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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
172 Chapter 5 Floating-point arithmetic
5.3 Floating-point operations
We now turn to consideration of arithmetic operations in floating-point systems, fol-
lowed by treatment of errors of such operations.
In Chapters 3 and 4 we established that the arithmetic in the subsets under D and
S and in all rows of Figure 1 can be defined by semimorphisms. We recall that if M
is any ringoid or vectoid and N M a symmetric lower or upper screen (or both) of
M , then a semimorphism
is defined by the following formulas:
(R1)
V
x2N
x D x,
(R2)
V
x,y2M
.x y ) x y/,
(R4)
V
x2M
.x/ D x,
(RG)
V
x,y2N
.x
ı
y :D .x ı y//,for ı2fC, , , =g with y 6D 0forıD=.
In general the operations ...
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Publisher Resources

ISBN: 9783110301731