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[[File:Nearest integer.svg|thumb|300px|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 <math>[x]</math>,<ref>{{MathWorld | title=Nearest Integer Function | urlname=NearestIntegerFunction | accessdate= 2008-08-15}}</ref> <math>\lfloor x \rceil</math>, <math>\Vert x \Vert</math>,<ref>{{cite book|author=J.W.S. Cassels|title=An introduction to Diophantine approximation|series=Cambridge Tracts in Mathematics and Mathematical Physics|volume=45|publisher=[[Cambridge University Press]]|year=1957|page=1}}</ref> nint(''x''), or Round(''x''), is a [[function (mathematics)|function]] which returns the nearest [[integer]] to ''x''. To avoid ambiguity when operating on [[half-integer]]s, a [[rounding]] rule must be chosen. On most computer implementations, the selected rule is to round half-integers to the nearest [[even number|even integer]]—for example, | |||
:<math>[1.25] = 1</math> | |||
:<math>[1.50] = 2</math> | |||
:<math>[1.75] = 2</math> | |||
:<math>[2.25] = 2</math> | |||
:<math>[2.50] = 2</math> | |||
:<math>[2.75] = 3</math> | |||
:<math>[3.25] = 3</math> | |||
:<math>[3.50] = 4</math> | |||
:<math>[3.75] = 4</math> | |||
:<math>[4.50] = 4</math> | |||
:etc. | |||
This is in accordance with the [[IEEE 754]] standards and helps reduce bias in the result. | |||
There are many other possible rules for [[rounding#Tie-breaking|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]] | |||
==References== | |||
<references/> | |||
[[Category:Mathematical notation]] | |||
[[Category:Special functions]] | |||
[[Category:Parity]] | |||
Revision as of 21:01, 31 May 2013
In computer science, the nearest integer function of real number x denoted variously by ,[1] , ,[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 [x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07548563c21e128890501e14eb7c80ee2d6fda4d)
- etc.
![[1.25]=1](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d8b62330a7765ad50617c4d1c965608630e4197)
![[1.50]=2](https://wikimedia.org/api/rest_v1/media/math/render/svg/470169bb1aa7adcbaacd34c7af9ab6f38eb1ded1)
![[1.75]=2](https://wikimedia.org/api/rest_v1/media/math/render/svg/5d703941147b405f40998f22606b6173d6958102)
![[2.25]=2](https://wikimedia.org/api/rest_v1/media/math/render/svg/5281e025d7b1e06c2edb4e655be82cd24c170ca9)
![[2.50]=2](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeb49207ff9ac1fdbd0968763927bfb6072eb48b)
![[2.75]=3](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b428a74b11a32b1a59aecfb2f656fbda5fb1d83)
![[3.25]=3](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a71be8e81bc46766821f9d2cc638df8e53df4e3)
![[3.50]=4](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc63c4373cba73f5f3fc3e244840a5824561c547)
![[3.75]=4](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4e258dcacadea31b24bdc242df5739e22a07250)
![[4.50]=4](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cab225f11f48e6878d1374e1f1512f0980a753e)
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
References
- ↑
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