Nearest integer function
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[citation needed], 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.
![{\displaystyle [1.25]=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d8b62330a7765ad50617c4d1c965608630e4197)
![{\displaystyle [1.50]=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/470169bb1aa7adcbaacd34c7af9ab6f38eb1ded1)
![{\displaystyle [1.75]=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5d703941147b405f40998f22606b6173d6958102)
![{\displaystyle [2.25]=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5281e025d7b1e06c2edb4e655be82cd24c170ca9)
![{\displaystyle [2.50]=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeb49207ff9ac1fdbd0968763927bfb6072eb48b)
![{\displaystyle [2.75]=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b428a74b11a32b1a59aecfb2f656fbda5fb1d83)
![{\displaystyle [3.25]=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a71be8e81bc46766821f9d2cc638df8e53df4e3)
![{\displaystyle [3.50]=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc63c4373cba73f5f3fc3e244840a5824561c547)
![{\displaystyle [3.75]=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4e258dcacadea31b24bdc242df5739e22a07250)
![{\displaystyle [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
- ^ Weisstein, Eric W. "Nearest Integer Function". MathWorld. Retrieved 2008-08-15.
{{cite web}}: More than one of|accessdate=and|access-date=specified (help) - ^ J.W.S. Cassels (1957). An introduction to Diophantine approximation. Cambridge Tracts in Mathematics and Mathematical Physics. Vol. 45. Cambridge University Press. p. 1.