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/*
Copyright (C) 2012 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 "fmpr.h"
slong
fmpr_rsqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd)
{
slong r;
if (fmpr_is_special(x))
{
if (fmpr_is_zero(x))
fmpr_pos_inf(y);
else if (fmpr_is_pos_inf(x))
fmpr_zero(y);
else
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
if (fmpr_sgn(x) < 0)
{
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
/* special case: 4^n */
if (fmpz_is_one(fmpr_manref(x)) && fmpz_is_even(fmpr_expref(x)))
{
r = fmpr_set_round(y, x, prec, rnd);
fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1);
fmpz_neg(fmpr_expref(y), fmpr_expref(y));
return r;
}
{
fmpr_t t;
fmpz_t e;
fmpr_init(t);
fmpz_init(e);
fmpz_neg(e, fmpr_expref(x));
if (fmpz_is_odd(e))
fmpz_add_ui(e, e, 1);
fmpr_mul_2exp_fmpz(t, x, e);
CALL_MPFR_FUNC(r, mpfr_rec_sqrt, y, t, prec, rnd);
fmpz_tdiv_q_2exp(e, e, 1);
fmpr_mul_2exp_fmpz(y, y, e);
fmpr_clear(t);
fmpz_clear(e);
return r;
}
}
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