Table-based polynomials for fast hardware function evaluation

Many general table-based methods for the evaluation in hardware of elementary functions have been published. The bipartite and multipartite methods implement a first-order approximation of the function using only table lookups and additions. Recently, a single multiplier second order method of similar inspiration has also been published. This paper extends such methods to approximations of arbitrary order, using adders, small multipliers, and very small ad hoc powering units. We obtain implementations that are both smaller and faster than previously published approaches. This paper also deals with the FPGA implementation of such methods. Previous work have consistently shown that increasing the approximation degree lead to not only smaller but also faster designs, as the reduction of the table size meant a reduction of its lookup time, which compensated for the addition and multiplication time. The experiments in this paper suggest that this still holds when going from order 2 to order 3, but no longer when using higher order approximations, where a tradeoff appears.