Approximate Hardware Generation using Symbolic Computer Algebra employing Gröbner Basis

Saman Fröhlich, Daniel Große, Rolf Drechsler

In: Design, Automation and Test in Europe (DATE). Design, Automation & Test in Europe (DATE-2018) March 19-23 Dresden Germany 2018.


Many applications are inherently error tolerant. Ap-proximate Computing is an emerging design paradigm, whichgives the opportunity to make use of this error tolerance, bytrading off accuracy for performance.The behavior of a circuit can be defined at an arithmetic level,by describing the input and output relation as a polynomial.Symbolic Computer Algebra (SCA) has been employed to verifythat a given circuit netlist matches the behavior specified at thearithmetic level.In this paper, we present a method that relaxes the exactnessrequirement of the implementation. We propose a heuristicmethod to generate an approximation for a given netlist and useSCA to ensure that the result is within application-specific boundsfor given error-metrics. In addition, our approach allows forautomatic generation of approximate hardware wrt. application-specific input probabilities. To the best of our knowledge takinginput probabilities, which are known for many practical appli-cations, into account has not been considered before. We employthe proposed approach to generate approximate adders andshow that the results outperform state-of-the-art, handcraftedapproximate hardware.


Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence