
146 Chapter 4 Interval arithmetic
4.11 Extended interval arithmetic on the computer
On a computer, only subsets of the real numbers are representable. We assume now
that F denotes the set of finite floating-point numbers representable in some floating-
point format and
F :D F [f1, C1g.ThenIF denotes the intervals of IR whose
bounds are in F,and
IF denotes the intervals of IR whose bounds are in F and the
empty set. An interval between two floating-point bounds represents the continuous
set o f real numbers between these bounds. Similarly, except for the empty set, also
extended intervals represent continuous sets of real numbers.
In this section w e summarize ...