Skip to Main Content
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
168 Chapter 5 Floating-point arithmetic
Using the function Œx (the greatest integer less than or equal to x) the description
of
5
x can be shortened:
5
x D
8
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
<
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
:
C1 for x DC1,
CB for C B x<C1,
Œm b
r
b
er
for b
e11
jxjCB,
C0.000 :::0 b
e1
for 0 x<b
e11
,
0.100 :::0 b
e1
for b
e11
x<0,
1 for 1x<B.
The more detailed description of
5
x above shows that a normalization may still be
necessary.
A few additional but very similar cases occur if for e<e1 the exponent e is set to
e1 and unnormalized mantissas are permitted.
Thus the implementation of the rounding
5
on a computer is simplified if the func-
tion Œx is available. In the algorithms ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Arithmetic and Logic in Computer Systems

Arithmetic and Logic in Computer Systems

Mi Lu
Interval Analysis

Interval Analysis

Günter Mayer

Publisher Resources

ISBN: 9783110301731