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/*
Copyright (C) 2020 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 "ulong_extras.h"
#include "qqbar.h"
int
qqbar_tan_pi(qqbar_t res, slong p, ulong q)
{
slong g;
g = n_gcd(FLINT_ABS(p), q);
if (g != 1)
{
p /= g;
q /= g;
}
if (q == 1)
{
qqbar_zero(res);
}
else if (q == 2)
{
return 0;
}
else if (q == 4)
{
if (p % 4 == 1 || p % 4 == -3)
qqbar_one(res);
else
qqbar_set_si(res, -1);
}
else if (q == 3)
{
qqbar_set_ui(res, 3);
qqbar_sqrt(res, res);
if (p % 3 == -1 || p % 3 == 2)
qqbar_neg(res, res);
}
else if (q == 6)
{
qqbar_set_ui(res, 3);
qqbar_sqrt(res, res);
qqbar_inv(res, res);
if (p % 6 == -1 || p % 6 == 5)
qqbar_neg(res, res);
}
else
{
qqbar_t t;
qqbar_init(t);
qqbar_exp_pi_i(res, 2 * p, q);
qqbar_add_ui(res, res, 1);
qqbar_inv(res, res);
qqbar_mul_2exp_si(res, res, 1);
qqbar_sub_ui(res, res, 1);
qqbar_i(t);
qqbar_mul(res, res, t);
arb_zero(acb_imagref(QQBAR_ENCLOSURE(res)));
qqbar_clear(t);
}
return 1;
}