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/*
Copyright (C) 2015 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 "acb.h"
#include "acb_elliptic.h"
void
acb_elliptic_e(acb_t res, const acb_t m, slong prec)
{
if (acb_is_zero(m))
{
acb_const_pi(res, prec);
acb_mul_2exp_si(res, res, -1);
}
else if (acb_is_one(m))
{
acb_one(res);
}
else
{
acb_struct t[2];
acb_init(t + 0);
acb_init(t + 1);
acb_elliptic_k_jet(t, m, 2, prec);
acb_mul(t + 1, t + 1, m, prec);
acb_mul_2exp_si(t + 1, t + 1, 1);
acb_add(t, t, t + 1, prec);
acb_sub_ui(t + 1, m, 1, prec);
acb_mul(res, t, t + 1, prec);
acb_neg(res, res);
acb_clear(t + 0);
acb_clear(t + 1);
}
}