/*=============================================================================

    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) 2010 Sebastian Pancratz
    Copyright (C) 2010 William Hart
    Copyright (C) 2011 Fredrik Johansson
    Copyright (C) 2012 Lina Kulakova
    Copyright (C) 2013 Martin Lee

******************************************************************************/

#undef ulong
#define ulong ulongxx/* interferes with system includes */

#include <stdlib.h>

#undef ulong

#include <gmp.h>

#define ulong mp_limb_t

#include "flint.h"
#include "fmpz_vec.h"
#include "fmpz_mod_poly.h"
#include "long_extras.h"

void
_fmpz_mod_poly_powmod_x_fmpz_preinv(fmpz * res, const fmpz_t e, const fmpz * f,
                                    slong lenf, const fmpz* finv, slong lenfinv,
                                    const fmpz_t p)
{
    fmpz * T, * Q;
    slong lenT, lenQ;
    slong i, window, l, c;

    lenT = 2 * lenf - 3;
    lenQ = lenT - lenf + 1;

    T = _fmpz_vec_init(lenT + lenQ);
    Q = T + lenT;

    fmpz_one (res);
    l = z_sizeinbase (lenf - 1, 2) - 2;
    window = WORD(0);
    window = (WORD(1) << l);
    c = l;
    i = fmpz_sizeinbase(e, 2) - 2;
    if (i <= l)
    {
      window = WORD(0);
      window = (WORD(1) << i);
      c = i;
      l = i;
    }

    if (c == 0)
    {
        _fmpz_mod_poly_shift_left(T, res, lenf - 1, window);
        _fmpz_mod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window, f,
                                              lenf, finv, lenfinv, p);
        c = l + 1;
        window = WORD(0);
    }

    for (; i >= 0; i--)
    {
        _fmpz_mod_poly_sqr(T, res, lenf - 1, p);
        _fmpz_mod_poly_divrem_newton_n_preinv(Q, res, T, 2 * lenf - 3, f, lenf,
                                              finv, lenfinv, p);

        c--;
        if (fmpz_tstbit(e, i))
        {
            if (window == WORD(0) && i <= l - 1)
                c = i;
            if ( c >= 0)
              window = window | (WORD(1) << c);
        }
        else if (window == WORD(0))
            c = l + 1;
        if (c == 0)
        {
            _fmpz_mod_poly_shift_left(T, res, lenf - 1, window);
            
            _fmpz_mod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window,
                                                  f, lenf, finv, lenfinv, p);
            c = l + 1;
            window = WORD(0);
        }
    }

    _fmpz_vec_clear(T, lenT + lenQ);
}


void
fmpz_mod_poly_powmod_x_fmpz_preinv(fmpz_mod_poly_t res, const fmpz_t e,
                           const fmpz_mod_poly_t f, const fmpz_mod_poly_t finv)
{
    slong lenf = f->length;
    slong trunc = lenf - 1;
    fmpz_mod_poly_t tmp;

    if (lenf == 0)
    {
        flint_printf("Exception (fmpz_mod_poly_powmod_x_fmpz_preinv)."
                     "Divide by zero\n");
        abort();
    }

    if (fmpz_sgn(e) < 0)
    {
        flint_printf("Exception (fmpz_mod_poly_powmod_x_fmpz_preinv)."
                     "Negative exp not implemented\n");
        abort();
    }

    if (lenf == 1)
    {
        fmpz_mod_poly_zero(res);
        return;
    }

    if (lenf == 2)
    {
        fmpz_mod_poly_t r, poly;
        fmpz_mod_poly_init(tmp, &res->p);
        fmpz_mod_poly_init(r, &res->p);
        fmpz_mod_poly_init2(poly, &res->p, 2);
        fmpz_mod_poly_set_coeff_ui (poly, 1, 1);
        fmpz_mod_poly_divrem(tmp, r, poly, f);
        fmpz_mod_poly_powmod_fmpz_binexp_preinv(res, r, e, f, finv);
        fmpz_mod_poly_clear(tmp);
        fmpz_mod_poly_clear(r);
        fmpz_mod_poly_clear(poly);
        return;
    }

    if (fmpz_abs_fits_ui(e))
    {
        ulong exp = fmpz_get_ui(e);

        if (exp <= 2)
        {
            if (exp == UWORD(0))
            {
                fmpz_mod_poly_fit_length(res, 1);
                fmpz_one(res->coeffs);
                _fmpz_mod_poly_set_length(res, 1);
            }
            else if (exp == UWORD(1))
            {
                fmpz_mod_poly_t r;
                fmpz_mod_poly_init2(r, &f->p, 2);
                fmpz_mod_poly_set_coeff_ui(r, 1, 1);
                fmpz_mod_poly_init(tmp, &f->p);
                fmpz_mod_poly_divrem(tmp, res, r, f);
                fmpz_mod_poly_clear(tmp);
                fmpz_mod_poly_clear(r);
            }
            else
            {
                fmpz_mod_poly_init2(tmp, &f->p, 3);
                fmpz_mod_poly_set_coeff_ui(tmp, 1, 1);
                fmpz_mod_poly_mulmod(res, tmp, tmp, f);
                fmpz_mod_poly_clear(tmp);
            }
            return;
        }
    }

    if ((res == f) || (res == finv))
    {
        fmpz_mod_poly_init2(tmp, &f->p, trunc);
        _fmpz_mod_poly_powmod_x_fmpz_preinv(tmp->coeffs, e, f->coeffs, lenf,
                                            finv->coeffs, finv->length, &f->p);
        fmpz_mod_poly_swap(res, tmp);
        fmpz_mod_poly_clear(tmp);
    }
    else
    {
        fmpz_mod_poly_fit_length(res, trunc);
        _fmpz_mod_poly_powmod_x_fmpz_preinv(res->coeffs, e, f->coeffs, lenf,
                                            finv->coeffs, finv->length, &f->p);
    }

    _fmpz_mod_poly_set_length(res, trunc);
    _fmpz_mod_poly_normalise(res);
}