Re: Motion 42: NO
Le lundi 11 février 2013 à 15:01 +0000, John Pryce a écrit :
> As for "com", classical intervals are nonempty & bounded, so those two
> conditions are of the essence of recognising common evaluation. Please
> explain what you propose as an alternative scheme.
I am proposing the same scheme, but with a simplified mathematical
definition. What I am saying is that you do not need to require the
input intervals to be bounded; you only need the output interval to be
bounded for "com" to work. The propagation rule for decorations will
then take care of the details: either the input intervals are "com" and
then the output can be "com", or they are not and the output cannot.
Note that it has a direct impact on whether the example below works or
not.
> > - 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.
>
> This is indeed a serious question. Do we want to record (a) that an
> evaluation actually *did* only use common intervals, or (b) that it
> *would* have done so, if we had used infinite precision? I thought I
> had a strong argument against the very attractive (b), but it
> escapes me at present.
>
> Arguments on either side please.
Is the result of f(x)=1/(2*x) applied to [1,M] bounded or not (from the
point of view of decorations)? I cannot think of a good reason for
forbidding it.
Sure, it means that if the user changes flavor and now uses one that
does not support wide intervals, the program will crash (or simply
return NaI). But I have a hard time imagining the purpose of a
decoration system that will behave differently if the system suddenly
supports a new flavor that puts more constraints on the range of
intervals. I do believe there should be some kind of reproducibility: a
flavor never used (or simply missing from the system) should have no
influence on a computation in a different flavor.
Best regards,
Guillaume