[boost] Re: lazy exact arithmetic

From: Brandon Kohn (bkohn_at_[hidden])
Date: 2005-02-22 15:04:49

I'm glad there is some interest. I've already begun implementing it (will be 
testing it with GMP). I noticed (I think 3) implementations of big_integer 
classes in the yahoo group files section. None of them has ripened into a 
solid library so far? Or are they just not entirely compatible with 
boost::rational?

Boost seems fairly ready for this stage of evolution what with interval and 
rational... so perhaps it's just a matter of time for big_int to be 
completed. At any rate, I'll continue my work and post more when I have 
something worth reporting (or ?s).

Thanks guys,

Brandon

"Paul A Bristow" <pbristow_at_[hidden]> wrote in message 
news:E1D3bdc-0007Gk-SA_at_he303war.uk.vianw.net...
> 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
>
> Paul A Bristow
> Prizet Farmhouse, Kendal, Cumbria UK LA8 8AB
> [phone]  [phone]
> 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
> |
> |
> |
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