An efficient implementation of numerical integration using logical computation on stochastic bit streams

Numerical integration is a widely used approach for computing an approximate result of a definite integral. Conventional digital implementations of numerical integration using binary radix encoding are costly in terms of hardware and have long computational delay. This work proposes a novel method for performing numerical integration based on the paradigm of logical computation on stochastic bit streams. In this paradigm, ordinary digital circuits are employed but they operate on stochastic bit streams instead of deterministic values; the signal value is encoded by the probability of obtaining a one versus a zero in the streams. With this type of computation, complex arithmetic operations can be implemented with very simple circuitry. However, typically, such stochastic implementations have long computational delay, since long bit streams are required to encode precise values. This paper proposes a stochastic design for numerical integration characterized by both small area and short delay — so, in contrast to previous applications, a win on both metrics. The design is based on mathematical analysis that demonstrates that the summation of a large number of terms in the numerical integration could lead to a significant delay reduction. An architecture is proposed for this task. Experiments confirm that the stochastic implementation has smaller area and shorter delay than conventional implementations.