flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2017 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_poly.h"
#include "acb_dirichlet.h"

void
acb_dirichlet_hurwitz(acb_t res, const acb_t s, const acb_t a, slong prec)
{
    if (acb_is_one(a))
    {
        acb_dirichlet_zeta(res, s, prec);
        return;
    }

    if (acb_is_zero(s))
    {
        acb_mul_2exp_si(res, a, 1);
        acb_sub_ui(res, res, 1, prec);
        acb_neg(res, res);
        acb_mul_2exp_si(res, res, -1);
        return;
    }

    if (acb_is_zero(a) && acb_is_int(s) &&
        arf_sgn(arb_midref(acb_realref(s))) < 0)
    {
        acb_dirichlet_zeta(res, s, prec);
        return;
    }

    if (acb_is_int(s) && arf_sgn(arb_midref(acb_realref(s))) < 0 &&
        arf_cmpabs_ui(arb_midref(acb_realref(s)), prec / 2) < 0)
    {
        slong n = arf_get_si(arb_midref(acb_realref(s)), ARF_RND_FLOOR);

        acb_bernoulli_poly_ui(res, 1 - n, a, prec);
        acb_div_si(res, res, n - 1, prec);
        return;
    }

    if (arb_contains_zero(acb_imagref(s)) && arb_contains_si(acb_realref(s), 1))
    {
        acb_indeterminate(res);
        return;
    }

    _acb_poly_zeta_cpx_series(res, s, a, 0, 1, prec);
}