  We consider the prospect of a processor that can perform interval arithmetic
at the same speed as conventional floating-point arithmetic. This makes it
possible for all arithmetic to be performed with the superior security of
interval methods without any penalty in speed. In such a situation the IEEE
floating-point standard needs to be compared with a version of floating-point
arithmetic that is ideal for the purpose of interval arithmetic. Such a
comparison requires a succinct and complete exposition of interval arithmetic
according to its recent developments. We present such an exposition in this
paper. We conclude that the directed roundings toward the infinities and the
definition of division by the signed zeros are valuable features of the
standard. Because the operations of interval arithmetic are always defined,
exceptions do not arise. As a result neither Nans nor exceptions are needed. Of
the status flags, only the inexact flag may be useful. Denormalized numbers
seem to have no use for interval arithmetic; in the use of interval
constraints, they are a handicap.
