An Optimized Twofold LUT architecture for fast function approximation

The efficient approximation of elementary and activation functions is crucial for the deployment of machine learning algorithms and deep learning on resource-constrained hardware like FPGAs. The twofold lookup table (t-LUT) architecture effectively reduces resource usage by exploiting redundancy in fixed-point activation functions. However, it lacks generalization to elementary and other function types. This paper enhances and extends the t-LUT concept to be an Optimized approach, enabling the efficient approximation of not only activation functions but also a wider range of elementary functions. The proposed architecture employs two lookup tables to store base values and successive differences, minimizing memory footprint while maintaining high precision. This study offers an in-depth evaluation of the architecture’s compressibility and validates its efficiency through experimental testing across multiple functions. The results show that the architecture achieves LUT compression of exponential and logarithmic functions by 39.2% and 32.7%, with the maximum absolute error 6.1×10 −5 and 4.87×10 −4 , respectively. In embedded machine learning applications, the Optimized t-LUT (Ot-LUT) architecture provides a flexible and effective way to implement logarithmic and exponential functions, among other functions. This allows complex algorithms to be deployed on devices with limited resources.