Datasheet

Floating-point Support

5.5.2 Arithmetic and rounding

Arithmetic is generally performed by computing the result of an operation as if it were

stored exactly (to infinite precision), and then rounding it to fit in the format. Apart from

operations whose result already fits exactly into the format (such as adding 1.0 to 1.0),

the correct answer is generally somewhere between two representable numbers in the

format. The system then chooses one of these two numbers as the rounded result. It uses

one of the following methods:

Round to nearest

The system chooses the nearer of the two possible outputs. If the correct

answer is exactly half-way between the two, the system chooses the one

where the least significant bit of Frac is zero. This behavior

(round-to-even) prevents various undesirable effects.

This is the default mode when an application starts up. It is the only mode

supported by the ordinary floating-point libraries. (Hardware

floating-point environments and the enhanced floating-point libraries,

g_avp

for example, support all four modes. See Library naming

conventions on page 4-105.)

Round up, or round toward plus infinity

The system chooses the larger of the two possible outputs (that is, the one

further from zero if they are positive, and the one closer to zero if they are

negative).

Round down, or round toward minus infinity

The system chooses the smaller of the two possible outputs (that is, the

one closer to zero if they are positive, and the one further from zero if they

are negative).

Round toward zero, or chop, or truncate

The system chooses the output that is closer to zero, in all cases.