ify by using the library. In that case, you are
  not really interested by the inclusion property; you are only interested by
  the computation algorithms the library provides. So you do not need to use
  any rounding; the checking also may not be useful. Use an "exact
  computation" rounding (you are allowed to think the name strangely applies
  to the situation) and a checking that never tests for any invalid numbers
  or empty intervals. By doing that, you will obtain library functions
  reduced to their