Nearest integer function

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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

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[edit]


  1. ^ Weisstein, Eric W., "Nearest Integer Function", 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.