Best platform independent pi constant?

Question

I know that you can use:

#define _USE_MATH_DEFINES

and then:

M_PI

to get the constant pi. However, if I r

Answer 1

The function below calculates pi without relying on any libraries at all.

Also, the type of its result is a template parameter.

Platform ueber-independence is stifled a bit because it only works with fixed-precision fractional types -- the calculated value needs to converge and remain constant over 2 iterations.

So if you specify some kind of arbitrary-precision rational or floating-point class which will automatically increase its precision as needed, a call to this function will not end well.

#include 
#include 

namespace golf {
    template  inline T calc_pi() {
        T sum=T(0), k8=T(0), fac=T(1);
        for(;;) {
            const T next = 
                sum + fac*(T(4)/(k8+T(1))-T(2)/(k8+T(4))-T(1)/(k8+T(5))-T(1)/(k8+T(6)));
            if(sum == next) return sum;
            sum=next;
            fac /= T(16);
            k8  += T(8);
    }   }
    static const auto PI = calc_pi();
}

int main() {
    std::cout << std::setprecision(16) << golf::PI << std::endl;
    return 0;
}