1. A CORDIC engine, comprising: an N-stage CORDIC processor configured for performing N micro-iterations and generating a 3-vector CORDIC output responsive to a 3-vector CORDIC input, the N-stage CORDIC processor comprising N CORDIC processors operably cascaded in series, each of the CORDIC processors comprising: a first variable shifter operably coupled to a first vector input and configured to generate a shifted first vector by an amount responsive to an iteration indicator from the counter; a second variable shifter operably coupled to a second vector input and configured to generate a shifted second vector by an amount responsive to the iteration indicator from the counter; a first adder/subtractor for arithmetically combining the first vector input and the shifted second vector to generate a first vector output; a second adder/subtractor for arithmetically combining the second vector input and the shifted first vector to generate a second vector output; and a third adder/subtractor for arithmetically combining a third vector input and a elementary angle input correlated to the iteration indicator to generate a third vector output; a counter configured for counting a number of M macro-iterations and indicating a start of the cycle iterations; and a multiplexer configured for selecting 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; wherein the 3-vector CORDIC output is configured to be complete after N*M clock cycles by generating the N micro-iterations for each of the M macro-iterations.