Computing Polynomials with Positive Coefficients using Stochastic Logic by Double-NAND Expansion
Sayed Ahmad Salehi, Yin Liu, Marc D. Riedel, Keshab K. Parhi · 2017
This paper proposes a novel method, referred to as \textit{double-NAND expansion}, to implement polynomials with all positive coefficients using unipolar stochastic logic. %The inputs and outputs of these circuits lie between 0 and 1, and are encoded using unary bit streams. Prior work has addressed implementation of polynomials with alternately positive and negative coefficients and non-increasing magnitudes, using stochastic logic based on Horner's rule. However, Horner's expansion is not applicable to implementation of polynomials with all positive coefficients. The proposed double-NAND expansion leads to implementations of polynomials using no more than 2n NAND gates where n represents the degree of the polynomial. %While the Horner's rule leads to cascaded AND-NAND gates, the proposed expansion leads to cascaded double-NAND gates.The proposed implementations are compared with those based on multiplexers, Bernstein polynomial method, finite state machine method and factorization. The paper also considers implementations of several functions expressed as polynomials using truncated Mclaurin series based on the proposed approach. The experimental results show that the proposed method outperforms the prior methods in terms of accuracy, hardware complexity, and critical path.