Version 2.11, Proposal for interval standardization
Interesting discussion between Sylvain Pion and Arnold Neumaier about
expression evaluation and constant expressions (section 2.6 in V2.11).
Sylvain Pion a ©crit:
> Arnold Neumaire schrieb:
> > The transformation (1/interval(3))*3 -> interval(3) is covered since
> > in 2.6., only requirements on the results are specified, not on the
> > means how to obtain them.
>
> Yes, but I was suggesting to remove section 2.6, by generalizing it with
> what I just proposed, hence the example that shows that it applies to
> constants as well, just like your current section 2.6.
Arnold himself forgot that section 2.6 only talks about REAL expressions
(and in fact CONSTANT real expressions), not INTERVAL expressions. This
is threfore completely different from expressions occurring in an interval
program. (Btw, Sylvain had a typo in this example, which got propagated
through several levels of quoting, but we all know what was meant.)
There is a reproducibility issue here however -- but I think that P1788
would be ill-advised to recommend, never mind mandate (under special mode
perhaps), reproducibility across implementations. I touched on that in
my comments about the Kearfott/Pryce/Revol P1788 draft of 2008-09-29.
The 754-2008 standard has a section on reproducibility, and recommends a
mode of calculation where the "literal meaning" of the program text has
to be followed, primitive by primitive (among other things). In the P1788
this would mean that (in 3-digit decimal, to simplify the example), the
program expression (NOT 2.6 text)
(1/interval(3))*3
must yield [.999,1.01].
The question remains how many rearrangements should be permitted. We all
agree that containment properties are crucial -- but is that all?
Michel.
Sent: 2008-11-18 15:40:18 UTC