How to use the CORDIC algorithm in your FPGA design

Adam P. Taylor, EADS Astrium
EETimes (5/12/2012 11:14 AM EDT)

Most engineers tasked with implementing a mathematical function such as sine, cosine or square root within an FPGA may initially think of doing so by means of a lookup table, possibly combined with linear interpolation or a power series if multipliers are available. However, in cases like this the CORDIC algorithm is one of the most important tools in your arsenal, albeit one that few engineers are aware of.

Invented by Jack Volder while designing a new navigation computer at Convair for the B-58A Hustler program in 1959, CORDIC – it stands for Coordinate Rotation Digital Computer – is a simple algorithm designed to calculate mathematical, trigonometric and hyperbolic mathematical functions.

The real beauty of this algorithm is that you can implement it with a very small FPGA footprint. CORDIC requires only a small lookup table, along with logic to perform shifts and additions. Importantly, the algorithm requires no dedicated multipliers or dividers.

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