A novel algorithm for accurate logarithmic number system subtraction

In this paper, a novel algorithm for the computation of Logarithmic Number System (LNS) subtraction is presented. The main feature of the proposed algorithm is that it circumvents the evaluation of the highly nonlinear function traditionally used in logarithmic subtraction. In some cases, this approach permits a reduction of up to 60% in the number of approximation intervals, thus making the realization of cost-effective LNS arithmetic units of very high accuracy feasible. The approach is extended to address certain algorithms that need to be implemented by an LNS processor. Moreover, alternative architectures that implement the computational approach and exhibit different time-area requirements are discussed. For the sake of completeness, upper bounds to the computational errors are offered.