Performance Engineering of Numerical Software on Multi- and Manycore Processors

The goal of performance engineering is to make the resource usage a controllable property of software. This thesis contributes to this field from the perspective of a computer scientist who is involved in scientific computing. In the beginning, it provides the necessary basis: This is first an understanding of the development process of numerical software and of the emergence of performance at the hardware/software interface. But further, methods to model, predict, analyze, measure, and assess software performance and a tool set of optimization techniques to improve it accordingly are required. Then adaption and application of established and novel approaches are described at numerical algorithms and applications. The first study is a port of a fluid simulation in complex geometries using a lattice Boltzmann method to the Cell Broadband Engine Architecture, in order to profit from its high arithmetic and memory throughput of its unique heterogeneous design. Although the previous data structures provided a good compromise between flexibility and regularity for cache-based architectures, a thorough adaption to the peculiarities of the accelerator cores of this architecture and subsequent low-level optimization are required. The Cell variant of the simulation can nearly saturate the memory interface when only about half of the accelerator cores are employed. Using single precision on an IBM QS 20 Cell blade, the program is able to update 200 million fluid lattice cells per second for a simple channel flow and 90 million when simulating the flow through a real intracranial vessel geometry with an aneurysm. The batch variant of the orthogonal matching pursuit algorithm allows to efficiently derive sparse representations for a large number of signals. It is based on common operations in linear algebra, i.e. on dense and sparse vectors and matrices. Eventually, comparable performance is achieved on an dual-socket system with a total of twelve cores (Intel Westmere microarchitecture), an IBM QS 20 Cell blade, and on an NVIDIA GeForce GTX 480 graphics card. Each architecture, however, needs a different approach to achieve this. On the general purpose processor, an implementation in C99 that has been primarily optimized on the algorithmic level is accelerated by addition of compiler hints and tuning of the compilation process. Preliminary tests show that this approach results in disappointing performance on the Cell Broadband Engine Architecture. Therefore a complete re-implementation that employs a sophisticated memory layout to enable platform-specific low-level optimizations is developed. The graphics card demands for reorganization of the algorithm to enable massive parallelism and a modified data layout to enable data access patterns that fit the architecture. Stencil computations on regular grids are often memory bound. They can then only be accelerated considerably by use of temporal blocking techniques that fuse multiple of such operations in order to reduce the associated memory transfer. As temporal blocking is generally tedious to implement, a novel generic approach is proposed. It enables temporal blocking on cache-based architectures as well as on the Cell Broadband Engine Architecture whose accelerator cores operate only on scratchpad memory, it can be strongly supported by a cross-platform framework, and it allows for good prediction of resulting main memory transfer. Implementations of a correction scheme multigrid method to solve Poisson’s equation as well as a Full Approximation Scheme multigrid method to solve a diffusive partial differential equation with complex numbers are described, analyzed, and measured on a Playstation 3 and on a common dual-socket workstation (Intel Harpertown microarchitecture). For the Poisson multigrid method, predicted and measured amount of memory transfer agree well on both test platforms, and its components are at least 1.5 and up three times as fast as optimistic estimates for alternative implementations that do not block temporally. For the complex diffusion multigrid method, prediction of data transfer agrees well on Playstation 3 and is rather close on the Xeon system. The kernels, however, could not be accelerated sufficiently, so that at least highly optimized alternatives could be competitive on the latter platform and that there is no benefit on the Playstation 3 in terms of run time. Design and implementation of a software program which is able to simulate heat conduction within rolls in hot rolling mills in real-time with the aid of graphics cards concludes the list of examples. As this application requires outstanding run time performance, a holistic co-design approach is taken which matches model, numerical method, implementation, and target platform. This study does therefore not only derive and verify a fast approach to numerically compute the heat equation in cylindrical geometries with rapidly changing boundary conditions, but also demonstrates the exertion and potential of performance engineering principles at its best.