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This basic problem is central to electronic computers' very existence. In turn, floating-point arithmetic goes back to the very beginning of electronic computing. Since the mistakes are usually small, we most often can just carry on regardless.Р”Р„lthough NaN itself technically goes back only to the IEEE 754 floating-point standard first published in 1985, the whole story includes the entire history of floating-point arithmetic.

Floating-point numbers technically violate most of the rules of basic algebra.

The real numbers are what most people learn about in their elementary education, and are often just called numbers.

Technically they act most like the real numbers.

We also describe alternatives to floating-point math that might work better in contexts where performance is less important. With this information, developers can understand floating-point arithmetic well enough to tell when they do and don't actually need it. WeРІР‚в„ўll also talk about some of its strange behavior. To better understand NaN, letРІР‚в„ўs consider why NaN exists at all. NaN is hardly the only example of this (the signed infinities are also oddly behaved), but it is certainly the most spectacular one. This can introduce many strange bugs and surprising behaviors to unprepared programmers. Despite that, many modern programming languages default to treating all non-integer arithmetic as floating-point arithmetic. The compromises that created modern floating-point math are very real and often still relevant, but don't always apply. The skeptics do have a point though, because NaN is a hack. In those contexts, we are not likely to get rid of NaN any time soon. Within contexts where floating-point numbers are the 'best tool for the job', NaN is a terrible hack, but it is also the best option we have found.

Even experienced programmers might think its existence a mistake or its behavior buggy. ItРІР‚в„ўs no surprise that programmers who stumble over NaN without warning are confused. With a few exceptions, numerical calculations involving NaN produce more NaNs, meaning that a single NaN in the wrong place can turn a large set of useful numbers into useless NaNs very quickly. Worse, NaNs can be a very serious problem because they are infectious. The only reliable way to test for NaN is to use a language-dependent built-in function the expression a = NaN is always false. This means, for instance, that NaN = 5 are both false. Numerical comparisons between NaN and other quantities are automatically false. ThatРІР‚в„ўs just the beginning of NaNРІР‚в„ўs misbehavior. For instance, in JavaScript you can create this amazing snippet: The most spectacular bit of weirdness is that NaN is not equal to itself. NaNРІР‚в„ўs actual behavior is even stranger, though. Only floating-point values can be NaN, meaning that from a type-system point of view, only numbers can be РІР‚Сљnot a numberРІР‚Сњ. Short for РІР‚СљNot a NumberРІР‚Сњ, even its name is a paradox.

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There are entire textbooks and university-level classes on how to get useful results out of floating-points numbers.Р”В®asily the strangest thing about floating-point numbers is the floating-point value РІР‚СљNaNРІР‚Сњ. The word РІР‚Сљalmost РІР‚Сљ hides an awful lot of complexity, though floating-point numbers cause an endless stream of strange behavior 2, odd edge cases, and general problems.

The problem is that floating-point numbers look and act almost like the numbers 1 we all learned about in school. A black box that РІР‚Сљjust worksРІР‚Сњ-until it doesnРІР‚в„ўt.

In modern programming, non-integer numbers often just are floating-point numbers. New programmers often donРІР‚в„ўt even realize they are using floating-point numbers, or know what floating-point numbers are. There are few things that can trip up even experienced programmers more easily than floating-point arithmetic.

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