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/* This file is part of the KDE project
Copyright (C) 2001, The Karbon Developers
Copyright (C) 2002, The Karbon Developers
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public
License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
This library 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public License
along with this library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301, USA.
*/
#include <math.h>
#include "vglobal.h"
int
VGlobal::binomialCoeff( unsigned n, unsigned k )
{
return
static_cast<int>(
0.5 +
exp(
factorialLn( n ) -
factorialLn( k ) -
factorialLn( n - k ) ) );
}
double
VGlobal::factorialLn( unsigned n )
{
const unsigned cacheSize = 100;
// A static array is initalized to zero.
static double cache[ cacheSize ];
if( n <= 1 )
return 0.0;
if( n <= cacheSize - 1 )
{
return cache[ n ]
? cache[ n ]
: ( cache[ n ] = gammaLn( n + 1.0 ) );
}
else
{
return gammaLn( n + 1.0 );
}
}
double
VGlobal::gammaLn( double x )
{
static double coeff[ 6 ] =
{
76.18009172947146,
-86.50532032941677,
24.01409824083091,
-1.231739572450155,
0.1208650973866179e-2,
-0.5395239384953e-5
};
double y = x;
double tmp = x + 5.5;
tmp -= ( x + 0.5 ) * log( tmp );
double ser = 1.000000000190015;
for( int i = 0; i < 5; ++i )
{
ser += coeff[ i ] / ++y;
}
return -tmp + log( 2.5066282746310005 * ser / x );
}
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