Redundant and on-line CORDIC: application to matrix triangularization and SVD

Abstract

Several modifications to the CORDIC method of computing angles and performing rotations are presented: (1) the use of redundant (carry-free) addition instead of a conventional (carry-propagate) one; (2) a representation of angles in a decomposed form to reduce area and communication bandwidth; (3) the use of on-line addition (left-to-right, digit-serial addition) to replace shifters by delays; and (4) the use of online multiplication, square root, and division to compute scaling factors and perform the scaling operations. The modifications improve the speed and the area of CORDIC implementations. The proposed scheme uses efficiently floating-point representations. The application of the modified CORDIC method to matrix triangularization by Givens' rotations and to the computation of the singular value decomposition (SVD) are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>