Efficient Table-Based Polynomial on FPGA

Field Programmable Gate Arrays (FPGAs) are gaining popularity in the context of scientific computing due to the recent advances of High-Level Synthesis (HLS) toolchains for customised hardware implementations combined with the increase in computing capabilities of modern FPGAs. As a result, developers are able to implement more complex scientific workloads which often require the evaluation of univariate numerical functions. In this study, we propose a methodology for table-based polynomial interpolation aiming at producing area-efficient implementations of such functions on FPGAs achieving the same accuracy and at similar performance as direct implementations. We also provide a rigorous error analysis to guarantee the correctness of the results. Our methodology covers the forecast of resource utilisation of the polynomial interpolator and, based on the characteristics of the function, guides the developer to the most area-efficient FPGA implementation. Our experiments show that in the case of a radiation spectrum of a Black Body application based on evaluating Planck's Law, it is possible to reduce resource utilisation by up to 90% when compared to direct implementations not using table-based methods. Moreover, when only the kernels are considered, our method uses up to two orders of magnitude fewer resources with no performance penalties. Based on previous more theoretical works, our study investigates practical applications of table-based methods in the context of high performance and scientific computing where it is used to implement common but more complex functions than the elementary functions widely studied in the related literature.