Re: Disjoint, subset, & interior, or more...???

[Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>]

> Date: Mon, 04 Oct 2010 05:24:57 -0500
> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Disjoint, subset, & interior, or more...???
> 
> On 10/3/2010 17:54, Dan Zuras Intervals wrote:
> > 	Folks,
> >
> > 	I have been having an offline discussion with John about
> > 	these comparison issues.  He has (indirectly) convinced
> > 	me that I should make my concerns more public.
> >
> .
> .
> .
> > 	You see, my attraction to his limited set of comparisons
> > 	is partially pedegogical rather than technical.  Sooner or
> > 	later we are going to have to deal with users of interval
> > 	software who are trained to think in floating-point rather
> > 	than interval terms.  The natural tendency will be to
> > 	attempt to convert their floating-point algorithms to
> > 	interval ones by, more or less, declaring all their
> > 	floating-point variables to be intervals instead.
> >
> 
> On the other hand, although 754 may not be perfect in this
> regard, it DOES provide an excellent framework upon which basic
> interval operations can be built.  In particular, I am thinking
> of the directed roundings, as well as recommended elementary
> functions (along with accuracy requirements).  It would be a
> shame (in my own opinion) not to take full advantage of what
> we can in crafting 1788.  The +/-0 and behavior of \infty may
> have been designed with interval continued fractions in mind,
> and that might be at odds with the most desired behavior in
> other applications.

	Yes, directed rounding was created over 30 years ago
	with you guys in mind.  Alas, it has gone largely
	unused & the floating-point hardware guys hate it &
	the state that surrounds it.

	The +/-0 more or less fell out of the format although
	the behavior WRT directed roundings had both you guys
	& cuts in the complex plane in mind.

	I forget what the rationale was behind +/-infinity.
	There was a discussion of affine versus projective
	infinity at the time.  Affine kinda won out after the
	8087 had alrady gone to silicon.  But you mostly get
	projective if you ignore the sign.

	Although I had some numerical analysis experience at
	the time, I was new to chip design & I just thought
	it was cool. :-)

> 
> > 	This would be, of course, a HUGE mistake.
> >
> > 	And what better way to convince them that it is a mistake
> > 	than to hit them right away with the fact that you cannot
> > 	compare two intervals as you once compared two floating-
> > 	point values?  Sure, some of them would try to hack around
> > 	it.  But at least some of them would look into why this is
> > 	the case&, just perhaps, learn something about how to do
> > 	REAL interval calculations.  Correct interval calculations.
> >
> 
> I personally find Juergen's Motion 21 attractive in this regard.
> It provides all possible comparisons, viewed in terms of the
> ordering on the reals, yet encompassing what we would desire
> with respect to set inclusion.  (Granted, some things we want
> would be compound operations, but we get both the numerical
> ordering and the set inclusion ordering with this set.)
> 
> > 	Its worth a shot, if for no other reason than that.
> >
> > 	But back to the technical issue, I am not convinced by
> > 	Arnold's big 3: disjoint, subset,&  interior.  I'm OK with
> > 	the first two but the 3rd bothers me.
> .
> .
> .
> > 	I believe Baker is correct that someone should make some
> > 	sort of unifying or simplifying motion on this matter.
> >
> > 	And I feel eminently unqualified to do so.
> >
> A couple of other people have expressed similar sentiments.
> I am willing to actually make that motion, just to move things
> along, if Arnold is still unwilling to formally register and
> participate officially.  However, it may add to the confusion
> if such a motion is put forward before 13.04, 20, and 21 are
> processed.  What do you think?

	Oh, it should come after them.
	Definitely.

> 
> > 	I am asking for your help.
> >
> 
> Just say the word.
> 
> Best regards,
> 
> Baker
> >
> > 				   Dan
> >

	I can make my own motions.
	I know how to do that.
	The problem is in knowing what to move.
	There I'm stumped.


			Dan