[std-interval] cset theory as fundamental

R. Baker Kearfott rbk at louisiana.edu
Mon Jun 5 14:21:21 PDT 2006


Lee (C++ standardization, and ISL),

At 05:29 PM 6/5/2006 +0000, first.i.last at comcast.net wrote:
> -------------- Original message ----------------------
>From: "R. Baker Kearfott" <rbk at louisiana.edu>
>> Guillaume, Lee,
>> 
>
>[...]
>

>> 
>> If I understand "twin," you envision it to hold two results,
>> such as returning [-\infty,-1] .union. [1,\infty] as the result
>> of [1,2] / [-1,1].  I can see a use for that.  However, there is a
>> "twin arithmetic" in the interval literature that is something else,
>> so I would recommend using a word other than "twin" in this context. 
>
>OK.  Good point.
>
>> I also recommend, if we go this route, that the actual
>> results returned be set based on the cset theory.
>
>What is it about disjoint results in particular that recommends the cset
theory over the alternative classical interval theories?
>

I am recommending cset arithmetic generally because it is an extensively
well-thought-out theory that guides specification of results and gives
results that are provable.  Having worked with extended interval
arithmetic for quite some time, I've found specifications to sometimes
be ad-hoc and to perhaps give unexpected results to someone not
familiar with the particular implementation. For instance, there is a
significant (>3) number of different ways I have seen division by 
an interval that contains zero defined. With a solid mathematical
theory, it both constrains the way the results can be define and 
allows one to predict what the computations will do. 

There is nothing about disjoint results in particular that leads me
to recommend cset theory, other than in cases, such as division by
an interval that contains zero, when the disjoint results are obtained
as limiting cases.

To what "alternative classical theory" are you referring?

In any case, John may have some additional comment on this.

Sincerely,

Baker

---------------------------------------------------------------
R. Baker Kearfott,    rbk at louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------



More information about the Std-interval mailing list