Re: Alternate floating-point results under directed rounding
On Mon, 2008-11-10 at 04:02 -0800, Arnold Neumaier wrote:
> Sylvain Pion schrieb:
> > Arnold Neumaier wrote:
> >> Nobody had suggested that. The question is only whether a
> >> floating-point +-inf or NaN should be converted into Empty,
> >> or into a substitute finite point interval, or into a substitute
> >> interval of positive width.
> >
> > Can't it be made an error?
> > I am not sure how to properly word this in the standard, but for
> > example one could define "undefined behavior", or raise some error
> flag...?
>
> Making it an error would perhaps be the best.
> On the other hand, one may want to be able to trap the error,
> to be able to do something alternative if the error occured...
> That's why I proposed to use the nonstandardNumber flag.
> I wouldn't mind using a different flag...
I prefer that IEEE NaN and IEEE inf be transformed to differently
represented "interval" objects. This allows users to interpret their
results without wondering whether some information has been lost.
Since IEEE FPA computations with NaN don't destroy NaN, intervals [x,y]
with either x or y NaN are reasonable representations of the empty set,
especially since division of an interval containing zero by the point
interval [0,0] using IEEE FPA naturally produces [NaN,NaN] with invalid
signaling.
A reasonable representation for intval(inf) is [inf,inf]. IEEE FPA
computations don't destroy inf, so if one wants to think of this as an
alternative representation of the empty set, one can do so. But it has
a different quality from sqrt([-1,1]) = [NaN,1].
If one computes (with variables instead of constants) 0.1*(2*HUGE) one
gets inf instead of 0.2*HUGE. If inf is then converted to [inf,inf] and
inf is interpreted as {x|x>HUGE} the correct result isn't in the
interval -- but it also isn't in the interval [NaN,NaN] so it's
difficult to produce a definitive argument that one is the better
representation of this result than the other. The argument I offer is
that [inf,inf] better represents the process by which the result arose
than does [NaN,NaN], and this might be useful information.
If P1788 is to be built atop P754 as much as possible, I see no reason
for yet another flag, nonstandardNumber, since P754 already has NaN, and
invalid and overflow signals.
--
Van Snyder | What fraction of Americans believe
Van.Snyder@xxxxxxxxxxxx | Wrestling is real and NASA is fake?
Any alleged opinions are my own and have not been approved or
disapproved by JPL, CalTech, NASA, the President, or anybody else.