Chapter 5
Floating-point arithmetic
Thus far our considerations have proceeded under the general assumption
that the set R in Figure 1 is a linearly ordered ringoid. We are now going
to be more specific and assume that R is the linearly ordered field of r eal
numbers R and that the subsets D and S are special screens, which are
called floating-point systems. In Section 5 .1 we briefly review the defi-
nition of the real numbers and their r e presentation by b-adic expansions.
Section 5.2 deals with floating-point numbers and systems. We also dis-
cuss several basic roundings of the real numbers into a floating-point sys-
tem, and we derive error bounds for these roundings.
In Section 5.3 we consider floating-point operations defined by semi-
morphisms, and we ...