
Roundoff Modes and Error Analysis 407
8o~!~ 10
Consequently, for B integer we obtain
1
B <-(2 e-2)-2 e-l-1 8.21
-2
For instance, for e -- 8 we can make B -- 127 and
E/3 -- E + 127 8.22
for a symmetric exponent range of- 127 < E < 127. Note that the maximum
value of Et3 is 255, so that this value can be used to represent E -- 128 (nonsym-
metric range) or as a singularity condition.
Special Values
These are values that are not representable in the floating-point system, but are
useful. Two examples, which are included in the IEEE Standard presented later,
are NAN (not a number) and infinity (positive and negative). For instance, ...