within values of type T.

```c++

  const int min_T = std::numeric_limits<T>::min();
  const int max_T = std::numeric_limits<T>::max();
  const float max_float = std::numeric_limits<float>::max();

  const float scale_factor_from_min_side =
      (min_T * min_range > 0) ? min_T / min_range : max_float;
  const float scale_factor_from_max_side =