MATLAB Implementation of the Cordic Algorithm with Code Description

The Cordic algorithm is an iterative method for efficiently computing mathematical operations such as trigonometric and hyperbolic functions, particularly suited for hardware implementation. This algorithm gradually approximates target values through simple shift and add/subtract operations, avoiding complex multiplication calculations.

When implementing the basic Cordic algorithm in MATLAB, the core process can be divided into three steps: initializing the rotation angle lookup table, iterative approximation calculation, and result scaling. The algorithm precomputes and stores a set of decreasing rotation angles (arctan(2^-i)), which are typically saved in external files for program access. During each iteration, the rotation direction is determined based on the current target angle, and these precomputed angles are accumulated/subtracted to approach the final result.

The unimproved version of Cordic has two key characteristics: when using circular rotation mode, the result requires correction by multiplying with the scaling factor K, and all iteration rounds must be executed fixedly without early termination. Although this implementation is less efficient than improved versions, it clearly demonstrates the algorithm's core concept - replacing direct function calculations with vector superposition through coordinate rotation.

This implementation is particularly helpful for understanding mathematical operation acceleration principles in hardware platforms like FPGAs, as Cordic utilizes hardware-friendly bit operations and pipeline techniques to replace expensive floating-point arithmetic units.