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

using namespace std;

# include "fresnel.hpp"

int main ( );
void fresnel_cos_plot ( );
void fresnel_cos_values ( int &n_data, double &x, double &fx );
void fresnel_cos_values_test ( );
void fresnel_phase_plot ( );
void fresnel_sin_plot ( );
void fresnel_sin_values ( int &n_data, double &x, double &fx );
void fresnel_sin_values_test ( );
void gnuplot_fx ( int n, double *x, double *y, string header );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_test() tests fresnel().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 July 2025
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );
  cout << "\n";
  cout << "fresnel_test():\n";
  cout << "  C++ version\n";
  cout << "  Test fresnel()\n";

  fresnel_cos_values_test ( );
  fresnel_sin_values_test ( );
  fresnel_cos_plot ( );
  fresnel_sin_plot ( );
  fresnel_phase_plot ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "fresnel_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void fresnel_cos_plot ( )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_cos_plot() tests fresnel_cos().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 July 2025
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n;
  double *x;
  double *y;

  cout << "\n";
  cout << "fresnel_cos_plot():\n";
  cout << "  Plot (X,C(X)), where C(X) is the Fresnel cosine integral.\n";

  a = -5.0;
  b = +5.0;
  n = 501;
  x = r8vec_linspace_new ( n, a, b );
  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = fresnel_cos ( x[i] );
  }

  header = "fresnel_cos_plot";
  gnuplot_fx ( n, x, y, header );

  delete [] x;
  delete [] y;

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

void fresnel_cos_values ( int &n_data, double &x, double &fx )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_cos_values() returns values of the Fresnel cosine integral function.
//
//  Discussion:
//
//    The Fresnel cosine integral is defined by:
//
//      C(X) = integral ( 0 <= T <= X ) cos ( PI * T^2 / 2 ) dT
//
//    In Mathematica, the function can be evaluated by:
//
//      FresnelC[x]
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    16 November 2015
//
//  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 &X, the argument of the function.
//
//    double &FX, the value of the function.
//
{
# define N_MAX 16

  static double fx_vec[N_MAX] = {
     0.0000000000000000E+00,
     0.1999210575944531E+00,
     0.3974807591723594E+00,
     0.5810954469916523E+00,
     0.7228441718963561E+00,
     0.7798934003768228E+00,
     0.7154377229230734E+00,
     0.5430957835462564E+00,
     0.3654616834404877E+00,
     0.3336329272215571E+00,
     0.4882534060753408E+00,
     0.6362860449033195E+00,
     0.5549614058564281E+00,
     0.3889374961919690E+00,
     0.4674916516989059E+00,
     0.6057207892976856E+00 };

  static double x_vec[N_MAX] = {
     0.0E+00,
     0.2E+00,
     0.4E+00,
     0.6E+00,
     0.8E+00,
     1.0E+00,
     1.2E+00,
     1.4E+00,
     1.6E+00,
     1.8E+00,
     2.0E+00,
     2.2E+00,
     2.4E+00,
     2.6E+00,
     2.8E+00,
     3.0E+00 };

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

  n_data = n_data + 1;

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

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

void fresnel_cos_values_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_cos_values_test() tests fresnel_cos_values().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 July 2025
//
//  Author:
//
//    John Burkardt
//
{
  double fx1;
  double fx2;
  int n_data;
  double x;

  cout << "\n";
  cout << "fresnel_cos_values_test():\n";
  cout << "  fresnel_cos_values() stores values of\n";
  cout << "  the Fresnel cosine integral C(X).\n";
  cout << "  fresnel_cos() evaluates the Fresnel cosine integral C(X).\n";
  cout << "\n";
  cout << "      X           C(X)\n";
  cout << "\n";

  n_data = 0;

  for ( ; ; )
  {
    fresnel_cos_values ( n_data, x, fx1 );

    if ( n_data == 0 )
    {
      break;
    }
    fx2 = fresnel_cos ( x );

    cout << "  " << setw(12) << x
         << "  " << setw(24) << fx1
         << "  " << setw(24) << fx2 << "\n";
  }
  return;
}
//****************************************************************************80

void fresnel_phase_plot ( )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_phase_plot() tests fresnel_cos() and fresnel_sin().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 July 2025
//
//  Author:
//
//    John Burkardt
//
//
{
  double a;
  double b;
  double *c;
  string header;
  int i;
  int n;
  double *s;
  double *x;

  cout << "\n";
  cout << "fresnel_phase_plot():\n";
  cout << "  Plot (C(X),S(X)), where C(X) and S(X) are\n";
  cout << "  the Fresnel cosine and sine integrals.\n";

  a = -5.0;
  b = +5.0;
  n = 501;
  x = r8vec_linspace_new ( n, a, b );
  c = new double[n];
  s = new double[n];

  for ( i = 0; i < n; i++ )
  {
    fresnel ( x[i], c[i], s[i] );
  }

  header = "fresnel_phase_plot";
  gnuplot_fx ( n, c, s, header );

  delete [] c;
  delete [] s;
  delete [] x;;

