Simit: A Language for Physical Simulation

Using existing programming tools, writing high-performance simulation code is labor intensive and requires sacrificing readability and portability. The alternative is to prototype simulations in a high-level language like Matlab, thereby sacrificing performance. The Matlab programming model naturally describes the behavior of an entire physical system using the language of linear algebra. However, simulations also manipulate individual geometric elements, which are best represented using linked data structures like meshes. Translating between the linked data structures and linear algebra comes at significant cost, both to the programmer and the machine. High-performance implementations avoid the cost by rephrasing the computation in terms of linked or index data structures, leaving the code complicated and monolithic, often increasing its size by an order of magnitude. In this paper, we present Simit, a new language for physical simulations that lets the programmer view the system both as a linked data structure in the form of a hypergraph, and as a set of global vectors, matrices and tensors depending on what is convenient at any given time. Simit provides a novel assembly construct that makes it conceptually easy and computationally efficient to move between the two abstractions. Using the information provided by the assembly construct, the compiler generates efficient in-place computation on the graph. We demonstrate that Simit is easy to use: a Simit program is typically shorter than a Matlab program; that it is high-performance: a Simit program running sequentially on a CPU performs comparably to hand-optimized simulations; and that it is portable: Simit programs can be compiled for GPUs with no change to the program, delivering 5-25x speedups over our optimized CPU code

Generating Fast Sparse Matrix Vector Multiplication From a High Level Generic Functional IR

Usage of high-level intermediate representations promises the generation of fast code from a high-level description, improving the productivity of developers while achieving the performance traditionally only reached with low-level programming approaches. High-level IRs come in two flavors: 1) domain-specific IRs designed only for a specific application area; or 2) generic high-level IRs that can be used to generate high-performance code across many domains. Developing generic IRs is more challenging but offers the advantage of reusing a common compiler infrastructure across various applications. In this paper, we extend a generic high-level IR to enable efficient computation with sparse data structures. Crucially, we encode sparse representation using reusable dense building blocks already present in the high-level IR. We use a form of dependent types to model sparse matrices in CSR format by expressing the relationship between multiple dense arrays explicitly separately storing the length of rows, the column indices, and the non-zero values of the matrix. We achieve high-performance compared to sparse low-level library code using our extended generic high-level code generator. On an Nvidia GPU, we outperform the highly tuned Nvidia cuSparse implementation of spmv multiplication across 28 sparse matrices of varying sparsity on average by 1.7×

Multilayered abstractions for partial differential equations

How do we build maintainable, robust, and performance-portable scientific applications? This thesis argues that the answer to this software engineering question in the context of the finite element method is through the use of layers of Domain-Specific Languages (DSLs) to separate the various concerns in the engineering of such codes. Performance-portable software achieves high performance on multiple diverse hardware platforms without source code changes. We demonstrate that finite element solvers written in a low-level language are not performance-portable, and therefore code must be specialised to the target architecture by a code generation framework. A prototype compiler for finite element variational forms that generates CUDA code is presented, and is used to explore how good performance on many-core platforms in automatically-generated finite element applications can be achieved. The differing code generation requirements for multi- and many-core platforms motivates the design of an additional abstraction, called PyOP2, that enables unstructured mesh applications to be performance-portable. We present a runtime code generation framework comprised of the Unified Form Language (UFL), the FEniCS Form Compiler, and PyOP2. This toolchain separates the succinct expression of a numerical method from the selection and generation of efficient code for local assembly. This is further decoupled from the selection of data formats and algorithms for efficient parallel implementation on a specific target architecture. We establish the successful separation of these concerns by demonstrating the performance-portability of code generated from a single high-level source code written in UFL across sequential C, CUDA, MPI and OpenMP targets. The performance of the generated code exceeds the performance of comparable alternative toolchains on multi-core architectures.Open Acces