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M. A. Clark

Publications and source records attributed to M. A. Clark.

At least 55 records · Page 3Linked to original sources

Optimizing performance per watt on GPUs in High Performance Computing: temperature, frequency and voltage effects

The magnitude of the real-time digital signal processing challenge attached to large radio astronomical antenna arrays motivates use of high performance computing (HPC) systems. The need for high power efficiency (performance per watt) at remote observatory sites parallels that in HPC broadly, where efficiency is an emerging critical metric. We investigate how the performance per watt of graphics processing units (GPUs) is affected by temperature, core clock frequency and voltage. Our results highlight how the underlying physical processes that govern transistor operation affect power efficiency. In particular, we show experimentally that GPU power consumption grows non-linearly with both temperature and supply voltage, as predicted by physical transistor models. We show lowering GPU supply voltage and increasing clock frequency while maintaining a low die temperature increases the power efficiency of an NVIDIA K20 GPU by up to 37-48% over default settings when running xGPU, a compute-bound code used in radio astronomy. We discuss how temperature-aware power models could be used to reduce power consumption for future HPC installations. Automatic temperature-aware and application-dependent voltage and frequency scaling (T-DVFS and A-DVFS) may provide a mechanism to achieve better power efficiency for a wider range of codes running on GPUs

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The Murchison Widefield Array Correlator

The Murchison Widefield Array (MWA) is a Square Kilometre Array (SKA) Precursor. The telescope is located at the Murchison Radio--astronomy Observatory (MRO) in Western Australia (WA). The MWA consists of 4096 dipoles arranged into 128 dual polarisation aperture arrays forming a connected element interferometer that cross-correlates signals from all 256 inputs. A hybrid approach to the correlation task is employed, with some processing stages being performed by bespoke hardware, based on Field Programmable Gate Arrays (FPGAs), and others by Graphics Processing Units (GPUs) housed in general purpose rack mounted servers. The correlation capability required is approximately 8 TFLOPS (Tera FLoating point Operations Per Second). The MWA has commenced operations and the correlator is generating 8.3 TB/day of correlation products, that are subsequently transferred 700 km from the MRO to Perth (WA) in real-time for storage and offline processing. In this paper we outline the correlator design, signal path, and processing elements and present the data format for the internal and external interfaces.

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Digital Signal Processing using Stream High Performance Computing: A 512-input Broadband Correlator for Radio Astronomy

A "large-N" correlator that makes use of Field Programmable Gate Arrays and Graphics Processing Units has been deployed as the digital signal processing system for the Long Wavelength Array station at Owens Valley Radio Observatory (LWA-OV), to enable the Large Aperture Experiment to Detect the Dark Ages (LEDA). The system samples a ~100MHz baseband and processes signals from 512 antennas (256 dual polarization) over a ~58MHz instantaneous sub-band, achieving 16.8Tops/s and 0.236 Tbit/s throughput in a 9kW envelope and single rack footprint. The output data rate is 260MB/s for 9 second time averaging of cross-power and 1 second averaging of total-power data. At deployment, the LWA-OV correlator was the largest in production in terms of N and is the third largest in terms of complex multiply accumulations, after the Very Large Array and Atacama Large Millimeter Array. The correlator's comparatively fast development time and low cost establish a practical foundation for the scalability of a modular, heterogeneous, computing architecture.

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A Framework for Lattice QCD Calculations on GPUs

Computing platforms equipped with accelerators like GPUs have proven to provide great computational power. However, exploiting such platforms for existing scientific applications is not a trivial task. Current GPU programming frameworks such as CUDA C/C++ require low-level programming from the developer in order to achieve high performance code. As a result porting of applications to GPUs is typically limited to time-dominant algorithms and routines, leaving the remainder not accelerated which can open a serious Amdahl's law issue. The lattice QCD application Chroma allows to explore a different porting strategy. The layered structure of the software architecture logically separates the data-parallel from the application layer. The QCD Data-Parallel software layer provides data types and expressions with stencil-like operations suitable for lattice field theory and Chroma implements algorithms in terms of this high-level interface. Thus by porting the low-level layer one can effectively move the whole application in one swing to a different platform. The QDP-JIT/PTX library, the reimplementation of the low-level layer, provides a framework for lattice QCD calculations for the CUDA architecture. The complete software interface is supported and thus applications can be run unaltered on GPU-based parallel computers. This reimplementation was possible due to the availability of a JIT compiler (part of the NVIDIA Linux kernel driver) which translates an assembly-like language (PTX) to GPU code. The expression template technique is used to build PTX code generators and a software cache manages the GPU memory. This reimplementation allows us to deploy an efficient implementation of the full gauge-generation program with dynamical fermions on large-scale GPU-based machines such as Titan and Blue Waters which accelerates the algorithm by more than an order of magnitude.

