ABSTRACT
Conventional high-level synthesis techniques are not able to manipulate polynomial expressions efficiently due to the lack of suitable optimization techniques for redundancy elimination over Z2n.
This paper, in comparison with [1], presents 1) an improved partitioning heuristic based on single-variable monomials instead of checking all sub-polynomials, 2) an improved compensation heuristic which is able to compensate monomials as well as coefficients, and 3) a combined area-delay-optimized factorization approach to extract the most frequently used sub-expressions from multi-output polynomials over Z2n. Experimental results have shown an average saving of 32% and 27.2% in the number of logic gates and critical path delay respectively compared to the state-of-the-art techniques. Regarding the comparison with [1], the number of gates and delay are improved by 14.3% and 13.9% respectively. Furthermore, the results show that the combined area-delay optimization can reduce the average delay by 26.4%.
- O. Sarbishei, B. Alizadeh and M. Fujita, "Polynomial Datapath Optimization using Partitioning and Compensation Heuristics", in 46th Design Automation Conference (DAC), pp. 931--936, 2009. Google ScholarDigital Library
- B. Alizadeh and M. Fujita, "Modular-HED: A Canonical Decision Diagram for Modular Equivalence Verification of Polynomial Functions", in the fifth Workshop on Constraints in Formal Verification (CFV), pp. 22--40, 2008.Google Scholar
- A. V. Aho, S. C. Johnson, and J. D. Ullman, "Code Generation for Expressions with Common Subexpressions," in Journal of the ACM, vol. 24, pp. 146--160, 1977. Google ScholarDigital Library
- M. A. Breuer, "Generation of Optimal Code for Expressions via Factorization," in Communications of the ACM, vol. 12, pp. 333--340, 1969. Google ScholarDigital Library
- A. Peymandoust and G. DeMicheli, "Application of Symbolic Computer Algebra in High-Level Data-Flow Synthesis", in IEEE Trans. CAD, vol. 22, pp. 1154--11656, 2003. Google ScholarDigital Library
- S. Gopalakrishnan and P. Kalla, "Optimization of polynomial datapaths using finite ring algebra", in ACM Trans. Design Automation of Electronics Systems, vol. 12, no. 4, pp. 49:1--30, 2007. Google ScholarDigital Library
- S. Gopalakrishnan, P. Kalla, B. Meredith, and F. Enescu, "Finding linear building-blocks for RTL synthesis of polynomial datapaths with fixed-size bit-vectors", in International Conference on CAD, pp. 143--148, 2007. Google ScholarDigital Library
- A. Hosangadi, F. Fallah, R. Kastner, "Factoring and Eliminating Common Subexpressions in Polynomial Expressions", in International Conference on CAD, pp. 169--174, 2004. Google ScholarDigital Library
- JuanCSE, "Extensible, programmable and reconfigurable embedded systems group", Available at: http://express.ece.ucsb.edu/suif/cse.html.Google Scholar
- E. Kaltofen, J. P. May, Z. Yang, L. Zhi, "Approximate Factorization of Multivariate Polynomials Using Singular Value Decomposition", in Journal of Symbolic Computation, pp. 359--376, 2008. Google ScholarDigital Library
- J. Krumm, "Savitzky-Golay Filters for 2D Images", Available at: http://homepages.inf.ed.ac.uk/rf/CVonline/LOCAL_COPIES/KRUMMI/SavGol.htm.Google Scholar
- A. Hosangadi, F. Fallah, and R. Kastner, "Optimizing polynomial expressions by algebraic factorization and common subexpression elimination", in IEEE Trans. CAD, vol. 25, pp. 2012--2022, 2006. Google ScholarDigital Library
Index Terms
- Improved heuristics for finite word-length polynomial datapath optimization
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