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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 3.7 Rounding nea r zero 81
Since o 2 S, (R1) and (RG) yield immediately that for every a 2 S the element a
is an additive inverse of a in S:
a
+
.a/ :D
(RG)
.a C .a// D o D
(R1)
o,foralla 2 S.
However, in a normalized floating-point system a is not in general the only addi-
tiveinverseofa in S. This was already shown by the example above. An affirmative
second example is:
1
4
+
3
8
D
1
8
D 0.
So
1
4
and
3
8
form a pair of additive inverses. More generally, whenever the real
sum of two numbers in S falls into the interval
1
4
,
1
4
their sum a
+
b in S is zer o.
We shall derive necessary and sufficient conditions for the existence of unique addi-
tive inverses ...
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Publisher Resources

ISBN: 9783110301731