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

    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) 2015 Fredrik Johansson

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

#include "acb.h"

slong
acb_rel_error_bits(const acb_t x)
{
    int am, ar, bm, br;
    slong result;
    const fmpz * radmag;
    const fmpz * midmag;
    fmpz_t t;

    am = !arf_is_zero(arb_midref(acb_realref(x)));
    ar = !mag_is_zero(arb_radref(acb_realref(x)));

    bm = !arf_is_zero(arb_midref(acb_imagref(x)));
    br = !mag_is_zero(arb_radref(acb_imagref(x)));

    /* no radius -- exact */
    if (!ar && !br)
        return -ARF_PREC_EXACT;

    /* no midpoint -- infinite relative error */
    if (!am && !bm)
        return ARF_PREC_EXACT;

    if (!acb_is_finite(x))
        return ARF_PREC_EXACT;

#define ame ARF_EXPREF(arb_midref(acb_realref(x)))
#define are MAG_EXPREF(arb_radref(acb_realref(x)))
#define bme ARF_EXPREF(arb_midref(acb_imagref(x)))
#define bre MAG_EXPREF(arb_radref(acb_imagref(x)))

    if (am && bm)
        midmag = fmpz_cmp(ame, bme) >= 0 ? ame : bme;
    else if (am)
        midmag = ame;
    else
        midmag = bme;

    if (ar && br)
        radmag = fmpz_cmp(are, bre) >= 0 ? are : bre;
    else if (ar)
        radmag = are;
    else
        radmag = bre;

    fmpz_init(t);
    fmpz_add_ui(t, radmag, 1);
    result = _fmpz_sub_small(t, midmag);
    fmpz_clear(t);

    return result;
}