Nearest integer function

In computer science, the nearest integer function of real number x denoted variously by [x]^[1], $\lfloor x \rceil$, $\Vert x \Vert$,^[2] nint(x), or Round(x), is a function which returns the nearest integer to x. To avoid ambiguity when operating on half-integers, a rounding rule must be chosen. On most computer implementations, the selected rule is to round half-integers to the nearest even integer — for example,

[1.25] = 1

[1.50] = 2

[1.75] = 2

[2.25] = 2

[2.50] = 2

[2.75] = 3

[3.25] = 3

[3.50] = 4

[3.75] = 4

[4.50] = 4

etc.

This is in accordance with the IEEE 754 standards and helps reduce bias in the result.

There are many other possible rules for tie breaking when rounding a half integer include rounding up, rounding down, rounding to or away from zero, or random rounding up or down.

See also

• Floor and ceiling functions

References

1. ^ Weisstein, Eric W., "Nearest Integer Function" from MathWorld.
2. ^ J.W.S. Cassels (1957). An introduction to Diophantine approximation. Cambridge Tracts in Mathematics and Mathematical Physics. 45. Cambridge University Press. p. 1.