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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"
int
qqbar_sgn_re(const qqbar_t x)
{
if (qqbar_degree(x) == 1)
{
return -fmpz_sgn(QQBAR_COEFFS(x));
}
else if (arb_is_zero(acb_realref(QQBAR_ENCLOSURE(x))))
{
return 0;
}
else if (!arb_contains_zero(acb_realref(QQBAR_ENCLOSURE(x))))
{
return arf_sgn(arb_midref(acb_realref(QQBAR_ENCLOSURE(x))));
}
else
{
slong d, i;
slong prec;
int res, maybe_zero;
acb_t t, u;
acb_init(t);
acb_init(u);
d = qqbar_degree(x);
maybe_zero = 1;
for (i = 1; i < d && maybe_zero; i += 2)
if (!fmpz_is_zero(QQBAR_COEFFS(x) + i))
maybe_zero = 0;
acb_set(t, QQBAR_ENCLOSURE(x));
res = 0;
for (prec = QQBAR_DEFAULT_PREC / 2; ; prec *= 2)
{
_qqbar_enclosure_raw(t, QQBAR_POLY(x), t, prec);
if (!arb_contains_zero(acb_realref(t)) || arb_is_zero(acb_realref(t)))
{
res = arf_sgn(arb_midref(acb_realref(t)));
break;
}
if (maybe_zero)
{
acb_set(u, t);
arb_zero(acb_realref(u));
if (_qqbar_validate_existence_uniqueness(u, QQBAR_POLY(x), u, prec * 2))
{
res = 0;
break;
}
}
}
acb_clear(t);
acb_clear(u);
return res;
}
}