CORDIC algorithms in four dimensions

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Abstract
CORDIC algorithms offer an attractive alternative to multiply-and-add based algorithms for the implementation of two-dimensional rotations preserving either norm: (x2 + 2) or (x2 _ y2)/2 Indeed these norms whose computation is a significant part of the evaluation of the two-dimensional rotations are computed much more easily by the CORDIC algorithms. However the part played by norm computations in the evaluation of rotations becomes quickly small as the dimension of the space increases. Thus in spaces of dimension 5 or more there is no practical alternative to multiply-and-add based algorithms. In the intermediate region dimensions 3 and 4 extensions of the CORDIC algorithms are an interesting option. The four-dimensional extensions are particularly elegant and are the main object of this paper.
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