Characterizing the behavior of sparse algorithms on caches
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Adaptive use of iterative methods in interior point methods for linear programming
Adaptive use of iterative methods in interior point methods for linear programming
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
Applied numerical linear algebra
Applied numerical linear algebra
A relational approach to the automatic generation of sequential sparse matrix codes
A relational approach to the automatic generation of sequential sparse matrix codes
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
Automatic Nonzero Structure Analysis
SIAM Journal on Computing
A scalable cross-platform infrastructure for application performance tuning using hardware counters
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Automatically tuned linear algebra software
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Optimizing Sparse Matrix Computations for Register Reuse in SPARSITY
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Performance optimizations and bounds for sparse matrix-vector multiply
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Optimization of sparse matrix-vector multiplication on emerging multicore platforms
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Parallel memory prediction for fused linear algebra kernels
ACM SIGMETRICS Performance Evaluation Review - Special issue on the 1st international workshop on performance modeling, benchmarking and simulation of high performance computing systems (PMBS 10)
Performance tuning of matrix triple products based on matrix structure
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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This paper presents uniprocessor performance optimizations, automatic tuning techniques, and an experimental analysis of the sparse matrix operation, y = AT Ax, where A is a sparse matrix and x, y are dense vectors. We describe an implementation of this computational kernel which brings A through the memory hierarchy only once, and which can be combined naturally with the register blocking optimization previously proposed in the Sparsity tuning system for sparse matrix-vector multiply. We evaluate these optimizations on a benchmark set of 44 matrices and 4 platforms, showing speedups of up to 4.2×. We also develop platform-specific upper-bounds on the performance of these implementations. We analyze how closely we can approach these bounds, and show when low-level tuning techniques (e.g., better instruction scheduling) are likely to yield a significant pay-off. Finally, we propose a hybrid off-line/run-time heuristic which in practice automatically selects nearoptimal values of the key tuning parameters, the register block sizes.