Re: More on trits & tetrits... (long)
Dan Zuras, Vincent Lefèvre, Dan Zuras:
> > > We do not know whether or not an actual pole was encountered.
> > That's the problem.
>
> In essence, your definition is adding one bit to the range
> just as decorating this problem with 'exact' or 'inexact'
> would add one bit to the precision.
Actually, "Exact" adds infinitely many bits of precision. The
Exact vs Inexact distinction also applies to Inf-as-Pole (Exact)
and Inf-as-Overflow (Inexact).
The question then becomes whether this distinction can be carried
over from 754 to 1788 by means of decorations. This is a tall order,
because even in 754 the distinction is not carried forward by the
normal rules of arithmetic. For example, Inf(exact) - Inf(overflow)
or Inf(exact)/Inf(overflow) should be Inf(exact) and not NaN -- but
the only way to do that is to attach the Inexact flag to the datum,
i.e. to use decorated floats -- a topic that was never addressed.
The float result of an operation would however depend on both the
input floats and the input decorations.
So the question becomes whether the deliberate separation of
bare interval results and decorations is good or bad.
Michel.
---Sent: 2010-04-22 15:19:30 UTC