On 12/30/19 12:06 AM, Andrew Barnert wrote:
On Dec 29, 2019, at 20:04, Richard Damon <rich...@damon-family.org> wrote:
Thus your total_order, while not REALLY a total order, is likely good enough
for most purposes.
Well, it is a total order of equivalence classes (with all IEEE-equal values
being equivalent, all negative NaNs being equivalent, and all positive NaNs
being equivalent).
But whether it’s good enough for most purposes depends on what those purposes
are.
I’m having a hard time imagining any purposes where “some well-defined but
arbitrary, unnatural, and idiosyncratic total order of equivalence classes of
the binary64 values” is of any use at all. Maybe that’s just a failure of my
imagination. But “the specific well-defined but arbitrary, unnatural order that
almost every other similar bit of code in every language is likely to use”
seems a lot more likely to be useful.
(And, needless to say, so does “this specific order that I defined myself”. I
don’t know why the OP wanted to treat all NaNs as equivalents values greater
than inf, but presumably he does know, and that’s fine. So, I don’t think that
needs to be built into the module as one of the options, but I don’t see why he
shouldn’t be able to specify it explicitly.)
But it DOESN'T make all positive NaNs equivalent, as they do not compare
'equal'. Neither is less than the other, but they don't compare equal.
If you use a sort function (not the one that Python currently uses) that
uses an equality test as part of its sort (rather than just letting the
falsehood of a < b and b< a imply that a == b) then it will break and
perhaps return illogical results. This is getting into the weeds of
corner cases, so may not be important.
I will admit that if you want to sort a list that contains a mix of
floats, Decimals, and Rationals, then the tuple approach might be better
then the conversion to a 64 bit int as the key, since that doesn't work
for the other types except by converting them to float first.
As to why NaNs are greater than infinity, that comes from the IEEE
specification on the total_order relationship of floating point numbers.
--
Richard Damon
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