Polynomial datapath synthesis and optimization based on vanishing polynomial over Z2m and algebraic techniques

The growing market for Digital Signal Processing (DSP), Computer graphics and embedded systems applications that can be modeled as polynomial computations in their datapath designs, requires improvements in high-level synthesis and optimization techniques for such systems. This paper concentrates on how to find common sub-expressions between s given polynomial functions over Z_2n1 × Z_2n2 × ... × Z_2nd to Z_2m in order to optimize the area and delay as much as possible. Our main contributions in this paper is proposing an optimization method based on adding/deleting vanishing polynomials over Z₂^m, i.e., those polynomials that are equivalent to zero over Z₂^m, to/from given polynomial functions in the hope of achieving further common sub-expressions. After applying our optimization techniques, experimental comparisons with the state-of-the-art techniques show an average improvement in the area by 36.80% with an average delay decrease of 2.41%. Regarding the comparison with our previous works, the area and delay are improved by 21.4% and 8.7% respectively.