Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier-Stokes equations, with a highly parallel fast multipole method (FMM) as numerical engine, and match the current record in mesh size for this application, a cube of 4096^3 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the FFT algorithm as numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm-based vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpus per node of the TSUBAME-2.0 system). The FFT-based spectral method is able to achieve just 14% parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the FFT algorithm. The calculation time for one time step was 108 seconds for the vortex method and 154 seconds for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex method calculations to date

Beyond the socket: NUMA-aware GPUs

GPUs achieve high throughput and power efficiency by employing many small single instruction multiple thread (SIMT) cores. To minimize scheduling logic and performance variance they utilize a uniform memory system and leverage strong data parallelism exposed via the programming model. With Moore's law slowing, for GPUs to continue scaling performance (which largely depends on SIMT core count) they are likely to embrace multi-socket designs where transistors are more readily available. However when moving to such designs, maintaining the illusion of a uniform memory system is increasingly difficult. In this work we investigate multi-socket non-uniform memory access (NUMA) GPU designs and show that significant changes are needed to both the GPU interconnect and cache architectures to achieve performance scalability. We show that application phase effects can be exploited allowing GPU sockets to dynamically optimize their individual interconnect and cache policies, minimizing the impact of NUMA effects. Our NUMA-aware GPU outperforms a single GPU by 1.5×, 2.3×, and 3.2× while achieving 89%, 84%, and 76% of theoretical application scalability in 2, 4, and 8 sockets designs respectively. Implementable today, NUMA-aware multi-socket GPUs may be a promising candidate for scaling GPU performance beyond a single socket.We would like to thank anonymous reviewers and Steve Keckler for their help in improving this paper. The first author is supported by the Ministry of Economy and Competitiveness of Spain (TIN2012-34557, TIN2015-65316-P, and BES-2013-063925)Peer ReviewedPostprint (published version

A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the order of billions of unknowns. That work led to an extremely parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This paper reports on a a campaign of performance tuning and scalability studies using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were parallelized using OpenMP, and a test using 10^7 particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using SIMD instructions resulted in 4x speed-up of the overall algorithm on single-core tests with 10^3 - 10^7 particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 10^8 particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2x faster). The weak scaling test used 10^6 particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that FMM is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape

Memory Subsystem Optimization Techniques for Modern High-Performance General-Purpose Processors

abstract: General-purpose processors propel the advances and innovations that are the subject of humanity’s many endeavors. Catering to this demand, chip-multiprocessors (CMPs) and general-purpose graphics processing units (GPGPUs) have seen many high-performance innovations in their architectures. With these advances, the memory subsystem has become the performance- and energy-limiting aspect of CMPs and GPGPUs alike. This dissertation identifies and mitigates the key performance and energy-efficiency bottlenecks in the memory subsystem of general-purpose processors via novel, practical, microarchitecture and system-architecture solutions. Addressing the important Last Level Cache (LLC) management problem in CMPs, I observe that LLC management decisions made in isolation, as in prior proposals, often lead to sub-optimal system performance. I demonstrate that in order to maximize system performance, it is essential to manage the LLCs while being cognizant of its interaction with the system main memory. I propose ReMAP, which reduces the net memory access cost by evicting cache lines that either have no reuse, or have low memory access cost. ReMAP improves the performance of the CMP system by as much as 13%, and by an average of 6.5%. Rather than the LLC, the L1 data cache has a pronounced impact on GPGPU performance by acting as the bandwidth filter for the rest of the memory subsystem. Prior work has shown that the severely constrained data cache capacity in GPGPUs leads to sub-optimal performance. In this thesis, I propose two novel techniques that address the GPGPU data cache capacity problem. I propose ID-Cache that performs effective cache bypassing and cache line size selection to improve cache capacity utilization. Next, I propose LATTE-CC that considers the GPU’s latency tolerance feature and adaptively compresses the data stored in the data cache, thereby increasing its effective capacity. ID-Cache and LATTE-CC are shown to achieve 71% and 19.2% speedup, respectively, over a wide variety of GPGPU applications. Complementing the aforementioned microarchitecture techniques, I identify the need for system architecture innovations to sustain performance scalability of GPG- PUs in the face of slowing Moore’s Law. I propose a novel GPU architecture called the Multi-Chip-Module GPU (MCM-GPU) that integrates multiple GPU modules to form a single logical GPU. With intelligent memory subsystem optimizations tailored for MCM-GPUs, it can achieve within 7% of the performance of a similar but hypothetical monolithic die GPU. Taking a step further, I present an in-depth study of the energy-efficiency characteristics of future MCM-GPUs. I demonstrate that the inherent non-uniform memory access side-effects form the key energy-efficiency bottleneck in the future. In summary, this thesis offers key insights into the performance and energy-efficiency bottlenecks in CMPs and GPGPUs, which can guide future architects towards developing high-performance and energy-efficient general-purpose processors.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Matching non-uniformity for program optimizations on heterogeneous many-core systems

As computing enters an era of heterogeneity and massive parallelism, it exhibits a distinct feature: the deepening non-uniform relations among the computing elements in both hardware and software. Besides traditional non-uniform memory accesses, much deeper non-uniformity shows in a processor, runtime, and application, exemplified by the asymmetric cache sharing, memory coalescing, and thread divergences on multicore and many-core processors. Being oblivious to the non-uniformity, current applications fail to tap into the full potential of modern computing devices.;My research presents a systematic exploration into the emerging property. It examines the existence of such a property in modern computing, its influence on computing efficiency, and the challenges for establishing a non-uniformity--aware paradigm. I propose several techniques to translate the property into efficiency, including data reorganization to eliminate non-coalesced accesses, asynchronous data transformations for locality enhancement and a controllable scheduling for exploiting non-uniformity among thread blocks. The experiments show much promise of these techniques in maximizing computing throughput, especially for programs with complex data access patterns

Virtualizing Data Parallel Systems for Portability, Productivity, and Performance.

Computer systems equipped with graphics processing units (GPUs) have become increasingly common over the last decade. In order to utilize the highly data parallel architecture of GPUs for general purpose applications, new programming models such as OpenCL and CUDA were introduced, showing that data parallel kernels on GPUs can achieve speedups by several orders of magnitude. With this success, applications from a variety of domains have been converted to use several complicated OpenCL/CUDA data parallel kernels to benefit from data parallel systems. Simultaneously, the software industry has experienced a massive growth in the amount of data to process, demanding more powerful workhorses for data parallel computation. Consequently, additional parallel computing devices such as extra GPUs and co-processors are attached to the system, expecting more performance and capability to process larger data. However, these programming models expose hardware details to programmers, such as the number of computing devices, interconnects, and physical memory size of each device. This degrades productivity in the software development process as programmers must manually split the workload with regard to hardware characteristics. This process is tedious and prone to errors, and most importantly, it is hard to maximize the performance at compile time as programmers do not know the runtime behaviors that can affect the performance such as input size and device availability. Therefore, applications lack portability as they may fail to run due to limited physical memory or experience suboptimal performance across different systems. To cope with these challenges, this thesis proposes a dynamic compiler framework that provides the OpenCL applications with an abstraction layer for physical devices. This abstraction layer virtualizes physical devices and memory sub-systems, and transparently orchestrates the execution of multiple data parallel kernels on multiple computing devices. The framework significantly improves productivity as it provides hardware portability, allowing programmers to write an OpenCL program without being concerned of the target devices. Our framework also maximizes performance by balancing the data parallel workload considering factors like kernel dependencies, device performance variation on workloads of different sizes, the data transfer cost over the interconnect between devices, and physical memory limits on each device.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113361/1/jhaeng_1.pd