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

From: Andras Erdei (aerdei_at_[hidden])
Date: 2005-09-14 08:57:20

On 9/13/05, Andy Little <andy_at_[hidden]> wrote:
> 
> Are there really libraries that have unlimited precision?
> What happens when the result of a computation is irrational?
> 

as i understand the possible range of arithmetic types, there are

_fixed_ precision representations, like the built-in int or float,
or (extended precision) user-defined types, like a 2048 bit integer
for RSA operations (likely implemented using modular arithmetic)

we are all familiar with these

_arbitrary_ precision numbers (same as above, but the precision is
set at runtime, rather than selected at compile time); if i understand
correctly, Joel is proposing this kind of library

i have never used such a beast, nor seen it used, so i only have
guesses about it

_unlimited_ precision types (i think these are referred as 'unlimited'
rather than as 'infinite' -- except by the current C++ Standard
Library proposal :O) -- intentionally)

these usually do not have functions like sin/log/sqrt, as they are
used for problems like solving a set of linear equations, or
maintaining your account balance in a bank, in both cases
exactly

sometimes they do have some of those functions, coupled with
the cabaility to represent the results, but i only have read about 
such ones in articles, never seen or used one

_symbolic_ calculation

i have never used such a thing (beyond the capabilities of my
HP128S calculator long ago), but i think a really general implementation
is impossible (e.g. finding a primitive function could be a hard AI
problem :O), still, there are such things in use (i think mathematica
is an example, although i could be wrong)

so my answer is: unlimited precision types do not have operations
that would lead out from the set of numbers representable in that type

this does not mean that boost::rational cannot have an sqrt() function,
but it will work just like the one for float, returning an approximate 
result

br,
andras