A CORDIC engine includes an N-stage CORDIC processor for performing N micro-iterations of a CORDIC algorithm and generating a 3-vector CORDIC output responsive to a 3-vector CORDIC input. A counter counts a number of M macro-iterations for the CORDIC algorithm and indicates a start of the cycle iterations. A multiplexer selects an input to the N-stage CORDIC processor as the 3-vector CORDIC input at the start of the cycle iterations or the 3-vector CORDIC output at other times. The CORDIC algorithm is complete after N*M clock cycles by generating N micro-iterations for each of the M macro-iterations. In some embodiments, the CORDIC engine is coupled to programmable logic blocks as part of a programmable logic array.