Nearest integer function

File:Nearest integer.svg

A plot of the nearest integer function, rounding to the nearest even integer

In computer science, the nearest integer function of real number x denoted variously by $[x]$, $\lfloor x \rceil$, $\Vert x \Vert$, 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