vglobal.cpp

/* 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 );
}