VLSI implementation of rotations in pseudo-Euclidean spaces

Digital feedback is at the heart of implementations of many functions and can be used for the evaluation and application of rotations in definite and indefinite metrics. The CORDIC algorithms exploit this concept to perform rotations in two dimensions. These algorithms are analyzed as a first step before extending them to higher dimensions. A side result of this analysis is the simultaneous reduction of the number of steps and the enlargement of the domain of convergence of the algorithms. A few guidelines for their extension and a worked out three-dimensional example are then presented.