Le mardi 13 septembre 2005 à 12:28 +0100, Andy Little a écrit :
"Daryle Walker" <darylew@hotmail.com> 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.