Re: [boost] Interest in an arbitrary precision library?

From: Martin Bonner (martin.bonner_at_[hidden])
Date: 2005-09-14 03:54:26

----Original Message----
From: Daryle Walker [mailto:darylew_at_[hidden]]
Sent: 14 September 2005 07:12
To: Boost mailing list
Subject: Re: [boost] Interest in an arbitrary precision library?

> On 9/13/05 7:28 AM, "Andy Little" <andy_at_[hidden]>
> wrote: 
> 
>> "Daryle Walker" <darylew_at_[hidden]> wrote
>> 
>>> OK.  When you say "arbitrary precision," you mean that a precision
>>> limit must be set (at run-time) before an operation.  Most people
>>> use "arbitrary precision" to mean unlimited precision, not your
>>> "run-time cut-off" precision.
>> 
>> Are  there really libraries that have unlimited precision?
>> What happens when the result of a computation is irrational?
> 
> You can't store it conventionally, since such numbers would need an
> infinite amount of memory.  You would just give up and have to define
> some sort of rounding/cut-off philosophy.  As another poster said,
> you could store the irrational components of a number with some sort
> of formula (but only for algebraically irrational numbers, not
> transcendentally irrational numbers). 

Why only for algebraiclly irrational numbers?  There is no reason (in
principle) that the representation of an irrational shouldn't include trig /
hyperbolic / bessel functions of irrationals, or even definite integrals.  

Of course, at this point you get close to rewriting a chunk of Matlab or
Mathematica.  On the other hand, simplifying
(sqrt(5)-sqrt(3))*(sqrt(5)+sqrt(3)) to exactly 2 is quite a challenge too
(and if you don't then the unlimited precision representation doesn't really
buy you anything).

-- 
Martin Bonner
Martin.Bonner_at_[hidden]
Pi Technology, Milton Hall, Ely Road, Milton, Cambridge, CB4 6WZ,
ENGLAND Tel: [phone]