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/*
Copyright (C) 2013 Fredrik Johansson
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "arb.h"
void
arb_acos(arb_t z, const arb_t x, slong prec)
{
arb_t t, u;
if (arb_is_exact(x))
{
int side;
if (arf_is_zero(arb_midref(x)))
{
arb_const_pi(z, prec);
arb_mul_2exp_si(z, z, -1);
return;
}
side = arf_cmpabs_2exp_si(arb_midref(x), 0);
/* +/- 1 */
if (side == 0)
{
if (arf_is_one(arb_midref(x)))
arb_zero(z);
else
arb_const_pi(z, prec);
return;
}
else if (side > 0)
{
arb_indeterminate(z);
return;
}
}
arb_init(t);
arb_init(u);
arb_one(t);
arb_submul(t, x, x, prec);
arb_rsqrt(t, t, prec);
arb_mul(t, x, t, prec);
arb_atan(t, t, prec);
arb_const_pi(u, prec);
arb_mul_2exp_si(u, u, -1);
arb_sub(z, u, t, prec);
arb_clear(t);
arb_clear(u);
}