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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
210 Chapter 6 Implementation of floating-point arithmetic on a computer
(1) x D 0.1000 10
6
and y D0.5001 10
1
.Then
x Cy D 0.0999
ˇ
ˇ
9499
ˇ
ˇ
9 10
6
,
.x C y/ D 0.9999
ˇ
ˇ
4999 10
5
,
5
.x C y/ D 0.9999 10
5
,
4.x C y/ D 0.1000 10
6
,
.x C y/ D 0.9999 10
5
for 5 9.
(2) x D 0.1000 10
6
and y D0.5000 10
1
.Then
x Cy D 0.0999
ˇ
ˇ
9500
ˇ
ˇ
0 10
6
,
.x C y/ D 0.9999
ˇ
ˇ
5000 10
5
,
5
.x C y/ D 0.9999 10
5
,
4.x C y/ D 0.1000 10
6
,
.x C y/ D 0.1000 10
6
for D 5.
In the last two examples the operands are identical except for the last digit of y.If
the .2r C1/th digit of the accumulator was in fact not present, the corresponding sums
x Cy would be identical. Since these ...
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Publisher Resources

ISBN: 9783110301731