nf_gammaFunctions.cc File Reference

#include "nf_specialFunctions.h"

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Macros
#define	MAXGAM   171.624376956302725
#define	MAXSTIR   143.01608
#define	MAXLGM   2.556348e305

Functions
static double	stirf (double x, nfu_status *status)
static double	lgam (double x, int *sgngam, nfu_status *status)
double	nf_gammaFunction (double x, nfu_status *status)
double	nf_logGammaFunction (double x, nfu_status *status)

Variables
static double	P []
static double	Q []
static double	LOGPI = 1.14472988584940017414
static double	SQTPI = 2.50662827463100050242E0
static double	STIR [5] = { 7.873113957930936284e-4, -2.2954996161337812638e-4, -2.6813261780578123283e-3, 3.472222216054586673e-3, 8.3333333333348225713e-2 }
static double	A []
static double	B []
static double	C []
static double	LS2PI = 0.91893853320467274178

Macro Definition Documentation

#define MAXGAM   171.624376956302725

Definition at line 93 of file nf_gammaFunctions.cc.

#define MAXLGM   2.556348e305

Definition at line 201 of file nf_gammaFunctions.cc.

#define MAXSTIR   143.01608

Definition at line 99 of file nf_gammaFunctions.cc.

Function Documentation

static double lgam ( double  x, int *  sgngam, nfu_status *  status  )

static

Definition at line 219 of file nf_gammaFunctions.cc.

                                                                {

    double p, q, u, w, z;
    int i;

    *sgngam = 1;

    if( x < -34.0 ) {
        q = -x;
        w = lgam( q, sgngam, status );                  /* note this modifies *sgngam! */
        p = floor( q );
        if( p == q ) goto lgsing;
        i = (int) p;
        if( ( i & 1 ) == 0 ) {
            *sgngam = -1; }
        else {
            *sgngam = 1;
        }
        z = q - p;
        if( z > 0.5 ) {
            p += 1.0;
            z = p - q;
        }
        z = q * sin( M_PI * z );
        if( z == 0.0 ) goto lgsing;
        z = LOGPI - G4Log( z ) - w;
        return( z );
    }

    if( x < 13.0 ) {
        z = 1.0;
        p = 0.0;
        u = x;
        while( u >= 3.0 ) {
            p -= 1.0;
            u = x + p;
            z *= u;
        } // Loop checking, 11.06.2015, T. Koi
        while( u < 2.0 ) {
            if( u == 0.0 ) goto lgsing;
            z /= u;
            p += 1.0;
            u = x + p;
        } // Loop checking, 11.06.2015, T. Koi
        if( z < 0.0 ) {
            *sgngam = -1;
            z = -z; }
        else {
            *sgngam = 1;
        }
        if( u == 2.0 ) return( G4Log( z ) );
        p -= 2.0;
        x = x + p;
        p = x * nf_polevl( x, B, 5 ) / nf_p1evl( x, C, 6);
        return( G4Log( z ) + p );
    }

    if( x > MAXLGM ) goto lgsing;
    q = ( x - 0.5 ) * G4Log( x ) - x + LS2PI;
    if( x > 1.0e8 ) return( q );

    p = 1.0 / ( x * x );
    if( x >= 1000.0 ) {
        q += ( ( 7.9365079365079365079365e-4 * p - 2.7777777777777777777778e-3 ) * p + 0.0833333333333333333333 ) / x; }
    else {
        q += nf_polevl( p, A, 4 ) / x;
    }
    return( q );

lgsing:
    return( *sgngam * DBL_MAX );
}

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double nf_gammaFunction	(	double	x,
		nfu_status *	status
	)

Definition at line 126 of file nf_gammaFunctions.cc.

                                                        {

    double p, q, z;
    int i, sgngam = 1;

