Boost logo

Boost :

From: Paul A Bristow (pbristow_at_[hidden])
Date: 2005-02-22 10:07:46

This looks very useful - if a minority pastime,
but since Boost has yet to get a yet-to-be Boost big_integer to work with
Boost rational,
it might be running before walking.

However, exposing your impressive work to Boosters view must be good.


Paul A Bristow
Prizet Farmhouse, Kendal, Cumbria UK LA8 8AB
+44 1539 561830 +44 7714 330204
mailto: pbristow_at_[hidden]

| -----Original Message-----
| From: boost-bounces_at_[hidden]
| [mailto:boost-bounces_at_[hidden]] On Behalf Of Brandon Kohn
| Sent: 19 February 2005 10:15
| To: boost_at_[hidden]
| Subject: [boost] lazy exact arithmetic
| Hello,
| I was just posting to see if there is any interest in
| developing a library
| to help with exact arithmetic using the lazy arithmetic strategy?
| I've been working for the last couple of years with
| computational geometry
| algorithms, and have found that such a library is really essential to
| overcoming problems due to floating point precision/round off
| errors in most
| computational geometry algorithms with non-brute force
| complexity. The idea
| behind the lazy paradigm is that exact computation (using rational
| arithmetic with arbitrary sized integers) is too costly to be
| used all the
| time. So the exact computations are delayed until such a time
| as you cannot
| reliably make decisions with the information you have from the 'lazy'
| filters. The lazy filters are implemented as a layer of
| calculation that
| uses interval arithmetic to compare numerical quantities. If
| the intervals
| being compared are non-overlapping, the result is considered to be
| sufficient and exact computation is avoided. If the intervals
| do overlap,
| exact computation is required to unambiguously decide how the
| quantities
| compare.
| This is just a rough outline of how the method works, and I'm
| sure there
| will be plenty of kinks to work out (my background is in physics and
| computer science... so perhaps a mathematician in the group
| would step up to
| help guide my efforts :).
| A library such as this one exists in the CGAL kernel library which is
| available under the LGPL. I find that while the LGPL can be
| useful in cases
| where the library is already organized as a single DLL/shared object
| library, it is generally difficult to implement into
| commercial solutions
| due to the dynamic linking constraints imposed by the
| library. Further, I
| think that this type of algorithm (which solves a very big
| problem with
| floating point arithmetic in computing) is really something
| that should be
| standardized and freely available.
| Sorry for the long post :)
| What do you guys think?
| Kind regards,
| Brandon
| _______________________________________________
| Unsubscribe & other changes:

Boost list run by bdawes at, gregod at, cpdaniel at, john at