Radix-2(R) Recoding With Common Subexpression Elimination For Multiple Constant Multiplication

In a recent work on multiple constant multiplication (MCM) problems, a fully predictable sub-linear runtime heuristic was introduced, called Radix-2(R) MCM. This method shows competitive results in speed, power and area, comparatively with the leading algorithms. In this study, the authors combine Radix-2(R) MCM with an exact common subexpression elimination (CSE) algorithm. The resulting algorithm denoted Radix-2(R)-CSE allows a substantial reduction in the number of addition/subtraction operations in MCM by maximising the sharing of partial terms after an initial recoding in Radix-2(R) MCM. The savings over Radix-2(R) MCM ranges from 4.34 to 18.75% (10% on average) when considering a set of 14 benchmark finite impulse response filters of varying complexity.