Very High Accuracy Hyperbolic Tangent Function Implementation in FPGAs

Abstract

The paper presents in detail a relatively simple implementation method of the hyperbolic tangent function, particularly targeted for FPGAs. The research goal of the proposed method was to examine the usage of the approximation of ordinary or Chebyshev polynomials for the implementation of the function. Several miscellaneous implementation versions have been considered. They differ in the polynomial degree, number of intervals for which the domain of the function is divided, etc. Both floatingpoint and fixed-point implementations have been presented. An impact on the FPGA resources utilization and calculations time for the implementation versions has also been briefly analyzed. Special attention has been paid to the accuracy of the calculations of the function. It turned out that applying the proposed method, a very high calculations accuracy can be achieved, while simultaneously maintaining reasonable resources utilization and short calculations time. The proposed method can be an effective alternative to other encountered implementation methods such as CORDIC. Additionally, the presented hardware architecture is more versatile and can be easily adapted for the implementation of other mathematical functions.

A Tanh Control Method for the Third Mirror’s Z Axis of Large Optical Telescope

“…The hyperbolic function is a very common function that is widely studied and used in neural networks, filters [18], tracking differentiators [19], etc. Zhang proposed a fuzzy hyperbolic model (FHM) based on hyperbolic tangent [20]- [24], and the analysis showed that the control algorithm has very strong nonlinearity coping ability.…”