Re: about com (was: Motion 42: NO)
Le jeudi 07 février 2013 à 14:38 +0100, Vincent Lefevre a écrit :
> On 2013-02-06 22:07:15 +0100, Guillaume Melquiond wrote:
> > - I do not agree with com requiring the computed interval to be bounded
> > at level 2. I feel that the boundedness should only be required at level
> > 1. In particular, I do not see what is gained from stripping com in case
> > of a harmless overflow. What is the point of com if an unbounded
> > interval from the point of view of the interval type is necessarily
> > unbounded from the point of view of the decorations? Any information
> > about what the mathematical function actually computes is lost.
>
> The primary goal of com is not to give a property of the function
> but to record whether the evaluation does not depend on the flavor
> (assuming identical rounding and some form of reproducibility). As
> some flavors (e.g. Kaucher) do not have unbounded intervals, it was
> necessary to reject overflows.
It might not have been the primary goal, but the motion explicitly
defines com as "Definition: x is a bounded, nonempty subset of Dom(f); f
is continuous at each point of x; and the computed interval f(x) is
bounded". The fact that it talks about the domain and continuity of the
mathematical function does not leave much leeway for interpretation.
Now, if the actual goal was that the evaluation does not depend on the
flavor, it could have been defined just as that: "Definition: the exact
same interval would have been computed for f(x) with any of the other
flavors available." At least it would not suffer from the
reproducibility issue which you point out.
Best regards,
Guillaume