# Nearest integer function

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 ${\displaystyle [x]}$,[1] ${\displaystyle \lfloor x\rceil }$, ${\displaystyle \Vert x\Vert }$,[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,

${\displaystyle [1.25]=1}$
${\displaystyle [1.50]=2}$
${\displaystyle [1.75]=2}$
${\displaystyle [2.25]=2}$
${\displaystyle [2.50]=2}$
${\displaystyle [2.75]=3}$
${\displaystyle [3.25]=3}$
${\displaystyle [3.50]=4}$
${\displaystyle [3.75]=4}$
${\displaystyle [4.50]=4}$
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.