  If the non-zero finite floating-point numbers are interpreted as point
intervals, then the effect of rounding can be interpreted as computing one of
the bounds of the result according to interval arithmetic. We give an interval
interpretation for the signed zeros and infinities, so that the undefined
operations 0*inf, inf - inf, inf/inf, and 0/0 become defined.
  In this way no operation remains that gives rise to an error condition.
Mathematically questionable features of the floating-point standard become
well-defined sets of reals. Interval semantics provides a basis for the
verification of numerical algorithms. We derive the results of the newly
defined operations and consider the implications for hardware implementation.
