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).