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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
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 ...
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Publisher Resources

ISBN: 9783110301731