Representation-transparent matrix algorithms with scalable performance

Abstract

Positive results from new object-oriented tools for scientific programming are reported. Using template classes, abstractions of matrix representations are available that subsume conventional row-major, column-major, either Z-or IMorton-order, as well as block-wise combinations of these. Moreover, the design of the Matrix Template Library (MTL) has been independently extended to provide recursators, to support block-recursive algorithms, supplementing MTL's iterators. Data types modeling both concepts enable the programmer to implement both iterative and recursive algorithms (or even both) on all of the aforementioned matrix representations at once for a wide family of important scientific operations.We illustrate the unrestricted applicability of our matrixrecursator on matrix multiplication. The same generic blockrecursive function, unaltered, is instantiated on different triplets of matrix types. Within a base block, either a library multiplication or a user-provided, platform-specific code provides excellent performance. We achieve 77% of peak-performance using hand-tuned base cases without explicit prefetching. This excellent performance becomes available over a wide family of matrix representations from a single program. The techniques generalize to other applications in linear algebra.

Window Memory Layout Scheme for Alternate Row-Wise/Column-Wise Matrix Access

“…First, methods for program transformation have been explored to improve the cache hit rate in uniprocessor systems, or to improve the data locality in distributed-memory parallel computers [9], [10]. Gottschling [11] proposed a representation-transparent matrix algorithm for multicore chip and developed matrix template library (MTL) for matrix application, such as matrix multiplication. Ruetsch [12] and Podlozhnyuk [13] combine features of the GPU warp access memory and the shared memory structure to enhance matrix transpose performance.…”

The STAPL parallel container framework

“…Sequential libraries such as STL [19], BGL [10], and MTL [9], provide data structures such as arrays, vectors, lists, maps, matrices, and graphs. A parallel container is an object oriented implementation of a data structure designed to be used efficiently in a parallel environment.…”

“…pContainers can be constructed from any base container, sequential or parallel, so long as it can support the required interface. The pContainers currently provided in STAPL use the corresponding STL containers (e.g., the STAPL pVector uses the STL vector), containers from other sequential libraries (e.g., MTL [9] for matrices), containers available in libraries developed for multicore (e.g., TBB [14] concurrent containers), or other pContainers. This flexibility allows for code reuse and supports interoperability with other libraries.…”

“…Thus, the PCF makes developing a pContainer almost as easy as developing its sequential counterpart. Moreover, the PCF facilitates interoperability by enabling the use of parallel or sequential containers from other libraries, e.g., MTL [9], BGL [10] or TBB [14].…”

“…The STAPL runtime system includes a communication library (ARMI) and an executor that executes pRanges. Sequential libraries such as STL [19], BGL [10], and MTL [9], provide the user with a collection of data structures that simplifies the application development process. Similarly, STAPL provides the Parallel Container Framework (PCF) which includes a set of elementary pContainers and tools to facilitate the customization and specialization of existing pContainers and the development of new ones.…”