A bit-serial arithmetic unit for rational arithmetic

Abstract

We describe a binary implementation of an algorithm of Gosper to compute the sum, difference, product, quotient and certain rational functions of two rational operands applicable to integrated approximate and exact rational computation. The arithmetic unit we propose is an eight register computation cell with bit serial input and output employing the binary lexicographic continued fraction (LCF) representation of the rational operands. The operands and results are processed in a most-significant-bit first on-line fashion with bit level logic leading to less delay in the computation cell when compared to operation on the full partial quotients of the standard continued fraction representation. Minimization of delay is investigated with the aim of supporting greater throughput in cascaded parallel computation with such computation cells.