Fredrik Kjolstad

Ghost Cell Pattern

Many problems consist of a structured grid of points that are updated repeatedly based on the values of a fixed set of neighboring points in the same grid. To parallelize these problems we can geometrically divide the grid into chunks that are processed by different processors. One challenge with this approach is that the update of points at the periphery of a chunk requires values from neighboring chunks. These are often located in remote memory belonging to different processes. The naive implementation results in a lot of time spent on communication leaving less time for useful computation. By using the Ghost Cell Pattern communication overhead can be reduced. This results in faster time to completion.

Transformation for class immutability

It is common for object-oriented programs to have both mutable and immutable classes. Immutable classes simplify programing because the programmer does not have to reason about side-effects. Sometimes programmers write immutable classes from scratch, other times they transform mutable into immutable classes. To transform a mutable class, programmers must find all methods that mutate its transitive state and all objects that can enter or escape the state of the class. The analyses are non-trivial and the rewriting is tedious. Fortunately, this can be automated. We present an algorithm and a tool, Immutator, that enables the programmer to safely transform a mutable class into an immutable class. Two case studies and one controlled experiment show that Immutator is useful. It (i) reduces the burden of making classes immutable, (ii) is fast enough to be used interactively, and (iii) is much safer than manual transformations.

Perspectives: Why New Programming Languages for Simulation?

Writing highly performant simulations requires a lot of human effort to optimize for an increasingly diverse set of hardware platforms, such as multi-core CPUs, GPUs, and distributed machines. Since these optimizations cut across both the design of geometric data structures and numerical linear algebra, code reusability and portability is frequently sacrificed for performance. We believe the key to make simulation programmers more productive at developing portable and performant code is to introduce new linguistic abstractions, as in rendering and image processing. In this perspective, we distill the core ideas from our two languages, Ebb and Simit, that are published in this journal.

Simit: A Language for Physical Simulation

With 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 to 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 article, 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 4 to 20× speedups over our optimized CPU code.

MPI datatype processing using runtime compilation

Data packing before and after communication can make up as much as 90% of the communication time on modern computers. Despite MPIs well-defined datatype interface for non-contiguous data access, many codes use manual pack loops for performance reasons. Programmers write access-pattern specific pack loops (e.g., do manual unrolling) for which compilers emit optimized code. In contrast, MPI implementations in use today interpret datatypes at pack time, resulting in high overheads. In this work we explore the effectiveness of using runtime compilation techniques to generate efficient and optimized pack code for MPI datatypes at commit time. Thus, none of the overhead of datatype interpretation is incurred at pack time and pack setup is as fast as calling a function pointer. We have implemented a library called libpack that can be used to compile and (un)pack MPI datatypes. The library optimizes the datatype representation and uses the LLVM framework to produce vectorized machine code for each datatype at commit time. We show several examples of how MPI datatype pack functions benefit from runtime compilation and analyze the performance of compiled pack functions for the data access patterns in many applications. We show that the pack/unpack functions generated by our packing library are seven times faster than those of prevalent MPI implementations for 73% of the datatypes used in a scientific application and in many cases outperform manual pack loops.

Automatic datatype generation and optimization

Many high performance applications spend considerable time packing noncontiguous data into contiguous communication buffers. MPI Datatypes provide an alternative by describing noncontiguous data layouts. This allows sophisticated hardware to retrieve data directly from application data structures. However, packing codes in real-world applications are often complex and specifying equivalent datatypes is difficult, time-consuming, and error prone. We present an algorithm that automates the transformation. We have implemented the algorithm in a tool that transforms packing code to MPI Datatypes, and evaluated it by transforming 90 packing codes from the NAS Parallel Benchmarks. The transformation allows easy porting of applications to new machines that benefit from datatypes, thus improving programmer productivity.

The tensor algebra compiler

Tensor algebra is a powerful tool with applications in machine learning, data analytics, engineering and the physical sciences. Tensors are often sparse and compound operations must frequently be computed in a single kernel for performance and to save memory. Programmers are left to write kernels for every operation of interest, with different mixes of dense and sparse tensors in different formats. The combinations are infinite, which makes it impossible to manually implement and optimize them all. This paper introduces the first compiler technique to automatically generate kernels for any compound tensor algebra operation on dense and sparse tensors. The technique is implemented in a C++ library called taco. Its performance is competitive with best-in-class hand-optimized kernels in popular libraries, while supporting far more tensor operations.

Taco: A tool to generate tensor algebra kernels

Tensor algebra is an important computational abstraction that is increasingly used in data analytics, machine learning, engineering, and the physical sciences. However, the number of tensor expressions is unbounded, which makes it hard to develop and optimize libraries. Furthermore, the tensors are often sparse (most components are zero), which means the code has to traverse compressed formats. To support programmers we have developed taco, a code generation tool that generates dense, sparse, and mixed kernels from tensor algebra expressions. This paper describes the taco web and command-line tools and discusses the benefits of a code generator over a traditional library. See also the demo video at tensor-compiler.org/ase2017.

Format abstraction for sparse tensor algebra compilers

This paper shows how to build a sparse tensor algebra compiler that is agnostic to tensor formats (data layouts). We develop an interface that describes formats in terms of their capabilities and properties, and show how to build a modular code generator where new formats can be added as plugins. We then describe six implementations of the interface that compose to form the dense, CSR/CSF, COO, DIA, ELL, and HASH tensor formats and countless variants thereof. With these implementations at hand, our code generator can generate code to compute any tensor algebra expression on any combination of the aforementioned formats. To demonstrate our technique, we have implemented it in the taco tensor algebra compiler. Our modular code generator design makes it simple to add support for new tensor formats, and the performance of the generated code is competitive with hand-optimized implementations. Furthermore, by extending taco to support a wider range of formats specialized for different application and data characteristics, we can improve end-user application performance. For example, if input data is provided in the COO format, our technique allows computing a single matrix-vector multiplication directly with the data in COO, which is up to 3.6× faster than by first converting the data to CSR.