NaN (or "not a number") in the IEEE 754-2019 standard is a symbolic floating-point representation which
is neither a signed infinity nor a finite number.
In general, NaNs occur as the output of computations
which are somehow "indeterminate," e.g.,
when attempting to compute quantities such as 
, 
, or 
.
NaN representations were already included in IEEE 754-2008 and its predecessors. Traditionally, the computation
of indeterminate quantities such as 
or 
was treated as an unrecoverable error which caused a computation
to halt. In practice, however, it sometimes makes sense for a computation
to continue despite encountering such a scenario; in these situations, unnecessary
halting can be avoided by specifying that the computation
of expressions like 
and 
output NaN rather than halting
the program (Goldberg 1991).
Ostensibly, a NaN output should carry with it some degree of diagnostic information regarding the circumstances and/or operations which created it. The diagnostic information contained in a NaN is called its payload.
In IEEE 754-2019, there are two distinct kinds of NaN representations, namely quiet NaN (or qNaN) and signaling NaN (or sNaN). Most operations within IEEE 754 propagate qNaNs without signaling exceptions while signaling an invalid operation exception when given an sNaN as input (IEEE Computer Society 2008).
