Compile-time calculation of Pi

gistfile1.cpp

#include <cstdio>
#include <ratio>

template <typename R, intmax_t N>
struct ratio_pow {
  using prev = typename ratio_pow<R, N-1>::value;
  using value = std::ratio<R::num * prev::num, R::den * prev::den>;
};

template <typename R>
struct ratio_pow<R, 0> {
  using value = std::ratio<1, 1>;
};


template <typename X, intmax_t I, intmax_t N>
struct arctan_impl {
  using coefficient = 
    std::ratio_multiply<
      typename ratio_pow<std::ratio<-1, 1>, I>::value,
      std::ratio<1, 2 * I + 1>
    >;
  using value = std::ratio_add<
    std::ratio_multiply<
      coefficient,
      typename ratio_pow<X, 2 * I + 1>::value
    >,
    typename arctan_impl<X, I+1, N-1>::value
  >;
};

template <typename X, intmax_t I>
struct arctan_impl<X, I, 0> {
  using value = std::ratio<0, 1>;
};


template <typename X, intmax_t N>
struct arctan {
  using value = typename arctan_impl<X, 0, N>::value;
};
    

template <class R>
void dump() {
  printf("%.10lf\n", (double(R::num) / R::den));
}


using pi = 
  std::ratio_subtract<
    std::ratio_multiply<
      std::ratio<16, 1>,
      typename arctan<std::ratio<1, 5>, 6>::value
    >,
    std::ratio_multiply<
      std::ratio<4, 1>,
      typename arctan<std::ratio<1, 239>, 2>::value
    >
  >;


int main () {
  dump<pi>();
  return 0;
}