Research on Optimal Performance of Sparse Matrix-Vector Multiplication and Convoulution Using the Probability-Process-Ram Model

Performance models provide insightful perspectives to allow us to predict performance and propose optimization guidance. Although there has been much research, pinpointing bottlenecks of various memory access patterns and reaching high performance of both regular and irregular programs on various hardware configurations are still not trivial. In this work, we propose a novel model called probability-process-ram (PPR) to quantify the amount of compute and data transfer time on general-purpose multicore processors. The PPR model predicts the number of instruction for single-core and probability of memory access between each memory hierarchy through a newly designed cache simulator. By using the automatically extracted best optimization method and expectation, we use PPR model for analyzing and optimizing sparse matrix-vector multiplication and 1D convolution as case study for typical irregular and regular computational kernels. Then we obtain best block sizes for sparse matrices with various sparsity structures, as well as optimal optimization guidance for 1D convolution with different instruction sets support and data sizes. Comparison with Roofline model and ECM model, the proposed PPR model greatly improves prediction accuracy by the newly designed cache simulator and achieves comprehensive feedback ability.