Mark Dickinson <dicki...@gmail.com> added the comment:
> We should consider biting the bullet and revising the default NaN sort order.
If we went that route, I think we wouldn't need to consider payload or
identity. We could just do:
NaN < NaN -> False
NaN < non-NaN -> True
non-NaN < NaN -> False
non-NaN < non-NaN -> usual numeric comparison
That then satisfies the axioms for a total ordering, albeit that the implied
equality isn't Python's == (and it can't be, if we're going to keep the
property that NaN != NaN): all NaNs compare equal for the equality determined
by the above order, and the stability of the sort means that those NaNs will
retain their order relative to each other in the sorted output.
Making `NaN < non-NaN` return `True` (which happens under both the proposal
above and Raymond's more elaborate proposal) _would_ be a break with IEEE 754,
though.
There's also a somewhat arbitrary choice to be made here: do we consider NaNs
to be negative or positive? That is, do we want NaNs to sort to the beginning
of the list, or the end?
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<https://bugs.python.org/issue44370>
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