NDLI: Optimization of polynomial datapaths using finite ring algebra

Content Provider	ACM Digital Library
Author	Gopalakrishnan, Sivaram Kalla, Priyank
Copyright Year	2007
Abstract	This article presents an approach to area optimization of arithmetic datapaths at register-transfer level (RTL). The focus is on those designs that perform polynomial computations (add, mult) over finite word-length operands (bit-vectors). We model such polynomial computations over $\textit{m}-bit$ vectors as algebra over finite integer rings of residue classes $Z_{2}^{m}.$ Subsequently, we use the number-theoretic and algebraic properties of such rings to transform a given datapath computation into another, bit-true equivalent computation. We also derive a cost model to estimate, at RTL, the area cost of the computation. Using the transformation procedure along with the cost model, we devise algorithmic procedures to search for a lower-cost implementation. We show how these theoretical concepts can be applied to RTL optimization of arithmetic datapaths within practical CAD settings. Experiments conducted over a variety of benchmarks demonstrate substantial optimizations using our approach.
File Format	PDF
ISSN	10844309
e-ISSN	15577309
DOI	10.1145/1278349.1278362
Volume Number	12
Issue Number	4
Journal	ACM Transactions on Design Automation of Electronic Systems (TODAES)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2007-09-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	High-level synthesis Arithmetic datapaths Finite ring algebra Modulo arithmetic Polynomial datapaths
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Computer Science Applications Electrical and Electronic Engineering

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