Re: More on trits & tetrits... (long)
Ian McIntosh wrote:
> It should be possible to always compute correct results without using
> decorations. This situation is the sort of issue that led me to conclude
> that 754 should have distinguished, and ideally 1788 should distinguish,
> between Infinity versus Overflow.
Would be nice, I agree. But you'd have to give up a bit in the format to
be consistent, because the same problem exists for zero, which could be
exact or due to underflow. What's the inverse of the two kinds of Inf?
One is exact signed zero, the other is underflow to zero.
Now you get into trouble defining arithmetic with exact and inexact zeros.
For example, the inexact zeros resulting from underflow have a valid sign,
but the sum or difference of two inexact zeros does not. Should that be
a NaN, just like Inf-Inf?
If you don't have inexact zeros, you can't decide whether the inverse of
zero should be Inf-Overflow or Inf-Pole.
So the only way to track this information is in some kind of decoration,
and you need an additional means to annotate an unsigned inexact zero.
Intervals have the capability of tracking the amount of inexactness, and
with suitable decorations we can keep track of it all. The only sensible
decoration for a float is in fact a decorated interval!
So unfortunately there is little to be gained from exploiting NaNcodes
and Infcodes. The latter are technically possible in DFP, whereas in
BFP one would have to reserve certain NaNcodes to denote flavours of Inf,
after deciding which flavour deserves to be the one with SNaNcode zero
(the current definition of BFP Inf, in the preferred definition of SNaN).
Michel.
---Sent: 2010-04-22 21:29:25 UTC