On 9/13/05, Andy Little <andy@servocomm.freeserve.co.uk> 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