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/*
* Project: The SPD Image correction and azimuthal regrouping
* http://forge.epn-campus.eu/projects/show/azimuthal
*
* Copyright (C) 2005-2010 European Synchrotron Radiation Facility
* Grenoble, France
*
* Principal authors: P. Boesecke (boesecke@esrf.fr)
* R. Wilcke (wilcke@esrf.fr)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* and the GNU Lesser General Public License along with this program.
* If not, see <http://www.gnu.org/licenses/>.
*/
/*+++
NAME
gamma.c --- Gamma Function
SYNOPSIS
double gamma( double X );
HISTORY
2000-11-28 V1.0 Peter Boesecke
translated from PEARL function GAMMA PB 19-APR-1988
from COLLECTED ALGORITHMS FROM CACM 31-P 1- 0
ALGORITHM 31 (in ALGOL )
2000-12-01 V1.01 calculation corrected
2000-12-04 V1.02 -> gamma.c, .h
2000-12-06 V1.03 Stirling's formula for x>20
---*/
/****************************************************************************
* Include *
****************************************************************************/
# include "gamma.h"
# define GAMMA_PI 3.1415926535897932384626
double _loggamma( double x )
{ // by Stirling's formula Knuth I: 111
double invx, invx2, invx3, invx5, invx7;
double sum=0.0;
x -= 1.0;
if (x <= 1.0) return( 1.0 );
invx = 1.0 / x;
invx2 = invx * invx;
invx3 = invx2 * invx;
invx5 = invx3 * invx2;
invx7 = invx5 * invx2;
sum = ((x + 0.5) * log(x)) - x;
sum += log(2*GAMMA_PI) * 0.5;
sum += (invx / 12.0) - (invx3 / 360.0);
sum += (invx5 / 1260.0) - (invx7 / 1680.0);
return ( sum );
} /* _loggamma */
/*+++------------------------------------------------------------------------
NAME
gamma --- gamma function
SYNOPSIS
double gamma( double X );
DESCRIPTION
For 2<=x<=3 gamma is approximated. In this interval the absolut
error abs(eps(x))<0.25*1e-7. For x>3 gamma(x) is calculated
by iteration gamma(x) = (x-1) * (x-2) * ... * (x-n)*gamma(x-n),
with 2<=(x-n)<=3. For x<2 gamma(x) = gamma(x+n) / ( x*(x+1)...(x+n-1) )
again with 2<=(x-n)<=3. For x=0 or a negative integer gamma(x) is
set to DBL_MAX.
RETURN VALUE
gamma(x)
----------------------------------------------------------------------------*/
double gamma( double X )
{
const double EPSMIN = 1e-30;
const double EPS = 1e-6;
const double DUMVAL = DBL_MAX;
const double a0=.9999999758, a1=.4227874605, a2=.4117741955, a3=.0821117404;
const double a4=.0721101567, a5=.0044511400, a6=.0051589951, a7=.0016063118;
double GAMMA_WERT;
double H,Y;
H = 1.0; Y = X;
while ( (fabs(Y-2.0)) >= EPS ) {
if ( fabs(Y)<EPSMIN ) { H=DUMVAL; break; }
else if (Y<2.0) { H = H/Y; Y=Y+1.0; }
else if (Y>=20.0) { H = exp(_loggamma( Y )); break; }
else if (Y>=3.0) { Y = Y-1.0;H=H*Y; }
else { Y=Y-2.0;
H = (((((((a7*Y+a6)*Y+a5)*Y+a4)*Y+a3)*Y+a2)*Y+a1)*Y+a0)*H;
break; }
}
GAMMA_WERT = H;
return ( GAMMA_WERT );
} /* gamma */
/*+++------------------------------------------------------------------------
NAME
loggamma --- natural logarithm of gamma function
SYNOPSIS
double loggamma( double X );
DESCRIPTION
Calculation of the natural logarithm of gamma for positive X.
For X==0 or negative X DBL_MAX is returned.
RETURN VALUE
loggamma(x)
----------------------------------------------------------------------------*/
double loggamma( double X )
{
const double EPSMIN = 1e-30;
const double EPS = 1e-6;
const double DUMVAL = DBL_MAX;
const double a0=.9999999758, a1=.4227874605, a2=.4117741955, a3=.0821117404;
const double a4=.0721101567, a5=.0044511400, a6=.0051589951, a7=.0016063118;
double LOGGAMMA_WERT;
double logH, Y;
logH = 0.0; Y = X;
while ( (fabs(Y-2.0)) >= EPS ) {
if ( Y<EPSMIN ) { logH=DUMVAL; break; }
else if (Y<2.0) { logH = logH-log(Y); Y=Y+1.0; }
else if (Y>=20.0) { logH = _loggamma( Y ); break; }
else if (Y>=3.0) { Y = Y-1.0;logH=logH+log(Y); }
else { Y=Y-2.0;
logH = logH + log(((((((a7*Y+a6)*Y+a5)*Y+a4)*Y+a3)*Y+a2)*Y+a1)*Y+a0);
break; }
}
LOGGAMMA_WERT = logH;
return ( LOGGAMMA_WERT );
} /* loggamma */
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