Round half to even

A tie-breaking rule that is less biased is round half to even, namely:

• If the fraction of y is 0.5, then q is the even integer nearest to y.

Thus, for example, +23.5 becomes +24, as does +24.5; while −23.5 becomes −24, as does −24.5.

This method treats positive and negative values symmetrically, and is therefore free of sign bias. More importantly, for reasonable distributions of y values, the expected (average) value of the rounded numbers is the same as that of the original numbers. However, this rule will introduce a towards-zero bias when y − 0.5 is even, and a towards-infinity bias for when it is odd.

This variant of the round-to-nearest method is also called unbiased rounding, convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding,^[3] or bankers' rounding.

This is the default rounding mode used in IEEE 754 computing functions and operators.