pqc/external/flint-2.4.3/arith/bernoulli_number_size.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT 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.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <math.h>
#include "arith.h"
double arith_bernoulli_number_size(ulong n)
{
double x;
/* |B_n| < 2 */
if (n <= 14)
return 1.0;
x = 2 + (n + 1) * log(n + 1) * 1.44269504088897; /* 1/log(2) */
x -= n * 4.0941911703612822; /* log2(2*pi*e) */
return x + 2;
}