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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.