Some results on Taylor-series function approximation on FPGA

This paper presents results from the design of a parameterised function approximation unit on FPGA. The Taylor-series expansion is used to approximate a function f(x) of 8 to 26-bits over a given domain [a, b]. A search of the 1^st, 2^nd and 3^rd order Taylor expansions is performed for each operand length to find the most area efficient implementation in terms of LUT usage of a representative FPGA technology. Results show that trading lookup-logic and arithmetic-logic reduces the exponential logic requirement that occurs if a predominantly ROM based approximation is used.