An On-Line Arithmetic Unit for Bit-Pipelined Rational Arithmetic

Abstract We derive a binary version 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 a binary continued fraction representation of the rational operands. The operands and results are processed in a most-significant-bit first on-line fashion with bit level logic. Individual bits of the input/output in our binary continued fraction representation are shown to correspond in a one-to-one manner with primitive shift and shift-and-add/subtract operations on pairs of registers in the computation cell. Extension to a redundant signed-bit format is shown feasible toward the ultimate goal of achieving small on-line delay and near uniform throughput in cascaded pipelined computation with these computation cells.