Rounding directions

Some of the classes of operators presented in the following sections are templated by a rounding direction. This is the direction chosen when converting a real number that cannot be exactly represented in the destination format.

There are eleven directions:

zr

toward zero

aw

away from zero

dn

toward minus infinity (down)

up

toward plus infinity

od

to odd mantissas

ne

to nearest, tie breaking to even mantissas

no

to nearest, tie breaking to odd mantissas

nz

to nearest, tie breaking toward zero

na

to nearest, tie breaking away from zero

nd

to nearest, tie breaking toward minus infinity

nu

to nearest, tie breaking toward plus infinity

The rounding directions mandated by the IEEE-754 standard are ne (default mode, rounding to nearest), zr, dn, up, and na (introduced for decimal arithmetic).