This paper introduces a binary encoding that supports arbitrarily large, small and precise decimals. It completely preserves information and order. It does not rely on any arbitrary use-case-based choice of calibration and is readily implementable and usable, as is. Finally, it is also simple to explain and understand.
@cite_6: We describe a new binary encoding for numbers termed lexicographic continued fraction (LCF) representation that provides a one-to-one order preserving finite bit string representation for every rational. Conversion either way between binary integer numerator-denominator pair representation and LCF representation is shown feasible in time linear with bit string length, given registers of length sufficient to hold the numerator and denominator. LCF bit string length is about 2 max log 2 p, log 2 q for the irreducible fraction p q. Realization of arithmetic (+, −, ×, ÷ on LCF bit string encoded operands is shown feasible. Some relations between the theory of best rational approximation and the values represented by truncated LCF bit strings are noted to assess the feasibility of a finite precision arithmetic based on LCF representation.
The Rishe encoding was itself proposed as an improvement upon the Matula-Kornerup encoding @cite_6 , which relies on a representation of the decimal as a continuous fraction. The latter did not scale up with exponents. The exponent part of Rishe scales up logarithmically in the decimal, while that of decimalInfinite scales up double-logarithmically (see Section ).