FPGA based floating-point library for CORDIC algorithms

Abstract

Computation of floating-point transcendental functions has a relevant importance in a wide variety of scientific applications, where the area cost, error and latency are important requirements to be attended. This paper describes a flexible FPGA implementation of a parameterizable floating-point library for computing sine, cosine, arctangent and exponential functions using the CORDIC algorithm. The novelty of the proposed architecture is that by sharing the same resources the CORDIC algorithm can be used in two operation modes, allowing it to compute the sine, cosine or arctangent functions. Additionally, in case of the exponential function, the architectures change automatically between the CORDIC or a Taylor approach, which helps to improve the precision characteristics of the circuit, specifically for small input values after the argument reduction. Synthesis of the circuits and an experimental analysis of the errors have demonstrated the correctness and effectiveness of the implemented cores and allow the designer to choose, for general-purpose applications, a suitable bit-width representation and number of iterations of the CORDIC algorithm.