Approximate Hardware Generation using Symbolic Computer Algebra employing Gröbner Basis
Saman Froehlicha, Daniel Großeb and Rolf Drechslerc
Cyber-Physical Systems, DFKI GmbH and Group of Computer Architecture, University of Bremen, Germany
asaman.froehlich@dfki.de
bgrosse@cs.uni-bremen.de
cdrechsle@cs.uni-bremen.de
ABSTRACT
Many applications are inherently error tolerant. Approximate Computing is an emerging design paradigm, which gives the opportunity to make use of this error tolerance, by trading 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 verify that a given circuit netlist matches the behavior specified at the arithmetic level. In this paper, we present a method that relaxes the exactness requirement of the implementation. We propose a heuristic method to generate an approximation for a given net list and use SCA to ensure that the result is within application‐specific bounds for given error‐metrics. In addition, our approach allows for automatic generation of approximate hardware wrt. application specific input probabilities. To the best of our knowledge taking input probabilities, which are known for many practical applications, into account has not been considered before. We employ the proposed approach to generate approximate adders and show that the results outperform state‐of‐the‐art, handcrafted approximate hardware.
