Am Mi., 20. Okt. 2021 um 20:57 Uhr schrieb Edward Kmett
Interestingly, I'd always assumed the answer was that all comparison functions should return False for NaN, and mentally just assumed that would include (/=). I never actually tested if (/=) returned False, but apparently this isn't the case. [...]
NaN is the only value where the result of "x == x" is *swapped*. The reasoning behind this by Kahan himself in e.g. https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF: Were there no way to get rid of NaNs, they would be as useless as
Indefinites on CRAYs; as soon as one were encountered, computation would be best stopped rather than continued for an indefinite time to an Indefinite conclusion. That is why some operations upon NaNs must deliver non-NaN results. Which operations? Disagreements about some of them are inevitable, but that grants no license to resolve the disagreements by making arbitrary choices. Every real ( not logical ) function that produces the same floating-point result for all finite and infinite numerical values of an argument should yield the same result when that argument is NaN. ( Recall hypot above.) The exceptions are C predicates “ x == x ” and “ x != x ”, which are respectively 1 and 0 for every infinite or finite number x but reverse if x is Not a Number ( NaN ); these provide the only simple unexceptional distinction between NaNs and numbers in languages that lack a word for NaN and a predicate IsNaN(x). Overoptimizing compilers that substitute 1 for x == x violate IEEE 754.
IEEE 754 Wonderland... :-D