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

From: Guillaume Melquiond (guillaume.melquiond_at_[hidden])
Date: 2005-09-13 07:17:12

Le mardi 13 septembre 2005 à 12:28 +0100, Andy Little a écrit :
> "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?

It all depends on which representation you choose for your numbers;
rational representations are not the only ones. Some formats can
represent any real number as long as it is constructible [1] (and you
have enough memory, but no need for an infinite memory for a given
number). There are lots of such formats and an abundant literature about
them, so I will only give one single example: functional Cauchy
sequences of rational numbers.

Best regards,

Guillaume

[1] Rational numbers are constructible. Irrational numbers are
constructible. Pi, E, and other common mathematical constants are
constructible. Numbers derived from them are constructible. Omega (the
halting problem encoding) is not constructible.