Editing NaN (section)

{{Short description|Value for unrepresentable data}}
{{Other uses|Nan (disambiguation)}}

In [[computing]], '''NaN''' ({{IPAc-en|n|æ|n}}), standing for '''Not a Number''', is a particular [[value (computer science)|value]] of a numeric [[data type]] (often a [[floating-point arithmetic|floating-point number]]) which is undefined as a number, such as the result of [[0/0]]. Systematic use of NaNs was introduced by the [[IEEE&nbsp;754]] floating-point standard in 1985, along with the representation of other non-finite quantities such as [[Infinity|infinities]].

In [[mathematics]], the result of {{sfrac|0|0}} is typically not defined as a number{{efn|0/0 is undefined as a number in both the [[real number]] and [[extended real number]] systems, while 1/±0, for example, could be consistently assigned a value of ±∞ in the latter system, assuming a [[signed zero]].}} and may therefore be represented by NaN in computing systems.<!-- Warning: computing systems include integer types, where one may compute 0/0 and NaN usually doesn't exist. Possibly clarify or expand the section on integers (which currently only considers the conversion of a floating-point NaN to an integer type, which is not the same thing as doing 0/0 in integer arithmetic). -->

The [[square root]] of a [[negative number]] is not a [[real number]], and is therefore also represented by NaN in compliant computing systems. NaNs may also be used to represent missing values in computations.<ref name=idl>{{cite book|last=Bowman|first=Kenneth|date=2006|title=An Introduction to Programming with IDL: Interactive Data Language|url=https://archive.org/details/introductiontopr00bowm|url-access=limited|publisher=Academic Press|page=[https://archive.org/details/introductiontopr00bowm/page/n26 26]|isbn=978-0-12-088559-6}}</ref><ref>{{cite book|last1=Press|first1=William H.|last2=Teukolsky|first2=Saul A.|last3=Vetterling|first3=William T.|last4=Flannery|first4=Brian P.|date=2007|title=Numerical Recipes: The Art of Scientific Computing|url=https://archive.org/details/numericalrecipes00pres_033|url-access=limited|publisher=Cambridge University Press|page=[https://archive.org/details/numericalrecipes00pres_033/page/n57 34]|isbn=978-0-521-88068-8}}</ref>

Two separate kinds of NaNs are provided, termed ''quiet NaNs'' and ''signaling NaNs''.  Quiet NaNs are used to propagate errors resulting from invalid operations or values. Signaling NaNs can support advanced features such as mixing numerical and [[computer algebra|symbolic computation]] or other extensions to basic floating-point arithmetic.