Bit and word-level common subexpression elimination for the synthesis of linear computations

In this paper, we propose a transformation technique for the multiplications of one variable with multiple constants, which are frequently seen in the various applications of signal processing, image processing, and so forth. The method is based on the exploration of common subexpressions among constants and reduces the number of shifts, additions, and subtractions to implement linear computations with hardware. Our method searches for regularity among elements of a linear transform using matrix decomposition and generates a reduced data-flow graph which preserves the full regularity. We show experimental results obtained using Discrete Cosine Transform (DCT) and Fast Fourier Transform (FFT) and illustrate the effectiveness of the method.