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/*
Copyright (C) 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 "mag.h"
const int mag_bernoulli_div_fac_ui_tab[32] =
{
1, 536870912,
-3, 715827883,
-9, 763549742,
-14, 581752185,
-20, 930803495,
-25, 752164440,
-30, 609225645,
-36, 987456906,
-41, 800365631,
-46, 648744507,
-52, 1051701970,
-57, 852476898,
-62, 690991623,
-67, 560096688,
-73, 907994540,
-78, 735992650,
};
/* computes upper bound for B_n / n! */
void
mag_bernoulli_div_fac_ui(mag_t z, ulong n)
{
if (n % 2 == 1)
{
if (n == 1)
{
mag_one(z);
mag_mul_2exp_si(z, z, -1);
}
else
{
mag_zero(z);
}
}
else if (n < 32)
{
_fmpz_demote(MAG_EXPREF(z));
MAG_EXP(z) = mag_bernoulli_div_fac_ui_tab[n];
MAG_MAN(z) = mag_bernoulli_div_fac_ui_tab[n + 1];
}
else
{
/* upper bound for 1/(2pi) */
mag_set_ui_2exp_si(z, 683565276, -32);
/* 2 (1/(2pi))^n */
mag_pow_ui(z, z, n);
mag_mul_2exp_si(z, z, 1);
/* we should multiply by an upper bound for zeta(n),
but the error in the upper bound for 1/(2pi)
used above is already larger than this factor
when n >= 32, so there is no need */
}
}
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