Re: Nitpick with FLOOR etc.

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``` | Date: Thu, 21 Jul 2005 20:50:05 -0400
| From: Paul Schlie <schlie@xxxxxxxxxxx>
|
| 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?

| - 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 ..
|                        |

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

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