# include <math.h>
# include <stdio.h>
# include <stdlib.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 MIT 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;
}
/******************************************************************************/

void gamma_inc_p_values ( int *n_data, double *a, double *x, double *fx )

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

    gamma_inc_p_values(): values of the normalized incomplete Gamma function P(A,X).

  Discussion:

    The (normalized) incomplete Gamma function is defined as:

      P(A,X) = 1/Gamma(A) * Integral ( 0 <= T <= X ) T^(A-1) * exp(-T) dT.

    With this definition, for all A and X,

      0 <= P(A,X) <= 1

    and

      P(A,oo) = 1.0

    In Mathematica, the function can be evaluated by:

      1 - GammaRegularized[A,X]

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    11 April 2010

  Author:

    John Burkardt

  Reference:

    Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.

    Stephen Wolfram,
    The Mathematica Book,
    Fourth Edition,
    Cambridge University Press, 1999,
    ISBN: 0-521-64314-7,
    LC: QA76.95.W65.

  Input:

    int *N_DATA.  The user sets N_DATA to 0 before the first call.

  Output:

    int *N_DATA.  The routine increments N_DATA by 1, and
    returns the corresponding data; when there is no more data, the
    output value of N_DATA will be 0 again.

    double *A, the parameter of the function.

    double *X, the argument of the function.

    double *FX, the value of the function.
*/
{
# define N_MAX 20

  static double a_vec[N_MAX] = {
     0.10E+00,
     0.10E+00,
     0.10E+00,
     0.50E+00,
     0.50E+00,
     0.50E+00,
     0.10E+01,
     0.10E+01,
     0.10E+01,
     0.11E+01,
     0.11E+01,
     0.11E+01,
     0.20E+01,
     0.20E+01,
     0.20E+01,
     0.60E+01,
     0.60E+01,
     0.11E+02,
     0.26E+02,
     0.41E+02  };

  static double fx_vec[N_MAX] = {
     0.7382350532339351E+00,
     0.9083579897300343E+00,
     0.9886559833621947E+00,
     0.3014646416966613E+00,
     0.7793286380801532E+00,
     0.9918490284064973E+00,
     0.9516258196404043E-01,
     0.6321205588285577E+00,
     0.9932620530009145E+00,
     0.7205974576054322E-01,
     0.5891809618706485E+00,
     0.9915368159845525E+00,
     0.1018582711118352E-01,
     0.4421745996289254E+00,
     0.9927049442755639E+00,
     0.4202103819530612E-01,
     0.9796589705830716E+00,
     0.9226039842296429E+00,
     0.4470785799755852E+00,
     0.7444549220718699E+00 };

  static double x_vec[N_MAX] = {
     0.30E-01,
     0.30E+00,
     0.15E+01,
     0.75E-01,
     0.75E+00,
     0.35E+01,
     0.10E+00,
     0.10E+01,
     0.50E+01,
     0.10E+00,
     0.10E+01,
     0.50E+01,
     0.15E+00,
     0.15E+01,
     0.70E+01,
     0.25E+01,
     0.12E+02,
     0.16E+02,
     0.25E+02,
     0.45E+02 };

  if ( *n_data < 0 )
  {
    *n_data = 0;
  }

  *n_data = *n_data + 1;

  if ( N_MAX < *n_data )
  {
    *n_data = 0;
    *a = 0.0;
    *x = 0.0;
    *fx = 0.0;
  }
  else
  {
    *a = a_vec[*n_data-1];
    *x = x_vec[*n_data-1];
    *fx = fx_vec[*n_data-1];
  }

  return;
# undef N_MAX
}