Nitpick with FLOOR etc. Michael Sperber (07 Jul 2005 08:46 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (09 Jul 2005 00:50 UTC)
Re: Nitpick with FLOOR etc. Michael Sperber (11 Jul 2005 06:55 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (16 Jul 2005 02:01 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (16 Jul 2005 08:38 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (16 Jul 2005 17:42 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (16 Jul 2005 09:12 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (16 Jul 2005 18:19 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (17 Jul 2005 17:23 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (17 Jul 2005 17:35 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (17 Jul 2005 22:43 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (18 Jul 2005 01:43 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (18 Jul 2005 02:31 UTC)
Re: Nitpick with FLOOR etc. bear (18 Jul 2005 05:59 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (18 Jul 2005 18:57 UTC)
Re: Nitpick with FLOOR etc. bear (19 Jul 2005 01:35 UTC)
Re: Nitpick with FLOOR etc. Alan Watson (19 Jul 2005 20:30 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (21 Jul 2005 17:35 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (24 Jul 2005 23:15 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (18 Jul 2005 03:24 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (18 Jul 2005 18:24 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (18 Jul 2005 18:41 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (21 Jul 2005 23:36 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (22 Jul 2005 00:50 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (25 Jul 2005 00:54 UTC)
Re: Nitpick with FLOOR etc. bear (27 Jul 2005 15:56 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (01 Aug 2005 16:33 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (25 Jul 2005 01:16 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (25 Jul 2005 02:38 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (28 Jul 2005 01:11 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (28 Jul 2005 18:15 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (01 Aug 2005 16:59 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (02 Aug 2005 13:58 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (18 Jul 2005 17:39 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (18 Jul 2005 18:15 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (20 Jul 2005 19:24 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (20 Jul 2005 21:35 UTC)
Re: Nitpick with FLOOR etc. bear (20 Jul 2005 22:41 UTC)
Re: Nitpick with FLOOR etc. Paul Schlie (20 Jul 2005 22:47 UTC)
Re: Nitpick with FLOOR etc. Aubrey Jaffer (21 Jul 2005 01:31 UTC)

Re: Nitpick with FLOOR etc. Aubrey Jaffer 25 Jul 2005 01:15 UTC

 | Date: Thu, 21 Jul 2005 20:50:05 -0400
 | From: Paul Schlie <xxxxxx@comcast.net>
 |
 | After attempting to digest everything discusses, although realizing
 | your desire to not require any corresponding impact to either rsrx
 | or exact semantics; I don't believe it's reasonably possible, as it
 | seems that the only way to achieve what you desire, and maintain
 | reasonable consistency with mixed exact/inexact arithmetic would be
 | to:
 |
 | - as suggested by "bear", define the requirement that exact and
 | inexact value representations be constrained to the same value
 | range.

I am reluctant to add that requirement unless someone can provide an
example from practice where the ranges being unequal caused bad
software behavior.

 | - define infinites and their reciprocals to abstractly commonly
 | represent the greatest/smallest values at bounds of the
 | representable numerical range,

As I written previously, using the boundary for the nominal value is
the worst choice from that neighborhood.  Doing so means that nearly
every calculation which projects into #i+/0 is larger than the nominal
value.

 | exclusive of 0 representing an absolute 0, who's reciprocal is
 | itself 0.

This would mean (* 0 (/ 0)) would no longer signal an error or return
0/0, thus failing to meet some of the original goals of SRFI-70.

What would (/ 0.0) return (exact or inexact)?
What would (/ 0 0) do?
How about (/ 0 0.0)?

 | - thereby the range of all numerical transforms map to a
 | correspondingly representable domain (although may optionally
 | signal a run-time exception as may be desired in certain
 | circumstances).

This would have been nice, but the smallest (unnormalized) numbers in
IEEE-754 are not symmetrical with the largest magnitude numbers:

(/ 179.76931348623157e306) ==> 5.562684646268003e-309
(/ 5.562684646268003e-309) ==> #i+/0

There are unnormalized numbers down to 4.0e-324, all of whose
reciprocals are #i+/0.

 | Which overall seems to eliminate all the contentious issues, as
 | long as one is willing to accept the consequences saturating
 | arithmetic, in lieu of an typically arguably less useful more
 | abstract treatment of infinites.
 |
 | Effectively resulting in:
 |
 |        .. -1.0 ..      |      .. +1.0 ..
 |   -1/0 .. -1/1 .. -0/1 | +0/1 .. +1/1 .. +1/0
 |   -------------------- 0 --------------------- (multiplicative inverse axis)
 |   -0/1 .. -1/1 .. -1/0 | +1/0 .. +1/1 .. +0/1
 |        .. -1.0 ..      |      .. +1.0 ..
 |                        |
 |             (additive inverse axis)

How is this different from your "more abstract treatment of
infinities"?