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/*
Copyright (C) 2012, 2013 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_root(fmpr_t y, const fmpr_t x, ulong k, slong prec, fmpr_rnd_t rnd)
{
slong r;
if (k == 0)
{
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
else if (k == 1)
{
return fmpr_set_round(y, x, prec, rnd);
}
else if (k == 2)
{
return fmpr_sqrt(y, x, prec, rnd);
}
if (fmpr_is_special(x))
{
if (fmpr_is_zero(x))
fmpr_zero(y);
else if (fmpr_is_pos_inf(x))
fmpr_pos_inf(y);
else
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
if (fmpr_sgn(x) < 0)
{
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
{
fmpr_t t;
fmpz_t a, b;
fmpr_init(t);
fmpz_init(a);
fmpz_init(b);
/* (m * 2^(aq+b))^(1/q) = (m*2^b)^(1/q) * 2^a */
fmpz_set_ui(a, k);
fmpz_fdiv_qr(a, b, fmpr_expref(x), a);
fmpz_set(fmpr_manref(t), fmpr_manref(x));
fmpz_set(fmpr_expref(t), b);
#if MPFR_VERSION_MAJOR >= 4
CALL_MPFR_FUNC_K(r, mpfr_rootn_ui, y, t, k, prec, rnd);
#else
CALL_MPFR_FUNC_K(r, mpfr_root, y, t, k, prec, rnd);
#endif
fmpr_mul_2exp_fmpz(y, y, a);
fmpr_clear(t);
fmpz_clear(a);
fmpz_clear(b);
return r;
}
}
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