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Sorry to continue on this subject, but...



1. I'm glad to see that -0 will be removed.  In the current reference
implementation, (+ 1 -1) returns 0, as does (+ -1 1), and it's very hard
for me to see why 0 is privileged over -0 in this case.

2. As you can probably guess from the fuss created by -0, exact
infinities sure as hell are not reciprocals of 0.  Infinities can be
created by calculating a limit of lim x->(+)0 (1/x), but the existence
of a limit is required.  This is because 0 _really is_ -0, and
consequently, 1/0 _really is_ 1/-0, that is, undefined.

So you might have two things to do, which are relatively orthogonal:

(a) define an exact NaN value, which is the result of division by zero,
and provide rules for handling NaN wrt basic arithmetic and boolean
operations (things like (> 0 NaN) are especially problematic);

(b) define exact (negative and positive) infinity, which are greater in
magnitude than any finitary exact number, but cannot be manipulated much
in any way; for example, (+ 1 inf) cannot evaluate to inf, because this
will break the numeric system.  These infinities cannot be obtained as a
result from any calculation, but one can use them as literals.

I think the latter might have some value, for example as initialisation
values for algorithms searching for a maximum value in a list etc.

Panu

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