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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 "fmpq.h"
#include "fmpz_poly.h"
#include "qqbar.h"
int
qqbar_cmp_re(const qqbar_t x, const qqbar_t y)
{
slong prec;
acb_t z1, z2;
int res, both_real;
if (!arb_overlaps(acb_realref(QQBAR_ENCLOSURE(x)), acb_realref(QQBAR_ENCLOSURE(y))))
{
return arf_cmp(arb_midref(acb_realref(QQBAR_ENCLOSURE(x))),
arb_midref(acb_realref(QQBAR_ENCLOSURE(y))));
}
if (qqbar_sgn_re(y) == 0)
return qqbar_sgn_re(x);
if (qqbar_sgn_re(x) == 0)
return -qqbar_sgn_re(y);
if (qqbar_degree(x) == 1 && qqbar_degree(y) == 1)
{
/* Reversed order since the signs are reversed */
return _fmpq_cmp(QQBAR_COEFFS(y), QQBAR_COEFFS(y) + 1,
QQBAR_COEFFS(x), QQBAR_COEFFS(x) + 1);
}
/* Likely complex conjugates */
if (fmpz_poly_equal(QQBAR_POLY(x), QQBAR_POLY(y)))
{
qqbar_t t;
/* Complex conjugate quadratics */
if (qqbar_degree(x) == 2 &&
!arb_overlaps(acb_imagref(QQBAR_ENCLOSURE(x)), acb_imagref(QQBAR_ENCLOSURE(y))))
return 0;
qqbar_init(t);
qqbar_conj(t, y);
res = qqbar_equal(x, t);
qqbar_clear(t);
if (res == 1)
return 0;
}
/* Subtraction is a scalar operation and will be quick */
if ((qqbar_degree(x) == 1 || qqbar_degree(y) == 1))
{
qqbar_t t;
qqbar_init(t);
qqbar_sub(t, x, y);
res = qqbar_sgn_re(t);
qqbar_clear(t);
return res;
}
acb_init(z1);
acb_init(z2);
acb_set(z1, QQBAR_ENCLOSURE(x));
acb_set(z2, QQBAR_ENCLOSURE(y));
both_real = -1;
res = 0;
for (prec = QQBAR_DEFAULT_PREC; ; prec *= 2)
{
_qqbar_enclosure_raw(z1, QQBAR_POLY(x), z1, prec);
_qqbar_enclosure_raw(z2, QQBAR_POLY(y), z2, prec);
if (!arb_overlaps(acb_realref(z1), acb_realref(z2)))
{
res = arf_cmp(arb_midref(acb_realref(z1)), arb_midref(acb_realref(z2)));
break;
}
if (both_real == -1)
both_real = qqbar_is_real(x) && qqbar_is_real(y);
/* Force an exact computation (may be slow) */
/* Todo: tune the cutoff based on degrees, bit sizes. */
/* Todo: use the improved closures we have computed. */
/* Todo: when is it better to compute and compare the real
parts? */
if (!both_real && prec >= 4 * QQBAR_DEFAULT_PREC)
{
qqbar_t t;
qqbar_init(t);
qqbar_sub(t, x, y);
res = qqbar_sgn_re(t);
qqbar_clear(t);
break;
}
}
acb_clear(z1);
acb_clear(z2);
return res;
}