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/*
Copyright (C) 2014 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 "acb_elliptic.h"
#include "acb_modular.h"
void
acb_elliptic_p(acb_t r, const acb_t z, const acb_t tau, slong prec)
{
acb_struct t0[4], tz[4];
acb_t t;
int i, real;
real = acb_is_real(z) && arb_is_int_2exp_si(acb_realref(tau), -1) &&
arb_is_positive(acb_imagref(tau));
acb_init(t);
for (i = 0; i < 4; i++)
{
acb_init(t0 + i);
acb_init(tz + i);
}
acb_modular_theta(tz + 0, tz + 1, tz + 2, tz + 3, z, tau, prec);
acb_zero(t);
acb_modular_theta(t0 + 0, t0 + 1, t0 + 2, t0 + 3, t, tau, prec);
acb_mul(t, t0 + 1, t0 + 2, prec);
acb_mul(t, t, tz + 3, prec);
acb_div(t, t, tz + 0, prec);
acb_mul(t, t, t, prec);
acb_pow_ui(t0 + 1, t0 + 1, 4, prec);
acb_pow_ui(t0 + 2, t0 + 2, 4, prec);
acb_add(r, t0 + 1, t0 + 2, prec);
acb_div_ui(r, r, 3, prec);
acb_sub(r, t, r, prec);
acb_const_pi(t, prec);
acb_mul(t, t, t, prec);
acb_mul(r, r, t, prec);
if (real)
arb_zero(acb_imagref(r));
acb_clear(t);
for (i = 0; i < 4; i++)
{
acb_clear(t0 + i);
acb_clear(tz + i);
}
}
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