```c++

  const int min_expected_T = std::numeric_limits<T>::min() +
    (narrow_range ? 1 : 0);
  const int max_expected_T = std::numeric_limits<T>::max();
  const float max_expected_T = std::numeric_limits<float>::max();

  const float scale_factor =
    (std::numeric_limits<T>::min() == 0) ? (max_range / max_expected_T)
                                         : std::max(min_range / min_expected_T,