/*
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2010 William Hart
    Copyright (C) 2011 Fredrik Johansson
    Copyright (C) 2013 Martin Lee
    Copyright (C) 2020 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 2.1 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#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 "nmod_vec.h"
#include "nmod_poly.h"
#include "ulong_extras.h"
#include "long_extras.h"

void
_nmod_poly_powmod_x_fmpz_preinv (mp_ptr res, fmpz_t e, mp_srcptr f, slong lenf,
                                      mp_srcptr finv, slong lenfinv, nmod_t mod)
{
    mp_ptr T, Q;
    slong lenT, lenQ, window;
    slong i, l, c;

    lenT = 2*lenf - 3;
    lenQ = FLINT_MAX(lenT - lenf + 1, 1);

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

    flint_mpn_zero (res, lenf - 1);
    res[0] = 1;

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

    if (c == 0)
    {
        _nmod_poly_shift_left(T, res, lenf - 1, window);

        _nmod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window, f,
                                                     lenf, finv, lenfinv, mod);

        c = l + 1;
        window = 0;
    }

    for (; i >= 0; i--)
    {
        _nmod_poly_mul(T, res, lenf - 1, res, lenf - 1, mod);

        _nmod_poly_divrem_newton_n_preinv(Q, res, T, 2*lenf - 3, f,
                                                     lenf, finv, lenfinv, mod);

        c--;

        if (fmpz_tstbit(e, i))
        {
            if (window == 0 && i <= l - 1)
                c = i;
        
            if (c >= 0)
              window = window | (WORD(1) << c);
        } else if (window == 0)
            c = l + 1;

        if (c == 0)
        {
            _nmod_poly_shift_left(T, res, lenf - 1, window);
          
            _nmod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window, f,
                                                     lenf, finv, lenfinv, mod);

            c = l + 1;
            window = 0;
        }
    }

    _nmod_vec_clear(T);
}


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

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

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

    if (lenf == 2)
    {
        nmod_poly_t r, poly;

        nmod_poly_init_mod(tmp, res->mod);
        nmod_poly_init_mod(r, res->mod);
        nmod_poly_init2_preinv(poly, res->mod.n, res->mod.ninv, 2);
        
        nmod_poly_set_coeff_ui(poly, 1, 1);
        
        nmod_poly_divrem(tmp, r, poly, f);
        
        nmod_poly_powmod_fmpz_binexp_preinv(res, r, e, f, finv);
        
        nmod_poly_clear(tmp);
        nmod_poly_clear(r);
        nmod_poly_clear(poly);
        
        return;
    }

    if (fmpz_cmp_ui(e, 2) <= 0)
    {
        if (fmpz_is_zero(e))
        {
            nmod_poly_fit_length(res, 1);
          
            res->coeffs[0] = 1;
            res->length = 1;
        } else if (fmpz_is_one(e))
        {
            nmod_poly_t r;
          
            nmod_poly_init2_preinv(r, res->mod.n, res->mod.ninv, 2);
            nmod_poly_set_coeff_ui(r, 1, 1);

            nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv);
            
            nmod_poly_divrem (tmp, res, r, f);
            
            nmod_poly_clear(tmp);
            nmod_poly_clear(r);
        }
        else
        {
            nmod_poly_init2_preinv(tmp, res->mod.n, res->mod.ninv, 3);
            nmod_poly_set_coeff_ui(tmp, 1, 1);
            
            nmod_poly_mulmod(res, tmp, tmp, f);
            
            nmod_poly_clear(tmp);
        }
        return;
    }

    if (res == f || res == finv)
    {
        nmod_poly_init2(tmp, res->mod.n, trunc);
        
        _nmod_poly_powmod_x_fmpz_preinv(tmp->coeffs, e, f->coeffs, lenf,
                                           finv->coeffs, finv->length, f->mod);
        
        nmod_poly_swap(res, tmp);
        nmod_poly_clear(tmp);
    }
    else
    {
        nmod_poly_fit_length(res, trunc);
        
        _nmod_poly_powmod_x_fmpz_preinv(res->coeffs, e, f->coeffs, lenf,
                                           finv->coeffs, finv->length, f->mod);
    }

    res->length = trunc;
    _nmod_poly_normalise(res);
}