CS 267 Dense Linear Algebra: History and Structure, Parallel Matrix
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Life As a Developer of Numerical Software
A Brief History of Numerical Libraries Sven Hammarling NAG Ltd, Oxford & University of Manchester First – Something about Jack Jack’s thesis (August 1980) 30 years ago! TOMS Algorithm 589 Small Selection of Jack’s Projects • Netlib and other software repositories • NA Digest and na-net • PVM and MPI • TOP 500 and computer benchmarking • NetSolve and other distributed computing projects • Numerical linear algebra Onto the Rest of the Talk! Rough Outline • History and influences • Fortran • Floating Point Arithmetic • Libraries and packages • Proceedings and Books • Summary Ada Lovelace (Countess Lovelace) Born Augusta Ada Byron 1815 – 1852 The language Ada was named after her “Is thy face like thy mother’s, my fair child! Ada! sole daughter of my house and of my heart? When last I saw thy young blue eyes they smiled, And then we parted,-not as now we part, but with a hope” Childe Harold’s Pilgramage, Lord Byron Program for the Bernoulli Numbers Manchester Baby, 21 June 1948 (Replica) 19 Kilburn/Tootill Program to compute the highest proper factor 218 218 took 52 minutes 1.5 million instructions 3.5 million store accesses First published numerical library, 1951 First use of the word subroutine? Quality Numerical Software • Should be: – Numerically stable, with measures of quality of solution – Reliable and robust – Accompanied by test software – Useful and user friendly with example programs – Fully documented – Portable – Efficient “I have little doubt that about 80 per cent. of all the results printed from the computer are in error to a much greater extent than the user would believe, ...'' Leslie Fox, IMA Bulletin, 1971 “Giving business people spreadsheets is like giving children circular saws. -
Microbenchmarks in Big Data
M Microbenchmark Overview Microbenchmarks constitute the first line of per- Nicolas Poggi formance testing. Through them, we can ensure Databricks Inc., Amsterdam, NL, BarcelonaTech the proper and timely functioning of the different (UPC), Barcelona, Spain individual components that make up our system. The term micro, of course, depends on the prob- lem size. In BigData we broaden the concept Synonyms to cover the testing of large-scale distributed systems and computing frameworks. This chap- Component benchmark; Functional benchmark; ter presents the historical background, evolution, Test central ideas, and current key applications of the field concerning BigData. Definition Historical Background A microbenchmark is either a program or routine to measure and test the performance of a single Origins and CPU-Oriented Benchmarks component or task. Microbenchmarks are used to Microbenchmarks are closer to both hardware measure simple and well-defined quantities such and software testing than to competitive bench- as elapsed time, rate of operations, bandwidth, marking, opposed to application-level – macro or latency. Typically, microbenchmarks were as- – benchmarking. For this reason, we can trace sociated with the testing of individual software microbenchmarking influence to the hardware subroutines or lower-level hardware components testing discipline as can be found in Sumne such as the CPU and for a short period of time. (1974). Furthermore, we can also find influence However, in the BigData scope, the term mi- in the origins of software testing methodology crobenchmarking is broadened to include the during the 1970s, including works such cluster – group of networked computers – acting as Chow (1978). One of the first examples of as a single system, as well as the testing of a microbenchmark clearly distinguishable from frameworks, algorithms, logical and distributed software testing is the Whetstone benchmark components, for a longer period and larger data developed during the late 1960s and published sizes. -
Overview of the SPEC Benchmarks
