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Re: Nitpick with FLOOR etc.



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.

- define infinites and their reciprocals to abstractly commonly represent
the greatest/smallest values at bounds of the representable numerical range,
exclusive of 0 representing an absolute 0, who's reciprocal is itself 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).

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)