Compile Time sqrt(2)

main.cpp

#include <cstdio>
#include <cstdlib>

template<int x>
struct from_int
{
  const static double value;
};
template<int x>
const double from_int<x>::value = x;




template<
  bool flag,
  typename T,
  typename F
  >
struct ternary;


template<
  typename T,
  typename F
  >
struct ternary<true, T, F>
{
  const static double value;
};
template<
  typename T,
  typename F
  >
const double ternary<true, T, F>::value = T::value;


template<
  typename T,
  typename F
  >
struct ternary<false, T, F>
{
  const static double value;
};
template<
  typename T,
  typename F
  >
const double ternary<false, T, F>::value = F::value;






namespace newton
{

  template<typename X0, typename Y>
  struct advance
  {
    const static double value;
  };
  template<typename X0, typename Y>
  const double advance<X0, Y>::value =
    X0::value - (X0::value*X0::value - Y::value) / (2*X0::value) ;


  

  template<typename X0, typename Y>
  struct is_converged
  {
    const static bool value;
  };
  template<typename X0, typename Y>
  const bool is_converged<X0, Y>::value =
    X0::value*X0::value<Y::value*(1+1e-15) &&
    X0::value*X0::value>Y::value*(1-1e-15) ;


  template<typename X0, typename Y>
  struct solve_impl
  {
    typedef advance<X0, Y> adv_t;
    const static double value;
  };
  template<typename X0, typename Y>
  const double solve_impl<X0, Y>::value =
    ternary<is_converged<X0, Y>::value, X0, solve_impl<adv_t, Y> >::value;

  template<typename Y>
  struct solve : public solve_impl<from_int<1>, Y> { };
    

}



int main()
{
  typedef from_int<2> f2;
  printf("sqrt(2)=%.16g\n", newton::solve<f2>::value);
}