#include <iostream>
#include <cstdlib>
#include <cmath>
// niklaus wirth
//
using namespace std;

int main(int nargs, char* args[])
{
   double sn= 0.0, sv;
   double x= 0.5, p= x;
   int    sig= 1;
   int    k= 0;
   do {
      sv= sn;
      sn= sn +  sig * p/ (2.0*k+1.0) ;
      sig= -sig;
      p= p*x*x;
      k= k+1;
   } while ( abs(sv-sn) >= 1e-8);

   cout << "k= " << k << "\tsuma=" << sn;
   cout << "\tpi=" << 4*sn << endl;
   return EXIT_SUCCESS;
}