Java Reference
In-Depth Information
PROJECTIVE
CLOSURE
NEGATIVE
NUMBERS
POSITIVE
NUMBERS
0
0
+
-
AFFINE CLOSURE
Figure21-2IEEE754RepresentationsofInfinity
Thestandardalsoprovidesthatarithmeticoperationswithoneor
moreinfinityoperandsmustbeexact.Nevertheless,certainoperations
oninfinityareconsideredinvalidandgeneratethecorrespondingexcep-
tion,specifically:
1.Addition(orsubtraction)ofinfinitieswithoppositesigns,forinstance,(-
∞)
+(+∞
).
2.Multiplicationof0times
∞.
3.Divisionof
∞
by
∞
.
4.Remainderoperationsintheform
x
REM
y
,when
x
=
∞.
5.Wheninfinityiscreatedbytheoverflowofafiniteoperand.
Thepracticalconsequenceoftheaffinetreatmentofinfinitiesisthat
wheninfinityformspartofanarithmeticoperationtheresultsarealge-
braicallyvalid.
Notein
Table21-2
thatinthebasicencodingofthesingleformatthe
exponent (bias 127) is in the range +127 to -126. This leaves unrepre-
sented the exponent values 0H and FFH. Also, in the encoding of the dou-
ble format, the exponent values 0H and 7FFH are unrepresented. These
values are intentionally left unused by the standard so that they are avail-
able for encoding un-normalized numbers, infinity, and non-numeric val-
ues that represent invalid operations.
In the single and double formats infinity is represented with an expo-
nent of all one bits, and a significand of all zeros in the fractional portion.
