Michael E. Wolf and Monica S. Lam. A data locality optimising algorithm. In Proceedings of the Conference on Programming Language Design and Implementation, pages 30-44, Toronto, Canada, June 1991. ACM Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....CHAPTER 2. PROGRAM OPTIMISATION 36 Unimodular Transformations A rst really abstract attempt for a framework came from Banerjee [13] It uses unimodular matrices to map any point from the iteration space onto a new point in a di erent iteration space. More work on this was done by Wolf and Lam [87, 86]. But its applicability is restricted to perfectly nested loops and it can only represent a subset of loop transformations, namely interchange, skewing and reversal. Conversely, any unimodular matrix can be constructed using a combination of these three transformations. Given an iteration p, ....

Michael E. Wolf and Monica S. Lam. A data locality optimising algorithm. In Proceedings of the Conference on Programming Language Design and Implementation, pages 30-44, Toronto, Canada, June 1991. ACM Press.

.... use template metaprogramming to perform register blocking in linear algebra kernels Complete unrolling for operations on small arrays [55] matrix constructor interface [16, 18] compile time prime number calculations [54] Tuned MTL algorithms for high performance Tiling and blocking techniques [10, 11, 12, 14, 32, 34, 35, 39, 60, 61], automatically tuned libraries [7, 59] Proved that iterators can be used in high performance arenas Optimizing compilers [33, 41] lightweight object optimization, inlining Created the Mayfly pattern Andrew Lumsdaine thought of the name Designed the ITL interface ITL implementation by Andrew ....

....generation and optimization to be built into a library, which is then called from an application program. 3.2. 1 The Optimizing Compiler Approach A large amount of research has been done in the compiler community with regards to loop optimizations, especially for dense linear algebra operations [34, 10, 61, 35, 60, 12, 11, 39, 14, 32]. The results of this research has proved extremely valuable in selecting the performance optimization used in MTL. Many of the performance optimizations used in MTL would not be necessary if commercial compilers implemented more transformations in a consistent and reliable fashion. The difficulty ....

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M. E. Wolf and M. S. Lam. A data locality optimising algorithm. In B. Hailpern, editor, Proceedings of the ACM SIGPLAN ' 91 Conference on Programming Language Design and Implementation, pages 30--44, Toronto, ON, Canada, June 1991. ACM Press.

....different optimization techniques in the various programs can readily be seen in Fig. 4 (left) and manifest themselves quite strongly as a function of matrix size. In the region from N = 10 to N = 256, performance is dominated by register usage and pipeline performance. Unroll and jam techniques [5, 21] are used to attain high levels of performance in this region. In the region from 256 to approximately 1024, performance is dominated by data locality. Loop blocking for cache usage is used to attain high levels of performance here. Finally, for matrix sizes larger than approximately N = 1024, ....

Michael E. Wolf and Monica S. Lam. A data locality optimising algorithm. In Brent Hailpern, editor, Proceedings of the ACM SIGPLAN '91 Conference on Programming Language Design and Implementation, pages 30--44, Toronto, ON, Canada, June 1991. ACM Press.

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