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Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision.

With discrete Intel GPUs entering the high-performance computing landscape, there is an urgent need for production-ready software stacks for these platforms. In this article, we report how we enable the Ginkgo math library to execute on Intel GPUs by developing a kernel backed based on the DPC++ programming environment. We discuss conceptual differences between the CUDA and DPC++ programming models and describe workflows for simplified code conversion. We evaluate the performance of basic and advanced sparse linear algebra routines available in Ginkgo's DPC++ backend in the hardware-specific performance bounds and compare against routines providing the same functionality that ship with Intel's oneMKL vendor library.

[EN] The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator-like a preconditioner-in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings., H. Anzt and T. Cojean were supported by the "Impuls und Vernetzungsfond of the Helmholtz Association" under grant VH-NG-1241. G. Flegar and E. S. Quintana-Orti were supported by project TIN2017-82972-R of the MINECO and FEDER and the H2020 EU FETHPC Project 732631 "OPRECOMP". This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. The authors want to acknowledge the access to the Piz Daint supercomputer at the Swiss National Supercomputing Centre (CSCS) granted under the project #d100 and the Summit supercomputer at the Oak Ridge National Lab (ORNL).

We contribute to the optimization of the sparse matrix-vector product on graphics processing units by introducing a variant of the coordinate sparse matrix layout that compresses the integer representation of the matrix indices. In addition, we employ a look-ahead table to avoid the storage of repeated numerical values in the sparse matrix, yielding a more compact data representation that is easier to maintain in the cache. Our evaluation on the two most recent generations of NVIDIA GPUs, the V100 and the A100 architectures, shows considerable performance improvements over the kernels for the sparse matrix-vector product in cuSPARSE (CUDA 11.0.167). This work was partially sponsored by the EU H2020 project 732631 OPRECOMP and project TIN2017-82972-R of the Spanish MINECO. Hartwig Anzt and Yuhsiang M. Tsai were supported by the “Impuls und Vernetzungsfond” of the Helmholtz Association under grant VH-NG-1241 and by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. The authors would like to thank the Steinbuch Centre for Computing (SCC) of the Karlsruhe Institute of Technology for providing access to an NVIDIA A100 GPU.

In this work, we present highly efficient mixed precision GPU-implementations of an Incomplete Sparse Approximate Inverse (ISAI) preconditioner for general non-symmetric matrices and a Factorized Sparse Approximate Inverse (FPSAI) preconditioner for symmetric positive definite matrices. While working with full double precision in all arithmetic operations, we demonstrate the benefit of decoupling the memory precision and storing the preconditioner in a more compact low precision floating point format to reduce the memory access volume and therefore preconditioner application time.

Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin.

We contribute to the optimization of the sparse matrix-vector product by introducing a variant of the coordinate sparse matrix format that balances the workload distribution and compresses both the indexing arrays and the numerical information. Our approach is multi-platform, in the sense that the realizations for (general-purpose) multicore processors as well as graphics accelerators (GPUs) are built upon common principles, but differ in the implementation details, which are adapted to avoid thread divergence in the GPU case or maximize compression element-wise (i.e., for each matrix entry) for multicore architectures. Our evaluation on the two last generations of NVIDIA GPUs as well as Intel and AMD processors demonstrate the benefits of the new kernels when compared with the optimized implementations of the sparse matrix-vector product in NVIDIA's cuSPARSE and Intel's MKL, respectively. J. I. Aliaga, E. S. Quintana-Ortí, and A. E. Tomás were supported by TIN2017-82972-R of the Spanish MINECO. H. Anzt and T. Grützmacher were supported by the “Impuls und Vernetzungsfond” of the Helmholtz Association under grant VH-NG-1241 and by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. The authors would like to thank the Steinbuch Centre for Computing (SCC) of the Karlsruhe Institute of Technology for providing access to an NVIDIA A100 GPU.