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Re: Nitpick with FLOOR etc.
> From: Paul Schlie <schlie@xxxxxxxxxxx>
>> From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
>> | Date: Tue, 02 Aug 2005 21:48:52 -0400
>> | From: Paul Schlie <schlie@xxxxxxxxxxx>
>> | > From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
>> | > | From: Paul Schlie <schlie@xxxxxxxxxxx>
>> | > |
>> | > | - I still don't understand how it's acceptable for (/ 1/-0.0)
>> | > | => 0.0, as it seems neither necessary, nor desirable to
>> | > | propagate IEEE-754 mistake.
>> | >
>> | > (limit / -/0. -1.0e222) ==> 0.0
>> | - which is only the case as you don't differentiate between -0.0
>> | and +0.0;
>> The `limit' procedure does not call `/' at the limit point.
>> Its last call to `+' generating the return value is
>> (+ 999.9999999999999e-225 -999.9999999999999e-225) ==> 0.0
> - Therefore it would appear the implementation of limit is flawed,
> as if it is agreed that: #i-1/0 :: -1.0/0 :: 1/-0.0 :: -Inf.0
> then it follows that it's reciprocal must then be correspondingly
> both infinitesimally small and negative (not positive). Apparently
> resulting from it's implementation not treating +-0.0 as special
> case reciprocal infinite, as in general the magnitude of the
> deviation about a value should never be greater than the magnitude
> of the value itself, as otherwise the limit calculation will be
> erroneous, where the only arguable exception would be about an
> absolute 0, where by definition any deviation about itself will
> result in varying signed magnitudes (where absolute 0 has neither
> a sign nor magnitude).
- more specifically, deviations about a point should only likely be
considered generically acceptable iff they remain within the region
of a function's continuity; where for division this deviations of
greater magnitude than the limit point will produce errinous results.