PLAC: Piecewise Linear Approximation Computation for All Nonlinear Unary Functions

Abstract

This article presents a piecewise linear approximation computation (PLAC) method for all nonlinear unary functions, which is an enhanced universal and error-flattened piecewise linear (PWL) approximation approach. Compared with the previous methods, PLAC features two main parts, an optimized segmenter to seek the minimum number of segments under the predefined software maximum absolute error (MAE), raising the segmentation performance to the highest theoretical level for logarithm, and a novel quantizer to completely simulate the hardware behavior and determine the required bit width and ${\text {MAE}}_{c}$ (MAE in circuits) for hardware implementation. In addition, the hardware architecture is also improved by simplifying the indexing logic, leading to nonredundant hardware overhead. The ASIC implementation results reveal that the proposed PLAC can improve all metrics without any compromise. Compared with the state-of-the-art methods, when computing logarithmic function, PLAC reduces 2.80% area, 3.77% power consumption, and 1.83% ${\text {MAE}}_{c}$ with the same delay; when approximating hyperbolic tangent function, PLAC reduces 6.25% area, 4.31% power consumption, and 18.86% ${\text {MAE}}_{c}$ with the same delay; when evaluating sigmoid function, PLAC reduces 16.50% area, 4.78% power consumption with the same delay, and ${\text {MAE}}_{c}$ ; and when calculating softsign function, PLAC reduces 17.28% area, 11.34% power consumption, 12.50% delay, and 33.28% ${\text {MAE}}_{c}$ .