CORDIC Implementation

What is CORDIC Algorithm ? 

The CORDIC (COordinate Rotation DIgital Computer) algorithm is an efficient, iterative method for calculating trigonometric, hyperbolic, logarithmic, and square root functions using only additions, subtractions, and bit shifts. It is highly valued in hardware design (FPGAs, ASICs) and microcontrollers because it eliminates the need for expensive hardware multipliers.

How CORDIC Algorithm Works

• Concept: CORDIC computes functions by rotating a 2D vector by smaller and smaller, predetermined angles (pseudo-rotations).
• Operations: Instead of complex multiplication, it uses binary shifts (to divide by powers of 2) and adds/subtracts to rotate the vector, making it very fast.
• Iterative Process: Through several iterations, the algorithm converges to the desired output, with accuracy improving as more iterations are performed.
• Modes:Rotation Mode: Given an input angle, it computes the corresponding sine and cosine components.
• Vectoring Mode: Given the
• coordinates, it rotates the vector to the
• -axis to calculate its magnitude and angle.

Key Features and Applications

• Hardware Efficiency: It is ideal for digital signal processing (DSP), digital communication systems, and simple calculators.
• Versatility: Beyond basic trigonometry, it is used for Cartesian-to-polar conversions, square roots, and complex multiplications.
• Examples: It is implemented in ARM-based processors like the STM32G4, Intel 8087, and Hewlett Packard’s HP-35 calculator.