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

# include "steinerberger.h"

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

double harmonic_number ( int n )

/******************************************************************************/
/*
  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;
}
/******************************************************************************/

double steinerberger_function ( int n, double x )

/******************************************************************************/
/*
  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;
}
/******************************************************************************/

double steinerberger_integral01 ( int n )

/******************************************************************************/
/*
  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;
}