Symmetric Indefinite Linear Solver using OpenMP Task on Multicore Architectures

Recently, the Open Multi-Processing (OpenMP) standard has incorporated task-based programming, where a function call with input and output data is treated as a task. At run time, OpenMP’s superscalar scheduler tracks the data dependencies among the tasks and executes the tasks as their dependencies are resolved. On a shared-memory architecture with multiple cores, the independent tasks are executed on different cores in parallel, thereby enabling parallel execution of a seemingly sequential code. With the emergence of many-core architectures, this type of programming paradigm is gaining attention—not only because of its simplicity, but also because it breaks the artificial synchronization points of the program and improves its thread-level parallelization. In this paper, we use these new OpenMP features to develop a portable high-performance implementation of a dense symmetric indefinite linear solver. Obtaining high performance from this kind of solver is a challenge because the symmetric pivoting, which is required to maintain numerical stability, leads to data dependencies that prevent us from using some common performance-improving techniques. To fully utilize a large number of cores through tasking, while conforming to the OpenMP standard, we describe several techniques. Our performance results on current many-core architectures—including Intel’s Broadwell, Intel’s Knights Landing, IBM’s Power8, and Arm’s ARMv8—demonstrate the portable and superior performance of our implementation compared with the Linear Algebra PACKage (LAPACK). The resulting solver is now available as a part of the PLASMA software package.