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/*
Copyright (C) 2023 Arb authors
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 "arb.h"
void
arb_minmax(arb_t z1, arb_t z2, const arb_t x, const arb_t y, slong prec)
{
arf_t xleft, xright, yleft, yright, xr, yr;
if (!arb_overlaps(x, y))
{
arb_t t; /* For handling aliasing */
arb_init(t);
if (arf_cmp(arb_midref(x), arb_midref(y)) < 0) {
arb_set(t, y);
arb_set(z1, x);
arb_set(z2, t);
} else {
arb_set(t, x);
arb_set(z1, y);
arb_set(z2, t);
}
arb_clear(t);
return;
}
if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y)))
{
arb_indeterminate(z1);
arb_indeterminate(z2);
return;
}
if (!arb_is_finite(x) || !arb_is_finite(y))
{
if (z1 != x && z1 != y)
{
arb_min(z1, x, y, prec);
arb_max(z2, x, y, prec);
}
else
{
arb_t t;
arb_init(t);
arb_min(t, x, y, prec);
arb_max(z2, x, y, prec);
arb_swap(z1, t);
arb_clear(t);
}
return;
}
arf_init(xleft);
arf_init(xright);
arf_init(yleft);
arf_init(yright);
arf_init_set_mag_shallow(xr, arb_radref(x));
arf_init_set_mag_shallow(yr, arb_radref(y));
arf_sub(xleft, arb_midref(x), xr, prec, ARF_RND_FLOOR);
arf_sub(yleft, arb_midref(y), yr, prec, ARF_RND_FLOOR);
arf_add(xright, arb_midref(x), xr, prec, ARF_RND_CEIL);
arf_add(yright, arb_midref(y), yr, prec, ARF_RND_CEIL);
if (arf_cmp(xleft, yleft) < 0)
{
/* xleft < yleft */
if (arf_cmp(xright, yright) < 0)
{
/* xright < yright */
arb_set_interval_arf(z1, xleft, xright, prec);
arb_set_interval_arf(z2, yleft, yright, prec);
} else {
/* xright >= yright */
arb_set_interval_arf(z1, xleft, yright, prec);
arb_set_interval_arf(z2, yleft, xright, prec);
}
} else {
/* xleft >= yleft */
if (arf_cmp(xright, yright) < 0)
{
/* xright < yright */
arb_set_interval_arf(z1, yleft, xright, prec);
arb_set_interval_arf(z2, xleft, yright, prec);
} else {
/* xright >= yright */
arb_set_interval_arf(z1, yleft, yright, prec);
arb_set_interval_arf(z2, xleft, xright, prec);
}
}
arf_clear(xleft);
arf_clear(xright);
arf_clear(yleft);
arf_clear(yright);
}
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