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A Scalable Hybrid FPGA/GPU FX Correlator

Radio astronomical imaging arrays comprising large numbers of antennas, O(10^2-10^3) have posed a signal processing challenge because of the required O(N^2) cross correlation of signals from each antenna and requisite signal routing. This motivated the implementation of a Packetized Correlator architecture that applies Field Programmable Gate Arrays (FPGAs) to the O(N) "F-stage" transforming time domain to frequency domain data, and Graphics Processing Units (GPUs) to the O(N^2) "X-stage" performing an outer product among spectra for each antenna. The design is readily scalable to at least O(10^3) antennas. Fringes, visibility amplitudes and sky image results obtained during field testing are presented.

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Shadow Hamiltonians, Poisson Brackets, and Gauge Theories

Numerical lattice gauge theory computations to generate gauge field configurations including the effects of dynamical fermions are usually carried out using algorithms that require the molecular dynamics evolution of gauge fields using symplectic integrators. Sophisticated integrators are in common use but are hard to optimise, and force-gradient integrators show promise especially for large lattice volumes. We explain why symplectic integrators lead to very efficient Monte Carlo algorithms because they exactly conserve a shadow Hamiltonian. The shadow Hamiltonian may be expanded in terms of Poisson brackets, and can be used to optimize the integrators. We show how this may be done for gauge theories by extending the formulation of Hamiltonian mechanics on Lie groups to include Poisson brackets and shadows, and by giving a general method for the practical computation of forces, force-gradients, and Poisson brackets for gauge theories.

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Multigrid Algorithms for Domain-Wall Fermions

We describe an adaptive multigrid algorithm for solving inverses of the domain-wall fermion operator. Our multigrid algorithm uses an adaptive projection of near-null vectors of the domain-wall operator onto coarser four-dimensional lattices. This extension of multigrid techniques to a chiral fermion action will greatly reduce overall computation cost, and the elimination of the fifth dimension in the coarse space reduces the relative cost of using chiral fermions compared to discarding this symmetry. We demonstrate near-elimination of critical slowing as the quark mass is reduced and small volume dependence, which may be suppressed by taking advantage of the recursive nature of the algorithm.

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Improving dynamical lattice QCD simulations through integrator tuning using Poisson brackets and a force-gradient integrator

We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow Hamiltonian $\tilde{H}$. This property allows for a new tuning method of the molecular dynamics integrator and also allows for a new class of integrators (force-gradient integrators) which is expected to reduce significantly the computational cost of future large-scale gauge field ensemble generation.

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Scaling Lattice QCD beyond 100 GPUs

Over the past five years, graphics processing units (GPUs) have had a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations in nuclear and particle physics. While GPUs have been applied with great success to the post-Monte Carlo "analysis" phase which accounts for a substantial fraction of the workload in a typical LQCD calculation, the initial Monte Carlo "gauge field generation" phase requires capability-level supercomputing, corresponding to O(100) GPUs or more. Such strong scaling has not been previously achieved. In this contribution, we demonstrate that using a multi-dimensional parallelization strategy and a domain-decomposed preconditioner allows us to scale into this regime. We present results for two popular discretizations of the Dirac operator, Wilson-clover and improved staggered, employing up to 256 GPUs on the Edge cluster at Lawrence Livermore National Laboratory.

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Accelerating Radio Astronomy Cross-Correlation with Graphics Processing Units

We present a highly parallel implementation of the cross-correlation of time-series data using graphics processing units (GPUs), which is scalable to hundreds of independent inputs and suitable for the processing of signals from "Large-N" arrays of many radio antennas. The computational part of the algorithm, the X-engine, is implementated efficiently on Nvidia's Fermi architecture, sustaining up to 79% of the peak single precision floating-point throughput. We compare performance obtained for hardware- and software-managed caches, observing significantly better performance for the latter. The high performance reported involves use of a multi-level data tiling strategy in memory and use of a pipelined algorithm with simultaneous computation and transfer of data from host to device memory. The speed of code development, flexibility, and low cost of the GPU implementations compared to ASIC and FPGA implementations have the potential to greatly shorten the cycle of correlator development and deployment, for cases where some power consumption penalty can be tolerated.

