#include <iostream>
#include <iomanip>  //for the i/o manipulator setprecision
#include <cstdlib>
#include <numbers>  //for std::numbers::pi  Compile with -std=c++20
using namespace std;

/*
Get closer and closer to the value of pi by adding up
4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...
*/

template <typename T>
T f()
{
	T pi {0};
	T sign {1};

	for (T i {1}; i < 32500000; i += 2) {
		pi += sign/i;
		sign = -sign;	
	}

	return 4 * pi;
}

int main()
{
	cout << fixed << setprecision(8);  //digits to right of decimal point
	cout << "pi =    " << numbers::pi << "\n";

	cout << "float:  " << f<float>()  << "\n";
	cout << "double: " << f<double>() << "\n";
	return EXIT_SUCCESS;
}