Abstract: A CORDIC unit for the iterative approximation of a vector rotation through a rotary angle ? by a number of elementary rotations through elementary angles ?i, including elementary rotation stages for respectively effecting an elementary rotation through an elementary angle ?i as an iteration step in the iterative approximation. After such an elementary rotation there remains a residual angle through which rotation is still to be effected. The elementary rotation stages of the CORDIC unit are adapted for rotation through elementary angles a( given by powers of two with a negative integral exponent. The CORDIC unit can also include a triggering device for triggering the elementary rotations, a triggering device which is adapted prior to each iteration step to compare the residual angle to at least one of the elementary angles and to omit those elementary rotation stages whose elementary angles are greater than the residual angle.