How arithmetic should work in an ideal programming language

How arithmetic should work in an ideal programming language

ToonTalk's ability to do exact rational arithmetic was very successfully exploited by the WebLabs Project. This is described in detail in this paper. If feasible this should be extended to include irrational numbers (and maybe complex numbers as well). Libraries exist for implementing exact (computable) real arithmetic. The limitation to computable numbers is not an issue since one will never encounter a non-computable definable real such as the Chaitin constant. What perhaps is an issue is that some comparisons of computable numbers may never terminate.

The shrinking digit format of ToonTalk is particularly well-suited for dealing with irrational numbers by only computing those digits that are greater than a pixel in size.