Verified lifting of stencil computations

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counter-example guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. For example, our experiments show that the lifted summaries can enable domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. We demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1X and up to 24X for non-trivial stencils as compared to the original implementation.United States. Department of Energy. Office of Science (Award DE-SC0008923)United States. Department of Energy. Office of Science (Award DE-SC0005288

Doctor of Philosophy

dissertationIn the static analysis of functional programs, control- ow analysis (k-CFA) is a classic method of approximating program behavior as a infinite state automata. CFA2 and abstract garbage collection are two recent, yet orthogonal improvements, on k-CFA. CFA2 approximates program behavior as a pushdown system, using summarization for the stack. CFA2 can accurately approximate arbitrarily-deep recursive function calls, whereas k-CFA cannot. Abstract garbage collection removes unreachable values from the store/heap. If unreachable values are not removed from a static analysis, they can become reachable again, which pollutes the final analysis and makes it less precise. Unfortunately, as these two techniques were originally formulated, they are incompatible. CFA2's summarization technique for managing the stack obscures the stack such that abstract garbage collection is unable to examine the stack for reachable values. This dissertation presents introspective pushdown control-flow analysis, which manages the stack explicitly through stack changes (pushes and pops). Because this analysis is able to examine the stack by how it has changed, abstract garbage collection is able to examine the stack for reachable values. Thus, introspective pushdown control-flow analysis merges successfully the benefits of CFA2 and abstract garbage collection to create a more precise static analysis. Additionally, the high-performance computing community has viewed functional programming techniques and tools as lacking the efficiency necessary for their applications. Nebo is a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena. For efficient execution, Nebo exploits a version of expression templates, based on the C++ template system, which is a type-less, completely-pure, Turing-complete functional language with burdensome syntax. Nebo's declarative syntax supports functional tools, such as point-wise lifting of complex expressions and functional composition of stencil operators. Nebo's primary abstraction is mathematical assignment, which separates what a calculation does from how that calculation is executed. Currently Nebo supports single-core execution, multicore (thread-based) parallel execution, and GPU execution. With single-core execution, Nebo performs on par with the loops and code that it replaces in Wasatch, a pre-existing high-performance simulation project. With multicore (thread-based) execution, Nebo can linearly scale (with roughly 90% efficiency) up to 6 processors, compared to its single-core execution. Moreover, Nebo's GPU execution can be up to 37x faster than its single-core execution. Finally, Wasatch (the pre-existing high-performance simulation project which uses Nebo) can scale up to 262K cores

An Automatic and Symbolic Parallelization System for Distributed Memory Parallel Computers

This paper describes ASPAR (Automatic and Symbolic PARallelization) which consists of a source-to-source parallelizer and a set of interactive graphic tools. While the issues of data dependency have already been explored and used in many parallel computer systems such as vector and shared memory machines, distributed memory parallel computers require, in addition, explicit data decomposition. New symbolic analysis and data-dependency analysis methods are used to determine an explicit data decomposition scheme. Automatic parallelization models using high level communications are also described in this paper. The target applications are of the “regular-mesh" type typical of many scientific calculations. The system has been implemented for the language C, and is designed for easy modification for other languages such as Fortran

AIMES: advanced computation and I/O methods for earth-system simulations

Dealing with extreme scale Earth-system models is challenging from the computer science perspective, as the required computing power and storage capacity are steadily increasing. Scientists perform runs with growing resolution or aggregate results from many similar smaller-scale runs with slightly different initial conditions (the so-called ensemble runs). In the fifth Coupled Model Intercomparison Project (CMIP5), the produced datasets require more than three Petabytes of storage and the compute and storage requirements are increasing significantly for CMIP6. Climate scientists across the globe are developing next-generation models based on improved numerical formulation leading to grids that are discretized in alternative forms such as an icosahedral (geodesic) grid. The developers of these models face similar problems in scaling, maintaining and optimizing code. Performance portability and the maintainability of code are key concerns of scientists as, compared to industry projects, model code is continuously revised and extended to incorporate further levels of detail. This leads to a rapidly growing code base that is rarely refactored. However, code modernization is important to maintain productivity of the scientist working with the code and for utilizing performance provided by modern and future architectures. The need for performance optimization is motivated by the evolution of the parallel architecture landscape from homogeneous flat machines to heterogeneous combinations of processors with deep memory hierarchy. Notably, the rise of many-core, throughput-oriented accelerators, such as GPUs, requires non-trivial code changes at minimum and, even worse, may necessitate a substantial rewrite of the existing codebase. At the same time, the code complexity increases the difficulty for computer scientists and vendors to understand and optimize the code for a given system. Storing the products of climate predictions requires a large storage and archival system which is expensive. Often, scientists restrict the number of scientific variables and write interval to keep the costs balanced. Compression algorithms can reduce the costs significantly but can also increase the scientific yield of simulation runs. In the AIMES project, we addressed the key issues of programmability, computational efficiency and I/O limitations that are common in next-generation icosahedral earth-system models. The project focused on the separation of concerns between domain scientist, computational scientists, and computer scientists

Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.Comment: 24 pages, 1 figure. Corresponds to journal versio