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> 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.