Re: [boost] Numerical Quadrature Library/Boost.Accumulators

From: John Maddock (john_at_[hidden])
Date: 2006-12-08 09:04:29

Guillaume Melquiond wrote:
> Le vendredi 08 décembre 2006 à 09:25 +0000, Paul A Bristow a écrit :
>
>> I strongly support thinking about (computational) uncertainty
>> estimates.
>>
>> (Uncertainty seems to be the 'modern' term for what was called
>> error).
>>
>> But I am not clear exactly how to achieve this.  We've got Interval
>> but it's doubtful if this is the right weapon to use.
>
> Interval as a generic notion is the right tool for bounding errors and
> representing uncertain inputs. Most papers on "reliable computing" are
> related to intervals (the name may change for higher dimensions, like
> ellipsoids, but they are still convex sets).
>
> Then there is the matter of representing intervals. With lower-upper
> bounds as in Boost.Interval, the representation is fine as long as the
> precision of the intervals is "small". For precisions of thousands of
> bits, a midpoint-radius representation is more efficient, as the
> radius
> can be stored in reduced form to improve performance and memory
> footprint.

Isn't the Boost.Interval interface agnostic of the underlying 
representation?

Of course one would probably have to specialise boost::interval<T> for each 
type T you want to work with :-(  Unless someone has a generic 
implementation?

John.