
Section 3.6 Un ique ness of the minus operator 79
by the monotone downwardly directed rounding
5
alone. Apart from 4,noother
monotone rounding has this property.
This implies that on a computer, in principle, every monotone rounding can be per-
formed if either the monotone downwardly or upwardly directed rounding
5
or 4 is
available. Since non-monotone roundings are of little interest, this points out the poly-
tone role of the monotone directed roundings
5
and 4 for all rounded computations.
Beyond this result, the monotone directed roundings
5
and 4 are needed for all
interval computations as we shall see in Chapter 4. Interval arithmetic is a fundamen- ...