Faithful bipartite ROM reciprocal tables

Abstract

We describe bipartite reciprocal tables that employ separate table lookup of the positive and negative portions of a borrow-save reciprocal value. The fusion of the parts includes a rounding so the output reciprocals are guaranteed correct to a unit in the last place, and typically provide a round-to-nearest reciprocal for over 90% of input arguments. The output rounding can be accomplished in conjunction with multiplier recoding yielding practically no cost in logic complexity or time in employing bipartite tables. We demonstrate these tables to be 2 to 4 times smaller than conventional 4-bit reciprocal tables. For 10-16 bit reciprocal table lookup the compression grows from a factor of 4 to over 16, making possible the use of larger seed reciprocals than previously considered cost effective.<>