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/*
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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
#include "fmpz.h"
#include "fmpz_factor.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);
}