Nonlinear array layouts for hierarchical memory systems
ICS '99 Proceedings of the 13th international conference on Supercomputing
Recursive array layouts and fast parallel matrix multiplication
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Language support for Morton-order matrices
PPoPP '01 Proceedings of the eighth ACM SIGPLAN symposium on Principles and practices of parallel programming
New Generalized Data Structures for Matrices Lead to a Variety of High Performance Algorithms
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
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Hierarchically-blocked non-linear storage layouts, such as the Morton ordering, have been shown to be a potentially attractive compromise between row-major and column-major for two-dimensional arrays. When combined with appropriate optimizations, Morton layout offers some spatial locality whether traversed row- or column-wise. However, for linear algebra routines with larger problem sizes, the layout shows diminishing returns. It is our hypothesis that associativity conflicts between Morton blocks cause this behavior and we show that carefully arranging the Morton blocks can minimize this effect. We explore one such arrangement and report our preliminary results.