9 Overview of the SPEC Benchmarks Kaivalya M. Dixit IBM Corporation “The reputation of current benchmarketing claims regarding system performance is on par with the promises made by politicians during elections.” Standard Performance Evaluation Corporation (SPEC) was founded in October, 1988, by Apollo, Hewlett-Packard,MIPS Computer Systems and SUN Microsystems in cooperation with E. E. Times. SPEC is a nonprofit consortium of 22 major computer vendors whose common goals are “to provide the industry with a realistic yardstick to measure the performance of advanced computer systems” and to educate consumers about the performance of vendors’ products. SPEC creates, maintains, distributes, and endorses a standardized set of application-oriented programs to be used as benchmarks. 489 490 CHAPTER 9 Overview of the SPEC Benchmarks 9.1 Historical Perspective Traditional benchmarks have failed to characterize the system performance of modern computer systems. Some of those benchmarks measure component-level performance, and some of the measurements are routinely published as system performance. Historically, vendors have characterized the performances of their systems in a variety of confusing metrics. In part, the confusion is due to a lack of credible performance information, agreement, and leadership among competing vendors. Many vendors characterize system performance in millions of instructions per second (MIPS) and millions of floating-point operations per second (MFLOPS). All instructions, however, are not equal. Since CISC machine instructions usually accomplish a lot more than those of RISC machines, comparing the instructions of a CISC machine and a RISC machine is similar to comparing Latin and Greek. 9.1.1 Simple CPU Benchmarks Truth in benchmarking is an oxymoron because vendors use benchmarks for marketing purposes. -
Hypervisors Vs. Lightweight Virtualization: a Performance Comparison
2015 IEEE International Conference on Cloud Engineering Hypervisors vs. Lightweight Virtualization: a Performance Comparison Roberto Morabito, Jimmy Kjällman, and Miika Komu Ericsson Research, NomadicLab Jorvas, Finland [email protected], [email protected], [email protected] Abstract — Virtualization of operating systems provides a container and alternative solutions. The idea is to quantify the common way to run different services in the cloud. Recently, the level of overhead introduced by these platforms and the lightweight virtualization technologies claim to offer superior existing gap compared to a non-virtualized environment. performance. In this paper, we present a detailed performance The remainder of this paper is structured as follows: in comparison of traditional hypervisor based virtualization and Section II, literature review and a brief description of all the new lightweight solutions. In our measurements, we use several technologies and platforms evaluated is provided. The benchmarks tools in order to understand the strengths, methodology used to realize our performance comparison is weaknesses, and anomalies introduced by these different platforms in terms of processing, storage, memory and network. introduced in Section III. The benchmark results are presented Our results show that containers achieve generally better in Section IV. Finally, some concluding remarks and future performance when compared with traditional virtual machines work are provided in Section V. and other recent solutions. Albeit containers offer clearly more dense deployment of virtual machines, the performance II. BACKGROUND AND RELATED WORK difference with other technologies is in many cases relatively small. In this section, we provide an overview of the different technologies included in the performance comparison. -
Numerical and Parallel Libraries
Numerical and Parallel Libraries Uwe Küster University of Stuttgart High-Performance Computing-Center Stuttgart (HLRS) www.hlrs.de Uwe Küster Slide 1 Höchstleistungsrechenzentrum Stuttgart Numerical Libraries Public Domain commercial vendor specific Uwe Küster Slide 2 Höchstleistungsrechenzentrum Stuttgart 33. — Numerical and Parallel Libraries — 33. 33-1 Overview • numerical libraries for linear systems – dense – sparse •FFT • support for parallelization Uwe Küster Slide 3 Höchstleistungsrechenzentrum Stuttgart Public Domain Lapack-3 linear equations, eigenproblems BLAS fast linear kernels Linpack linear equations Eispack eigenproblems Slatec old library, large functionality Quadpack numerical quadrature Itpack sparse problems pim linear systems PETSc linear systems Netlib Server best server http://www.netlib.org/utk/papers/iterative-survey/packages.html Uwe Küster Slide 4 Höchstleistungsrechenzentrum Stuttgart 33. — Numerical and Parallel Libraries — 33. 33-2 netlib server for all public domain numerical programs and libraries http://www.netlib.org Uwe Küster Slide 5 Höchstleistungsrechenzentrum Stuttgart Contents of netlib access aicm alliant amos ampl anl-reports apollo atlas benchmark bib bibnet bihar blacs blas blast bmp c c++ cephes chammp cheney-kincaid clapack commercial confdb conformal contin control crc cumulvs ddsv dierckx diffpack domino eispack elefunt env f2c fdlibm fftpack fishpack fitpack floppy fmm fn fortran fortran-m fp gcv gmat gnu go graphics harwell hence hompack hpf hypercube ieeecss ijsa image intercom itpack -