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

void fresnel_sin_plot ( )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_sin_plot() tests fresnel_sin().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 July 2025
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n;
  double *x;
  double *y;

  cout << "\n";
  cout << "fresnel_sin_plot():\n";
  cout << "  Plot (X,S(X)), where S(X) is the Fresnel sine integral.\n";

  a = -5.0;
  b = +5.0;
  n = 501;
  x = r8vec_linspace_new ( n, a, b );
  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = fresnel_sin ( x[i] );
  }

  header = "fresnel_sin_plot";
  gnuplot_fx ( n, x, y, header );

  delete [] x;
  delete [] y;

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

void fresnel_sin_values ( int &n_data, double &x, double &fx )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_sin_values() returns some values of the Fresnel sine integral function.
//
//  Discussion:
//
//    The Fresnel sine integral is defined by
//
//      S(X) = integral ( 0 <= T <= X ) sin ( pi * T^2 / 2 ) dT
//
//    In Mathematica, the function can be evaluated by:
//
//      FresnelS[x]
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    16 November 2015
//
//  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 &X, the argument of the function.
//
//    double &FX, the value of the function.
//
{
# define N_MAX 16

  static double fx_vec[N_MAX] = {
     0.0000000000000000E+00,
     0.4187609161656762E-02,
     0.3335943266061318E-01,
     0.1105402073593870E+00,
     0.2493413930539178E+00,
     0.4382591473903548E+00,
     0.6234009185462497E+00,
     0.7135250773634121E+00,
     0.6388876835093809E+00,
     0.4509387692675831E+00,
     0.3434156783636982E+00,
     0.4557046121246569E+00,
     0.6196899649456836E+00,
     0.5499893231527195E+00,
     0.3915284435431718E+00,
     0.4963129989673750E+00 };

  static double x_vec[N_MAX] = {
     0.0E+00,
     0.2E+00,
     0.4E+00,
     0.6E+00,
     0.8E+00,
     1.0E+00,
     1.2E+00,
     1.4E+00,
     1.6E+00,
     1.8E+00,
     2.0E+00,
     2.2E+00,
     2.4E+00,
     2.6E+00,
     2.8E+00,
     3.0E+00 };

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

  n_data = n_data + 1;

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

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

void fresnel_sin_values_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    fresnel_sin_values_test() tests fresnel_sin_values().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 July 2025
//
//  Author:
//
//    John Burkardt
//
{
  double fx1;
  double fx2;
  int n_data;
  double x;

  cout << "\n";
  cout << "fresnel_sin_values_test():\n";
  cout << "  fresnel_sin_values() stores values of\n";
  cout << "  the Fresnel sine integral S(X).\n";
  cout << "  fresnel_sin() evaluates the Fresnel sine integral S(X).\n";
  cout << "\n";
  cout << "      X           S(X)\n";
  cout << "\n";

  n_data = 0;

  for ( ; ; )
  {
    fresnel_sin_values ( n_data, x, fx1 );

    if ( n_data == 0 )
    {
      break;
    }
    fx2 = fresnel_sin ( x );

    cout << "  " << setw(12) << x
         << "  " << setw(24) << fx1
         << "  " << setw(24) << fx2 << "\n";
  }
  return;
}
//****************************************************************************80

void gnuplot_fx ( int n, double *x, double *y, string header )

//****************************************************************************80
//
//  Purpose:
//
//    gnuplot_fx() plots functional data x, f(x).
//
//  Discussion:
//
//    Actually, we simply create two files for processing by gnuplot().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  int i;
  string png_filename;
//
//  Create a graphics data file.
//
  data_filename = header + "_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < n; i++ )
  {
    data_unit << x[i] << "  "
              << y[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '" << data_filename << "'\n";

  png_filename = header + ".png";
//
//  Create graphics command file.
//
  command_filename = header + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );
  command_unit << "# " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "# Usage:\n";
  command_unit << "#  gnuplot < " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "set term png\n";
  command_unit << "set output '" << png_filename << "'\n";
  command_unit << "set xlabel '<--- X --->'\n";
  command_unit << "set ylabel '<-- Y(X) -->'\n";
  command_unit << "set title '" << header << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << 
    "plot '" << data_filename << "' using 1:2 lw 3 linecolor rgb 'blue'\n";
  command_unit.close ( );
  cout << "  Created command file '" << command_filename << "'\n";

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

double *r8vec_linspace_new ( int n, double a_first, double a_last )

//****************************************************************************80
//
//  Purpose:
//
//    r8vec_linspace_new() creates a vector of linearly spaced values.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12.
//
//    In other words, the interval is divided into N-1 even subintervals,
//    and the endpoints of intervals are used as the points.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    29 March 2011
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the vector.
//
//    double A_FIRST, A_LAST, the first and last entries.
//
//  Output:
//
//    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
//
{
  double *a;
  int i;

  a = new double[n];

  if ( n == 1 )
  {
    a[0] = ( a_first + a_last ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      a[i] = ( ( double ) ( n - 1 - i ) * a_first 
             + ( double ) (         i ) * a_last ) 
             / ( double ) ( n - 1     );
    }
  }
  return a;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    timestamp() prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    19 March 2018
//
//  Author:
//
//    John Burkardt
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}