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

#include "nmod.h"
#include "nmod_vec.h"
#include "nmod_poly.h"

nn_ptr * _nmod_poly_tree_alloc(slong len)
{
    nn_ptr * tree = NULL;

    if (len)
    {
        slong i, height = FLINT_CLOG2(len);

        tree = flint_malloc(sizeof(nn_ptr) * (height + 1));
        for (i = 0; i <= height; i++)
            tree[i] = _nmod_vec_init(len + (len >> i) + 1);
    }

    return tree;
}

void _nmod_poly_tree_free(nn_ptr * tree, slong len)
{
    if (len)
    {
        slong i, height = FLINT_CLOG2(len);

        for (i = 0; i <= height; i++)
            flint_free(tree[i]);

        flint_free(tree);
    }
}

void
_nmod_poly_tree_build(nn_ptr * tree, nn_srcptr roots, slong len, nmod_t mod)
{
    slong height, pow, left, i;
    nn_ptr pa, pb;

    if (len == 0)
        return;

    height = FLINT_CLOG2(len);

    /* zeroth level, (x-a) */
    for (i = 0; i < len; i++)
    {
        tree[0][2 * i + 1] = 1;
        tree[0][2 * i] = nmod_neg(roots[i], mod);
    }

    /* first level, (x-a)(x-b) = x^2 + (-a-b)*x + a*b */
    if (height > 1)
    {
        pa = tree[1];

        for (i = 0; i < len / 2; i++)
        {
            ulong a, b;

            a = roots[2 * i];
            b = roots[2 * i + 1];

            pa[3 * i] = nmod_mul(a, b, mod);
            pa[3 * i + 1] = nmod_neg(nmod_add(a, b, mod), mod);
            pa[3 * i + 2] = 1;
        }

        if (len & 1)
        {
            pa[3 * (len / 2)] = nmod_neg(roots[len-1], mod);
            pa[3 * (len / 2) + 1] = 1;
        }
    }

    for (i = 1; i < height - 1; i++)
    {
        left = len;
        pow = WORD(1) << i;
        pa = tree[i];
        pb = tree[i + 1];

        while (left >= 2 * pow)
        {
            _nmod_poly_mul(pb, pa, pow + 1, pa + pow + 1, pow + 1, mod);
            left -= 2 * pow;
            pa += 2 * pow + 2;
            pb += 2 * pow + 1;
        }

        if (left > pow)
            _nmod_poly_mul(pb, pa, pow + 1, pa + pow + 1, left - pow + 1, mod);
        else if (left > 0)
            _nmod_vec_set(pb, pa, left + 1);
    }
}