Power Measurement Tutorial for the Green500 List
Power Measurement Tutorial for the Green500 List R. Ge, X. Feng, H. Pyla, K. Cameron, W. Feng June 27, 2007 Contents 1 The Metric for Energy-Efficiency Evaluation 1 2 How to Obtain P¯(Rmax)? 2 2.1 The Definition of P¯(Rmax)...................................... 2 2.2 Deriving P¯(Rmax) from Unit Power . 2 2.3 Measuring Unit Power . 3 3 The Measurement Procedure 3 3.1 Equipment Check List . 4 3.2 Software Installation . 4 3.3 Hardware Connection . 4 3.4 Power Measurement Procedure . 5 4 Appendix 6 4.1 Frequently Asked Questions . 6 4.2 Resources . 6 1 The Metric for Energy-Efficiency Evaluation This tutorial serves as a practical guide for measuring the computer system power that is required as part of a Green500 submission. It describes the basic procedures to be followed in order to measure the power consumption of a supercomputer. A supercomputer that appears on The TOP500 List can easily consume megawatts of electric power. This power consumption may lead to operating costs that exceed acquisition costs as well as intolerable system failure rates. In recent years, we have witnessed an increasingly stronger movement towards energy-efficient computing systems in academia, government, and industry. Thus, the purpose of the Green500 List is to provide a ranking of the most energy-efficient supercomputers in the world and serve as a complementary view to the TOP500 List. However, as pointed out in [1, 2], identifying a single objective metric for energy efficiency in supercom- puters is a difficult task. Based on [1, 2] and given the already existing use of the “performance per watt” metric, the Green500 List uses “performance per watt” (PPW) as its metric to rank the energy efficiency of supercomputers. -
The High Performance Linpack (HPL) Benchmark Evaluation on UTP High Performance Computing Cluster by Wong Chun Shiang 16138 Diss
The High Performance Linpack (HPL) Benchmark Evaluation on UTP High Performance Computing Cluster By Wong Chun Shiang 16138 Dissertation submitted in partial fulfilment of the requirements for the Bachelor of Technology (Hons) (Information and Communications Technology) MAY 2015 Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh Perak Darul Ridzuan CERTIFICATION OF APPROVAL The High Performance Linpack (HPL) Benchmark Evaluation on UTP High Performance Computing Cluster by Wong Chun Shiang 16138 A project dissertation submitted to the Information & Communication Technology Programme Universiti Teknologi PETRONAS In partial fulfillment of the requirement for the BACHELOR OF TECHNOLOGY (Hons) (INFORMATION & COMMUNICATION TECHNOLOGY) Approved by, ____________________________ (DR. IZZATDIN ABDUL AZIZ) UNIVERSITI TEKNOLOGI PETRONAS TRONOH, PERAK MAY 2015 ii CERTIFICATION OF ORIGINALITY This is to certify that I am responsible for the work submitted in this project, that the original work is my own except as specified in the references and acknowledgements, and that the original work contained herein have not been undertaken or done by unspecified sources or persons. ________________ WONG CHUN SHIANG iii ABSTRACT UTP High Performance Computing Cluster (HPCC) is a collection of computing nodes using commercially available hardware interconnected within a network to communicate among the nodes. This campus wide cluster is used by researchers from internal UTP and external parties to compute intensive applications. However, the HPCC has never been benchmarked before. It is imperative to carry out a performance study to measure the true computing ability of this cluster. This project aims to test the performance of a campus wide computing cluster using a selected benchmarking tool, the High Performance Linkpack (HPL). -
A Study on the Evaluation of HPC Microservices in Containerized Environment
ReceivED XXXXXXXX; ReVISED XXXXXXXX; Accepted XXXXXXXX DOI: xxx/XXXX ARTICLE TYPE A Study ON THE Evaluation OF HPC Microservices IN Containerized EnVIRONMENT DeVKI Nandan Jha*1 | SaurABH Garg2 | Prem PrAKASH JaYARAMAN3 | Rajkumar Buyya4 | Zheng Li5 | GrAHAM Morgan1 | Rajiv Ranjan1 1School Of Computing, Newcastle UnivERSITY, UK Summary 2UnivERSITY OF Tasmania, Australia, 3Swinburne UnivERSITY OF TECHNOLOGY, AustrALIA Containers ARE GAINING POPULARITY OVER VIRTUAL MACHINES (VMs) AS THEY PROVIDE THE ADVANTAGES 4 The UnivERSITY OF Melbourne, AustrALIA OF VIRTUALIZATION WITH THE PERFORMANCE OF NEAR bare-metal. The UNIFORMITY OF SUPPORT PROVIDED 5UnivERSITY IN Concepción, Chile BY DockER CONTAINERS