Arithmetic on the European logarithmic microprocessor

A new European research project aims to develop a microprocessor based on t he logarithmic number system, in which a real number is represented as a fi xed-point logarithm. Multiplication and division therefore proceed in minim al time with no rounding error. However, the system can only offer an overa ll advantage over floating-point if addition and subtraction can be perform ed with speed and accuracy at least equal to that of floating-point, but th ese operations require the interpolation of a nonlinear function which has hitherto been either time-consuming or inaccurate. We present a procedure b y 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 o f both speed and accuracy.