Module Hardcaml_circuits.Cordic

Coordinate rotation digital computer.

CORDIC is an iterative shift-add algorithm for computing trig and hyperbolic functions like sin, cosh, atan etc.

Generally it requires 3 adders, 2 barrel shifters and a fairly small lookup table.

Gain

The x and y outputs from the CORDIC are (usually) scaled by the CORDIC gain. The exact value of the gain depends on the number of iterations performed, but tends towards about 1.647.

For some functions the gain can be adjusted for by altering input constants. Where it cannot, and it's a problem, it should be removed with a constant multiplier.

Hyperbolic mode

In hyperbolic mode the standard iteration scheme needs to be adjusted. Generally the iterations run from 0,1,...,(iters-1). In hyperbolic mode the iterations are 1,2,..,4,4,...13,13,.... That is they start at 1 and iterations 3k+1 (starting with k=4, then 13, 40, 121 etc) are repeated.

The hardware designs require a fixed number of iterations regardless of the mode. Therefore the number of iterations specified is exactly the number run regardless of mode (indices are modified internally in hyperbolic mode). Some care might need to be taken to not stop processing in hyperbolic mode on one of the double iterations to ensure convergence.