Numerical Representation of real numbers, alternative to floating-point format

Question

are there any formats to describe real numbers, other than floating point format?

In particular, I ask for formats which still provide feasible computation performance (compared to floating point), in contrast to, say, symbolic computation.

Thank you.

Addendum: I am interested in this from a perspective of theoretical computer science. Indeed I have found a scientific paper which gives a (small list) of number systems to 'represent' a real number. perso.ens-lyon.fr/jean-michel.muller/chapitre1.pdf

The term 'symbolic' is ambigious, I admit. I have been thinking about mathematica like computing, which is a term used in theoretical CS. Btw, 'describe' does not mean 'describe precisely. The term 'float' however does not apply, because that wouldn't make much sense. But this is far adrift from the actual question, being more philosophical.

Answer 1

I really like continued fraction representations. Done lazily, they can let you generate precision as needed. They will, of course, be slower than "native" representations such as floating point.