Re: (/ 0 0.0) ==> 0

[Matthew Flatt <mflatt@cs.utah.edu>]

Quoting Wolfgang Hukriede:
> Hello!
> 
>     Welcome to MzScheme version 100alpha1, 
>     Copyright (c) 1995-99 PLT (Matthew Flatt)
> 
>     > (/ 0 0.0)
>     0
> 
> Is this result intented? 

Yes.

Inexact zero is interpreted as "a positive number arbitrarily close to
zero, but not quite zero". Similarly, -0.0 is "a negative number
arbitrarily close to zero". Hence, (/ 1 0.0) is not undefined, but
rather an arbitrarily large positive number, +inf.0, and so on.

You can find holes in this interpretation easily. For example, why
should (+ 0.0 -0.0) be 0.0?

For summary of the issues, see Brad Lucier's notes from the '98
workshop:
  http://www.neci.nj.nec.com/homepages/kelsey/lucier.txt

I believe the only way that MzScheme disagrees with Brad's
recommendation is that (real? +0.0i) = #t. Chez and Gambit take
essentially the same position, as far as I can tell, including the
concession in `real?'.

One final note --- I found an inconsistency in MzScheme that survived
in version 101: (angle 0.0) reports an error. (angle 0.0) should
instead be 0, and (angle -0.0) should be pi. This is consistent with
MzScheme's distinction between 0.0+0i and 0.0+0.0i, and with the notion
of 0.0 as "infinitesimally small". Also, (angle +nan.0) didn't return
+nan.0.

Obviously, almost none of this is documented in the MzScheme manual at
the moment...

Matthew