/*
    Copyright (C) 2010 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 "fmpz.h"

void
fmpz_factor_euler_phi(fmpz_t res, const fmpz_factor_t fac)
{
    fmpz_t t;
    slong i;

    fmpz_init(t);

    fmpz_one(res);

    for (i = 0; i < fac->num; i++)
    {
        fmpz_sub_ui(t, fac->p + i, 1);
        fmpz_mul(res, res, t);

        if (fac->exp[i] != 1)
        {
            fmpz_pow_ui(t, fac->p + i, fac->exp[i] - 1);
            fmpz_mul(res, res, t);
        }
    }

    fmpz_clear(t);
}

void
fmpz_euler_phi(fmpz_t res, const fmpz_t n)
{
    fmpz_factor_t fac;

    if (fmpz_sgn(n) <= 0)
    {
        fmpz_zero(res);
        return;
    }

    if (fmpz_abs_fits_ui(n))
    {
        fmpz_set_ui(res, n_euler_phi(fmpz_get_ui(n)));
        return;
    }

    fmpz_factor_init(fac);
    fmpz_factor(fac, n);
    fmpz_factor_euler_phi(res, fac);
    fmpz_factor_clear(fac);
}