Harmonized Parabolic Synthesis: A High-Precision, Low-Latency FPGA Implementation of the Hyperbolic Tangent Function for Neural Networks

Activation functions such as Sigmoid and Tanh play a crucial role in introducing nonlinear characteristics to artificial neural networks. However, existing hardware implementations of these functions often struggle to simultaneously achieve high precision, low latency, and efficient resource utilization. This paper proposes a novel hardware-oriented function approximation method based on a harmonized parabolic synthesis algorithm. By decomposing the target function into the product of a first-order function and a piecewise parabolic function, the proposed approach transforms complex mathematical operations into hardware-friendly shift-add-multiply operations. Experimental results demonstrate an order-of-magnitude improvement in the synergistic performance metrics of latency and precision. Implemented on the Artix-7 AC701 evaluation board, the proposed approximation method achieves an average hardware error of only 10 -4 and a computational latency of merely 17.3 ns, which is at least 10% shorter than other methods, exhibiting significant advantages in reducing both latency and error overhead. The proposed architecture provides an effective solution for applications requiring high-precision nonlinear function implementations.