HP 3000 Manuals

HP C/iX Reference Manual

IEEE Floating-Point Format 

The internal representation of floating-point numbers conforms to the
IEEE floating-point standard, ANSI/IEEE 754-1985, as shown in Figure 9-1.


          Figure 9-1.  Internal Representation of Floating-Point Numbers 

The s field contains the sign of the number.  The exp field contains the
biased exponent (exp = E + bias, where E is the real exponent) of the
number.  The values of bias and the maximum and minimum values of the
unbiased exponent appear in the following table:

-------------------------------------------------------------------------------------------------
|                       |                       |                       |                       |
|                       |         float         |        double         |      long double      |
|                       |                       |                       |                       |
-------------------------------------------------------------------------------------------------
|                       |                       |                       |                       |
| bias                  | +127                  | +1023                 | +16383                |
|                       |                       |                       |                       |
| Emax                  | +127                  | +1023                 | +16383                |
|                       |                       |                       |                       |
| Emin                  | -126                  | -1022                 | -16382                |
|                       |                       |                       |                       |
-------------------------------------------------------------------------------------------------

Emin-1 is used to encode 0 and denormalized numbers.

Emax+1 is used to encode infinities and NaNs.

NaNs are binary floating-point numbers that have all ones in the exponent
and a nonzero fraction.  NaN is the term used for a binary floating-point
number that has no value (that is, "Not A Number").

If E is within the range

     Emin <= E <= Emax 

the mantissa field contains the number in a normalized form, preceded by
an implicit 1 and binary point.

In accordance with the IEEE standard, floating-point operations are
performed with traps not enabled, and the result of such an operation is
that defined by the standard.  This means, for example, that dividing a
positive finite number by zero will yield positive infinity, and no trap
will occur.  Dividing zero by zero or infinity by infinity will yield a
NaN, again with no trap.  For a discussion of infinity arithmetic and
operations with NaNs, in the context of the IEEE standard, see the HP 
Precision Architecture and Instruction Set Reference Manual (HP part
number 09740-90014).

Note that infinities and NaNs propagate through a sequence of operations.
For example, adding any finite number to infinity will yield infinity.
An operation on a NaN will yield a NaN. This means that you may be able
to perform a sequence of calculations and then check just the final
result for infinity or NaN.

MPE/iX 5.0 Documentation