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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 "mag.h"
void
mag_root(mag_t y, const mag_t x, ulong n)
{
if (n == 0)
{
mag_inf(y);
}
else if (n == 1 || mag_is_special(x))
{
mag_set(y, x);
}
else if (n == 2)
{
mag_sqrt(y, x);
}
else if (n == 4)
{
mag_sqrt(y, x);
mag_sqrt(y, y);
}
else
{
fmpz_t e, f;
fmpz_init_set_ui(e, MAG_BITS);
fmpz_init(f);
/* We evaluate exp(log(1+2^(kn)x)/n) 2^-k where k is chosen
so that 2^(kn) x ~= 2^30. TODO: this rewriting is probably
unnecessary with the new exp/log functions. */
fmpz_sub(e, e, MAG_EXPREF(x));
fmpz_cdiv_q_ui(e, e, n);
fmpz_mul_ui(f, e, n);
mag_mul_2exp_fmpz(y, x, f);
mag_log1p(y, y);
mag_div_ui(y, y, n);
mag_exp(y, y);
fmpz_neg(e, e);
mag_mul_2exp_fmpz(y, y, e);
fmpz_clear(e);
fmpz_clear(f);
}
}
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