What is the fastest way to get the value of π?

Question

I\'m looking for the fastest way to obtain the value of π, as a personal challenge. More specifically, I\'m using ways that don\'t involve using #define constan

Answer 1

In the interests of completeness, a C++ template version, which, for an optimised build, will compute an approximation of PI at compile time, and will inline to a single value.

#include 

template
struct sign
{
    enum {value = (I % 2) == 0 ? 1 : -1};
};

template
struct pi_calc
{
    inline static double value ()
    {
        return (pi_calc::value () + pi_calc::value ()) / 2.0;
    }
};

template
struct pi_calc<0, J>
{
    inline static double value ()
    {
        return (sign::value * 4.0) / (2.0 * J + 1.0) + pi_calc<0, J-1>::value ();
    }
};


template<>
struct pi_calc<0, 0>
{
    inline static double value ()
    {
        return 4.0;
    }
};

template
struct pi
{
    inline static double value ()
    {
        return pi_calc::value ();
    }
};

int main ()
{
    std::cout.precision (12);

    const double pi_value = pi<10>::value ();

    std::cout << "pi ~ " << pi_value << std::endl;

    return 0;
}

Note for I > 10, optimised builds can be slow, likewise for non-optimised runs. For 12 iterations I believe there are around 80k calls to value() (in the absence of memoisation).