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SLEEF: A Portable vectorized Library of C Standard Mathematical Functions

IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2020年第6期31卷 1316-1327页

作者： Shibata, Naoki Petrogalli, Francesco Nara Inst Sci & Technol Grad Sch Informat Sci Nara 6300192 Japan ARM110 Cambridge CB1 9NJ England

In this article, we present techniques used to implement our portable vectorized library of C standard mathematical functions written entirely in C language. In order to make the library portable while maintaining good performance, intrinsic functions of vector extensions are abstracted by inline functions or preprocessor macros. We implemented the functions so that they can use sub-features of vector extensions such as fused multiply-add, mask registers, and extraction of mantissa. In order to make computation with SIMD instructions efficient, the library only uses a small number of conditional branches, and all the computation paths are vectorized. We devised a variation of the Payne-Hanek argument reduction for trigonometric functions and a floating point remainder, both of which are suitable for vector computation. We compare the performance with our library to Intel SVML.

关键词： parallel and vector implementations SIMD processors elementary functions floating-point arithmetic

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Adaptive Particle Swarm Optimization with Heterogeneous Multicore parallelism

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IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2017年第10期28卷 2784-2793页

作者： Wachowiak, Mark P. Timson, Mitchell C. DuVal, David J. Nipissing Univ Dept Comp Sci & Math North Bay ON P1B 8L7 Canada

Much progress has recently been made in global optimization, with particular attention devoted to robust nature-inspired stochastic methods for difficult, high-dimensional problems. This paper presents a computational study of an adaptation of one such method, particle swarmoptimization(PSO), which is analyzed for parallelization on readily-available heterogeneous parallel computational hardware: specifically, multicore technologies accelerated by graphics processing units (GPUs), as well as Intel Xeon Phi co-processors accelerated with vectorization. In this heterogeneous approach, computationally-intensive, task-parallel components are performed with multicore parallelism and data-parallel elements are executed via co-processing (GPUs or vectorization). A computationally intensive adaptive PSO technique is parallelized according to this schema. In experiments with two high-dimensional and complex functions, large speedups can be obtained. Thus, a heterogeneous approach mitigates the time complexity of PSO adaptations, suggesting that other time-intensive stochastic methods can also benefit from the techniques proposed here.

关键词： Applications parallel and vector implementations optimization stochastic programming unconstrained optimization

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A Fast parallel Stochastic Gradient Method for Matrix Factorization in Shared Memory Systems

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ACM TRANSACTIONS ON INTELLIGENT SYSTEMS AND TECHNOLOGY 2015年第1期6卷 2-2页

作者： Chin, Wei-Sheng Zhuang, Yong Juan, Yu-Chin Lin, Chih-Jen Natl Taiwan Univ Dept Comp Sci Taipei Taiwan

Matrix factorization is known to be an effective method for recommender systems that are given only the ratings from users to items. Currently, stochastic gradient (SG) method is one of the most popular algorithms for matrix factorization. However, as a sequential approach, SG is difficult to be parallelized for handling web-scale problems. In this article, we develop a fast parallel SG method, FPSG, for shared memory systems. By dramatically reducing the cache-miss rate and carefully addressing the load balance of threads, FPSG is more efficient than state-of-the-art parallel algorithms for matrix factorization.

关键词： parallel and vector implementations Recommender system matrix factorization stochastic gradient descent parallel computing shared memory algorithm

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An Optimized FFT-Based Direct Poisson Solver on CUDA GPUs

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IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2014年第3期25卷 550-559页

作者： Wu, Jing JaJa, Joseph Balaras, Elias Univ Maryland Dept Elect & Comp Engn Inst Adv Comp Studies College Pk MD 20742 USA George Washington Univ Dept Mech & Aerosp Engn Acad Ctr 720F Washington DC 20052 USA

