A Flexible Dynamic Master–User Look-Up Table Approach for Evaluation of Trigonometric Values

Abstract

Systems which are computationally complex often include the calculation of sine/cosine values, which frequently uses its Taylor series expansion. For high accuracy the Taylor series expansion becomes computationally intensive. Therefore, the calculation of sine (or cosine) values may become the bottleneck of the system. In this paper, a novel concept is proposed that employs dynamic master–user look-up table (DMU-LUT) configuration for the calculation of trigonometric values with user defined precision. Initially, samples on a unit circle are evaluated at regular interval of $\Phi$, where $\Phi$ denotes the sampling angle. This results in $2\pi \Phi$ total number of samples for creation of master table. The values of sine/cosine are calculated at each sample and then stored in the master table. The application-specific user table is obtained by three proposed sampling scenarios (constant distance, section, and probabilistic sampling) of master table. The main advantage of this scheme is to provide flexibility to achieve the desired accuracy according to system requirements. For FPGA implementations of user table, $7{\times}$ delay improvement and 48% reduced components utilization has been observed while achieving better accuracy over high speed combinational CORDIC algorithm.