Re: [boost] [review] Multiprecision review scheduled for June 8th - 17th, 2012

Subject: Re: [boost] [review] Multiprecision review scheduled for June 8th - 17th, 2012
From: Jeffrey Lee Hellrung, Jr. (jeffrey.hellrung_at_[hidden])
Date: 2012-06-05 11:14:55

On Thu, May 31, 2012 at 5:31 PM, Marc Glisse <marc.glisse_at_[hidden]> wrote:
[...]

> On Thu, 31 May 2012, John Maddock wrote:
>
[...]

>  * what about infinite precision floats? By that I mean something like
>>> bigint*2^n, where operations + - * are computed exactly. It can be quite a
>>> bit faster than rationals, when it is sufficient.
>>>
>>
>> Wouldn't those get horribly large very quickly?
>>
>
> You can see them as a special case of rationals where the denominator is
> always a power of 2, so they grow more slowly than rationals.
>
>  Off hand I know of no other library that implements such a beast?
>>
>
> CGAL. If you want to evaluate exactly the sign of a polynomial of double,
> your best bets are this or a sum-of-double representation, depending on the
> degree.
>

I want to echo Marc's comment that algorithms and numeric types where you
only perform ring operations are common in computational geometry. You can
often bound the size of your expression tree (as a function of your spatial
dimension), hence bound the size of your rationals. It might be worth
considering this application within the scope of (proposed)
Boost.Multiprecision. Indeed, I've used a C++ implementation of Jonathan
Shewchuck's exact arithmetic algorithms [1] for such purposes.

[1] http://www.cs.cmu.edu/~quake/robust.html

- Jeff