Re: What is your philosophy? Tracking or Static?
> Date: Wed, 25 May 2011 17:06:12 +0200
> From: Dominique Lohez <dominique.lohez@xxxxxxx>
> To: "Corliss, George" <george.corliss@xxxxxxxxxxxxx>
> CC: "<stds-1788@xxxxxxxxxxxxxxxxx>" <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: What is your philosophy? Tracking or Static?
Dominique is correct in that we often choose examples
which are mathematically difficult when perhaps some
simpler example would suffice for this argument.
Very well, let me see if I can come up with one off
the top of my head.
f(x,y,z) = max(x,y,z)
Now, max() is basically a selection function. It is
formally equivalent to:
max(x,y) = if x < y then y else x
Therefore, it takes on the properties of the selected
thing no matter what happened to the unselected thing.
Indeed, code like:
if x < 0 then sqrt(-x) else sqrt(x)
DEPENDS on the not taken path having no effect on the
taken path.
Therefore, I argue that the result of max() should be
decorated with the selected thing (or things, in the
case of overlapping intervals) & discard the unselected
items.
So, what is the answer to f(sqrt([-2,-1]),sqrt([-1,1]),
sqrt([4,9]))?
The intermediate result is max({empty,undefined},
{[0,1],discontinuous},{[2,3],defined&continuous}).
The tracking philosophy would have us return {[2,3],
undefined}. The static philosophy would have us return
{[2,3],defined&continuous}.
Which is more imformative? The one that correctly tells
us that SOME calculation was undefined even though it did
not participate in the final result? Or the one that WAS
the final result?
Note that the answer is NOT a slam dunk. It COULD be that
one of the unselected answers WAS unselected due to a bug
in the code as easily as because the programmer always
intended that it not be selected. Tracking warns us of
both the bug & the false positive. Static ignores both.
So it requires some thought to decide which is best.
What do you think?
Dan
>
> George,
> IMHO your examples are not illustrative of argument in favor of some
> philosophy.
> They show how problems must be reformulated when interval arithmetic is
> aimed
> Corliss, George a écrit :
> > Dan,
> >
> > Thank you for the useful characterization. I, too, began assuming tracking, but I am coming more to the static view.
> >
> > Early in AD, a frequently cited difficulty was scaling:
> >
> > x is a vector
> > s = max(|x|)
> > x = x / s // Normalize
> > y = lots of computations
> > y = y * s // Rescale back
> >
> > Is y a differentiable function of x? AD is forced to assume not. Intervals can help decide this question more precisely, but the analogy is whether we care about the history or only the result.
> >
> When x is replaced with a box X, the scaling factor must be calculated
> for the box as a whole, so it a constant for all the vector in the box.
> So the problematic dependence of s with a particular vector is removed.
>
> > Or, suppose
> > x is a scalar
> > f(x) = sign(x)
> > y = 0 * f(x)
> >
> > Is y a continuous function of x?
> >
> This problem is ill-posed.
> The interval arithmetic provide a correct enclosure of the exact result.
> Since sign is discontinuous , the continuity is definitely lost for
> future calculation
> exactly in the same way a the result of a interval arithmetic
> calculation may provide a heavy overestimation of the the exact result.
>
> The rule must be
> the system must not lie
> Nothing more.
>
> Best regards,
>
> Dominique
>
> > I am becoming a static-ist.
> >
> > George
> >
> > On May 25, 2011, at 6:17 AM, Dan Zuras Intervals wrote:
> >
> >
> >>> Date: Tue, 24 May 2011 19:05:38 -0500
> >>> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
> >>> To: Nate Hayes <nh@xxxxxxxxxxxxxxxxx>
> >>> CC: John Pryce <j.d.pryce@xxxxxxxxxxxx>,
> >>> stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> >>> Subject: Re: Ar we succeeding?
> >>>
> >>> All,
> >>>
> >>> Does someone else also have an opinion concerning this (please)?
> >>>
> >>> Baker
> >>>
> >>>
> >> Baker, et al,
> >>
> >> I find I do have an opinion on this. And as long as Nate's
> >> motion is in its discussion period, now is as good a time
> >> as any to discuss it.
> >>
> >> Let me put it in the form of a question I put to Nate:
> >>
> >> Is your philosophy about decorations a tracking approach or
> >> a static approach?
> >>
> >> There seem to be two schools of thought about the meaning
> >> of decorations.
> >>
> >> There is the TRACKING school in which decorations are the
> >> maximal (most pessimistic) result of the tree of evaluations
> >> that led up to the result to which they are attached. That
> >> is, every exceptional or noteworthy incident in that tree is
> >> recorded for all to see whether it is relevant to the final
> >> result or not.
> >>
> >> Then there is the STATIC school in which decorations are
> >> information concerning the current result only. Earlier
> >> decorations may pass through to this result if they still
> >> apply & may be discarded if they do not. In this case the
> >> decoration must be able to be interpreted in the context
> >> of the final result whatever happened before.
> >>
> >> (In either school, the decoration must be ordered WRT to
> >> subsets of arguments. I believe this is both necessary &
> >> sufficient for an FTDIA to be proved.)
> >>
> >> I asked this question of Nate because his motion seemed to
> >> be primarily of the tracking school but with some static
> >> features thrown in.
> >>
> >> I think we need to be consistent on this point. As much
> >> for our own understanding as to explain the meaning of
> >> decorations to the rest of the world.
> >>
> >> I will admit that I started out in the Tracking school.
> >> But some remarks I've heard in this forum & privately have
> >> suggested to me that the Static school might serve us better
> >> as a standard.
> >>
> >> So I ask of all of you: Which philosophy should we espouse?
> >> Tracking or Static?
> >>
> >> I believe that once we decide this many of our more
> >> difficult questions will fall out as obvious.
> >>
> >> Yours,
> >>
> >> Dan
> >>
> >
> > Dr. George F. Corliss
> > Electrical and Computer Engineering
> > Marquette University
> > P.O. Box 1881
> > 1515 W. Wisconsin Ave
> > Milwaukee WI 53201-1881 USA
> > 414-288-6599; GasDay: 288-4400; Fax 288-5579
> > George.Corliss@xxxxxxxxxxxxx
> > www.eng.mu.edu/corlissg
> >
> >
> >
>
>
> --
> Dr Dominique LOHEZ
> ISEN
> 41, Bd Vauban
> F59046 LILLE
> France
>
> Phone : +33 (0)3 20 30 40 71
> Email: Dominique.Lohez@xxxxxxx