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The current proposal

Dear all,

we are discussing the standardization of interval arithmetic. This
is not intended to pass and put into the cabinet, but intended to use.

May I ask how many of you have experience in using interval arithmetic?

Here is why I must insist that the current proposal is academic and
puts burden of case distinctions on the user.

Trust me, it is very natural in interval arithmetic to do interval
calculations with the bounds.
For a given function F, for example, X=F(interval(A.sup)) should give an
inclusion of the value of F at the right bound of A.

With the current proposal, this needs a case distinction:

   if A.sup==Inf
     X = F(interval(realmax,Inf));
   else
     X = F(interval(A.sup));
   end

This burden is on the part of the user. Even worse, it is likely to be
forgotten and to pass unoticed. And then false results may appear, the
worst what can happen to a verication method.

Let me transpose this to the floating-point world.

Imagine the question "What is the result of -0==0" is at stake. There
are good arguments that it should be true, like in IEEE 754, but one
may also argue that these are two different quantities, so how can they
be equal.

Now suppose it is voted for the latter, so that from now on one cannot
just write

   res = ( x==y );

but must use

   if abs(x)==0
     res = ( abs(x)==abs(y) );
   else
     res = ( x==y );
   end

or alike. It may be perfectly documented, but is this reasonable?

IMHO the current proposal for interval arithmetic is very similar.

Best wishes

Siegfried M. Rump


--
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
Schwarzenbergstr. 95
21071 Hamburg
Germany
phone  +49 40 42878 3027
fax    +49 40 42878 2489
http://www.ti3.tu-harburg.de

and

Visiting Professor at Waseda University
Faculty of Science and Engineering
Shinjuku Lambdax Bldg. 902
2-4-12 Okubo, Shinjuku-ku
Tokyo 169-0072
Japan
phone/fax in Japan  +81 3 5286 3414