Which programming languages correctly handle irrational/transcendental numbers? | Hacker News Reader

Which programming languages correctly handle irrational/transcendental numbers?

3 pointsmathodical3 comments

Which programming languages properly handle irrational and transcendental numbers such that loss of precision, etc. is not a problem theoretically? (It doesn't matter whether the ability is built-in to the language or available via existing libraries.)

View on HN

You're looking for the search term "symbolic math". You can get specialized programs like Matlab, Octave, or Mathematica and hope their general purpose stuff will be enough to carry you through, or you can hook to them from your general-purpose language. You can also search for a "symbolic math library" for the language of your choice. Test anything you find very thoroughly for your needs.

Without more details, I doubt you'll get more than a search term. With more details, maybe somebody else can give you a more specific recommendation. (Not me, though, I've done little more than fiddle in this domain.)

There is an implementation of exact real arithmetic that has been verified in in Coq[1] and also an implementation in Haskell[2] which may or may not do what you want to do.

It really does depend on what you want to compute. For instance, I can provide a simple implementation in Haskell that includes addition, multiplication and square roots: data Real = Real

  add :: Real -> Real -> Real
  add _ _ = Real 

  multiply :: Real -> Real -> Real
  multiply _ _ = Real

  squareRoot :: Real -> Real -> Real
  squareRoot _ _ = Real
 
  zero :: Real
  zero = Real

  one :: Real 
  one = Real

but it isn't very interesting as you can't print things or test for equality...Any implementation of real numbers that includes those is going to be much harder[3].

[1]http://videolectures.net/aug09_spitters_oconnor_cvia/ [2]http://www.haskell.org/haskellwiki/Exact_real_arithmetic [3]http://en.wikipedia.org/wiki/Tarskis_undefinability_theorem

This is not exactly what you are asking for, but you may find Gosper's ideas on using continued fractions for exact arithmetic useful

http://www.inwap.com/pdp10/hbaker/hakmem/cf.html

http://www.strw.leidenuniv.nl/~gurkan/gosper.pdf

I think this would be most naturally implemented in something like LISP, Ruby or Python.

Reply on news.ycombinator.com