The Synthesis of Stochastic Logic to Perform Multivariate Polynomial Arithmetic

As the feature size of integrated circuits scales to ever smaller regimes, maintaining the paradigm of deterministic Boolean computation is increasingly challenging. Indeed, mounting concerns over noise and uncertainty in signal values motivate a new approach: the design of stochastic logic, that is to say, digital circuitry that processes signals probabilistically, and so can cope with errors and uncertainty. In this paper, we present a general methodology for synthesizing stochastic logic for the computation of multivariate polynomials, a category that is important for applications such as digital signal processing. The method is based on converting polynomials into a particular mathematical form – multivariate Bernstein polynomials – and then implementing the computation with stochastic logic. The resulting logic processes serial or parallel streams that are random at the bit level. In the aggregate, the computation becomes accurate, since the results depend only on the precision of the statistics. Experiments show that our method produces circuits that are highly tolerant of errors in the input stream, while the area-delay product of the circuit is comparable to that of deterministic implementations.