New non-uniform segmentation technique for software function evaluation

Embedded applications use more and more sophisticated computations. These computations can integrate composition of elementary functions and can easily be approximated by polynomials. Indeed, polynomial approximation methods allow to find a trade-off between accuracy and computation time. Software implementation of polynomial approximation in fixed-point processors is considered in this paper. To obtain a moderate approximation error, segmentation of the interval I on which the function is computed is necessary. This paper proposes a new method to compute the values of a function on I using non-uniform segmentation and polynomial approximation. Non-uniform segmentation allows one to minimize the number of segments created and is modeled by a tree-structure. The specifications of the segmentation set the balance between memory space requirement and computation time. Besides, compared to table-based methods or the CORDIC algorithm, our approach significantly reduces, the memory size and the function evaluation time respectively.