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bug#16365: (* 0 +inf.0) rationale is flawed

From: Zefram
Subject: bug#16365: (* 0 +inf.0) rationale is flawed
Date: Tue, 21 Jun 2016 15:21:30 +0100

Mark H Weaver wrote:
>         I also suspect that (/ 0 <anything_but_exact_0>) should be 0,
>although that conflicts with R6RS.  We should probably investigate the
>rationale behind R6RS's decision to specify that (/ 0 0.0) returns a NaN
>before changing that, though.

I think R6RS makes sense for (/ 0 0.0).  A flonum zero really represents
a range of values including both small non-zero numbers and actual zero.
The mathematical result of the division could therefore be either zero or
undefined.  To return zero for it would be picking a particular result,
on the assumption that the flonum zero actually represented a non-zero
value, and that's not justified.  So to use the flonum behaviour seems
the best thing available.

(/ 0 3.5) is a different case.  Here the mathematical result is an
exact zero, and I'm surprised that R6RS specifies that this should be
an inexact zero.  This seems inconsistent with (* 1.0 0), for which it
specifies that the result may be either 0 or 0.0.

I'd also question R6RS in the related case of (/ 0.0 0).  Mathematically
this division is definitely an error, regardless of whether the dividend
represents zero or a non-zero number.  So it would make sense for this
to raise an exception in the same manner as (/ 3 0) or (/ 0 0), rather
than get flonum treatment as R6RS specifies.

But deviating from R6RS, even with a good rationale for other behaviour,
would be a bad idea.  The questionable R6RS requirements are not crazy,
just suboptimal.  The case I originally raised, (* 0 +inf.0), is one
for which R6RS offers the choice.


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