/* $Id: beta.c,v 1.1 2003/04/15 03:20:17 cher Exp $ */

/* This file is taken from Cephes math library */

/*
  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 "cephes.h"
#include "mconf.h"

#include <math.h>

/*							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
 *
 */

#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
cephes_beta(double a, double 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 = cephes_lgam(y);
    sign *= sgngam; /* keep track of the sign */
    y = cephes_lgam(b) - y;
    sign *= sgngam;
    y = cephes_lgam(a) + y;
    sign *= sgngam;
    if( y > MAXLOG ) goto over;
    return( sign * exp(y) );
  }

  y = cephes_gamma(y);
  if( y == 0.0 ) goto over;

  if( a > b ) {
    y = cephes_gamma(a)/y;
    y *= cephes_gamma(b);
  } else {
    y = cephes_gamma(b)/y;
    y *= cephes_gamma(a);
  }

  return (y);

 over:
  cephes_mtherr( "beta", OVERFLOW );
  return( sign * MAXNUM );
}

/* Natural log of |beta|.  Return the sign of beta in sgngam.  */
double
lbeta( double a, double 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 = cephes_lgam(y);
    sign *= sgngam; /* keep track of the sign */
    y = cephes_lgam(b) - y;
    sign *= sgngam;
    y = cephes_lgam(a) + y;
    sign *= sgngam;
    sgngam = sign;
    return( y );
  }

  y = cephes_gamma(y);
  if( y == 0.0 ) {
    goto over;
  }

  if( a > b ) {
    y = cephes_gamma(a)/y;
    y *= cephes_gamma(b);
  } else {
    y = cephes_gamma(b)/y;
    y *= cephes_gamma(a);
  }

  if( y < 0 ) {
    sgngam = -1;
    y = -y;
  } else
    sgngam = 1;

  return( log(y) );

over:
  cephes_mtherr( "lbeta", OVERFLOW );
  return( sign * MAXNUM );
}

/*
 * Local variables:
 *  compile-command: "make -C .."
 * End:
 */