/*=============================================================================

    This file is part of ARB.

    ARB is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    ARB is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with ARB; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2013 Fredrik Johansson

******************************************************************************/

#include "bernoulli.h"
#include "zeta.h"

void zeta_inv_ui_euler_product(fmprb_t z, ulong s, long prec);

void
bernoulli_fmprb_ui_zeta(fmprb_t b, ulong n, long prec)
{
    long wp, piwp;

    fmprb_t t, u;

    if (n < 10 || n % 2 != 0)
        abort();

    wp = prec + 8;
    piwp = wp + 2*FLINT_BIT_COUNT(n);

    fmprb_init(t);
    fmprb_init(u);

    /* |B_n| = 2 * n! / (2*pi)^n * zeta(n) */
    fmprb_fac_ui(b, n, piwp);
    fmprb_const_pi(t, piwp);
    fmprb_mul_2exp_si(t, t, 1);
    fmprb_pow_ui(t, t, n, piwp);

    if (n > 0.7 * wp)
    {
        zeta_ui_asymp(u, n, wp);
        fmprb_mul(b, b, u, wp);
    }
    else
    {
        zeta_inv_ui_euler_product(u, n, wp);
        fmprb_mul(t, t, u, wp);
    }

    fmprb_div(b, b, t, prec);
    fmprb_mul_2exp_si(b, b, 1);

    if (n % 4 == 0)
        fmprb_neg(b, b);

    fmprb_clear(t);
    fmprb_clear(u);
}