A highly multithreaded FFT-based direct Poisson solver that makes effective use of the capabilities of the current NVIDIA graphics processing units (GPUs) is presented. Our algorithms carefully manage the multiple layers of the memory hierarchy of the GPUs such that almost all the global memory accesses are coalesced into 128-byte device memory transactions, and all computations are carried out directly on the registers. A new strategy to interleave the FFT computation along each dimension with other computations is used to minimize the total number of accesses to the 3D grid. We illustrate the performance of our algorithms on the NVIDIA Tesla and Fermi architectures for a wide range of grid sizes, up to the largest size that can fit on the device memory (512 x 512 x 512 on the Tesla C1060/C2050 and 512 x 256 x 256 on the GeForce GTX 280/480). We achieve up to 140 GFLOPS and a bandwidth of 70 GB/s on the Tesla C1060, and up to 375 GFLOPS with a bandwidth of 120GB/s on the GTX 480. The performance of our algorithms is superior to what can be achieved using the CUDA FFT library in combination with well-known parallel algorithms for solving tridiagonal linear systems of equations.

关键词： Fast-Fourier transforms parallel and vector implementations elliptic equations

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Optimized FFT computations on heterogeneous platforms with application to the Poisson equation

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JOURNAL OF parallel AND DISTRIBUTED COMPUTING 2014年第8期74卷 2745-2756页

作者： Wu, Jing Jaja, Joseph Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Maryland Inst Adv Comp Studies College Pk MD 20742 USA

We develop optimized multi-dimensional FFT implementations on CPU-GPU heterogeneous platforms for the case when the input is too large to fit on the GPU global memory, and use the resulting techniques to develop a fast Poisson solver. The solver involves memory bound computations for which the large 3D data may have to be transferred over the PCIe bus several times during the computation. We develop a new strategy to decompose and allocate the computation between the GPU and the CPU such that the 3D data is transferred only once to the device-memory, and the executions of the GPU kernels are almost completely overlapped with the PCI data transfer. We were able to achieve significantly better performance than what has been reported in previous related work, including over 145 GFLOPS for the three periodic boundary conditions (single precision version), and over 105 GFLOPS for the two periodic, one Neumann boundary conditions (single precision version). The effective bidirectional PCIe bus bandwidth achieved is 9-10 GB/s, which is close to the best possible on our platform. For all the cases tested, the single 3D data PCIe transfer time, which constitutes a lower bound on what is possible on our platform, takes almost 70% of the total execution time of the Poisson solver. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Fast Fourier transforms parallel and vector implementations CUDA GPU Poisson equations

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Performance evaluation and comparison of parallel conjugate gradient on modern multi-core accelerator and massively parallel systems

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INTERNATIONAL JOURNAL OF parallel EMERGENT AND DISTRIBUTED SYSTEMS 2014年第1期29卷 38-67页

作者： Sibai, Fadi N. El-Moursy, Ali Saudi Aramco R&D Ctr Dhahran 31311 Saudi Arabia Univ Sharjah Dept Elect & Comp Engn Sharjah U Arab Emirates

Two parallel computer paradigms available today are multi-core accelerators such as the Sony, Toshiba and IBM Cell or Graphics Processing Unit (GPUs), and massively parallel message-passing machines such as the IBM Blue Gene (BG). The solution of systems of linear equations is one of the most central processing unit-intensive steps in engineering and simulation applications and can greatly benefit from the multitude of processing cores and vectorisation on today's parallel computers. We parallelise the conjugate gradient (CG) linear equation solver on the Cell Broadband Engine and the IBM Blue Gene/L machine. We perform a scalability analysis of CG on both machines across 1, 8 and 16 synergistic processing elements and 1-32 cores on BG with heptadiagonal matrices. The results indicate that the multi-core Cell system outperforms by three to four times the massively parallel BG system due to the Cell's higher communication bandwidth and accelerated vector processing capability.

关键词： parallel and vector implementations mathematical software multiple processor systems Special-purpose and application-based systems multi-core accelerators message-passing systems

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High Performance FFT Based Poisson Solver on a CPU-GPU Heterogeneous Platform

High Performance FFT Based Poisson Solver on a CPU-GPU Heter...

