#include "iostream"
#include "math.h"
using namespace std;

double arctan(double x);
double atan(double x);
int main (){
	double x;
	double PI;
	cout << "Input x:" << endl;
	cin >> x;
	double s = arctan(x) ;
	cout << "before:"<<s <<endl;
	cout << "later:"<< 	 atan(x) <<endl;
		
	PI = 16 * arctan(1.0/5) - 4 * arctan( 1.0/239 );
	cout << "PI:" << PI ;
	
	return 0;
}

double arctan(double x){
	
	int n(1);
	double sum1,sum2,sum(1);
	double sqrt = x*x;
	int flag(1);
	sum1 = x;
	sum = x;
	while(sum1/n > 1e-20 ){
		sum1 *= sqrt;
		n += 2;
		int j;
		( flag++ % 2 == 1) ? j=-1 : j = 1;
		sum += sum1 / (j * n);
		
		 
	}
	return sum;
	
}