Framework for Quantifying and Managing Accuracy in Stochastic Circuit Design
Florian Neugebauer1,a, Ilia Polian1,b and John P. Hayes2
1Faculty of Computer Science and Mathematics, University of Passau, Innstr. 43, D-94032 Passau, Germany.
aflorian.neugebauer@uni-passau.de
bilia.polian@uni-passau.de
2Computer Engineering Laboratory, University of Michigan, Ann Arbor, MI 48109, USA.
jhayes@eecs.umich.edu
ABSTRACT
Stochastic circuits (SCs) offer tremendous areaand power-consumption benefits at the expense of computational inaccuracies. Managing accuracy is a central problem in SC design and has no counterpart in conventional circuit synthesis. It raises a basic question: how to build a systematic design flow for stochastic circuits? We present, for the first time, a systematic design approach to control the accuracy of SCs and balance it against other design parameters. We express the (in)accuracy of a circuit processing n-bit stochastic numbers by the numerical deviation of the computed value from the expected result, in conjunction with a confidence level. Using the theory of Monte Carlo simulation, we derive expressions for the stochastic number length required for a desired level of accuracy, or vice versa. We discuss the integration of the theory into a design framework that is applicable to both combinational and sequential SCs. We show that for combinational SCs, accuracy is independent of the circuit's size or complexity, a surprising result. We also show how the analysis can identify subtle errors in both combinational and sequential designs.
Keywords: Emerging technologies, Error analysis, Simulation, Stochastic computing.