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IEEE 27th International parallel and Distributed Processing Symposium (IPDPS)

作者： Wu, Jing JaJa, Joseph Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA

ISBN: (纸本)9780769549712

We develop an optimized FFT based Poisson solver on a CPU-GPU heterogeneous platform for the case when the input is too large to fit on the GPU global memory. The solver involves memory bound computations such as 3D FFT in which the large 3D data may have to be transferred over the PCIe bus several times during the computation. We develop a new strategy to decompose and allocate the computation between the GPU and the CPU such that the 3D data is transferred only once to the device memory, and the executions of the GPU kernels are almost completely overlapped with the PCI data transfer. We were able to achieve significantly better performance than what has been reported in previous related work, including over 50 GFLOPS for the three periodic boundary conditions, and over 40 GFLOPS for the two periodic, one Neumann boundary conditions. The PCIe bus bandwidth achieved is over 5GB/s, which is close to the best possible on our platform. For all the cases tested, the single 3D PCIe transfer time, which constitutes a lower bound on what is possible on our platform, takes almost 70% of the total execution time of the Poisson solver.

关键词： Fast Fourier Transforms parallel and vector implementations GPU CUDA Poisson Equations

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Three Applications of GPU Computing in Neuroscience

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COMPUTING IN SCIENCE & ENGINEERING 2012年第3期14卷 40-47页

作者： Baladron, Javier Fasoli, Diego Faugeras, Olivier INRIA NeuroMathComp Grp NeuroMathComp Project Team Sophia Antipolis France

Three scenarios outlined here show the benefits of using a computer system with multiple GPUs in theoretical neuroscience. In each instance, it's clear that the GPU speedup considerably helps answer a scientific o... 详细信息

关键词： Graphics Processing Units GPU Computing Neuroscience Computer System Computational Modeling Mathematical Model Numerical Models Brain Modeling Visualization Computational Neuroscience parallel and vector implementations GP Us Scientific Computing

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Accelerating Matrix Operations with Improved Deeply Pipelined vector Reduction

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IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2012年第2期23卷 202-210页

作者： Tai, Yi-Gang Lo, Chia-Tien Dan Psarris, Kleanthis Univ Texas San Antonio Dept Comp Sci San Antonio TX 78249 USA So Polytech State Univ Dept Comp Sci & Software Engn Marietta GA 30060 USA

Many scientific or engineering applications involve matrix operations, in which reduction of vectors is a common operation. If the core operator of the reduction is deeply pipelined, which is usually the case, dependencies between the input data elements cause data hazards. To tackle this problem, we propose a new reduction method with low latency and high pipeline utilization. The performance of the proposed design is evaluated for both single data set and multiple data set scenarios. Further, QR decomposition is used to demonstrate how the proposed method can accelerate its execution. We implement the design on an FPGA and compare its results to other methods.

关键词： Reconfigurable hardware pipeline processors parallel algorithms parallel and vector implementations algorithm design and analysis

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An Optimized Cell BE Special Function Library Generated by Coconut

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IEEE TRANSACTIONS ON COMPUTERS 2009年第8期58卷 1126-1138页

作者： Anand, Christopher Kumar Kahl, Wolfram McMaster Univ Dept Comp & Software ITB202 Hamilton ON L8S 4K1 Canada

Coconut, a tool for developing high-assurance, high-performance kernels for scientific computing, contains an extensible domain-specific language (DSL) embedded in Haskell. The DSL supports interactive prototyping and unit testing, simplifying the process of designing efficient implementations of common patterns. Unscheduled C and scheduled assembly language output are supported. Using the patterns, even nonexpert users can write efficient function implementations, leveraging special hardware features. A production-quality library of elementary functions for the Cell BE SPU compute engines has been developed. Coconut-generated and -scheduled vector functions were more than four times faster than commercially distributed functions written in C with intrinsics (a nicer syntax for in-line assembly), wrapped in loops and scheduled by spuxIc. All Coconut functions were faster, but the difference was larger for hard-to-approximate functions for which register-level SIMD lookups made a bigger difference. Other helpful features in the language include facilities for translating interval and polynomial descriptions between GHCi, a Haskell interpreter used to prototype in the DSL, and Maple, used for exploration and minimax polynomial generation. This makes it easier to match mathematical properties of the functions with efficient calculational patterns in the SPU ISA. By using single, literate source files, the resulting functions are remarkably readable.

关键词： Special function approximations parallel and vector implementations code generation specialized application languages SIMD processors applicative (functional) programming

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