notanumber

Notanumber, commonly written NaN, stands for Not a Number and is a value used to denote an undefined or unrepresentable result in floating-point arithmetic.

In IEEE 754 floating-point systems, NaN values are represented with all exponent bits set to 1 and a nonzero significand. There are two main types: quiet NaN (qNaN) and signaling NaN (sNaN). The bits in the significand can carry a payload that some implementations use to encode diagnostic information about the source of the NaN.

NaN has distinctive arithmetic behavior: any operation that involves NaN typically yields NaN, and NaN participates in comparisons in a non-standard way. In most languages, NaN is not equal to any value, including itself, so NaN == NaN is false while NaN != NaN is true. To detect NaN, programs usually rely on language-specific predicates such as isnan or isNaN.

NaN is generated by invalid or undefined operations, such as 0/0, the square root of a negative number in real arithmetic, or applying a function to inappropriate inputs. It is distinct from infinity and is used to signal errors without interrupting program flow, allowing subsequent computations to handle or propagate the issue.

Across programming languages and platforms, the exact handling and exposure of NaN can vary. Some environments offer tools to inspect or manipulate the NaN payload, while others provide standard predicates and arithmetic rules consistent with the IEEE 754 standard.

See also: IEEE 754, floating-point arithmetic, NaN payload.