Developer's Topics
Chapter 1, Floating point operations
Special-case values

Special-case values

The following table gives the names of special cases and how each is represented. 

 --------------------------------------------------------------
 Value name            Sign   Exponent          Fraction
 --------------------------------------------------------------
                                         MSB   Rest of fraction
                                        -----------------------
 NaN (non-trapping)     X     Max         0    Nonzero
 Trapping NaN           X     Max         1    X
                                        -----------------------
 Positive Infinity      0     Max        Min
 Negative Infinity      1     Max        Min
 Positive Zero          0     Min        Min
 Negative Zero          1     Min        Min
 Denormalized number    X     Min        Nonzero
 Normalized number      X     NotMM      X
Key:

X
does not matter

Max
maximum value that can be stored in the field (all 1's)

Min
minimum value that can be stored in the field (all 0's)

NaN
not a number

NotMM
field is not equal to either Min or Max values

Nonzero
field contains at least one ``1'' bit

MSB
Most Significant Bit
The algorithm for classification of a value into special cases follows:

If (Exponent==Max)
If (Fraction==Min)
Then the number is Infinity (Positive or Negative
as determined by the Sign bit).
Else the number is NaN (Trapping if FractionMSB==0,
non-Trapping if FractionMSB==1).

Else If (Exponent==Min)
If (Fraction==Min)
Then the number is Zero (Positive or Negative
as determined by the Sign bit).
Else the number is Denormalized.
Else the number is Normalized.