    *status = nfu_badInput;
    if( !isfinite( x ) ) return( x );
    *status = nfu_Okay;

    q = fabs( x );

    if( q > 33.0 ) {
        if( x < 0.0 ) {
            p = floor( q );
            if( p == q ) goto goverf;
            i = (int) p;
            if( ( i & 1 ) == 0 ) sgngam = -1;
            z = q - p;
            if( z > 0.5 ) {
                p += 1.0;
                z = q - p;
            }
            z = q * sin( M_PI * z );
            if( z == 0.0 ) goto goverf;
            z = M_PI / ( fabs( z ) * stirf( q, status ) );
        }
        else {
            z = stirf( x, status );
        }
        return( sgngam * z );
    }

    z = 1.0;
    while( x >= 3.0 ) {
        x -= 1.0;
        z *= x;
    } // Loop checking, 11.06.2015, T. Koi

    while( x < 0.0 ) {
        if( x > -1.E-9 ) goto small;
        z /= x;
        x += 1.0;
    } // Loop checking, 11.06.2015, T. Koi

    while( x < 2.0 ) {
        if( x < 1.e-9 ) goto small;
        z /= x;
        x += 1.0;
    } // Loop checking, 11.06.2015, T. Koi

    if( x == 2.0 ) return( z );

    x -= 2.0;
    p = nf_polevl( x, P, 6 );
    q = nf_polevl( x, Q, 7 );
    return( z * p / q );

small:
    if( x == 0.0 ) goto goverf;
    return( z / ( ( 1.0 + 0.5772156649015329 * x ) * x ) );

goverf:
    return( sgngam * DBL_MAX );
}

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double nf_logGammaFunction	(	double	x,
		nfu_status *	status
	)

Definition at line 206 of file nf_gammaFunctions.cc.

                                                           {
/* Logarithm of gamma function */

    int sgngam;

    *status = nfu_badInput;
    if( !isfinite( x ) ) return( x );
    *status = nfu_Okay;
    return( lgam( x, &sgngam, status ) );
}

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static double stirf ( double  x, nfu_status *  status  )

static

Definition at line 106 of file nf_gammaFunctions.cc.

                                                {
/* Gamma function computed by Stirling's formula. The polynomial STIR is valid for 33 <= x <= 172.  */

    double y, w, v;

    w = 1.0 / x;
    w = 1.0 + w * nf_polevl( w, STIR, 4 );
    y = G4Exp( x );
    if( x > MAXSTIR ) {                     /* Avoid overflow in pow() */
        v = G4Pow::GetInstance()->powA( x, 0.5 * x - 0.25 );
        y = v * (v / y); }
    else {
        y = G4Pow::GetInstance()->powA( x, x - 0.5 ) / y;
    }
    y = SQTPI * y * w;
    return( y );
}

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Variable Documentation

double A[]

static

Initial value:

= { 8.11614167470508450300E-4, -5.95061904284301438324E-4, 7.93650340457716943945E-4,
                     -2.77777777730099687205E-3, 8.33333333333331927722E-2 }

Definition at line 194 of file nf_gammaFunctions.cc.

double B[]

static

Initial value:

= { -1.37825152569120859100E3, -3.88016315134637840924E4, -3.31612992738871184744E5,
                      -1.16237097492762307383E6, -1.72173700820839662146E6, -8.53555664245765465627E5 }

Definition at line 196 of file nf_gammaFunctions.cc.

double C[]

static

Initial value:

= { -3.51815701436523470549E2, -1.70642106651881159223E4, -2.20528590553854454839E5,
                      -1.13933444367982507207E6, -2.53252307177582951285E6, -2.01889141433532773231E6 }

Definition at line 198 of file nf_gammaFunctions.cc.

double LOGPI = 1.14472988584940017414

static

Definition at line 94 of file nf_gammaFunctions.cc.

double LS2PI = 0.91893853320467274178

static

Definition at line 200 of file nf_gammaFunctions.cc.

double P[]

static

Initial value:

= { 1.60119522476751861407E-4, 1.19135147006586384913E-3, 1.04213797561761569935E-2, 4.76367800457137231464E-2,
                      2.07448227648435975150E-1, 4.94214826801497100753E-1, 9.99999999999999996796E-1 }

Definition at line 89 of file nf_gammaFunctions.cc.

double Q[]

static

Initial value:

= { -2.31581873324120129819E-5, 5.39605580493303397842E-4, -4.45641913851797240494E-3, 1.18139785222060435552E-2,
                       3.58236398605498653373E-2, -2.34591795718243348568E-1, 7.14304917030273074085E-2, 1.00000000000000000320E0 }

Definition at line 91 of file nf_gammaFunctions.cc.

double SQTPI = 2.50662827463100050242E0

static

Definition at line 95 of file nf_gammaFunctions.cc.

double STIR[5] = { 7.873113957930936284e-4, -2.2954996161337812638e-4, -2.6813261780578123283e-3, 3.472222216054586673e-3, 8.3333333333348225713e-2 }

static

Definition at line 98 of file nf_gammaFunctions.cc.