Re: Nitpick with FLOOR etc.

[Paul Schlie <schlie@xxxxxxxxxxx>]

> From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
>  | Date: Sun, 24 Jul 2005 22:38:24 -0400
>  | From: Paul Schlie <schlie@xxxxxxxxxxx>
>  | 
>  | > From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
>  | >  | Date: Thu, 21 Jul 2005 20:50:05 -0400
>  | >  | From: Paul Schlie <schlie@xxxxxxxxxxx>
>  |  ....
>  | >  | - 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:
>  | 
>  | - which would imply that unnormalized values would be invalid
>  | inexact values. (as only normalized floats would satisfy the
>  | symmetry specified)
> 
> 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)

>                           The way to achieve symmetry is to choose a
> different bias for the exponent.  But you have work through the math;
> possibly one of the exponent values would also need to be unused.