On Linear Skewing Schemes and d-Ordered Vectors

Linear skewing schemes were introduced by Kuck et al. in the nineteen sixties, to provide a simple class of storage mappings for N × N matrices for use in vector processors with a large number of memory banks. Conditions on linear skewing schemes that guarantee conflict-free access to rows, columns, and/or (anti-) diagonals are usually presented in terms of conditions on so-called d-ordered vectors. We shall argue that these formulations are mathematically imprecise, and revise and extend the existing theory. Several claims are proved to bound the minimum number of memory banks needed for successful linear skewing by, e.g., the smallest prime number ≥ N.