Re: Tightest representable interval in mid-rad (cf. Motion 16)
> Date: Sun, 27 Jun 2010 20:54:23 -2000
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> From: Michel Hack <hack@xxxxxxxxxxxxxx>
> Subject: Tightest representable interval in mid-rad (cf. Motion 16)
>
> Vincent Lefèvre wrote:
> > "the tightest representable interval in the target type"
> > is not defined in case of mid-rad and mid-rad1-rad2.
>
> Is there a problem in defining a tie-breaking rule? The cases where
> it applies are pretty rare (intervals of width 1 ulp), and one could
> decide that the midpoint have an even significand, for example. Or
> there could be a formula, e.g. as provided in the Vienna proposal,
> where the rounding applied to the division by two would decide.
>
> (Actually, an odd significand might be better, because in the case of
> the inf-sup interval [0, MinSubnormal] the sign could be preserved.)
>
> For mid-rad1-rad2 we don't have a precise definition on the table, so
> that point is moot. Motion 16 simply says what properties are needed.
>
> We will eventually have to settle these details, but I don't think that
> was the intent of Motion 16.
>
> Michel.
> ---Sent: 2010-06-28 01:07:28 UTC
Gentlemen,
Yes, any reasonable tie-breaking rule will work here.
But it is not the issue.
Narrow intervals play into the strengths of both inf-sup
& mid-rad methods. The problem lies in their weaknesses.
Wide intervals are poorly represented in mid-rad & semi-
infinite intervals not at all.
While there is a diverse group of applications which
ONLY use narrow intervals, as a standards body we cannot
assume we know what the user is doing or why.
Providing correct (i.e. containing) arithmetic is not
enough. The user must KNOW it is correct. It must be
provable to the satisfaction of others. Therefore, it
must be testable & reproducable from machine to machine.
Any 'standard' vague enough to admit both methods as if
they were identical will permit results that, while
formally correct, are incapable of being independently
verified.
Users will not believe in such a standard.
And if they don't believe they won't use it.
And if they won't use it we might as well not write it.
If we don't believe in the need for a standard I'm sure
we all have better things to do with our lives.
I know I do. :-)
Dan