Rounding Modes

This pages describes the different rounding modes which can be selected for numeric field elements.

Round up

This modes rounds away from zero. It increases the absolute value of the number to round, if there is any fractional remainder.

Round down

This modes rounds towards zero. It decreases the absolute value of the number to round, if there is any fractional remainder.

Round ceiling

This modes rounds towards positive infinity. It increases the value of the number to round, if there is any fractional remainder. That way the rounded value will always be greater or equal to the value to round.

Round floor

This modes rounds towards negative infinity. It decreases the value of the number to round, if there is any fractional remainder. That way the rounded value will always be lesser or equal to the value to round.

Round half up

This modes rounds towards the nearest neighbor. If both neighbors are equidistant, this mode will have the same effect as round up.

Round half down

This modes rounds towards the nearest neighbor. If both neighbors are equidistant, this mode will have the same effect as round down.

Round half even

This modes rounds towards the nearest neighbor. If both neighbors are equidistant, this mode will round towards the even neighbor. Round half even has the minimum cumulative error and is therefore the default rounding mode.

Comparison of rounding modes

Input	Up	Down	Ceil	Floor	Half up	Half down	Half even
-2.50	-3	-2	-2	-3	-3	-2	-2
-1.50	-2	-1	-1	-2	-2	-1	-2
-1.00	-1	-1	-1	-1	-1	-1	-1
-0.60	-1	0	0	-1	-1	-1	-1
0.60	1	0	1	0	1	1	1
1.00	1	1	1	1	1	1	1
1.50	2	1	2	1	2	1	2
2.50	3	2	3	2	3	2	2