
402
c H A ~.~,T E ~~ ~8
Floating-Point Representation, Algorithms, and Implementations
Significand
0.100
0.101
0.110 I
0.111
Denormals
I,,,I,,,I
I'''1'''1
1 1
0 "g a"
1 1 1
[A, B] -- negative floating-point numbers (normalized)
[D, E] -- positive floating-point numbers (normalized)
(B, b] & [d, D) -- denormals
C -- zero
> E -- positive overflow
< A -- negative overflow
(B, C)- negative underflow (normalized)
(C, D) -- positive underflow (normalized)
(a)
I I I I I I I "- "-
1
1 2
Exponent -2 -1 0 1
(b)
F ! G U R E S.2 (a) Regions in floating-point representation. (b) Example for m -- f = 3, r -- 2,
and-2 <