6,460 research outputs found
Generating optimized Fourier interpolation routines for density function theory using SPIRAL
© 2015 IEEE.Upsampling of a multi-dimensional data-set is an operation with wide application in image processing and quantum mechanical calculations using density functional theory. For small up sampling factors as seen in the quantum chemistry code ONETEP, a time-shift based implementation that shifts samples by a fraction of the original grid spacing to fill in the intermediate values using a frequency domain Fourier property can be a good choice. Readily available highly optimized multidimensional FFT implementations are leveraged at the expense of extra passes through the entire working set. In this paper we present an optimized variant of the time-shift based up sampling. Since ONETEP handles threading, we address the memory hierarchy and SIMD vectorization, and focus on problem dimensions relevant for ONETEP. We present a formalization of this operation within the SPIRAL framework and demonstrate auto-generated and auto-tuned interpolation libraries. We compare the performance of our generated code against the previous best implementations using highly optimized FFT libraries (FFTW and MKL). We demonstrate speed-ups in isolation averaging 3x and within ONETEP of up to 15%
Efficient multicore-aware parallelization strategies for iterative stencil computations
Stencil computations consume a major part of runtime in many scientific
simulation codes. As prototypes for this class of algorithms we consider the
iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient
parallel implementations for cache-based multicore architectures. Temporal
cache blocking is a known advanced optimization technique, which can reduce the
pressure on the memory bus significantly. We apply and refine this optimization
for a recently presented temporal blocking strategy designed to explicitly
utilize multicore characteristics. Especially for the case of Gauss-Seidel
smoothers we show that simultaneous multi-threading (SMT) can yield substantial
performance improvements for our optimized algorithm.Comment: 15 pages, 10 figure
Automatic Loop Kernel Analysis and Performance Modeling With Kerncraft
Analytic performance models are essential for understanding the performance
characteristics of loop kernels, which consume a major part of CPU cycles in
computational science. Starting from a validated performance model one can
infer the relevant hardware bottlenecks and promising optimization
opportunities. Unfortunately, analytic performance modeling is often tedious
even for experienced developers since it requires in-depth knowledge about the
hardware and how it interacts with the software. We present the "Kerncraft"
tool, which eases the construction of analytic performance models for streaming
kernels and stencil loop nests. Starting from the loop source code, the problem
size, and a description of the underlying hardware, Kerncraft can ideally
predict the single-core performance and scaling behavior of loops on multicore
processors using the Roofline or the Execution-Cache-Memory (ECM) model. We
describe the operating principles of Kerncraft with its capabilities and
limitations, and we show how it may be used to quickly gain insights by
accelerated analytic modeling.Comment: 11 pages, 4 figures, 8 listing
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
Beyond Reuse Distance Analysis: Dynamic Analysis for Characterization of Data Locality Potential
Emerging computer architectures will feature drastically decreased flops/byte
(ratio of peak processing rate to memory bandwidth) as highlighted by recent
studies on Exascale architectural trends. Further, flops are getting cheaper
while the energy cost of data movement is increasingly dominant. The
understanding and characterization of data locality properties of computations
is critical in order to guide efforts to enhance data locality. Reuse distance
analysis of memory address traces is a valuable tool to perform data locality
characterization of programs. A single reuse distance analysis can be used to
estimate the number of cache misses in a fully associative LRU cache of any
size, thereby providing estimates on the minimum bandwidth requirements at
different levels of the memory hierarchy to avoid being bandwidth bound.
However, such an analysis only holds for the particular execution order that
produced the trace. It cannot estimate potential improvement in data locality
through dependence preserving transformations that change the execution
schedule of the operations in the computation. In this article, we develop a
novel dynamic analysis approach to characterize the inherent locality
properties of a computation and thereby assess the potential for data locality
enhancement via dependence preserving transformations. The execution trace of a
code is analyzed to extract a computational directed acyclic graph (CDAG) of
the data dependences. The CDAG is then partitioned into convex subsets, and the
convex partitioning is used to reorder the operations in the execution trace to
enhance data locality. The approach enables us to go beyond reuse distance
analysis of a single specific order of execution of the operations of a
computation in characterization of its data locality properties. It can serve a
valuable role in identifying promising code regions for manual transformation,
as well as assessing the effectiveness of compiler transformations for data
locality enhancement. We demonstrate the effectiveness of the approach using a
number of benchmarks, including case studies where the potential shown by the
analysis is exploited to achieve lower data movement costs and better
performance.Comment: Transaction on Architecture and Code Optimization (2014
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