本文提出了一种在Julia中实现的基于QR分解的奇异值计算算法的便携式GPU加速实现。奇异值分解（SVD）是科学计算和机器学习中的基础数值工具，提供最优低秩矩阵近似。其重要性在大规模机器学习流程中更加凸显，包括大型语言模型（LLMs），其中它支持低秩适应（LoRA）。所实现的算法基于经典的两阶段QR约简，包括连续将矩阵约简为带状形式和对角形式。我们的实现利用Julia的多重分派和元编程能力，与GPUArrays和KernelAbstractions框架集成，提供统一的类型和硬件无关函数。它支持多种GPU架构和数据类型，据我们所知，这是首个支持Apple Metal GPU和半精度的GPU加速奇异值实现。在多个GPU后端和数据类型上的性能结果表明，便携性并不需要牺牲性能：对于大于1024x1024的矩阵，该统一函数优于大多数线性代数库（MAGMA、SLATE、rocSOLVER、oneMKL），对于大矩阵，其性能达到cuSOLVER的80%-90%。
英文摘要：
This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value ecomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning, providing optimal low-rank matrix approximations. Its importance has increased even more in large-scale machine learning pipelines, including large language models (LLMs), where it enables low-rank adaptation (LoRA). The implemented algorithm is based on the classic two-stage QR reduction, consisting of successive matrix reduction to band form and bidiagonal form. Our implementation leverages Julia's multiple dispatch and metaprogramming capabilities, integrating with the GPUArrays and KernelAbstractions frameworks to provide a unified type and hardware-agnostic function. It supports diverse GPU architectures and data types, and is, to our knowledge, the first GPU-accelerated singular value implementation to support Apple Metal GPUs and half precision. Performance results on multiple GPU backends and data types demonstrate that portability does not require sacrificing performance: the unified function outperforms most linear algebra libraries (MAGMA, SLATE, rocSOLVER, oneMKL) for matrix sizes larger than 1024x1024, and achieves 80%-90% of the performance of cuSOLVER for large matrices.
Containers are an emerging technology that hold promise for improving productivity and code portability in scientific computing. We examine Linux container technology for the distribution of a non-trivial scientific computing software stack and its execution on a spectrum of platforms from laptop computers through to high performance computing (HPC) systems. We show on a workstation and a leadership-class HPC system that when deployed appropriately there are no performance penalties running scientific programs inside containers. For Python code run on large parallel computers, the run time is …
The Portable Extensible Toolkit for Scientific computation (PETSc) library delivers scalable solvers for nonlinear time-dependent differential and algebraic equations and for numerical optimization.The PETSc design for performance portability addresses fundamental GPU accelerator challenges and stresses flexibility and extensibility by separating the programming model used by the application from that used by the library, and it enables application developers to use their preferred programming model, such as Kokkos, RAJA, SYCL, HIP, CUDA, or OpenCL, on upcoming exascale systems. A blueprint fo…
GPU runtimes are historically implemented in CUDA or other vendor specific languages dedicated to GPU programming. In this work we show that OpenMP 5.1, with minor compiler extensions, is capable of replacing existing solutions without a performance penalty. The result is a performant and portable GPU runtime that can be compiled with LLVM/Clang to Nvidia and AMD GPUs without the need for CUDA or HIP during its development and compilation. While we tried to be OpenMP compliant, we identified the need for compiler extensions to achieve the CUDA performance with our OpenMP runtime. We hope that …
Meeting both scalability and performance portability requirements is a challenge for any HPC application, especially for adaptively refined ones. In Octo-Tiger, an astrophysics application for the simulation of stellar mergers, we approach this with existing solutions: We employ HPX to obtain fine-grained tasks to easily distribute work and finely overlap communication and computation. For the computations themselves, we use Kokkos to turn these tasks into compute kernels capable of running on hardware ranging from a few CPU cores to powerful accelerators. There is a missing link, however: whi…
Characterizing compute kernel execution behavior on GPUs for efficient task scheduling is a non-trivial task. We address this with a simple model enabling portable and fast predictions among different GPUs using only hardware-independent features. This model is built based on random forests using 189 individual compute kernels from benchmarks such as Parboil, Rodinia, Polybench-GPU and SHOC. Evaluation of the model performance using cross-validation yields a median Mean Average Percentage Error (MAPE) of 8.86-52.00% and 1.84-2.94%, for time respectively power prediction across five different G…
OpenMC is an open source Monte Carlo neutral particle transport application that has recently been ported to GPU using the OpenMP target offloading model. We examine the performance of OpenMC at scale on the Frontier, Polaris, and Aurora supercomputers, demonstrating that performance portability has been achieved by OpenMC across all three major GPU vendors (AMD, NVIDIA, and Intel). OpenMC's GPU performance is compared to both the traditional CPU-based version of OpenMC as well as several other state-of-the-art CPU-based Monte Carlo particle transport applications. We also provide historical c…
We present hipBone, an open source performance-portable proxy application for the Nek5000 (and NekRS) CFD applications. HipBone is a fully GPU-accelerated C++ implementation of the original NekBone CPU proxy application with several novel algorithmic and implementation improvements which optimize its performance on modern fine-grain parallel GPU accelerators. Our optimizations include a conversion to store the degrees of freedom of the problem in assembled form in order to reduce the amount of data moved during the main iteration and a portable implementation of the main Poisson operator kerne…
Georgia Institute of Technology（佐治亚理工学院）；Twentieth Century Fox（二十世纪福克斯）；Starfleet Academy（星际舰队学院）
