On energy efficiency and performance of polynomial and LUT-based approximation of elementary functions in floating-point systems
Andrey A. Chusov, Anna A. Shklyar, Yulia I. Efimova · Vestnik Tomskogo gosudarstvennogo universiteta Upravlenie vychislitel naya tekhnika i informatika · 2024
The paper presents results of theoretical and experimental analysis of common methods used for polynomial and table-based numerical approximation of transcendental elementary functions calculated in a finite precision with guarantees on maximal absolute errors, and, particularly, with correct rounding in a given rational or floatingpoint system. The methods of approximation of real-valued functions include Taylor-based polynomial approximation, also one based on the CORDIC “shift-and-add” LUT-based approximation as well as iterative evaluation of digits of a logarithm. The methods are analyzed with the purpose to achieve their energy efficiency and speed given the constraint on maximal absolute errors which is that the result must be off by no more than a half of a unit in the last place of mantissa, with rounding to nearest even in the case of a floating-point system. Experimentally, LUT-based approximation outperforms polynomial approximation by a large margin, and asymptotically, the former consumes resources linearly with the required accuracy while the latter is polynomial and non-linear.