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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
Section 4.10 Exception-free arithmetic for extended intervals 141
Table 4.8. Rules for use of 1 and C1 in interval operations.
Addition
1 b C1
1 1 1
a
1 C1
C1
C1 C1
Subtraction
1 b C1
1 1 1
a
C1 1
C1
C1 C1
Multiplication 1 b<00b>0 C1
1 C1 C1 0 1 1
a<0
C1 1
0
00
a>0
1 C1
C1
1 1 0 C1 C1
Division
1 C1
a 00
beyond IEEE 754 is
0 .1/ D .1/ 0 D 0 .C1/ D .C1/ 0 D 0.
This rule follows quite naturally from the definition of unbounded intervals. However,
it should not be taken as a new mathematical law. It is just a short cut to easily compute
the bounds of the result of an operation on unbounded intervals.
The calculus in
IR as defined here is free of exception ...
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Publisher Resources

ISBN: 9783110301731