A fast CORDIC algorithm based on a novel angle recoding scheme

This work proposes a new CORDIC algorithm, which considerably reduces rotation number. It is achieved by combining several design techniques. Particularly, a new angle recoding scheme for table lookup is developed to speed up the convergence rate of the rotation angle. The required lookup table is small. Other design techniques used include: the leading-one bit detection and the variable-scale-factor compensation algorithm. The number of the shift-and-add operations required in the compensation algorithm can be also further reduced by using the same residue recoding scheme. Simulations show that on average the new design needs only 3.5 iterations to generate results with 22-bit precision, which is much less than the existing designs (normally need 22 iterations). The new encoding scheme can be applied to other iterative convergence computation function such as the division operation.