Arithmetic on the European logarithmic microprocessor

A new European research project aims to develop a microprocessor based on the logarithmic number system, in which a real number is represented as a fixed-point logarithm. Multiplication and division therefore proceed in minimal time with no rounding error. However, the system can only offer an overall advantage over floating-point if addition and subtraction can be performed with speed and accuracy at least equal to that of floating-point, but these operations require the interpolation of a nonlinear function which has hitherto been either time-consuming or inaccurate. We present a procedure by which additions and subtractions can be performed rapidly and accurately and show that these operations are thereby competitive with their floating-point equivalents. We then present some large-scale case studies which show that the average performance of the LNS exceeds floating-point, in terms of both speed and accuracy.