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/*
Copyright (C) 2019 D.H.J Polymath
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_dirichlet.h"
/* out = 2*pi^(5/4)*exp(1/(8*h^2) - (t0^2)/(2*h^2) - pi*x) */
void
acb_dirichlet_platt_lemma_32(arb_t out, const arb_t h, const arb_t t0,
const arb_t x, slong prec)
{
arb_t pi, one_fourth;
arb_t x1, x2;
arb_init(pi);
arb_init(one_fourth);
arb_init(x1);
arb_init(x2);
arb_const_pi(pi, prec);
arb_set_d(one_fourth, 0.25);
arb_set_d(x1, 1.25);
arb_pow(x1, pi, x1, prec);
arb_mul_2exp_si(x1, x1, 1);
arb_sqr(x2, t0, prec);
arb_sub(x2, x2, one_fourth, prec);
arb_div(x2, x2, h, prec);
arb_div(x2, x2, h, prec);
arb_mul_2exp_si(x2, x2, -1);
arb_mul(out, pi, x, prec);
arb_add(out, out, x2, prec);
arb_neg(out, out);
arb_exp(out, out, prec);
arb_mul(out, out, x1, prec);
arb_clear(pi);
arb_clear(one_fourth);
arb_clear(x1);
arb_clear(x2);
}
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