26,467 research outputs found
An efficient sparse conjugate gradient solver using a Beneš permutation network
© 2014 Technical University of Munich (TUM).The conjugate gradient (CG) is one of the most widely used iterative methods for solving systems of linear equations. However, parallelizing CG for large sparse systems is difficult due to the inherent irregularity in memory access pattern. We propose a novel processor architecture for the sparse conjugate gradient method. The architecture consists of multiple processing elements and memory banks, and is able to compute efficiently both sparse matrix-vector multiplication, and other dense vector operations. A Beneš permutation network with an optimised control scheme is introduced to reduce memory bank conflicts without expensive logic. We describe a heuristics for offline scheduling, the effect of which is captured in a parametric model for estimating the performance of designs generated from our approach
New-Sum: A Novel Online ABFT Scheme for General Iterative Methods
Emerging high-performance computing platforms, with large component counts and lower power margins, are anticipated to be more susceptible to soft errors in both logic circuits and memory subsystems. We present an online algorithm-based fault tolerance (ABFT) approach to efficiently detect and recover soft errors for general iterative methods. We design a novel checksum-based encoding scheme for matrix-vector multiplication that is resilient to both arithmetic and memory errors. Our design decouples the checksum updating process from the actual computation, and allows adaptive checksum overhead control. Building on this new encoding mechanism, we propose two online ABFT designs that can effectively recover from errors when combined with a checkpoint/rollback scheme. These designs are capable of addressing scenarios under different error rates. Our ABFT approaches apply to a wide range of iterative solvers that primarily rely on matrix-vector multiplication and vector linear operations. We evaluate our designs through comprehensive analytical and empirical analysis. Experimental evaluation on the Stampede supercomputer demonstrates the low performance overheads incurred by our two ABFT schemes for preconditioned CG (0:4% and 2:2%) and preconditioned BiCGSTAB (1:0% and 4:0%) for the largest SPD matrix from UFL Sparse Matrix Collection. The evaluation also demonstrates the exibility and effectiveness of our proposed designs for detecting and recovering various types of soft errors in general iterative methods
Design Principles for Sparse Matrix Multiplication on the GPU
We implement two novel algorithms for sparse-matrix dense-matrix
multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the
popular compressed-sparse-row (CSR) format and thus do not require expensive
format conversion. While previous SpMM work concentrates on thread-level
parallelism, we additionally focus on latency hiding with instruction-level
parallelism and load-balancing. We show, both theoretically and experimentally,
that the proposed SpMM is a better fit for the GPU than previous approaches. We
identify a key memory access pattern that allows efficient access into both
input and output matrices that is crucial to getting excellent performance on
SpMM. By combining these two ingredients---(i) merge-based load-balancing and
(ii) row-major coalesced memory access---we demonstrate a 4.1x peak speedup and
a 31.7% geomean speedup over state-of-the-art SpMM implementations on
real-world datasets.Comment: 16 pages, 7 figures, International European Conference on Parallel
and Distributed Computing (Euro-Par) 201
GraphR: Accelerating Graph Processing Using ReRAM
This paper presents GRAPHR, the first ReRAM-based graph processing
accelerator. GRAPHR follows the principle of near-data processing and explores
the opportunity of performing massive parallel analog operations with low
hardware and energy cost. The analog computation is suit- able for graph
processing because: 1) The algorithms are iterative and could inherently
tolerate the imprecision; 2) Both probability calculation (e.g., PageRank and
Collaborative Filtering) and typical graph algorithms involving integers (e.g.,
BFS/SSSP) are resilient to errors. The key insight of GRAPHR is that if a
vertex program of a graph algorithm can be expressed in sparse matrix vector
multiplication (SpMV), it can be efficiently performed by ReRAM crossbar. We
show that this assumption is generally true for a large set of graph
algorithms. GRAPHR is a novel accelerator architecture consisting of two
components: memory ReRAM and graph engine (GE). The core graph computations are
performed in sparse matrix format in GEs (ReRAM crossbars). The
vector/matrix-based graph computation is not new, but ReRAM offers the unique
opportunity to realize the massive parallelism with unprecedented energy
efficiency and low hardware cost. With small subgraphs processed by GEs, the
gain of performing parallel operations overshadows the wastes due to sparsity.
The experiment results show that GRAPHR achieves a 16.01x (up to 132.67x)
speedup and a 33.82x energy saving on geometric mean compared to a CPU baseline
system. Com- pared to GPU, GRAPHR achieves 1.69x to 2.19x speedup and consumes
4.77x to 8.91x less energy. GRAPHR gains a speedup of 1.16x to 4.12x, and is
3.67x to 10.96x more energy efficiency compared to PIM-based architecture.Comment: Accepted to HPCA 201
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