214 lines
6.9 KiB
C
214 lines
6.9 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Lina Kulakova
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Copyright (C) 2013 Martin Lee
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******************************************************************************/
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#undef ulong
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#define ulong ulongxx/* interferes with system includes */
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#include <math.h>
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#undef ulong
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#include <gmp.h>
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#define ulong mp_limb_t
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#include "nmod_poly.h"
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void nmod_poly_factor_distinct_deg(nmod_poly_factor_t res,
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const nmod_poly_t poly, slong * const *degs)
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{
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nmod_poly_t f, g, v, vinv, reducedH0, tmp;
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nmod_poly_t *h, *H, *I;
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slong i, j, l, m, n, index, d;
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nmod_mat_t HH, HHH;
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double beta;
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n = nmod_poly_degree(poly);
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nmod_poly_init_preinv(v, poly->mod.n, poly->mod.ninv);
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nmod_poly_make_monic(v, poly);
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if (n == 1)
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{
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nmod_poly_factor_insert (res, v, 1);
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(*degs)[0]= 1;
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nmod_poly_clear (v);
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return;
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}
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beta = 0.5 * (1. - (log(2) / log(n)));
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l = ceil(pow (n, beta));
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m = ceil(0.5 * n / l);
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/* initialization */
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nmod_poly_init_preinv(f, poly->mod.n, poly->mod.ninv);
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nmod_poly_init_preinv(g, poly->mod.n, poly->mod.ninv);
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nmod_poly_init_preinv(vinv, poly->mod.n, poly->mod.ninv);
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nmod_poly_init_preinv(reducedH0, poly->mod.n, poly->mod.ninv);
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nmod_poly_init_preinv(tmp, poly->mod.n, poly->mod.ninv);
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if (!(h = flint_malloc((2 * m + l + 1) * sizeof(nmod_poly_struct))))
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{
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flint_printf("Exception (nmod_poly_factor_distinct_deg):\n");
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flint_printf("Not enough memory.\n");
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abort();
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}
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H = h + (l + 1);
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I = H + m;
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for (i = 0; i < l + 1; i++)
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nmod_poly_init_preinv(h[i], poly->mod.n, poly->mod.ninv);
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for (i = 0; i < m; i++)
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{
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nmod_poly_init_preinv(H[i], poly->mod.n, poly->mod.ninv);
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nmod_poly_init_preinv(I[i], poly->mod.n, poly->mod.ninv);
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}
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nmod_poly_reverse(vinv, v, v->length);
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nmod_poly_inv_series(vinv, vinv, v->length);
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/* compute baby steps: h[i]=x^{p^i}mod v */
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nmod_poly_set_coeff_ui(h[0], 1, 1);
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nmod_poly_powmod_x_ui_preinv(h[1], poly->mod.n, v, vinv);
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if (FLINT_BIT_COUNT(poly->mod.n) > ((n_sqrt(v->length - 1) + 1) * 3) / 4)
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{
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nmod_mat_init(HH, n_sqrt (v->length - 1) + 1, v->length - 1,
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poly->mod.n);
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nmod_poly_precompute_matrix(HH, h[1], v, vinv);
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for (i = 2; i < l + 1; i++)
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nmod_poly_compose_mod_brent_kung_precomp_preinv(h[i], h[i - 1],
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HH, v, vinv);
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nmod_mat_clear(HH);
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}
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else
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{
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for (i = 2; i < l + 1; i++)
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nmod_poly_powmod_ui_binexp_preinv(h[i], h[i - 1], poly->mod.n,
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v, vinv);
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}
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/* compute coarse distinct-degree factorisation */
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index = 0;
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nmod_poly_set(H[0], h[l]);
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nmod_poly_set(reducedH0, H[0]);
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nmod_mat_init(HH, n_sqrt(v->length - 1) + 1, v->length - 1, poly->mod.n);
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nmod_poly_precompute_matrix(HH, reducedH0, v, vinv);
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d = 1;
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for (j = 0; j < m; j++)
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{
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/* compute giant steps: H[j]=x^{p^(lj)}mod v */
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if (j > 0)
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{
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if (I[j - 1]->length > 1)
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{
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_nmod_poly_reduce_matrix_mod_poly(HHH, HH, v);
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nmod_mat_clear(HH);
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nmod_mat_init_set(HH, HHH);
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nmod_mat_clear(HHH);
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nmod_poly_rem(reducedH0, reducedH0, v);
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nmod_poly_rem(tmp, H[j - 1], v);
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nmod_poly_compose_mod_brent_kung_precomp_preinv(H[j], tmp, HH,
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v, vinv);
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}
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else
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nmod_poly_compose_mod_brent_kung_precomp_preinv(H[j], H[j - 1],
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HH, v, vinv);
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}
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/* compute interval polynomials */
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nmod_poly_set_coeff_ui(I[j], 0, 1);
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for (i = l - 1; (i >= 0) && (2 * d <= v->length - 1); i--, d++)
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{
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nmod_poly_rem(tmp, h[i], v);
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nmod_poly_sub(tmp, H[j], tmp);
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nmod_poly_mulmod_preinv(I[j], tmp, I[j], v, vinv);
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}
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/* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */
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/* F_j is stored on the place of I_j */
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nmod_poly_gcd(I[j], v, I[j]);
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if (I[j]->length > 1)
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{
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nmod_poly_remove(v, I[j]);
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nmod_poly_reverse(vinv, v, v->length);
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nmod_poly_inv_series(vinv, vinv, v->length);
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}
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if (v->length - 1 < 2 * d)
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{
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break;
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}
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}
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if (v->length > 1)
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{
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nmod_poly_factor_insert(res, v, 1);
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(*degs)[index++] = v->length - 1;
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}
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/* compute fine distinct-degree factorisation */
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for (j = 0; j < m; j++)
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{
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if (I[j]->length - 1 > (j + 1) * l || j == 0)
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{
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nmod_poly_set(g, I[j]);
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for (i = l - 1; i >= 0 && (g->length > 1); i-- )
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{
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/* compute f^{[l*(j+1)-i]} */
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nmod_poly_sub(tmp, H[j], h[i]);
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nmod_poly_gcd(f, g, tmp);
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if (f->length > 1)
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{
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/* insert f^{[l*(j+1)-i]} into res */
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nmod_poly_make_monic(f, f);
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nmod_poly_factor_insert(res, f, 1);
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(*degs)[index++] = l * (j + 1) - i;
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nmod_poly_remove(g, f);
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}
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}
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}
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else if (I[j]->length > 1)
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{
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nmod_poly_make_monic(I[j], I[j]);
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nmod_poly_factor_insert(res, I[j], 1);
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(*degs)[index++] = I[j]->length-1;
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}
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}
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/* cleanup */
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nmod_poly_clear(f);
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nmod_poly_clear(g);
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nmod_poly_clear(reducedH0);
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nmod_poly_clear(v);
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nmod_poly_clear(vinv);
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nmod_poly_clear(tmp);
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nmod_mat_clear (HH);
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for (i = 0; i < l + 1; i++)
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nmod_poly_clear(h[i]);
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for (i = 0; i < m; i++)
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{
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nmod_poly_clear(H[i]);
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nmod_poly_clear(I[i]);
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}
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flint_free(h);
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}
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