Approximate Divider Design Based on Counting-Based Stochastic Computing Division

Stochastic computing (SC) promises extremely low cost and energy efficiency for error-tolerant arithmetic operations in many emerging applications such as image processing and deep neural networks. Existing SC-based nonlinear functions like division, however, require highly correlated bit-streams, which does not fit well with the existing SC computing framework in which randomness is required for accuracy. In this paper, we propose a novel SC-based divider design based on recently proposed counting-based stochastic computing scheme, which is much more accurate and faster than traditional SC, and does not depend on randomness of bit-streams for accuracy. We show how such counting-based SC can be applied to nonlinear functions like division. The new divider, called counting-based divider, or CBDIV, exploits both the correlation requirement of existing SC-based division methods and high efficiency of counting-based SC scheme. It essentially combines the best of two worlds in SC and the resulting division operation can be performed as a more efficient partial counting process. Experimental results show that the proposed CBDIV implemented in a 32nm technology node outperforms state of art works by 77.8% in accuracy, 37.1% in delay, 21.5% in area, 50.6% in ADP (area delay product) and 25.9% in power. CBDIV also saves 31.9% in energy consumption when compared to the fixed-point division baseline, and is much more energy efficient than existing SC-based dividers for binary inputs and outputs required in efficient image process implementations. Furthermore, CBDIV with 5-bit precision can even outperform state of art works with 7-bit precision in accuracy by 15.4%. Finally, we compare CBDIV with other state of art SC dividers in contrast stretch application and show that CBDIV can improve the accuracy with 20.6dB in average, which is a huge improvement.