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/*
Copyright (C) 2014 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 "mag.h"
void
mag_rsqrt(mag_t y, const mag_t x)
{
if (mag_is_special(x))
{
if (mag_is_zero(x))
mag_inf(y);
else
mag_zero(y);
}
else
{
double t;
fmpz e;
t = MAG_MAN(x) * ldexp(1.0, -MAG_BITS);
if (MAG_IS_LAGOM(x))
{
e = MAG_EXP(x);
if (e % 2 != 0)
{
e = (1 - e) >> 1;
t *= 2.0;
}
else
{
e = (-e) >> 1;
}
t = (1.0 / sqrt(t)) * (1 + 1e-13);
_fmpz_demote(MAG_EXPREF(y));
MAG_SET_D_2EXP(MAG_MAN(y), MAG_EXP(y), t, e);
}
else
{
if (fmpz_is_odd(MAG_EXPREF(x)))
t *= 2.0;
fmpz_fdiv_q_2exp(MAG_EXPREF(y), MAG_EXPREF(x), 1);
fmpz_neg(MAG_EXPREF(y), MAG_EXPREF(y));
t = (1.0 / sqrt(t)) * (1 + 1e-13);
mag_set_d_2exp_fmpz(y, t, MAG_EXPREF(y));
}
}
}
void
mag_rsqrt_lower(mag_t y, const mag_t x)
{
if (mag_is_special(x))
{
if (mag_is_zero(x))
mag_inf(y);
else
mag_zero(y);
}
else
{
double t;
fmpz e;
t = MAG_MAN(x) * ldexp(1.0, -MAG_BITS);
if (MAG_IS_LAGOM(x))
{
e = MAG_EXP(x);
if (e % 2 != 0)
{
e = (1 - e) >> 1;
t *= 2.0;
}
else
{
e = (-e) >> 1;
}
t = (1.0 / sqrt(t)) * (1 - 1e-13);
_fmpz_demote(MAG_EXPREF(y));
MAG_SET_D_2EXP_LOWER(MAG_MAN(y), MAG_EXP(y), t, e);
}
else
{
if (fmpz_is_odd(MAG_EXPREF(x)))
t *= 2.0;
fmpz_fdiv_q_2exp(MAG_EXPREF(y), MAG_EXPREF(x), 1);
fmpz_neg(MAG_EXPREF(y), MAG_EXPREF(y));
t = (1.0 / sqrt(t)) * (1 - 1e-13);
mag_set_d_2exp_fmpz_lower(y, t, MAG_EXPREF(y));
}
}
}
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