The CCSD(T) coupled-cluster model with perturbative triples is considered a gold standard for computational modeling of the correlated behavior of electrons in molecular systems. A fundamental constraint is the relatively small global-memory capacity in GPUs compared to the main-memory capacity on host nodes, necessitating relatively smaller tile sizes for high-dimensional tensor contractions in NWChem's GPU-accelerated implementation of the CCSD(T) method. A coordinated redesign is described to address this limitation and associated data movement overheads, including a novel fused GPU kernel for a set of tensor contractions, along with inter-node communication optimization and data caching. The new implementation of GPU-accelerated CCSD(T) improves overall performance by 3.4×. Finally, we discuss the trade-offs in using this fused algorithm on current and future supercomputing platforms.

Tensor contractions are higher dimensional generalizations of matrix-matrix multiplication. They form the compute-intensive core of many applications in computational science and data science. In this paper, we describe a high-performance GPU code generator for arbitrary tensor contractions. It exploits domain-specific properties about data reuse in tensor contractions to devise an effective code generation schema, coupled with an effective model-driven search, to determine parameters for mapping of computation to threads and staging of data through the GPU memory hierarchy. Experimental evaluation using a set of tensor contraction benchmarks demonstrates performance improvement and/or significantly reduced code generation time over other state-of-the-art tensor contraction libraries and code generators.

Tensor contractions are higher dimensional analogs of matrix multiplications, used in many computational contexts such as high order models in quantum chemistry, deep learning, finite element methods etc. In contrast to the wide availability of high-performance libraries for matrix multiplication on GPUs, the same is not true for tensor contractions. In this paper, we address the optimization of a set of symmetrized tensor contractions that form the computational bottleneck in the CCSD(T) coupled-cluster method in computational chemistry suites like NWChem. Some of the challenges in optimizing tensor contractions that arise in practice from the variety of dimensionalities and shapes for tensors include effective mapping of the high-dimensional iteration space to threads, choice of data buffering in shared-memory and registers, and tile sizes for multi-level tiling. Furthermore, in the case of symmetrized tensor contractions in CCSD(T), it is also a challenge to fuse contractions to reduce data movement cost by exploiting reuse of intermediate tensors. In this paper, we develop an efficient GPU implementation of the tensor contractions in CCSD(T) using shared-memory buffering, register tiling, loop fusion and register transpose. Experimental results demonstrate significant improvement over the current state-of-the-art.

This paper presents a Tensor Transposition Library for GPUs (TTLG). A distinguishing feature of TTLG is that it also includes a performance prediction model, which can be used by higher level optimizers that use tensor transposition. For example, tensor contractions are often implemented by using the TTGT (Transpose-Transpose-GEMM-Transpose) approach - transpose input tensors to a suitable layout and then use high-performance matrix multiplication followed by transposition of the result. The performance model is also used internally by TTLG for choosing among alternative kernels and/or slicing/blocking parameters for the transposition. TTLG is compared with current state-of-the-art alternatives for GPUs. Comparable or better transposition times for the "repeated-use" scenario and considerably better "single-use" performance are observed.

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also due to the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact on accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

Graph coloring-in a generic sense-is used to identify subsets of independent tasks in parallel scientific computing applications. Traditional coloring heuristics aim to reduce the number of colors used as that number also corresponds to the number of parallel steps in the application. However, if the color classes produced have a skew in their sizes, utilization of hardware resources becomes inefficient, especially for the smaller color classes. Equitable coloring is a theoretical formulation of coloring that guarantees a perfect balance among color classes, and its practical relaxation is referred to here as balanced coloring. In this paper, we consider balanced coloring models in the context of parallel computing. The goal is to achieve a balanced coloring of an input graph without increasing the number of colors that an algorithm oblivious to balance would have used. We propose and study multiple heuristics that aim to achieve such a balanced coloring for two variants of coloring problem, distance-1 coloring (the standard coloring problem) and partial distance-2 coloring (defined on a bipartite graph). We present parallelization approaches for multi-core and manycore architectures and cross-evaluate their effectiveness with respect to the quality of balance achieved and performance. Furthermore, we study the impact of the proposed balanced coloring heuristics on a concrete application-viz. parallel community detection, which is an example of an irregular application. In addition, we propose several extensions to our basic balancing schemes and evaluate their balancing efficacy and performance characteristics. The thorough treatment of balanced coloring presented in this paper from algorithms to application is expected to serve as a valuable resource to parallel application developers who seek to improve parallel performance of their applications using coloring.

Preparing codes for next generation supercomputer systems is anticipated to require significant changes to the optimization strategies employed in established HPC applications. In this paper, we present our experience in applying term rewriting transformations for the optimization of such applications. We have designed application-specific term rewriting transformations to improve the scalability, enhance locality and reduce the communication overhead of the Self-Consistent Field computational chemistry benchmark. We present the rationale for the use of term rewriting in this manner, the design of our transformations, and the much enhanced performance of the resulting code.