Efficient algorithms for binary logarithmic conversion and addition

Abstract

The logarithm number system is an attractive alternative to the conventional number systems when data needs to be manipulated at a very high rate over a wide range. The major problem is deriving logarithms and antilogarithms quickly and accurately enough to allow conversions to and from conventional number representations. Efficient algorithms that convert the conventional number representation to binary logarithm representations are proposed. The algorithms adopt a factorisation approach to reduce the look-up table size and a nonlinear approximation method to reduce the computational complexity. Simulation results on IEEE single precision (24 bits) conversion are presented, and the conversion requires only one ROM table with 213×26 bits, one with 213×14 bits, and one with 213×5 bits, or a total of 360 kbits.