Polynomial Approximation with Non-Uniform Segmentation for Bivariate Functions

Embedded applications use more and more sophisticated computations. These computations can integrate the composition of elementary functions which have to be approximated. In the context of scientific computation, mathematical libraries are available but are inefficient for real-time embedded applications. In this context, the efficient evaluation of a complex function requires to design a specific source code or HW block dedicated to this function and the considered input range. Different solutions have been proposed for univariate functions. These techniques are based on iterative methods, look-up tables, bi-/multi-partite table methods or polynomial approximation. Significantly fewer methods are available for multivariate functions. In this paper, we propose a polynomial approximation for software implementation of bivariate-functions. A smart nonuniform segmentation is proposed to better fit irregularities of the approximated function. Furthermore, for best performances, the degree of the bivariate approximating polynomial is dynamic which avoids data and time waste. The experiment results underline the ability of the proposed approach to explore the trade-off between the memory footprint and execution time of the function evaluation.