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.

References

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

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Nearest integer function

See also

References