[std-interval] More on interval computations as proofs

Sylvain Pion Sylvain.Pion at sophia.inria.fr
Fri Oct 6 12:55:15 PDT 2006

Guillaume Melquiond wrote:
> Le jeudi 05 octobre 2006 à 22:42 +0200, Gabriel Dos Reis a écrit :
>>Guillaume Melquiond <guillaume.melquiond at ens-lyon.fr> writes:
>>| So, to qualify your point on straightforward translation, I would say
>>| that you are right for resolution algorithms (finding roots, solving
>>| differential equations, and so on), as they simply won't work. But for
>>| evaluation functions, you don't have to rewrite them.
>>so, are you suggesting that basically x +-> x * x should return [-1,
>>1] on [-1,1], instead of [0, 1]? (I though a simple function to keep
>>the question simple).
> I am obviously not saying that x*x "should" return [-1,1]. I'm just
> saying that, if it returns [-1,1] instead of [0,1], that doesn't matter
> for solving things. Rewriting an evaluation function to take into
> account interval decorrelation will improve the performance of solvers a
> bit (a few iterations less), but it generally won't have any influence
> on the quality of the results.

Anyway.  Going back to the original problem, I think that rewriting the
formulas to get sharper intervals is one thing.  But rewriting to pass
additional flag arguments to each function is not really nice.

My personnal opinion here is that the speed gains here are not worth
duplicating the interface of many functions.  So, for the proposal
right now I would go for a global (thread-local) flag.  If the committee
disagrees from a C++ point of view and wishes something else, then fine,
we'll adapt.  But we need to write something now.


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