Re: Table 4 proposal version 0.1...
On 2012-02-29 15:47:49 +0100, Arnold Neumaier wrote:
> After all this discussion, I think that mid(X) should be NaN whenever
> X is unbounded or empty. This is consistent with the usage of NaN in
> floating-point for a mathematically not well-determined case of an
> otherwise standard operation. No other assignment of midpoints is
> appropriate for level 1 (where ad hoc decisions should be avoided).
>
> Users in a branch and bound can catch the NaN and do something sensible
> in the context of their particular method. The best choice is
> user-dependent ans hence should be left to the user, which the result
> NaN does.
>
> Moreover, a naive user will not be able to form the interval
> [inf(X),mid(X)] if the constructors are well-designed, and hence will
> notice immediately that something has been done wrongly.
>
> Thus there is no danger at all that this compromises the standard.
>
>
> On the other hand, a function split(X) [if provided by the standard]
> should return a sensible splitting point if one exist, and NaN
> otherwise, i.e., if X contains at most two machine numbers. What is
> most sensible would have to be discussed. I thought for some time that
> returning the median of the machine numbers is good but this would
> split the interval [0,1] at an extremely tiny number, which is not
> warranted. It seems that there is no ''natural'' such function, thus
> the standard should not provide one.
>
> Instead, I propose to provide a function flmedian(X) that provided the
> median, so that users can make their own split routine based on mid,
> flmedian, and scaling considerations.
I think that this would be the best choice. Perhaps instead of
returning a splitting point, split(X) could return 2 intervals,
corresponding to the actual splitting (if this is more useful).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)