Elementary Function Implementation with Optimized Sub Range Polynomial Evaluation

Abstract

Efficient elementary function implementations require primitives optimized for modern FPGAs. Fixed-point function generators are one such type of primitives. When built around piecewise polynomial approximations they make use of memory blocks and embedded multipliers, mapping well to contemporary FPGAs. Another type of primitive which can exploit the power series expansions of some elementary functions is floating-point polynomial evaluation. The high costs traditionally associated with floating-point arithmetic made this primitive unattractive for elementary function implementation on FPGAs. In this work we present a novel and efficient way of implementing floating-point polynomial evaluators on a restricted input range. We show on the atan(x) function in double precision that this very different technique reduces memory block count by up to 50% while only slightly increasing DSP count compared to the best implementation built around polynomial approximation fixed-point primitives.