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/*
Copyright (C) 2020 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 "qqbar.h"
/* todo: might be worth it to detect p/q * root of unity */
void
qqbar_abs(qqbar_t res, const qqbar_t x)
{
if (qqbar_is_real(x))
{
if (qqbar_sgn_re(x) >= 0)
qqbar_set(res, x);
else
qqbar_neg(res, x);
}
else if (qqbar_is_root_of_unity(NULL, NULL, x))
{
qqbar_one(res);
}
else
{
qqbar_t t;
qqbar_init(t);
if (qqbar_sgn_re(x) == 0)
{
qqbar_i(t);
qqbar_mul(res, x, t);
if (qqbar_sgn_re(res) < 0)
qqbar_neg(res, res);
}
else
{
qqbar_conj(t, x);
qqbar_mul(t, x, t);
qqbar_sqrt(res, t);
}
qqbar_clear(t);
}
arb_zero(acb_imagref(QQBAR_ENCLOSURE(res)));
}