295 research outputs found
A GPU-based hyperbolic SVD algorithm
A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm,
using a massively parallel graphics processing unit (GPU), is developed. The
algorithm also serves as the final stage of solving a symmetric indefinite
eigenvalue problem. Numerical testing demonstrates the gains in speed and
accuracy over sequential and MPI-parallelized variants of similar Jacobi-type
HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are
discussed.Comment: Accepted for publication in BIT Numerical Mathematic
Investigating Single Precision Floating General Matrix Multiply in Heterogeneous Hardware
The fundamental operation of matrix multiplication is ubiquitous across a myriad of disciplines. Yet, the identification of new optimizations for matrix multiplication remains relevant for emerging hardware architectures and heterogeneous systems. Frameworks such as OpenCL enable computation orchestration on existing systems, and its availability using the Intel High Level Synthesis compiler allows users to architect new designs for reconfigurable hardware using C/C++. Using the HARPv2 as a vehicle for exploration, we investigate the utility of several of the most notable matrix multiplication optimizations to better understand the performance portability of OpenCL and the implications for such optimizations on this and future heterogeneous architectures. Our results give targeted insights into the applicability of best practices that were for existing architectures when used on emerging heterogeneous systems
Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication
Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many
high-performance graph algorithms as well as for some linear solvers, such as
algebraic multigrid. The scaling of existing parallel implementations of SpGEMM
is heavily bound by communication. Even though 3D (or 2.5D) algorithms have
been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi
matrices, those algorithms had not been implemented in practice and their
complexities had not been analyzed for the general case. In this work, we
present the first ever implementation of the 3D SpGEMM formulation that also
exploits multiple (intra-node and inter-node) levels of parallelism, achieving
significant speedups over the state-of-the-art publicly available codes at all
levels of concurrencies. We extensively evaluate our implementation and
identify bottlenecks that should be subject to further research
A Computational Model for Tensor Core Units
To respond to the need of efficient training and inference of deep neural
networks, a plethora of domain-specific hardware architectures have been
introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A
common feature of these architectures is a hardware circuit for efficiently
computing a dense matrix multiplication of a given small size. In order to
broaden the class of algorithms that exploit these systems, we propose a
computational model, named the TCU model, that captures the ability to natively
multiply small matrices. We then use the TCU model for designing fast
algorithms for several problems, including matrix operations (dense and sparse
multiplication, Gaussian Elimination), graph algorithms (transitive closure,
all pairs shortest distances), Discrete Fourier Transform, stencil
computations, integer multiplication, and polynomial evaluation. We finally
highlight a relation between the TCU model and the external memory model
Benchmarking a New Paradigm: An Experimental Analysis of a Real Processing-in-Memory Architecture
Many modern workloads, such as neural networks, databases, and graph
processing, are fundamentally memory-bound. For such workloads, the data
movement between main memory and CPU cores imposes a significant overhead in
terms of both latency and energy. A major reason is that this communication
happens through a narrow bus with high latency and limited bandwidth, and the
low data reuse in memory-bound workloads is insufficient to amortize the cost
of main memory access. Fundamentally addressing this data movement bottleneck
requires a paradigm where the memory system assumes an active role in computing
by integrating processing capabilities. This paradigm is known as
processing-in-memory (PIM).
Recent research explores different forms of PIM architectures, motivated by
the emergence of new 3D-stacked memory technologies that integrate memory with
a logic layer where processing elements can be easily placed. Past works
evaluate these architectures in simulation or, at best, with simplified
hardware prototypes. In contrast, the UPMEM company has designed and
manufactured the first publicly-available real-world PIM architecture.
This paper provides the first comprehensive analysis of the first
publicly-available real-world PIM architecture. We make two key contributions.
First, we conduct an experimental characterization of the UPMEM-based PIM
system using microbenchmarks to assess various architecture limits such as
compute throughput and memory bandwidth, yielding new insights. Second, we
present PrIM, a benchmark suite of 16 workloads from different application
domains (e.g., linear algebra, databases, graph processing, neural networks,
bioinformatics).Comment: Our open source software is available at
https://github.com/CMU-SAFARI/prim-benchmark
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