# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <cmath>
# include <ctime>

using namespace std;

# include "asa063.H"

//****************************************************************************80

double alogam ( double x, int *ifault )

//****************************************************************************80
//
//  Purpose:
//
//    ALOGAM computes the logarithm of the Gamma function.
//
//  Modified:
//
//    22 January 2008
//
//  Author:
//
//    Malcolm Pike, David Hill
//    C++ version by John Burkardt
//
//  Reference:
//
//    Malcolm Pike, David Hill,
//    Algorithm 291:
//    Logarithm of Gamma Function,
//    Communications of the ACM,
//    Volume 9, Number 9, September 1966, page 684.
//
//  Parameters:
//
//    Input, double X, the argument of the Gamma function.
//    X should be greater than 0.
//
//    Output, int *IFAULT, error flag.
//    0, no error.
//    1, X <= 0.
//
//    Output, double ALOGAM, the logarithm of the Gamma
//    function of X.
//
{
  double f;
  double value;
  double y;
  double z;

  if ( x <= 0.0 )
  {
    *ifault = 1;
    value = 0.0;
    return value;
  }

  *ifault = 0;
  y = x;

  if ( x < 7.0 )
  {
    f = 1.0;
    z = y;

    while ( z < 7.0 )
    {
      f = f * z;
      z = z + 1.0;
    }
    y = z;
    f = - log ( f );
  }
  else
  {
    f = 0.0;
  }

  z = 1.0 / y / y;

  value = f + ( y - 0.5 ) * log ( y ) - y 
    + 0.918938533204673 + 
    ((( 
    - 0.000595238095238   * z 
    + 0.000793650793651 ) * z 
    - 0.002777777777778 ) * z 
    + 0.083333333333333 ) / y;

  return value;
}
//****************************************************************************80

void beta_inc_values ( int *n_data, double *a, double *b, double *x, 
  double *fx )

//****************************************************************************80
//
//  Purpose:
//
//    BETA_INC_VALUES returns some values of the incomplete Beta function.
//
//  Discussion:
//
//    The incomplete Beta function may be written
//
//      BETA_INC(A,B,X) = Integral (0 to X) T**(A-1) * (1-T)**(B-1) dT
//                      / Integral (0 to 1) T**(A-1) * (1-T)**(B-1) dT
//
//    Thus,
//
//      BETA_INC(A,B,0.0) = 0.0;
//      BETA_INC(A,B,1.0) = 1.0
//
//    The incomplete Beta function is also sometimes called the
//    "modified" Beta function, or the "normalized" Beta function
//    or the Beta CDF (cumulative density function.
//
//    In Mathematica, the function can be evaluated by:
//
//      BETA[X,A,B] / BETA[A,B]
//
//    The function can also be evaluated by using the Statistics package:
//
//      Needs["Statistics`ContinuousDistributions`"]
//      dist = BetaDistribution [ a, b ]
//      CDF [ dist, x ]
//
//  Modified:
//
//    04 January 2005
//
//  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.
//
//    Karl Pearson,
//    Tables of the Incomplete Beta Function,
//    Cambridge University Press, 1968.
//
//    Stephen Wolfram,
//    The Mathematica Book,
//    Fourth Edition,
//    Cambridge University Press, 1999,
//    ISBN: 0-521-64314-7,
//    LC: QA76.95.W65.
//
//  Parameters:
//
//    Input/output, int *N_DATA.  The user sets N_DATA to 0 before the
//    first call.  On each call, 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.
//
//    Output, double *A, B, the parameters of the function.
//
//    Output, double *X, the argument of the function.
//
//    Output, double *FX, the value of the function.
//
{
# define N_MAX 42

  double a_vec[N_MAX] = { 
      0.5E+00,  
      0.5E+00,  
      0.5E+00,  
      1.0E+00,  
      1.0E+00,  
      1.0E+00,  
      1.0E+00,  
      1.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      5.5E+00,  
     10.0E+00,  
     10.0E+00,  
     10.0E+00,  
     10.0E+00,  
     20.0E+00,  
     20.0E+00,  
     20.0E+00,  
     20.0E+00,  
     20.0E+00,  
     30.0E+00,  
     30.0E+00,  
     40.0E+00,
      0.1E+01, 
      0.1E+01, 
      0.1E+01, 
      0.1E+01, 
      0.1E+01, 
      0.1E+01, 
      0.1E+01, 
      0.1E+01, 
      0.2E+01, 
      0.3E+01, 
      0.4E+01, 
      0.5E+01 };

  double b_vec[N_MAX] = { 
      0.5E+00,  
      0.5E+00,  
      0.5E+00,  
      0.5E+00,  
      0.5E+00,  
      0.5E+00,  
      0.5E+00,  
      1.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      2.0E+00,  
      5.0E+00,  
      0.5E+00,  
      5.0E+00,  
      5.0E+00,  
     10.0E+00,  
      5.0E+00,  
     10.0E+00,  
     10.0E+00,  
     20.0E+00,  
     20.0E+00,  
     10.0E+00,  
     10.0E+00,  
     20.0E+00,
      0.5E+00, 
      0.5E+00, 
      0.5E+00, 
      0.5E+00, 
      0.2E+01, 
      0.3E+01, 
      0.4E+01, 
      0.5E+01, 
      0.2E+01, 
      0.2E+01, 
      0.2E+01, 
      0.2E+01 };

