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CORDIC is an algorithm that enables estimating the angle of a phasor (i.e. a complex number) from its real and imaginary parts. It operates by rotaing the phasor by a predfined sequence of angles (e.g. 180, 90, 45, 22.5 ...) and after each rotation checking if the phasor has crossed the 0 angle. Based on the the outcome of this test, the predefined angle is added to the estimate of the angle.
See http://www.free-ip.com/cordic/ for more details