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Re: Nitpick with FLOOR etc.



> From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
>  | Date: Thu, 28 Jul 2005 14:14:55 -0400
>  | From: Paul Schlie <schlie@xxxxxxxxxxx>
>  | 
>  | > From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
>  | > 
>  | > If you eliminate unnormalized numbers, then the difference
>  | > between all pairs of positive flonums having the most negative
>  | > exponent is 0, which isn't right.
>  | 
>  | - Agreed it's not 0, but +/- 0.0, (i.e. the reciprocal of +/- Inf.0)
> 
> Then it is some new type of infinitesimal, because adding it to
> numbers with the most negative exponent returns different numbers.

Sorry, I'm not sure what you mean; as it's impossible for the difference
between every two adjacent values to be representable unless it's
anticipated that the representational format supports infinitesimally small
value representations. Just as the difference between the smallest adjacent
unnormatlized values are not representable either.

(as traditionally infinities and their reciprocals are non-accumulating, if
the difference between to values is too small to be represented and results
in a reciprocal infinity, then it's sum with either value will result in
that value; where if more precision is desired I'd guess some form of a more
precise exact representation would be necessary?)