  double fx_vec[N_MAX] = { 
     0.6376856085851985E-01,  
     0.2048327646991335E+00,  
     0.1000000000000000E+01,  
     0.0000000000000000E+00,  
     0.5012562893380045E-02,  
     0.5131670194948620E-01,  
     0.2928932188134525E+00,  
     0.5000000000000000E+00,  
     0.2800000000000000E-01,  
     0.1040000000000000E+00,  
     0.2160000000000000E+00,  
     0.3520000000000000E+00,  
     0.5000000000000000E+00,  
     0.6480000000000000E+00,  
     0.7840000000000000E+00,  
     0.8960000000000000E+00,  
     0.9720000000000000E+00,  
     0.4361908850559777E+00,  
     0.1516409096347099E+00,  
     0.8978271484375000E-01,  
     0.1000000000000000E+01,  
     0.5000000000000000E+00,  
     0.4598773297575791E+00,  
     0.2146816102371739E+00,  
     0.9507364826957875E+00,  
     0.5000000000000000E+00,  
     0.8979413687105918E+00,  
     0.2241297491808366E+00,  
     0.7586405487192086E+00,  
     0.7001783247477069E+00,
     0.5131670194948620E-01, 
     0.1055728090000841E+00, 
     0.1633399734659245E+00, 
     0.2254033307585166E+00, 
     0.3600000000000000E+00, 
     0.4880000000000000E+00, 
     0.5904000000000000E+00, 
     0.6723200000000000E+00, 
     0.2160000000000000E+00, 
     0.8370000000000000E-01, 
     0.3078000000000000E-01, 
     0.1093500000000000E-01 };

  double x_vec[N_MAX] = { 
     0.01E+00,  
     0.10E+00,  
     1.00E+00,  
     0.00E+00,  
     0.01E+00,  
     0.10E+00,  
     0.50E+00,  
     0.50E+00,  
     0.10E+00,  
     0.20E+00,  
     0.30E+00,  
     0.40E+00,  
     0.50E+00,  
     0.60E+00,  
     0.70E+00,  
     0.80E+00,  
     0.90E+00,  
     0.50E+00,  
     0.90E+00,  
     0.50E+00,  
     1.00E+00,  
     0.50E+00,  
     0.80E+00,  
     0.60E+00,  
     0.80E+00,  
     0.50E+00,  
     0.60E+00,  
     0.70E+00,  
     0.80E+00,  
     0.70E+00,
     0.10E+00, 
     0.20E+00, 
     0.30E+00, 
     0.40E+00, 
     0.20E+00, 
     0.20E+00, 
     0.20E+00, 
     0.20E+00, 
     0.30E+00, 
     0.30E+00, 
     0.30E+00, 
     0.30E+00 };

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

  *n_data = *n_data + 1;

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

  return;
# undef N_MAX
}
//****************************************************************************80

double betain ( double x, double p, double q, double beta, int *ifault )

//****************************************************************************80
//
//  Purpose:
//
//    BETAIN computes the incomplete Beta function ratio.
//
//  Modified:
//
//    23 January 2008
//
//  Author:
//
//    KL Majumder, GP Bhattacharjee
//    C++ version by John Burkardt
//
//  Reference:
//
//    KL Majumder, GP Bhattacharjee,
//    Algorithm AS 63:
//    The incomplete Beta Integral,
//    Applied Statistics,
//    Volume 22, Number 3, 1973, pages 409-411.
//
//  Parameters:
//
//    Input, double X, the argument, between 0 and 1.
//
//    Input, double P, Q, the parameters, which
//    must be positive.
//
//    Input, double BETA, the logarithm of the complete
//    beta function.
//
//    Output, int *IFAULT, error flag.
//    0, no error.
//    nonzero, an error occurred.
//
//    Output, double BETAIN, the value of the incomplete
//    Beta function ratio.
//
{
  double acu = 0.1E-14;
  double ai;
  double betain;
  double cx;
  bool indx;
  int ns;
  double pp;
  double psq;
  double qq;
  double rx;
  double temp;
  double term;
  double value;
  double xx;

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

  if ( x < 0.0 || 1.0 < x )
  {
    *ifault = 2;
    return value;
  }
//
//  Special cases.
//
  if ( x == 0.0 || x == 1.0 )
  {
    return value;
  }
//
//  Change tail if necessary and determine S.
//
  psq = p + q;
  cx = 1.0 - x;

  if ( p < psq * x )
  {
    xx = cx;
    cx = x;
    pp = q;
    qq = p;
    indx = true;
  }
  else
  {
    xx = x;
    pp = p;
    qq = q;
    indx = false;
  }

  term = 1.0;
  ai = 1.0;
  value = 1.0;
  ns = ( int ) ( qq + cx * psq );
//
//  Use the Soper reduction formula.
//
  rx = xx / cx;
  temp = qq - ai;
  if ( ns == 0 )
  {
    rx = xx;
  }

  for ( ; ; )
  {
    term = term * temp * rx / ( pp + ai );
    value = value + term;;
    temp = r8_abs ( term );

    if ( temp <= acu && temp <= acu * value )
    {
      value = value * exp ( pp * log ( xx ) 
      + ( qq - 1.0 ) * log ( cx ) - beta ) / pp;

      if ( indx )
      {
        value = 1.0 - value;
      }
      break;
    }

    ai = ai + 1.0;
    ns = ns - 1;

    if ( 0 <= ns )
    {
      temp = qq - ai;
      if ( ns == 0 )
      {
        rx = xx;
      }
    }
    else
    {
      temp = psq;
      psq = psq + 1.0;
    }
  }

  return value;
}
//****************************************************************************80

double r8_abs ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    R8_ABS returns the absolute value of an R8.
//
//  Modified:
//
//    14 November 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, the quantity whose absolute value is desired.
//
//    Output, double R8_ABS, the absolute value of X.
//
{
  double value;

  if ( 0.0 <= x )
  {
    value = x;
  } 
  else
  {
    value = -x;
  }
  return value;
}
//****************************************************************************80

void timestamp ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  size_t len;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  len = strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}