20,491 research outputs found
Performance Analysis and Optimization of Sparse Matrix-Vector Multiplication on Modern Multi- and Many-Core Processors
This paper presents a low-overhead optimizer for the ubiquitous sparse
matrix-vector multiplication (SpMV) kernel. Architectural diversity among
different processors together with structural diversity among different sparse
matrices lead to bottleneck diversity. This justifies an SpMV optimizer that is
both matrix- and architecture-adaptive through runtime specialization. To this
direction, we present an approach that first identifies the performance
bottlenecks of SpMV for a given sparse matrix on the target platform either
through profiling or by matrix property inspection, and then selects suitable
optimizations to tackle those bottlenecks. Our optimization pool is based on
the widely used Compressed Sparse Row (CSR) sparse matrix storage format and
has low preprocessing overheads, making our overall approach practical even in
cases where fast decision making and optimization setup is required. We
evaluate our optimizer on three x86-based computing platforms and demonstrate
that it is able to distinguish and appropriately optimize SpMV for the majority
of matrices in a representative test suite, leading to significant speedups
over the CSR and Inspector-Executor CSR SpMV kernels available in the latest
release of the Intel MKL library.Comment: 10 pages, 7 figures, ICPP 201
An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling
We present a sparse linear system solver that is based on a multifrontal
variant of Gaussian elimination, and exploits low-rank approximation of the
resulting dense frontal matrices. We use hierarchically semiseparable (HSS)
matrices, which have low-rank off-diagonal blocks, to approximate the frontal
matrices. For HSS matrix construction, a randomized sampling algorithm is used
together with interpolative decompositions. The combination of the randomized
compression with a fast ULV HSS factorization leads to a solver with lower
computational complexity than the standard multifrontal method for many
applications, resulting in speedups up to 7 fold for problems in our test
suite. The implementation targets many-core systems by using task parallelism
with dynamic runtime scheduling. Numerical experiments show performance
improvements over state-of-the-art sparse direct solvers. The implementation
achieves high performance and good scalability on a range of modern shared
memory parallel systems, including the Intel Xeon Phi (MIC). The code is part
of a software package called STRUMPACK -- STRUctured Matrices PACKage, which
also has a distributed memory component for dense rank-structured matrices
A Library for Pattern-based Sparse Matrix Vector Multiply
Pattern-based Representation (PBR) is a novel approach to improving the performance of Sparse Matrix-Vector Multiply (SMVM) numerical kernels. Motivated by our observation that many matrices can be divided into blocks that share a small number of distinct patterns, we generate custom multiplication kernels for frequently recurring block patterns.
The resulting reduction in index overhead significantly reduces memory bandwidth requirements and improves performance. Unlike existing methods, PBR requires neither detection of dense blocks nor zero filling, making it particularly advantageous for matrices that lack dense nonzero concentrations. SMVM kernels for PBR can benefit from explicit prefetching and vectorization, and are amenable to parallelization. The analysis and format conversion to PBR is implemented as a library, making it suitable for applications that generate matrices dynamically at runtime. We present sequential and parallel performance results for PBR on two current multicore architectures, which show that PBR outperforms available alternatives for the matrices to which it is applicable,
and that the analysis and conversion overhead is amortized in realistic application scenarios
Integer Echo State Networks: Hyperdimensional Reservoir Computing
We propose an approximation of Echo State Networks (ESN) that can be
efficiently implemented on digital hardware based on the mathematics of
hyperdimensional computing. The reservoir of the proposed Integer Echo State
Network (intESN) is a vector containing only n-bits integers (where n<8 is
normally sufficient for a satisfactory performance). The recurrent matrix
multiplication is replaced with an efficient cyclic shift operation. The intESN
architecture is verified with typical tasks in reservoir computing: memorizing
of a sequence of inputs; classifying time-series; learning dynamic processes.
Such an architecture results in dramatic improvements in memory footprint and
computational efficiency, with minimal performance loss.Comment: 10 pages, 10 figures, 1 tabl
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
The Parallelism Motifs of Genomic Data Analysis
Genomic data sets are growing dramatically as the cost of sequencing
continues to decline and small sequencing devices become available. Enormous
community databases store and share this data with the research community, but
some of these genomic data analysis problems require large scale computational
platforms to meet both the memory and computational requirements. These
applications differ from scientific simulations that dominate the workload on
high end parallel systems today and place different requirements on programming
support, software libraries, and parallel architectural design. For example,
they involve irregular communication patterns such as asynchronous updates to
shared data structures. We consider several problems in high performance
genomics analysis, including alignment, profiling, clustering, and assembly for
both single genomes and metagenomes. We identify some of the common
computational patterns or motifs that help inform parallelization strategies
and compare our motifs to some of the established lists, arguing that at least
two key patterns, sorting and hashing, are missing
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