Optimization of polynomial datapaths using finite ring algebra
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Algebraic Methods for Optimizing Constant Multiplications in Linear Systems
Journal of VLSI Signal Processing Systems
Finding linear building-blocks for RTL synthesis of polynomial datapaths with fixed-size bit-vectors
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
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Polynomial expressions are used to approximate a wide variety of functions commonly found in signal processing and computer graphics applications. Computing these polynomial expressions in hardware consumes a lot of energy and therefore careful optimization of these expressions is important in order to achieve low energy consumption. Unfortunately, current optimization techniques for reducing complexity of expressions such as Common Subexpression Elimination (CSE) cannot do a good optimization. In this paper, we present an algebraic technique to reduce the energy consumption of custom datapath implementation of polynomials by reducing the number of energy intensive operations. Our techniques can handle polynomial expressions of any order and containing any number of variables. Synthesis of a set of benchmark polynomials verified the advantages of our technique in reducing energy consumption, where we observed up to 58% improvement over CSE.