# include <math.h>
# include <stdio.h>
# include <stdlib.h>
# include <time.h>

# include "asa032.h"

/******************************************************************************/

double gamain ( double x, double p, int *ifault )

/******************************************************************************/
/*
  Purpose:

    GAMAIN computes the incomplete gamma ratio.

  Discussion:

    A series expansion is used if P > X or X <= 1.  Otherwise, a
    continued fraction approximation is used.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    29 June 2014

  Author:

    Original FORTRAN77 version by G Bhattacharjee.
    C version by John Burkardt.

  Reference:

    G Bhattacharjee,
    Algorithm AS 32:
    The Incomplete Gamma Integral,
    Applied Statistics,
    Volume 19, Number 3, 1970, pages 285-287.

  Parameters:

    Input, double X, P, the parameters of the incomplete 
    gamma ratio.  0 <= X, and 0 < P.

    Output, int *IFAULT, error flag.
    0, no errors.
    1, P <= 0.
    2, X < 0.
    3, underflow.
    4, error return from the Log Gamma routine.

    Output, double GAMAIN, the value of the incomplete gamma ratio.
*/
{
  double a;
  double acu = 1.0E-08;
  double an;
  double arg;
  double b;
  double dif;
  double factor;
  double g;
  double gin;
  int i;
  double oflo = 1.0E+37;
  double pn[6];
  double rn;
  double term;
  double uflo = 1.0E-37;
  double value;

  *ifault = 0;
/*
  Check the input.
*/
  if ( p <= 0.0 )
  {
    *ifault = 1;
    value = 0.0;
    return value;
  }

  if ( x < 0.0 )
  {
    *ifault = 2;
    value = 0.0;
    return value;
  }

  if ( x == 0.0 )
  {
    *ifault = 0;
    value = 0.0;
    return value;
  }

  g = lgamma ( p );

  arg = p * log ( x ) - x - g;

  if ( arg < log ( uflo ) )
  {
    *ifault = 3;
    value = 0.0;
    return value;
  }

  *ifault = 0;
  factor = exp ( arg );
/*
  Calculation by series expansion.
*/
  if ( x <= 1.0 || x < p )
  {
    gin = 1.0;
    term = 1.0;
    rn = p;

    for ( ; ; )
    {
      rn = rn + 1.0;
      term = term * x / rn;
      gin = gin + term;

      if ( term <= acu )
      {
        break;
      }
    }

    value = gin * factor / p;
    return value;
  }
/*
  Calculation by continued fraction.
*/
  a = 1.0 - p;
  b = a + x + 1.0;
  term = 0.0;

  pn[0] = 1.0;
  pn[1] = x;
  pn[2] = x + 1.0;
  pn[3] = x * b;

  gin = pn[2] / pn[3];

  for ( ; ; )
  {
    a = a + 1.0;
    b = b + 2.0;
    term = term + 1.0;
    an = a * term;
    for ( i = 0; i <= 1; i++ )
    {
      pn[i+4] = b * pn[i+2] - an * pn[i];
    }

    if ( pn[5] != 0.0 )
    {
      rn = pn[4] / pn[5];
      dif = fabs ( gin - rn );
/*
  Absolute error tolerance satisfied?
*/
      if ( dif <= acu )
      {
/*
  Relative error tolerance satisfied?
*/
        if ( dif <= acu * rn )
        {
          value = 1.0 - factor * gin;
          break;
        }
      }
      gin = rn;
    }

    for ( i = 0; i < 4; i++ )
    {
      pn[i] = pn[i+2];
    }

    if ( oflo <= fabs ( pn[4] ) )
    {
      for ( i = 0; i < 4; i++ )
      {
        pn[i] = pn[i] / oflo;
      }
    }
  }

  return value;
}