/*
    Copyright (C) 2009, 2013, 2016 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/>.
*/

#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"

ulong
n_powmod2_preinv(ulong a, slong exp, ulong n, ulong ninv)
{
    ulong norm;

    FLINT_ASSERT(n != 0);

    if (a >= n)
        a = n_mod2_preinv(a, n, ninv);

    if (exp < 0)
    {
        ulong g = n_gcdinv(&a, a, n);

        if (g != 1)
            flint_throw(FLINT_IMPINV, "Cannot invert modulo %wd*%wd\n", g,
                        n / g);

        exp = -exp;
    }

    count_leading_zeros(norm, n);

    return n_powmod_ui_preinv(a << norm, exp, n << norm, ninv, norm) >> norm;
}