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/*
Copyright (C) 2023 Jean Kieffer
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"
#include "acb_theta.h"
void
acb_theta_jet_ql_radius(arf_t eps, arf_t err, const arb_t c, const arb_t rho,
slong ord, slong g, slong prec)
{
slong lp = ACB_THETA_LOW_PREC;
slong b = ord + 1;
arb_t x, y;
arb_init(x);
arb_init(y);
/* Set x to min of (1/2g)^(1/b)*rho, (2^(-prec)/2cg)^(1/b)*rho^(2b-1)/b */
arb_set_si(x, 2 * g);
arb_inv(x, x, lp);
arb_root_ui(x, x, b, lp);
arb_mul(x, x, rho, lp);
arb_pow_ui(y, rho, 2 * b - 1, prec);
arb_mul_2exp_si(y, y, -prec);
arb_div(y, y, c, lp);
arb_div_si(y, y, 2 * g, lp);
arb_root_ui(y, y, b, lp);
arb_min(x, x, y, lp);
arb_get_lbound_arf(eps, x, lp);
arf_one(err);
arf_mul_2exp_si(err, err, -prec);
arb_clear(x);
arb_clear(y);
}