) (I[j], tmp, I[j], s, vinv, ctx);
}
/* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */
/* F_j is stored on the place of I_j */
TEMPLATE(T, poly_gcd) (I[j], s, I[j], ctx);
if (I[j]->length > 1)
{
TEMPLATE(T, poly_remove) (s, I[j], ctx);
TEMPLATE(T, poly_reverse) (vinv, s, s->length, ctx);
TEMPLATE(T, poly_inv_series_newton) (vinv, vinv, s->length, ctx);
}
if (s->length - 1 < 2 * d)
{
break;
}
}
if (s->length > 1)
{
TEMPLATE(T, poly_factor_insert) (res, s, 1, ctx);
(*degs)[index++] = s->length - 1;
}
/* compute fine distinct-degree factorisation */
for (j = 0; j < m; j++)
{
if (I[j]->length - 1 > (j + 1) * l || j == 0)
{
TEMPLATE(T, poly_set) (g, I[j], ctx);
for (i = l - 1; i >= 0 && (g->length > 1); i--)
{
/* compute f^{[l*(j+1)-i]} */
TEMPLATE(T, poly_sub) (tmp, H[j], h[i], ctx);
TEMPLATE(T, poly_gcd) (f, g, tmp, ctx);
if (f->length > 1)
{
/* insert f^{[l*(j+1)-i]} into res */
TEMPLATE(T, poly_make_monic) (f, f, ctx);
TEMPLATE(T, poly_factor_insert) (res, f, 1, ctx);
(*degs)[index++] = l * (j + 1) - i;
TEMPLATE(T, poly_remove) (g, f, ctx);
}
}
}
else if (I[j]->length > 1)
{
TEMPLATE(T, poly_make_monic) (I[j], I[j], ctx);
TEMPLATE(T, poly_factor_insert) (res, I[j], 1, ctx);
(*degs)[index++] = I[j]->length - 1;
}
}
/* cleanup */
fmpz_clear(q);
TEMPLATE(T, poly_clear) (f, ctx);
TEMPLATE(T, poly_clear) (g, ctx);
TEMPLATE(T, poly_clear) (s, ctx);
TEMPLATE(T, poly_clear) (reducedH0, ctx);
TEMPLATE(T, poly_clear) (v, ctx);
TEMPLATE(T, poly_clear) (vinv, ctx);
TEMPLATE(T, poly_clear) (tmp, ctx);
TEMPLATE(T, mat_clear) (HH, ctx);
for (i = 0; i < l + 1; i++)
TEMPLATE(T, poly_clear) (h[i], ctx);
for (i = 0; i < m; i++)
{
TEMPLATE(T, poly_clear) (H[i], ctx);
TEMPLATE(T, poly_clear) (I[i], ctx);
}
flint_free(h);
}
#endif
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