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/*
Copyright (C) 2015 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "arb_hypgeom.h"
#include "acb_hypgeom.h"
void
acb_hypgeom_erfc(acb_t res, const acb_t z, slong prec)
{
double x, y, abs_z2, log_z, log_erfc_z_asymp;
if (!acb_is_finite(z))
{
acb_indeterminate(res);
return;
}
if (acb_is_real(z))
{
arb_hypgeom_erfc(acb_realref(res), acb_realref(z), prec);
arb_zero(acb_imagref(res));
return;
}
if (acb_is_zero(z))
{
acb_one(res);
return;
}
if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -64) < 0 &&
arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -64) < 0) ||
arf_sgn(arb_midref(acb_realref(z))) < 0)
{
acb_hypgeom_erf(res, z, prec);
acb_sub_ui(res, res, 1, prec);
acb_neg(res, res);
return;
}
if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 64) > 0 ||
arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 64) > 0))
{
acb_hypgeom_erf_asymp(res, z, 1, prec, prec);
return;
}
x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN);
y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN);
abs_z2 = x * x + y * y;
if (abs_z2 > (prec + 8) * 0.69314718055994530942)
{
acb_hypgeom_erf_asymp(res, z, 1, prec, prec);
}
else
{
slong wp;
log_z = 0.5 * log(abs_z2);
log_erfc_z_asymp = y * y - x * x - log_z;
wp = prec + 2;
if (log_erfc_z_asymp < 0.0)
wp += (-log_erfc_z_asymp) * 1.4426950408889634074;
if (acb_rel_accuracy_bits(z) >= wp)
{
acb_hypgeom_erf(res, z, wp);
}
else
{
acb_t zmid;
mag_t re_err, im_err;
acb_init(zmid);
mag_init(re_err);
mag_init(im_err);
acb_hypgeom_erf_propagated_error(re_err, im_err, z);
arf_set(arb_midref(acb_realref(zmid)), arb_midref(acb_realref(z)));
arf_set(arb_midref(acb_imagref(zmid)), arb_midref(acb_imagref(z)));
acb_hypgeom_erf(res, zmid, wp);
arb_add_error_mag(acb_realref(res), re_err);
arb_add_error_mag(acb_imagref(res), im_err);
acb_clear(zmid);
mag_clear(re_err);
mag_clear(im_err);
}
acb_sub_ui(res, res, 1, prec);
acb_neg(res, res);
}
}
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