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Re: Nitpick with FLOOR etc.
> 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.