Approximating stochastic numbers to reduce latency

Abstract Approximate Computing (AC) and Stochastic Computing (SC) have been studied as new computing paradigms to achieve energy-efficient designs for error-tolerant applications. The hardware cost of SC generally can be small compared to that of AC, but SC has not been applied to a wide range of applications as AC because SC needs very long cycles to use long random bit strings called Stochastic Numbers (SNs) when we need to maintain the desired precision. To mitigate this disadvantage of SC, we propose a new idea to approximate numbers represented by SNs; our idea is to use multiple SNs to represent one number. Indeed our method can shorten the length of SNs drastically while keeping the precision level compared to conventional SNs. We study two specific cases where we use two and three shorter bit-strings to represent a single conventional SN, which we call a dual-rail and a triple-rail SNs, respectively. We also discuss a general case when we use many SNs corresponding to a single conventional SNs. We also compare triple-rail, dual-rail and conventional SNs in terms of hardware overhead and calculation errors in this paper. From the comparison, we can conclude that our idea can be used to shorten the necessary cycles for SC.