Efficient floating-point polynomial evaluation on FPGAS

Many applications require the evaluation of polynomials having floating-point coefficients - one example is rational polynomial approximation, often used to implement some special functions. The most resource efficient polynomial evaluation scheme (Horner) is costly to implement on FPGAs due to the high cost associated with floating-point arithmetic. Floating-point adders are particularly costly due to their alignment stages requiring large barrel shifters. In this work we present a novel FPGA-specific technique for evaluating polynomials using the Horner scheme. Our technique removes the majority of alignment shifters present in floating-point adders by building a fused evaluation operator. It pushes the possible alignment values of the monomials into tables containing multiple shifted coefficient instances which are selected using the exponent of the input argument. Compared to operator assembly this work reduces circuit latency by 30-50% and logic consumption by 40-60%. Our work can be easily extended to other polynomial evaluation methods.