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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
212 Chapter 6 Implementation of floating-point arithmetic on a computer
6.5 Multiplication
If x D 0ory D 0, then x y D 0and .x y/ D 0. Otherwise we determine
ez :D ex C ey (the possibility that ez lies outside the range Œe1, e2 is considered in
Section 6.9) and mz :D mx my . This multiplication can be executed correctly within
the long accumulator. Because b
2
jmxjjmy j < 1, a normalization consisting of
at most one left shift may be necessary. Figure 6.21 displays the flow diagram for mul-
tiplication. The relevant normalization procedure is described in the previous section.
ex :D exp.x/; mx :D mant.x/
my :D mant.y/ey :D exp.y/;
false
true
mx
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Publisher Resources

ISBN: 9783110301731