Thanks for replying.
I have tested the m-file in the thread that I mentioned previously, it works but I don't know the proof. And the proof is actually a simple geometry question:
In the attached figure which illustrates the CORDIC algorithm in the linear mode, YR must be equal to y_{R} = y_{in} + x_{in} * z_{in} but when I try to prove it I find a condition (tan(\thet)* y{in} / x_{in} << 1) which needs to be satisfied to have the above relationship.
By the way, since today's most processors have multipliers, how do you compare a CORDIC multiplier with a dedicated multiplier. I think the hardware complexity is almost the same, how much slower is CORDIC in comparison with a usual multiplier? What are the main advantages of a CORDIC multiplier?