NaNs

NaN stands for Not a Number and refers to a special value used in floating-point arithmetic to represent undefined or unrepresentable results. It is part of the IEEE 754 standard, which defines how floating-point numbers are stored and manipulated in most modern computer systems.

In IEEE 754 binary floating-point formats, a NaN is indicated by an exponent of all ones and a nonzero significand (mantissa). The sign bit may be 0 or 1. NaNs are further categorized as quiet NaNs (qNaN) and signaling NaNs (sNaN); the latter may trigger floating-point exceptions on certain operations, while quiet NaNs propagate through calculations without signaling.

NaN values arise from operations that have no well-defined numeric result, such as 0/0, ∞ − ∞, or the square root of a negative number in real arithmetic. They can also result from invalid transformations or from domain errors in functions. Once generated, NaN typically propagates through most arithmetic operations, producing another NaN, which helps detect downstream errors.

A fundamental property of NaN is that it is not equal to any value, including itself. Comparisons with NaN generally yield false, so languages provide special checks such as isnan or isNaN to determine if a value is NaN.

Practical use and language differences vary. JavaScript treats NaN as a numeric value and uses NaN !== NaN, with isNaN and Number.isNaN for checks. Python exposes NaN via float('nan') and math.nan, with math.isnan to test. C and C++ provide NAN or nan() macros and routines like isnan. In databases and numerical libraries, NaN handling is influenced by the specific implementation and the available functions for numeric checks and aggregations.

Overall, NaN serves as a standardized signaling mechanism for undefined results within floating-point computations, enabling error handling and debugging while preserving numerical workflows.