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 $[x]$,^[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

• Rounding
• Floor and ceiling functions

References

1. Weisstein, Eric W. "Nearest Integer Function". MathWorld. Retrieved 2008-08-15.
2. J.W.S. Cassels (1957). An introduction to Diophantine approximation. Cambridge Tracts in Mathematics and Mathematical Physics. 45. Cambridge University Press. p. 1.