General Matrix Multiplication or GEMM kernels take centre place in high performance computing and machine learning. Recent NVIDIA GPUs include GEMM accelerators, such as NVIDIA's Tensor Cores. Their exploitation is hampered by the two-language problem: it requires either low-level programming which implies low programmer productivity or using libraries that only offer a limited set of components. Because rephrasing algorithms in terms of established components often introduces overhead, the libraries' lack of flexibility limits the freedom to explore new algorithms. Researchers using GEMMs can…
We present a portable platform, called PIC_ENGINE, for accelerating Particle-In-Cell (PIC) codes on heterogeneous many-core architectures such as Graphic Processing Units (GPUs). The aim of this development is efficient simulations on future exascale systems by allowing different parallelization strategies depending on the application problem and the specific architecture. To this end, this platform contains the basic steps of the PIC algorithm and has been designed as a test bed for different algorithmic options and data structures. Among the architectures that this engine can explore, partic…
High-throughput structure-based screening of drug-like molecules has become a common tool in biomedical research. Recently, acceleration with graphics processing units (GPUs) has provided a large performance boost for molecular docking programs. Both cloud and high-performance computing (HPC) resources have been used for large screens with molecular docking programs; while NVIDIA GPUs have dominated cloud and HPC resources, new vendors such as AMD and Intel are now entering the field, creating the problem of software portability across different GPUs. Ideally, software productivity could be ma…
Belief Propagation (BP) is a message-passing algorithm for approximate inference over Probabilistic Graphical Models (PGMs), finding many applications such as computer vision, error-correcting codes, and protein-folding. While general, the convergence and speed of the algorithm has limited its practical use on difficult inference problems. As an algorithm that is highly amenable to parallelization, many-core Graphical Processing Units (GPUs) could significantly improve BP performance. Improving BP through many-core systems is non-trivial: the scheduling of messages in the algorithm strongly af…
Computed Tomography (CT) is a key 3D imaging technology that fundamentally relies on the compute-intense back-projection operation to generate 3D volumes. GPUs are typically used for back-projection in production CT devices. However, with the rise of power-constrained micro-CT devices, and also the emergence of CPUs comparable in performance to GPUs, back-projection for CPUs could become favorable. Unlike GPUs, extracting parallelism for back-projection algorithms on CPUs is complex given that parallelism and locality are not explicitly defined and controlled by the programmer, as is the case …
The task of multi-dimensional numerical integration is frequently encountered in physics and other scientific fields, e.g., in modeling the effects of systematic uncertainties in physical systems and in Bayesian parameter estimation. Multi-dimensional integration is often time-prohibitive on CPUs. Efficient implementation on many-core architectures is challenging as the workload across the integration space cannot be predicted a priori. We propose m-Cubes, a novel implementation of the well-known Vegas algorithm for execution on GPUs. Vegas transforms integration variables followed by calculat…
Graphic Processing Units (GPUs) have become ubiquitous in scientific computing. However, writing efficient GPU kernels can be challenging due to the need for careful code tuning. To automatically explore the kernel optimization space, several auto-tuning tools - like Kernel Tuner - have been proposed. Unfortunately, these existing auto-tuning tools often do not concern themselves with integration of tuning results back into applications, which puts a significant implementation and maintenance burden on application developers. In this work, we present Kernel Launcher: an easy-to-use C++ library…
Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that high-order methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs; these data structures also offer up to 2x benefit for linear elements. We demonstrate the reliability, efficiency, and scalability of matrix-free $p$-multigrid methods with algebraic multigrid coarse…
We present a new lock-free multiple-producer and multiple-consumer (MPMC) FIFO queue design which is scalable and, unlike existing high-performant queues, very memory efficient. Moreover, the design is ABA safe and does not require any external memory allocators or safe memory reclamation techniques, typically needed by other scalable designs. In fact, this queue itself can be leveraged for object allocation and reclamation, as in data pools. We use FAA (fetch-and-add), a specialized and more scalable than CAS (compare-and-set) instruction, on the most contended hot spots of the algorithm. How…
UC Berkeley（加州大学伯克利分校）；UC Davis（加州大学戴维斯分校）；UW–Madison（威斯康星大学麦迪逊分校）；AMD（超威半导体）；Tsinghua University（清华大学）；Amazon Web Services（亚马逊网络服务）；ICSI（信息与计算机科学研究所）；Broadcom & University Politehnica of Bucharest（博通与布加勒斯特理工大学）
The Liquid Argon Time Projection Chamber (LArTPC) technology plays an essential role in many current and future neutrino experiments. Accurate and fast simulation is critical to developing efficient analysis algorithms and precise physics model projections. The speed of simulation becomes more important as Deep Learning algorithms are getting more widely used in LArTPC analysis and their training requires a large simulated dataset. Heterogeneous computing is an efficient way to delegate computing-heavy tasks to specialized hardware. However, as the landscape of the compute accelerators is evol…
