infinite (fractional) precision

[Jerzy Karczmarczuk]

Ketil Z. Malde wrote:

> It seems one could easily (I'll get back to that in a moment)
> calculate the fractional part of numbers lazily, generating the needed
> precision, and nothing more.  Does any such implementation exist in
> Haskell?
> 
> I realize it's probably far from trivial, e.g. comparing two equal
> numbers could easily not terminate, and memory exhaustion would
> probably arise in many other cases.
> 
> So, if such implementations exist, how does one deal with these
> issues?  Is it indeed possible to make this useful in practice?

Well, I implemented such a stuff for fun. Look here:

http://users.info.unicaen.fr/~karczma/arpap/lazypi.ps.gz

This shows how to implement Bailey-Borwein-Plouffe formula for PI,
using lazy hexadec. fractions, and converting them to decimal. This
is a crazy idea, with algorithms which are partly co-recursive, and
partly recursive, borrowing the carry from the non-existing yet
future. It could be done in a safer way, but I repeat that I did it
for sheer joy. Perhaps one day I will return to it, unless somebody
does it first.


Jerzy Karczmarczuk