Stochastic functions using sequential logic

Stochastic computing is a novel approach to real arithmetic, offering better error tolerance and lower hardware costs over the conventional implementations. Stochastic modules are digital systems that process random bit streams representing real values in the unit interval. Stochastic modules based on finite state machines (FSMs) have been shown to realize complicated arithmetic functions much more efficiently than combinational stochastic modules. However, a general approach to synthesize FSMs for realizing arbitrary functions has been elusive. We describe a systematic procedure to design FSMs that implement arbitrary real-valued functions in the unit interval using the Taylor series approximation.