Efficient algorithms for binary logarithmic conversion and addition

Efficient algorithms that convert the conventional number representation to binary logarithm representation are proposed, and the algorithms adopt a factorization approach to reduce the look-up table size and a nonlinear approximation method to reduction the computational complexity.

Abstract

Logarithm number system is an attractive alternative to the conventional number systems when data need to be manipulated at very high rate over a wide data range. However, the major problem is deriving logarithm and anti-logarithm quickly and accurately enough to allow conversions to and from the conventional number representations. In this paper, efficient algorithms that convert the conventional number representation to binary logarithm representation are proposed. The algorithms adopt a factorization 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 2/sup 13//spl times/26 bits, one with 2/sup 13//spl times/14 bits, and one with 2/sup 13//spl times/5 bits, or a total of 360 kbits. The algorithm can also be adopted for binary logarithmic addition.