Algorithmic redistribution methods for block-cyclic decompositions

This article presents various data redistribution methods for block-partitioned linear algebra algorithms operating on dense matrices that are distributed in a block-cyclic fashion. Because the algorithmic partitioning unit and the distribution blocking factor are most often chosen to be equal, severe alignment restrictions are induced on the operands, and optimal values with respect to performance are architecture dependent. The techniques presented in this paper redistribute data `on the fly,' so that the user's data distribution blocking factor becomes independent from the architecture dependent algorithmic partitioning. These techniques are applied to the matrix-matrix multiplication operation. A performance analysis along with experimental results shows that alignment restrictions can then be removed and that high performance can be maintained across platforms independently from the user's data distribution blocking factor.