A new algorithm for elimination of common subexpressions

The problem of an efficient hardware implementation of multiplications with one or more constants is encountered in many different digital signal-processing areas, such as image processing or digital filter optimization. In a more general form, this is a problem of common subexpression elimination, and as such it also occurs in compiler optimization and many high-level synthesis tasks. An efficient solution of this problem can yield significant improvements in important design parameters like implementation area or power consumption. In this paper, a new solution of the multiple constant multiplication problem based on the common subexpression elimination technique is presented. The performance of our method is demonstrated primarily on a finite-duration impulse response filter design. The idea is to implement a set of constant multiplications as a set of add-shift operations and to optimize these with respect to the common subexpressions afterwards. We show that the number of add/subtract operations can be reduced significantly this way. The applicability of the presented algorithm to the different high-level synthesis tasks is also indicated. Benchmarks demonstrating the algorithm's efficiency are included as well.