Re: What is your philosophy? Tracking or Static?
> From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>,
> "Ralph Baker Kearfott" <rbk@xxxxxxxxxxxx>
> Cc: <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: What is your philosophy? Tracking or Static?
> Date: Wed, 25 May 2011 08:23:31 -0500
>
>
> There has been a lot of discussion about tracking vs. static methodologies.
> IMHO, it is a bit of a red-herring to couch things in these terms. Both are
> applications of a single FTDIA. The only difference is how pessimism due to
> unrecognized interval dependence is handled in the computation.
I agree that the only difference amounts to the pessimism
with which decorations are computed. But I do not think
the difference is a red herring.
>
> As a low-level hardware standard, I think P1788 needs to be realistic and
> mindful of what it can hope to achieve. In my view, to try and standardize
> interval computations in such a way that the non-pessimistic (what I believe
> people are referring to as "static") result is always returned is simply too
> big a problem. If P1788 tries to do this, it will fail.
THIS is the red herring & also is why the former is not.
You see, I'm pretty sure the basic functions of add, subtract,
multiply & divide are all the same WRT their decorations
behavior no matter WHAT your philosophy. It is precisely in
those functions which are NOT likely to find their way into
hardware where the difference matters. (Well, less likely
anyway.)
>
> My understanding is that P1788 is essentially a low-level standard aimed at
> efficient hardware implementations. If this is true, P1788 should probably
> think very carefully about what is realistically computable at the hardware
> level. From my perspective, this clearly leads to the tracking methodology.
>
> Nate
>
I agree with your premise (of permitting efficient interval
hardware) but not your conclusion.
If tracking & static are equivalent for the basic functions
then efficient decorations hardware are equivalent for both.
But for those functions for which it makes a difference (say
max or intersection or the like) the tracking philosophy
gives more pessimistic results than the static one. Possibly
much more pessimistic as George's examples suggest.
Don't get me wrong: We will still need something that cleans
decorations for fixed point algorithms like interval Newton's.
But I am coming to believe that it is best to give the
cleanist decorations we can WHEN we can.
This suggests a static approach.
IMHO, of course.
Anyone else?
Dan