# include <cmath>
# include <cstdlib>

using namespace std;

# include "steinerberger.hpp"

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

double harmonic_number ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    harmonic_number() computes the Nth harmonic number.
//
//  Discussion:
//
//    H(N) = Sum ( 1 <= I <= N ) 1 / I
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 March 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    integer N: the index of the harmonic number.
//
//  Output:
//
//    real VALUE: the value of the harmonic number.
//
{
  int i;
  double value;

  value = 0.0;

  for ( i = 1; i <= n; i++ )
  {
    value = value + 1.0 / i;
  }

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

double steinerberger_function ( int n, double x )

//****************************************************************************80
//
//  Purpose:
//
//    steinerberger_function() evaluates the Steinerberger function.
//
//  Discussion:
//
//    f(n,x) = sum ( 1 <= k <= n ) abs ( sin ( pi * k * x ) ) / k
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 March 2025
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    John D Cook,
//    Pushing numerical integration software to its limits,
//    https://www.johndcook.com/blog/2023/06/12/stressing-numerical-integration/
//    Posted 12 June 2023.
//
//    John D Cook,
//    Plotting a function with lots of local minima,
//    https://www.johndcook.com/blog/2023/06/12/lots-of-local-minima/
//    Posted 12 June 2023.
//
//    Stefan Steinerberger,
//    A amusing sequence of functions,
//    Mathematics Magazine,
//    Volume 91, Number 4, October 2018, pages 262-266.
//
//  Input:
//
//    integer N: the index of the function.
//
//    real X: the evaluation point.
//
//  Output:
//
//    real VALUE: the function value.
//
{
  int k;
  static double r8_pi = 3.141592653589793;
  double value;

  value = 0.0;
  for ( k = 1; k <= n; k++ )
  {
    value = value + fabs ( sin ( k * r8_pi * x ) ) / k;
  }

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

double steinerberger_integral01 ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    steinerberger_integral01() returns the Steinerberger integral from 0 to 1.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 March 2025
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    John D Cook,
//    Pushing numerical integration software to its limits,
//    https://www.johndcook.com/blog/2023/06/12/stressing-numerical-integration/
//    Posted 12 June 2023.
//
//    John D Cook,
//    Plotting a function with lots of local minima,
//    https://www.johndcook.com/blog/2023/06/12/lots-of-local-minima/
//    Posted 12 June 2023.
//
//    Stefan Steinerberger,
//    A amusing sequence of functions,
//    Mathematics Magazine,
//    Volume 91, Number 4, October 2018, pages 262-266.
//
//  Input:
//
//    integer N: the index of the function.
//
//  Output:
//
//    real VALUE: the value of the integral from 0 to 1.
//
{
  static double r8_pi = 3.141592653589793;
  double value;

  value = 2.0 * harmonic_number ( n ) / r8_pi;

  return value;
}