Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions are transformations. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer

Barrier elision for production parallel programs

Large scientific code bases are often composed of several layers of runtime libraries, implemented in multiple programming languages. In such situation, programmers often choose conservative synchronization patterns leading to suboptimal performance. In this paper, we present context-sensitive dynamic optimizations that elide barriers redundant during the program execution. In our technique, we perform data race detection alongside the program to identify redundant barriers in their calling contexts; after an initial learning, we start eliding all future instances of barriers occurring in the same calling context. We present an automatic on-the-fly optimization and a multi-pass guided optimization. We apply our techniques to NWChem - a 6 million line computational chemistry code written in C/C++/Fortran that uses several runtime libraries such as Global Arrays, ComEx, DMAPP, and MPI. Our technique elides a surprisingly high fraction of barriers (as many as 63%) in production runs. This redundancy elimination translates to application speedups as high as 14% on 2048 cores. Our techniques also provided valuable insight about the application behavior, later used by NWChem developers. Overall, we demonstrate the value of holistic context-sensitive analyses that consider the domain science in conjunction with the associated runtime software stack

Dataflow Programming Paradigms for Computational Chemistry Methods

The transition to multicore and heterogeneous architectures has shaped the High Performance Computing (HPC) landscape over the past decades. With the increase in scale, complexity, and heterogeneity of modern HPC platforms, one of the grim challenges for traditional programming models is to sustain the expected performance at scale. By contrast, dataflow programming models have been growing in popularity as a means to deliver a good balance between performance and portability in the post-petascale era. This work introduces dataflow programming models for computational chemistry methods, and compares different dataflow executions in terms of programmability, resource utilization, and scalability. This effort is driven by computational chemistry applications, considering that they comprise one of the driving forces of HPC. In particular, many-body methods, such as Coupled Cluster methods (CC), which are the gold standard to compute energies in quantum chemistry, are of particular interest for the applied chemistry community. On that account, the latest development for CC methods is used as the primary vehicle for this research, but our effort is not limited to CC and can be applied across other application domains. Two programming paradigms for expressing CC methods into a dataflow form, in order to make them capable of utilizing task scheduling systems, are presented. Explicit dataflow, is the programming model where the dataflow is explicitly specified by the developer, is contrasted with implicit dataflow, where a task scheduling runtime derives the dataflow. An abstract model is derived to explore the limits of the different dataflow programming paradigms