Cordic Algorithm Implementation for Transcendental Function Computation

In this documentation, I would like to share my experience in implementing the CORDIC (Coordinate Rotation Digital Computer) algorithm for computing transcendental functions. I have developed a MATLAB program that effectively calculates functions like sine, cosine, and hyperbolic functions using the iterative CORDIC approach, and successfully validated it through comprehensive simulations. The implementation utilizes the algorithm's core principle of vector rotation through a series of micro-rotations, achieving high precision while avoiding complex multiplication operations. During the programming process, I encountered several challenges including convergence issues, precision optimization, and proper angle selection. Through thorough literature research and experimental validation, I resolved these problems by implementing proper scaling factors, optimizing iteration counts, and incorporating angle normalization techniques. The key MATLAB functions developed include cordic_rotation for the core iterative process, angle_lut for precomputed arctangent values, and precision_analysis for error evaluation. I will share detailed insights into problem-solving strategies and provide important considerations when applying the CORDIC algorithm, such as handling the trade-off between iteration cycles and computational accuracy, managing numerical precision in fixed-point implementations, and optimizing the algorithm for specific transcendental functions. This documentation aims to assist developers and researchers who need to implement efficient CORDIC-based solutions for transcendental function computations in digital signal processing and embedded systems applications.