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.)
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