#include <chrono>
#include <cmath>

using namespace std;

class timer
{
  public:
    timer() : start_timing(hi_res_clock::now()) {}
    void reset()
    {
      start_timing = hi_res_clock::now();
    }
    double elapsed() const
    {
       return(std::chrono::duration_cast<second_>
            (hi_res_clock::now() - start_timing).count());
    }
  private:
    typedef std::chrono::high_resolution_clock hi_res_clock;
    typedef std::chrono::duration<double, std::ratio<1> > second_;
    std::chrono::time_point<hi_res_clock> start_timing;

};

#include <iostream>
#include <cassert>
#include <chrono>
#include <string>
#include <cstdlib>

using namespace std;

void print_time(const string & heading , const double & t)
{
  cout << heading << " : " ;
  cout.setf(ios::right);
  cout.setf(ios::showpoint);
  cout.setf(ios::fixed);
  cout.width(10);
  cout.precision(6);
  cout << t << endl;
}

double f(double x)
{
  double f;
  f = 4.0/(1.0+x*x);
  return(f);
}

int main()
{

  timer timer_01;
  timer timer_02;

  double t;

  string heading;

  int i, j;
  int n_intervals;
  double interval_width, x, total, pi;
  double cplusplus_internal_pi;
  double time_difference;

  heading = "\n Program starts ";

  t=timer_01.elapsed();
  print_time(heading , t);

  n_intervals = 1000000;

  cplusplus_internal_pi = 4.0*atan(1.0);

  cout << "\n C++ internal pi 4.0*atan(1.0) \n" << endl;
  cout << "            " ;

  cout.width(20);
  cout.precision(16);
  cout.setf(ios::right);
  cout.setf(ios::showpoint);
  cout.setf(ios::fixed);

  cout << cplusplus_internal_pi << endl;

  heading = " Loop time ";

  for(j=1;j<5;j++)
  {

    interval_width = 1.0/n_intervals;
    total = 0.0;

    for (i=1; i <= n_intervals;i++)
    {
      x = interval_width*(double(i)-0.5);
      total = total + f(x);
    }

    t = timer_01.elapsed();
    time_difference = t;
    timer_01.reset();

    pi = interval_width*total;

    cout << "                     ";
    cout << "                N intervals " ;  
    cout.width(12);
    cout <<  n_intervals ;
    cout << " time = " ;

    cout.width(8);
    cout.precision(6);
    cout.setf(ios::right);
    cout.setf(ios::showpoint);
    cout.setf(ios::fixed);

    cout << time_difference << endl;

    cout << " Calculated "  ;

    cout.width(20);
    cout.precision(16);
    cout.setf(ios::right);
    cout.setf(ios::showpoint);
    cout.setf(ios::fixed);

    cout << pi << endl;

    cout << " Difference " ;
    cout.width(20);
    cout.precision(16);
    cout.setf(ios::right);
    cout.setf(ios::showpoint);
    cout.setf(ios::fixed);

    cout << abs(pi-cplusplus_internal_pi) << endl;
    n_intervals = n_intervals*10;

  }

  t = timer_02.elapsed();
  heading = " \n Total time ";
  print_time(heading,t);  

  return(0);

}