LCF: A Lexicographic Binary Representation of the Rationals [chapter]

Peter Kornerup, David W. Matula
1996 J.UCS The Journal of Universal Computer Science  
A binary representation of the rationals derived from their continued fraction expansions is described and analysed. The concepts adjacency", mediant" and convergent" from the literature on Farey fractions and continued fractions are suitably extended to provide a foundation for this new binary representation system. Worst case representation-induced precision loss for any real number by a xed length representable number of the system is shown to be at most 19 of bit word length, with no
more » ... on loss whatsoever induced in the representation of any reasonably sized rational number. The representation is supported by a computer arithmetic system implementing exact rational and approximate real computations in an on-line fashion.
doi:10.1007/978-3-642-80350-5_41 fatcat:3bok4cu4mrb7tnfxwn23g72moa