Searching for geometric objects that are close in space is a fundamental component of many applications. The performance of search algorithms comes to the forefront as the size of a problem increases both in terms of total object count as well as in the total number of search queries performed. Scientific applications requiring modern leadership-class supercomputers also pose an additional requirement of performance portability, i.e. being able to efficiently utilize a variety of hardware architectures. In this paper, we introduce a new open-source C++ search library, ArborX, which we have des…
This paper is devoted to the development of highly efficient kernels performing vector operations relevant in linear system solvers. In particular, we focus on the low arithmetic intensity operations (i.e., streaming operations) performed within the conjugate gradient iterative method, using the parameters specified in the CEED benchmark problems for high-order hexahedral finite elements. We propose a suite of new Benchmark Streaming tests to focus on the distinct streaming operations which must be performed. We implemented these new tests using the OCCA abstraction framework to demonstrate po…
To achieve high performance on modern computers, it is vital to map algorithmic parallelism to that inherent in the hardware. From an application developer's perspective, it is also important that code can be maintained in a portable manner across a range of hardware. Here we present targetDP (target Data Parallel), a lightweight programming layer that allows the abstraction of data parallelism for applications that employ structured grids. A single source code may be used to target both thread level parallelism (TLP) and instruction level parallelism (ILP) on either SIMD multi-core CPUs or GP…
Building and deploying software on high-end computing systems is a challenging task. High performance applications have to reliably run across multiple platforms and environments, and make use of site-specific resources while resolving complicated software-stack dependencies. Containers are a type of lightweight virtualization technology that attempt to solve this problem by packaging applications and their environments into standard units of software that are: portable, easy to build and deploy, have a small footprint, and low runtime overhead. In this work we present an extension to the cont…
Atomistic simulation drives scientific advances in modern material science and accounts for a significant proportion of wall time on High Performance Computing facilities. It is important that algorithms are efficient and implementations are performant in a continuously diversifying hardware landscape. Furthermore, they have to be portable to make best use of the available computing resource. In this paper we assess the parallel performance of some key algorithms implemented in a performance portable framework developed by us. We consider Molecular Dynamics with short range interactions, the F…
Empirical Dynamic Modeling (EDM) is a state-of-the-art non-linear time-series analysis framework. Despite its wide applicability, EDM was not scalable to large datasets due to its expensive computational cost. To overcome this obstacle, researchers have attempted and succeeded in accelerating EDM from both algorithmic and implementational aspects. In previous work, we developed a massively parallel implementation of EDM targeting HPC systems (mpEDM). However, mpEDM maintains different backends for different architectures. This design becomes a burden in the increasingly diversifying HPC system…
High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based on sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this pape…
PetscSF, the communication component of the Portable, Extensible Toolkit for Scientific Computation (PETSc), is designed to provide PETSc's communication infrastructure suitable for exascale computers that utilize GPUs and other accelerators. PetscSF provides a simple application programming interface (API) for managing common communication patterns in scientific computations by using a star-forest graph representation. PetscSF supports several implementations based on MPI and NVSHMEM, whose selection is based on the characteristics of the application or the target architecture. An efficient a…
Hardware heterogeneity is here to stay for high-performance computing. Large-scale systems are currently equipped with multiple GPU accelerators per compute node and are expected to incorporate more specialized hardware in the future. This shift in the computing ecosystem offers many opportunities for performance improvement; however, it also increases the complexity of programming for such architectures. This work introduces a runtime framework that enables effortless programming for heterogeneous systems while efficiently utilizing hardware resources. The framework is integrated within a dis…
This paper investigates the suitability of the AnyDSL partial evaluation framework to implement tinyMD: an efficient, scalable, and portable simulation of pairwise interactions among particles. We compare tinyMD with the miniMD proxy application that scales very well on parallel supercomputers. We discuss the differences between both implementations and contrast miniMD's performance for single-node CPU and GPU targets, as well as its scalability on SuperMUC-NG and Piz Daint supercomputers. Additionaly, we demonstrate tinyMD's flexibility by coupling it with the waLBerla multi-physics framework…
With the appearance of the heterogeneous platform OpenPower,many-core accelerator devices have been coupled with Power host processors for the first time. Towards utilizing their full potential, it is worth investigating performance portable algorithms that allow to choose the best-fitting hardware for each domain-specific compute task. Suiting even the high level of parallelism on modern GPGPUs, our presented approach relies heavily on abstract meta-programming techniques, which are essential to focus on fine-grained tuning rather than code porting. With this in mind, the CUDA-based open-sour…
