flint-sys 0.9.0

/*
    Copyright (C) 2012 Lina Kulakova
    Copyright (C) 2013, 2014 Martin Lee
    Copyright (C) 2020, 2022 William Hart

    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 <math.h>
#include "ulong_extras.h"
#include "nmod_mat.h"
#include "nmod_poly.h"
#include "nmod_poly_factor.h"

void nmod_poly_factor_distinct_deg(nmod_poly_factor_t res,
                                  const nmod_poly_t poly, slong * const * degs)
{
    nmod_poly_t f, g, v, vinv, tmp;
    nmod_poly_struct * h, * H, * I;
    slong i, j, l, m, n, index, d;
    nmod_mat_t HH, HHH;
    double beta;

    n = nmod_poly_degree(poly);
    nmod_poly_init_mod(v, poly->mod);

    nmod_poly_make_monic(v, poly);

    if (n == 1)
    {
        nmod_poly_factor_insert(res, v, 1);
        (*degs)[0] = 1;
        nmod_poly_clear(v);
        return;
    }

    beta = 0.5*(1. - log(2)/log(n));
    l = ceil(pow(n, beta));
    m = ceil(0.5*n/l);

    /* initialization */
    nmod_poly_init_mod(f, poly->mod);
    nmod_poly_init_mod(g, poly->mod);
    nmod_poly_init_mod(vinv, poly->mod);
    nmod_poly_init_mod(tmp, poly->mod);

    h = flint_malloc((2 * m + l + 1) * sizeof(nmod_poly_struct));
    H = h + (l + 1);
    I = H + m;

    for (i = 0; i < 2*m + l + 1; i++)
	    nmod_poly_init_mod(h + i, poly->mod);

    nmod_poly_reverse(vinv, v, v->length);
    nmod_poly_inv_series(vinv, vinv, v->length);

/* compute baby steps: h[i] = x^{p^i}mod v */
    nmod_poly_set_coeff_ui(h + 0, 1, 1);
    nmod_poly_powmod_x_ui_preinv(h + 1, poly->mod.n, v, vinv);

    if (FLINT_BIT_COUNT(poly->mod.n) > ((n_sqrt(v->length - 1) + 1)*3)/4)
    {
        for (i = 1; i < (slong) FLINT_BIT_COUNT(l); i++)
            nmod_poly_compose_mod_brent_kung_vec_preinv(h + 1 +
                            (1 << (i - 1)), h + 1, (1 << (i - 1)),
                            (1 << (i - 1)), h + (1 << (i - 1)), v, vinv);
        nmod_poly_compose_mod_brent_kung_vec_preinv(h + 1 + (1 << (i - 1)),
                            h + 1, (1 << (i - 1)), l - (1 << (i - 1)),
						    h + (1 << (i - 1)), v, vinv);
    }
    else
    {
        for (i = 2; i < l + 1; i++)
        {
            nmod_poly_init_mod(h + i, poly->mod);
            nmod_poly_powmod_ui_binexp_preinv(h + i, h + i - 1, poly->mod.n,
                                              v, vinv);
        }
    }

    /* compute coarse distinct-degree factorisation */
    index = 0;
    nmod_poly_set(H + 0, h + l);
    nmod_mat_init(HH, n_sqrt(v->length - 1) + 1, v->length - 1, poly->mod.n);
    nmod_poly_precompute_matrix(HH, H + 0, v, vinv);

    d = 1;
    for (j = 0; j < m; j++)
    {
        /* compute giant steps: H[j] = x^{p^(lj)}mod v */
        if (j > 0)
        {
            if (I[j - 1].length > 1)
            {
                _nmod_poly_reduce_matrix_mod_poly(HHH, HH, v);

                nmod_mat_clear(HH);
                nmod_mat_init_set(HH, HHH);
                nmod_mat_clear(HHH);

                nmod_poly_rem(tmp, H + j - 1, v);
                nmod_poly_compose_mod_brent_kung_precomp_preinv(H + j, tmp, HH,
                                                                v, vinv);
            } else
                nmod_poly_compose_mod_brent_kung_precomp_preinv(H + j, H + j - 1,
                                                                HH, v, vinv);
        }
        /* compute interval polynomials */
        nmod_poly_set_coeff_ui(I + j, 0, 1);

        for (i = l - 1; i >= 0 && 2*d <= v->length - 1; i--, d++)
        {
            nmod_poly_rem(tmp, h + i, v);
            nmod_poly_sub(tmp, H + j, tmp);
            nmod_poly_mulmod_preinv(I + j, tmp, I + j, v, vinv);
        }

        /* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */
        /* F_j is stored on the place of I_j */
        nmod_poly_gcd(I + j, v, I + j);

        if (I[j].length > 1)
        {
            nmod_poly_remove(v, I + j);
            nmod_poly_reverse(vinv, v, v->length);
            nmod_poly_inv_series(vinv, vinv, v->length);
        }

        if (v->length - 1 < 2*d)
            break;
    }

    if (v->length > 1)
    {
        nmod_poly_factor_insert(res, v, 1);
        (*degs)[index++] = v->length - 1;
    }

    /* compute fine distinct-degree factorisation */
    for (j = 0; j < m; j++)
    {
        if (I[j].length - 1 > (j + 1)*l || j == 0)
        {
            nmod_poly_set(g, I + j);

            for (i = l - 1; i >= 0 && (g->length > 1); i-- )
            {
                /* compute f^{[l*(j+1)-i]} */
                nmod_poly_sub(tmp, H + j, h + i);
                nmod_poly_gcd(f, g, tmp);

                if (f->length > 1)
                {
                    /* insert f^{[l*(j+1)-i]} into res */
                    nmod_poly_make_monic(f, f);
                    nmod_poly_factor_insert(res, f, 1);
                    (*degs)[index++] = l*(j + 1) - i;

                    nmod_poly_remove(g, f);
                }
            }
        } else if (I[j].length > 1)
        {
            nmod_poly_make_monic(I + j, I + j);
            nmod_poly_factor_insert(res, I + j, 1);
            (*degs)[index++] = I[j].length - 1;
        }
    }

    /* cleanup */
    nmod_poly_clear(f);
    nmod_poly_clear(g);
    nmod_poly_clear(v);
    nmod_poly_clear(vinv);
    nmod_poly_clear(tmp);

    nmod_mat_clear(HH);

    for (i = 0; i < l + 1; i++)
        nmod_poly_clear(h + i);

    for (i = 0; i < m; i++)
    {
        nmod_poly_clear(H + i);
        nmod_poly_clear(I + i);
    }

    flint_free(h);
}