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/* beta.c
*
* Beta function
*
*
*
* SYNOPSIS:
*
* double a, b, y, beta();
*
* y = beta( a, b );
*
*
*
* DESCRIPTION:
*
* - -
* | (a) | (b)
* beta( a, b ) = -----------.
* -
* | (a+b)
*
* For large arguments the logarithm of the function is
* evaluated using lgam(), then exponentiated.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0,30 1700 7.7e-15 1.5e-15
* IEEE 0,30 30000 8.1e-14 1.1e-14
*
* ERROR MESSAGES:
*
* message condition value returned
* beta overflow log(beta) > MAXLOG 0.0
* a or b <0 integer 0.0
*
*/
/* beta.c */
/*
Cephes Math Library Release 2.0: April, 1987
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include "mconf.h"
#ifdef UNK
#define MAXGAM 34.84425627277176174
#endif
#ifdef DEC
#define MAXGAM 34.84425627277176174
#endif
#ifdef IBMPC
#define MAXGAM 171.624376956302725
#endif
#ifdef MIEEE
#define MAXGAM 171.624376956302725
#endif
extern double MAXLOG, MAXNUM;
extern int sgngam;
double beta( a, b )
double a, b;
{
double y;
int sign;
sign = 1;
if( a <= 0.0 )
{
if( a == floor(a) )
goto over;
}
if( b <= 0.0 )
{
if( b == floor(b) )
goto over;
}
y = a + b;
if( fabs(y) > MAXGAM )
{
y = lgam(y);
sign *= sgngam; /* keep track of the sign */
y = lgam(b) - y;
sign *= sgngam;
y = lgam(a) + y;
sign *= sgngam;
if( y > MAXLOG )
{
over:
mtherr( "beta", OVERFLOW );
return( sign * MAXNUM );
}
return( sign * exp(y) );
}
y = Gamma(y);
if( y == 0.0 )
goto over;
if( a > b )
{
y = Gamma(a)/y;
y *= Gamma(b);
}
else
{
y = Gamma(b)/y;
y *= Gamma(a);
}
return(y);
}
/* Natural log of |beta|. Return the sign of beta in sgngam. */
double lbeta( a, b )
double a, b;
{
double y;
int sign;
sign = 1;
if( a <= 0.0 )
{
if( a == floor(a) )
goto over;
}
if( b <= 0.0 )
{
if( b == floor(b) )
goto over;
}
y = a + b;
if( fabs(y) > MAXGAM )
{
y = lgam(y);
sign *= sgngam; /* keep track of the sign */
y = lgam(b) - y;
sign *= sgngam;
y = lgam(a) + y;
sign *= sgngam;
sgngam = sign;
return( y );
}
y = Gamma(y);
if( y == 0.0 )
{
over:
mtherr( "lbeta", OVERFLOW );
return( sign * MAXNUM );
}
if( a > b )
{
y = Gamma(a)/y;
y *= Gamma(b);
}
else
{
y = Gamma(b)/y;
y *= Gamma(a);
}
if( y < 0 )
{
sgngam = -1;
y = -y;
}
else
sgngam = 1;
return( log(y) );
}
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