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First Spectroscopic Imaging Observations of the Sun at Low Radio Frequencies with the Murchison Widefield Array Prototype

We present the first spectroscopic images of solar radio transients from the prototype for the Murchison Widefield Array (MWA), observed on 2010 March 27. Our observations span the instantaneous frequency band 170.9-201.6 MHz. Though our observing period is characterized as a period of `low' to `medium' activity, one broadband emission feature and numerous short-lived, narrowband, non-thermal emission features are evident. Our data represent a significant advance in low radio frequency solar imaging, enabling us to follow the spatial, spectral, and temporal evolution of events simultaneously and in unprecedented detail. The rich variety of features seen here reaffirms the coronal diagnostic capability of low radio frequency emission and provides an early glimpse of the nature of radio observations that will become available as the next generation of low frequency radio interferometers come on-line over the next few years.

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Multigrid solver for clover fermions

We present an adaptive multigrid Dirac solver developed for Wilson clover fermions which offers order-of-magnitude reductions in solution time compared to conventional Krylov solvers. The solver incorporates even-odd preconditioning and mixed precision to solve the Dirac equation to double precision accuracy and shows only a mild increase in time to solution for decreasing quark mass. We show actual time to solution on production lattices in comparison to conventional Krylov solvers and will also discuss the setup process and its relative cost to the total solution time.

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Better HMC integrators for dynamical simulations

We show how to improve the molecular dynamics step of Hybrid Monte Carlo, both by tuning the integrator using Poisson brackets measurements and by the use of force gradient integrators. We present results for moderate lattice sizes.

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Interferometric imaging with the 32 element Murchison Wide-field Array

The Murchison Wide-field Array (MWA) is a low frequency radio telescope, currently under construction, intended to search for the spectral signature of the epoch of re-ionisation (EOR) and to probe the structure of the solar corona. Sited in Western Australia, the full MWA will comprise 8192 dipoles grouped into 512 tiles, and be capable of imaging the sky south of 40 degree declination, from 80 MHz to 300 MHz with an instantaneous field of view that is tens of degrees wide and a resolution of a few arcminutes. A 32-station prototype of the MWA has been recently commissioned and a set of observations taken that exercise the whole acquisition and processing pipeline. We present Stokes I, Q, and U images from two ~4 hour integrations of a field 20 degrees wide centered on Pictoris A. These images demonstrate the capacity and stability of a real-time calibration and imaging technique employing the weighted addition of warped snapshots to counter extreme wide field imaging distortions.

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Adaptive multigrid algorithm for the lattice Wilson-Dirac operator

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called gamma_5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.

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Enabling a High Throughput Real Time Data Pipeline for a Large Radio Telescope Array with GPUs

The Murchison Widefield Array (MWA) is a next-generation radio telescope currently under construction in the remote Western Australia Outback. Raw data will be generated continuously at 5GiB/s, grouped into 8s cadences. This high throughput motivates the development of on-site, real time processing and reduction in preference to archiving, transport and off-line processing. Each batch of 8s data must be completely reduced before the next batch arrives. Maintaining real time operation will require a sustained performance of around 2.5TFLOP/s (including convolutions, FFTs, interpolations and matrix multiplications). We describe a scalable heterogeneous computing pipeline implementation, exploiting both the high computing density and FLOP-per-Watt ratio of modern GPUs. The architecture is highly parallel within and across nodes, with all major processing elements performed by GPUs. Necessary scatter-gather operations along the pipeline are loosely synchronized between the nodes hosting the GPUs. The MWA will be a frontier scientific instrument and a pathfinder for planned peta- and exascale facilities.

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The removal of critical slowing down

We present promising initial results of our adaptive multigrid solver developed for application directly to the non-Hermitian Wilson-Dirac system in 4 dimensions, as opposed to the solver developed in [1] for the corresponding normal equations. The key behind the success of this algorithm is the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix. We demonstrate that the resulting algorithm has weak dependence on the gauge coupling and exhibits extremely mild critical slowing down in the chiral limit.

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Solving Lattice QCD systems of equations using mixed precision solvers on GPUs

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

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