#include <iostream>
#include <iomanip>   //for setw and setprecision
#include <cstdlib>   //for abs (means "absolute value")
#include <numbers>   //for std::numbers::pi       Compile with c++ -std=c++20
using namespace std;

int main()
{
	double pi {numbers::pi};
	double sum {0.0};
	double sign {1.0};
	double denominator {1.0};

	cout << "             sum               error\n"
	     << "      -----------------  -----------------\n";

	for (int i {1}; i <= 1000; ++i) {
		//means sum = sum + sign * 4.0 / denominator 
		sum += sign * 4.0 / denominator;

		cout << setw(4) << i
			<< "  " << fixed << setprecision(15) << sum
			<< "  " << fixed << setprecision(15) << abs(pi - sum)
			<< "\n";

		sign *= -1.0;         //means sign = sign * -1.0
		denominator += 2.0;   //means denominator = denominator + 2.0
	}

	cout << pi << " is the actual value of pi.\n";
	return EXIT_SUCCESS;
}