Tradeoff of FPGA design of floating-point transcendental functions

Abstract

Several scientific applications need a high precision computation of transcendental functions. This paper presents a hardware implementation of a parameterizable floating-point library for computing sine, cosine and arctangent functions using both CORDIC algorithm and Taylor series expansion for different bit-width representations. The results include the accuracy as a design criterion of the proposed hardware architectures; therefore, a tradeoff analysis between the cost in area and the number of iterations against the error associated is done in order to choose a suitable format for computing transcendental functions. The proposed architectures were validated using the Matlab results as a statistical estimator in order to compute the Mean Square Error (MSE). Synthesis and simulation results demonstrate the correctness and effectiveness of the implemented hardware transcendental functions.