A recent development in radio astronomy is to replace traditional dishes with many small antennas. The signals are combined to form one large, virtual telescope. The enormous data streams are cross-correlated to filter out noise. This is especially challenging, since the computational demands grow quadratically with the number of data streams. Moreover, the correlator is not only computationally intensive, but also very I O intensive. The LOFAR telescope, for instance, will produce over 100 terabytes per day. The future SKA telescope will even require in the order of exaflops, and petabits s of I O. A recent trend is to correlate in software instead of dedicated hardware, to increase flexibility and to reduce development efforts. We evaluate the correlator algorithm on multi-core CPUs and many-core architectures, such as NVIDIA and ATI GPUs, and the Cell B.E. The correlator is a streaming, real-time application, and is much more I O intensive than applications that are typically implemented on many-core hardware today. We compare with the LOFAR production correlator on an IBM Blue Gene P supercomputer. We investigate performance, power efficiency, and programmability. We identify several important architectural problems which cause architectures to perform suboptimally. Our findings are applicable to data-intensive applications in general. The processing power and memory bandwidth of current GPUs are highly imbalanced for correlation purposes. While the production correlator on the Blue Gene P achieves a superb 96 of the theoretical peak performance, this is only 16 on ATI GPUs, and 32 on NVIDIA GPUs. The Cell B.E. processor, in contrast, achieves an excellent 92 . We found that the Cell B.E. and NVIDIA GPUs are the most energy-efficient solutions, they run the correlator at least 4 times more energy efficiently than the Blue Gene P. The research presented is an important pathfinder for next-generation telescopes.
Intel's Larrabee @cite_23 (to be released) is another promising architecture. Larrabee will be a hybrid between a GPU and a multi-core CPU. It will be compatible with the x86 architecture, but will have 4-way simultaneous multi-threading, 512-bit wide vector units, shuffle and multiply-add instructions, and special texturing hardware. Larrabee will use in-order execution, and will have coherent caches. Unlike current GPUs, but similar to the Cell B.E. , Larrabee will have a ring bus for communication between cores and for memory transactions.
@cite_23
2169150396 2206856102 1981534910 2171308769
This paper presents a many-core visual computing architecture code named Larrabee, a new software rendering pipeline, a manycore programming model, and performance analysis for several applications. Larrabee uses multiple in-order x86 CPU cores that are augmented by a wide vector processor unit, as well as some fixed function logic blocks. This provides dramatically higher performance per watt and per unit of area than out-of-order CPUs on highly parallel workloads. It also greatly increases the flexibility and programmability of the architecture as compared to standard GPUs. A coherent on-die 2nd level cache allows efficient inter-processor communication and high-bandwidth local data access by CPU cores. Task scheduling is performed entirely with software in Larrabee, rather than in fixed function logic. The customizable software graphics rendering pipeline for this architecture uses binning in order to reduce required memory bandwidth, minimize lock contention, and increase opportunities for parallelism relative to standard GPUs. The Larrabee native programming model supports a variety of highly parallel applications that use irregular data structures. Performance analysis on those applications demonstrates Larrabee's potential for a broad range of parallel computation. High performance fast multipole method is crucial for the numerical simulation of many physical problems. In a previous study, we have shown that task-based fast multipole method provides the flexibility required to process a wide spectrum of particle distributions efficiently on multicore architectures. In this paper, we now show how such an approach can be extended to fully exploit heterogeneous platforms. For that, we design highly tuned graphics processing unit GPU versions of the two dominant operators P2P and M2L as well as a scheduling strategy that dynamically decides which proportion of subsequent tasks is processed on regular CPU cores and on GPU accelerators. We assess our method with the StarPU runtime system for executing the resulting task flow on an Intel X5650 Nehalem multicore processor possibly enhanced with one, two, or three Nvidia Fermi M2070 or M2090 GPUs Santa Clara, CA, USA. A detailed experimental study on two 30 million particle distributions a cube and an ellipsoid shows that the resulting software consistently achieves high performance across architectures. Copyright © 2015 John Wiley & Sons, Ltd. Multicore architectures enhanced with multiple GPUs are likely to become mainstream High Performance Computing (HPC) platforms in a near future. In this paper, we present the design and implementation of an LU factorization using tile algorithm that can fully exploit the potential of such platforms in spite of their complexity. We use a methodology derived from previous work on Cholesky and QR factorizations. Our contributions essentially consist of providing new CPU GPU hybrid LU kernels, studying the impact on performance of the looking variants as well as the storage layout in presence of pivoting, tuning the kernels for two different machines composed of multiple recent NVIDIA Tesla S1070 (four GPUs total) and Fermi-based S2050 GPUs (three GPUs total), respectively. The hybrid tile LU asymptotically achieves 1 Tflop s in single precision on both hardwares. The performance in double precision arithmetic reaches 500 Gflop s on the Fermi-based system, twice faster than the old GPU generation of Tesla S1070. We also discuss the impact of the number of tiles on the numerical stability. We show that the numerical results of the tile LU factorization will be accurate enough for most applications as long as the computations are performed in double precision arithmetic. SUMMARY This paper presents a number of algorithms to run the fast multipole method (FMM) on NVIDIA CUDA-capable graphical processing units (GPUs) (Nvidia Corporation, Sta. Clara, CA, USA). The FMM is a class of methods to compute pairwise interactions between N particles for a given error tolerance and with computational cost of O(N). The methods described in the paper are applicable to any FMMs in which the multipole-to-local (M2L) operator is a dense matrix and the matrix is precomputed. This is the case for example in the black-box fast multipole method (bbFMM), which is a variant of the FMM that can handle large class of kernels. This example will be used in our benchmarks. In the FMM, two operators represent most of the computational cost, and an optimal implementation typically tries to balance those two operators. One is the nearby interaction calculation (direct sum calculation, line 29 in Listing 1), and the other is the M2L operation. We focus on the M2L. By combining multiple M2L operations and reordering the primitive loops of the M2L so that CUDA threads can reuse or share common data, these approaches reduce the movement of data in the GPU. Because memory bandwidth is the primary bottleneck of these methods, significant performance improvements are realized. Four M2L schemes are detailed and analyzed in the case of a uniform tree. The four schemes are tested and compared with an optimized, OpenMP parallelized, multi-core CPU code. We consider high and low precision calculations by varying the number of Chebyshev nodes used in the bbFMM. The accuracy of the GPU codes is found to be satisfactory and achieved performance over 200 Gflop s on one NVIDIA Tesla C1060 GPU (Nvidia Corporation, Sta. Clara, CA, USA). This was compared against two quad-core Intel Xeon E5345 processors (Intel Corporation, Sta. Clara, CA, USA) running at 2.33 GHz, for a combined peak performance of 149 Gflop s for single precision. For the low FMM accuracy case, the observed performance of the CPU code was 37 Gflop s, whereas for the high FMM accuracy case, the performance was about 8.5 Gflop s, most likely because of a higher frequency of cache misses. We also present benchmarks on an NVIDIA C2050 GPU (a Fermi processor)(Nvidia Corporation, Sta. Clara, CA, USA) in single and double precision. Copyright © 2011 John Wiley & Sons, Ltd.