#include <limits>
#include <cmath>

template <typename T>
T ulp_up(T x)
{
  T infty = std::numeric_limits<T>::infinity();
  T above = std::nextafter(x, infty);
  return above - x;
}

template <typename T>
T ulp_down(T x)
{
  T infty = std::numeric_limits<T>::infinity();
  T below = std::nextafter(x, -infty);
  return x - below;
}