Scaled Population Subtraction for Approximate Computing

In this paper we present Scaled Population Subtraction to fill a void in Scaled Population arithmetic. Scaled population (SP) arithmetic is a scheme that is inspired by stochastic computing (SC), a non-conventional approximate computing method that is well known for its simplicity, area efficiency and resilience to bit errors. SP arithmetic reduces the numerical errors compared to SC and also solves the serialization limitation of SC, since it is designed to have a O(1) gate delay. Previously, SP was limited to only addition and multiplication and did not have a way to perform subtraction. This paper introduces the basic SP subtraction idea, followed by a detailed study of several ways that the basic design can be improved to reduce the computational error. Our best SP design significantly improves the error compared to our basic SP subtraction idea (reducing it by 32.3%). We also study the trade-off between design complexity of the SP subtractor against output error. Also, our implementation of the SP subtractor exhibits an improved delay, power and area compared to fixed point realizations with the same size.