A graphical transform for subexpression elimination using genetic algorithms

A common way of implementing multiplication in digital filters is by a series of shift and add operations. If the multiplier is represented in canonical signed digit (CSD) format then the number of additions (subtractions) needed will be reduced. This can be further reduced through subexpression elimination in the vertical, horizontal or both dimensions. This paper presents a method to graphically transform the subexpression elimination problem into one that is easily solved by a standard genetic algorithm. It operates in the vertical or horizontal dimensions or optimises simultaneously in both dimensions.