/*
    Copyright (C) 2011 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 2.1 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include <gmp.h>
#include "flint.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "nmod_mat.h"
#include "ulong_extras.h"

void
_nmod_poly_compose_series_brent_kung(mp_ptr res, mp_srcptr poly1, slong len1, 
                            mp_srcptr poly2, slong len2, slong n, nmod_t mod)
{
    nmod_mat_t A, B, C;
    mp_ptr t, h;
    slong i, m;

    if (n == 1)
    {
        res[0] = poly1[0];
        return;
    }

    m = n_sqrt(n) + 1;

    nmod_mat_init(A, m, n, mod.n);
    nmod_mat_init(B, m, m, mod.n);
    nmod_mat_init(C, m, n, mod.n);

    h = _nmod_vec_init(n);
    t = _nmod_vec_init(n);

    /* Set rows of B to the segments of poly1 */
    for (i = 0; i < len1 / m; i++)
        _nmod_vec_set(B->rows[i], poly1 + i*m, m);
    _nmod_vec_set(B->rows[i], poly1 + i*m, len1 % m);

    /* Set rows of A to powers of poly2 */
    A->rows[0][0] = UWORD(1);
    _nmod_vec_set(A->rows[1], poly2, len2);
    for (i = 2; i < m; i++)
        _nmod_poly_mullow(A->rows[i], A->rows[i-1], n, poly2, len2, n, mod);

    nmod_mat_mul(C, B, A);

    /* Evaluate block composition using the Horner scheme */
    _nmod_vec_set(res, C->rows[m - 1], n);
    _nmod_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n, mod);

    for (i = m - 2; i >= 0; i--)
    {
        _nmod_poly_mullow(t, res, n, h, n, n, mod);
        _nmod_poly_add(res, t, n, C->rows[i], n, mod);
    }

    _nmod_vec_clear(h);
    _nmod_vec_clear(t);

    nmod_mat_clear(A);
    nmod_mat_clear(B);
    nmod_mat_clear(C);
}

void
nmod_poly_compose_series_brent_kung(nmod_poly_t res, 
                    const nmod_poly_t poly1, const nmod_poly_t poly2, slong n)
{
    slong len1 = poly1->length;
    slong len2 = poly2->length;
    slong lenr;

    if (len2 != 0 && poly2->coeffs[0] != 0)
    {
        flint_printf("Exception (nmod_poly_compose_series_brent_kung). Inner \n"
               "polynomial must have zero constant term.\n");
        flint_abort();
    }

    if (len1 == 0 || n == 0)
    {
        nmod_poly_zero(res);
        return;
    }

    if (len2 == 0 || len1 == 1)
    {
        nmod_poly_fit_length(res, 1);
        res->coeffs[0] = poly1->coeffs[0];
        res->length = 1;
        _nmod_poly_normalise(res);
        return;
    }

    lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
    len1 = FLINT_MIN(len1, lenr);
    len2 = FLINT_MIN(len2, lenr);

    if ((res != poly1) && (res != poly2))
    {
        nmod_poly_fit_length(res, lenr);
        _nmod_poly_compose_series_brent_kung(res->coeffs, poly1->coeffs, len1, 
                                        poly2->coeffs, len2, lenr, res->mod);
        res->length = lenr;
        _nmod_poly_normalise(res);
    }
    else
    {
        nmod_poly_t t;
        nmod_poly_init2_preinv(t, res->mod.n, res->mod.ninv, lenr);
        _nmod_poly_compose_series_brent_kung(t->coeffs, poly1->coeffs, len1,
                                        poly2->coeffs, len2, lenr, res->mod);
        t->length = lenr;
        _nmod_poly_normalise(t);
        nmod_poly_swap(res, t);
        nmod_poly_clear(t);
    }
}
