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

From: Guillaume Melquiond (guillaume.melquiond_at_[hidden])
Date: 2006-12-08 10:27:50

Le vendredi 08 décembre 2006 à 14:04 +0000, John Maddock a écrit :
> > 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?

Boost interval<T> uses a representation as a pair of T values: the lower
and upper bounds of the connected set [1]. Whatever the uncertainty on
the real results, it is enclosed between these two bounds.

> 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?

The implementation is generic; you just have to provide a mathematical
kernel as a policy (what the documentation calls the "rounding policy")
in order to describe how to perform operations on values of type T [2].
That is, once you said how to divide values of type T, you can divide
values of type interval<T>.

Best regards,

Guillaume

[1] For comparison, n2137 does not mandate a specific representation; an
implementation relying on a midpoint-radius one would still be compliant.

[2] n2137 does not need a policy, as it is not generic : its behavior is
not defined for user-defined types, only for native floating-point types.