GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems

While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring "standard" as well as "accelerated" resources. Today, such resources are available as multicore processors, graphics processing units (GPUs), and other accelerators such as the Intel Xeon Phi. Any software infrastructure that claims usefulness for such environments must be able to meet their inherent challenges: massive multi-level parallelism, topology, asynchronicity, and abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems. It implements the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We describe the details of its design with respect to the challenges posed by modern heterogeneous supercomputers and recent algorithmic developments. Implementation details which are indispensable for achieving high efficiency are pointed out and their necessity is justified by performance measurements or predictions based on performance models. The library code and several applications are available as open source. We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.Comment: 32 pages, 11 figure

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$\times$ faster than by first converting the data to CSR.Comment: Presented at OOPSLA 201

Efficient Generation of Sequences of Dense Linear Algebra through Auto-Tuning

It is rare for a programmer to solve a numerical problem with a single library call; most problems require a sequence of calls. In the case of linear algebra, programmers will chain a series of Basic Linear Algebra Subprogram (BLAS) library calls to achieve the desired result. When a sequence of BLAS calls is memory bound, a great deal of performance is missed because optimization has not occurred between library routines. It is not practical to create a library with every required sequence of linear algebra operations, but at the same time it is difficult for programmers to write their own high performance implementation. One solution is for programmers to use an auto-tuning tool capable of optimizing the sequence of operations that exactly suits their need. This thesis presents a matrix representation and type system that describes basic linear algebra operations, the loops required to implement those operations, and the legality of key optimizations. This is demonstrated in an auto-tuning tool which generates loops and performs data parallelism and loop fusion. Results show that this approach can match or exceed performance of vendor tuned BLAS libraries, general purpose optimizing compilers, and hand written code. Further, this approach is shown to be both portable and work with a range of dense matrix storage formats. All of this is achieved with search times in the range of several minutes to a few hours