Module mode 

Built-in rounding modes of the floating numbers.

Rounding Error

For different rounding modes, the Rounding error in the output of operations tells the error range, as described in the table below.

Mode	Rounding	Error (truth - estimation) Range
Zero	NoOp	(-1 ulp 0) or (0, 1 ulp)*
Away	AddOne	(-1 ulp, 0)
Away	SubOne	(0, 1 ulp)
Down	SubOne	(0, 1 ulp)
Up	AddOne	(-1 ulp, 0)
HalfAway	AddOne	[-1/2 ulp, 0)
HalfAway	NoOp	(-1/2 ulp, 1/2 ulp)
HalfAway	SubOne	(0, 1/2 ulp]
HalfEven	AddOne	[-1/2 ulp, 0)
HalfEven	NoOp	[-1/2 ulp, 1/2 ulp]
HalfEven	SubOne	(0, 1/2 ulp]

*: Dependends on the sign of the result

Structs

Away

Round away from 0

Down

Round toward -∞

HalfAway

Round to the nearest value, ties away from zero

HalfEven

Round to the nearest value, ties are rounded to an even value. (default mode for decimal float)

Up

Round toward +∞

Zero

Round toward 0 (default mode for binary float)