The ability to model, analyze, and predict execution time of computations is an important building block that supports numerous efforts, such as load balancing, benchmarking, job scheduling, developer-guided performance optimization, and the automation of performance tuning for high performance, parallel applications. In today’s increasingly heterogeneous computing environment, this task must be accomplished efficiently across multiple architectures, including massively parallel coprocessors like GPUs, which are increasingly prevalent in the world’s fastest supercomputers. To address this challenge, we present an approach for constructing customizable, cross-machine performance models for GPU kernels, including a mechanism to automatically and symbolically gather performance-relevant kernel operation counts, a tool for formulating mathematical models using these counts, and a customizable parameterized collection of benchmark kernels used to calibrate models to GPUs in a black-box fashion. With this approach, we empower the user to manage trade-offs between model accuracy, evaluation speed, and generalizability. A user can define their own model and customize the calibration process, making it as simple or complex as desired, and as application-targeted or general as desired. As application examples of our approach, we demonstrate both linear and nonlinear models; these examples are designed to predict execution times for multiple variants of a particular computation: two matrix-matrix multiplication variants, four discontinuous Galerkin differentiation operation variants, and two 2D five-point finite difference stencil variants. For each variant, we present accuracy results on GPUs from multiple vendors and hardware generations. We view this highly user-customizable approach as a response to a central question arising in GPU performance modeling: how can we model GPU performance in a cost-explanatory fashion while maintaining accuracy, evaluation speed, portability, and ease of use, an attribute we believe precludes approaches requiring manual collection of kernel or hardware statistics.
Register-based implementation of the sparse general matrix-matrix multiplication on GPUs
