/*
    Copyright (C) 2013, 2014 Fredrik Johansson

    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 "arb.h"

#define TABSIZE 256

/* bounds for log2(1/n!) */
static const short rec_fac_bound_2exp_si_tab[TABSIZE] = 
{
    0, 0, -1, -2, -4, -6, -9, -12, -15, -18, -21, -25, -28, -32, -36,
    -40, -44, -48, -52, -56, -61, -65, -69, -74, -79, -83, -88, -93, -97,
    -102, -107, -112, -117, -122, -127, -132, -138, -143, -148, -153,
    -159, -164, -169, -175, -180, -186, -191, -197, -202, -208, -214,
    -219, -225, -231, -237, -242, -248, -254, -260, -266, -272, -278,
    -284, -289, -295, -302, -308, -314, -320, -326, -332, -338, -344,
    -350, -357, -363, -369, -375, -382, -388, -394, -401, -407, -413,
    -420, -426, -433, -439, -446, -452, -458, -465, -472, -478, -485,
    -491, -498, -504, -511, -518, -524, -531, -538, -544, -551, -558,
    -564, -571, -578, -585, -591, -598, -605, -612, -619, -626, -632,
    -639, -646, -653, -660, -667, -674, -681, -688, -695, -702, -709,
    -716, -723, -730, -737, -744, -751, -758, -765, -772, -779, -786,
    -793, -801, -808, -815, -822, -829, -836, -844, -851, -858, -865,
    -872, -880, -887, -894, -901, -909, -916, -923, -931, -938, -945,
    -952, -960, -967, -975, -982, -989, -997, -1004, -1011, -1019, -1026,
    -1034, -1041, -1049, -1056, -1064, -1071, -1078, -1086, -1093, -1101,
    -1108, -1116, -1123, -1131, -1139, -1146, -1154, -1161, -1169, -1176,
    -1184, -1192, -1199, -1207, -1214, -1222, -1230, -1237, -1245, -1253,
    -1260, -1268, -1276, -1283, -1291, -1299, -1306, -1314, -1322, -1329,
    -1337, -1345, -1353, -1360, -1368, -1376, -1384, -1391, -1399, -1407,
    -1415, -1423, -1430, -1438, -1446, -1454, -1462, -1470, -1477, -1485,
    -1493, -1501, -1509, -1517, -1525, -1532, -1540, -1548, -1556, -1564,
    -1572, -1580, -1588, -1596, -1604, -1612, -1620, -1628, -1636, -1644,
    -1652, -1660, -1668, -1675
};

static __inline__ slong
rec_fac_bound_2exp_si(slong n)
{
    if (n < TABSIZE)
    {
        return rec_fac_bound_2exp_si_tab[n];
    }
    else
    {
        mag_t t;
        mag_init(t);
        mag_rfac_ui(t, n);  /* todo: check for overflow */
        return MAG_EXP(t);
    }
}

slong
_arb_exp_taylor_bound(slong mag, slong prec)
{
    slong i;

    /* assume x <= 1/4 */
    if (mag > -2)
    {
        flint_printf("_arb_exp_taylor_bound: too large input %wd\n", mag);
        flint_abort();
    }

    for (i = 1; ; i++)
    {
        if (mag * i + rec_fac_bound_2exp_si(i) < -prec - 1)
            return i;
    }
}