ACROSS DIFFERENT CLOUD PROVIDERS MAKES THEM A POPULAR CHOICE FOR DEVel- Correspondence opers. EvOLUTION OF MICROSERVICE ARCHITECTURE ALLOWS COMPLEX APPLICATIONS TO BE STRUCTURED INTO *DeVKI Nandan Jha Email: [email protected] INDEPENDENT MODULAR COMPONENTS MAKING THEM EASIER TO manage. High PERFORMANCE COMPUTING (HPC) APPLICATIONS ARE ONE SUCH APPLICATION TO BE DEPLOYED AS microservices, PLACING SIGNIfiCANT RESOURCE REQUIREMENTS ON THE CONTAINER FRamework. HoweVER, THERE IS A POSSIBILTY OF INTERFERENCE BETWEEN DIFFERENT MICROSERVICES HOSTED WITHIN THE SAME CONTAINER (intra-container) AND DIFFERENT CONTAINERS (inter-container) ON THE SAME PHYSICAL host. In THIS PAPER WE DESCRIBE AN Exten- SIVE EXPERIMENTAL INVESTIGATION TO DETERMINE THE PERFORMANCE EVALUATION OF DockER CONTAINERS EXECUTING HETEROGENEOUS HPC microservices. WE ARE PARTICULARLY CONCERNED WITH HOW INTRa- CONTAINER AND inter-container INTERFERENCE INflUENCES THE performance. MoreoVER, WE INVESTIGATE THE PERFORMANCE VARIATIONS IN DockER CONTAINERS WHEN CONTROL GROUPS (cgroups) ARE USED FOR RESOURCE limitation. FOR EASE OF PRESENTATION AND REPRODUCIBILITY, WE USE Cloud Evaluation Exper- IMENT Methodology (CEEM) TO CONDUCT OUR COMPREHENSIVE SET OF Experiments. -
Jack Dongarra: Supercomputing Expert and Mathematical Software Specialist
Biographies Jack Dongarra: Supercomputing Expert and Mathematical Software Specialist Thomas Haigh University of Wisconsin Editor: Thomas Haigh Jack J. Dongarra was born in Chicago in 1950 to a he applied for an internship at nearby Argonne National family of Sicilian immigrants. He remembers himself as Laboratory as part of a program that rewarded a small an undistinguished student during his time at a local group of undergraduates with college credit. Dongarra Catholic elementary school, burdened by undiagnosed credits his success here, against strong competition from dyslexia.Onlylater,inhighschool,didhebeginto students attending far more prestigious schools, to Leff’s connect material from science classes with his love of friendship with Jim Pool who was then associate director taking machines apart and tinkering with them. Inspired of the Applied Mathematics Division at Argonne.2 by his science teacher, he attended Chicago State University and majored in mathematics, thinking that EISPACK this would combine well with education courses to equip Dongarra was supervised by Brian Smith, a young him for a high school teaching career. The first person in researcher whose primary concern at the time was the his family to go to college, he lived at home and worked lab’s EISPACK project. Although budget cuts forced Pool to in a pizza restaurant to cover the cost of his education.1 make substantial layoffs during his time as acting In 1972, during his senior year, a series of chance director of the Applied Mathematics Division in 1970– events reshaped Dongarra’s planned career. On the 1971, he had made a special effort to find funds to suggestion of Harvey Leff, one of his physics professors, protect the project and hire Smith. -
Randnla: Randomized Numerical Linear Algebra
review articles DOI:10.1145/2842602 generation mechanisms—as an algo- Randomization offers new benefits rithmic or computational resource for the develop ment of improved algo- for large-scale linear algebra computations. rithms for fundamental matrix prob- lems such as matrix multiplication, BY PETROS DRINEAS AND MICHAEL W. MAHONEY least-squares (LS) approximation, low- rank matrix approxi mation, and Lapla- cian-based linear equ ation solvers. Randomized Numerical Linear Algebra (RandNLA) is an interdisci- RandNLA: plinary research area that exploits randomization as a computational resource to develop improved algo- rithms for large-scale linear algebra Randomized problems.32 From a foundational per- spective, RandNLA has its roots in theoretical computer science (TCS), with deep connections to mathemat- Numerical ics (convex analysis, probability theory, metric embedding theory) and applied mathematics (scientific computing, signal processing, numerical linear Linear algebra). From an applied perspec- tive, RandNLA is a vital new tool for machine learning, statistics, and data analysis. Well-engineered implemen- Algebra tations have already outperformed highly optimized software libraries for ubiquitous problems such as least- squares,4,35 with good scalability in par- allel and distributed environments. 52 Moreover, RandNLA promises a sound algorithmic and statistical foundation for modern large-scale data analysis. MATRICES ARE UBIQUITOUS in computer science, statistics, and applied mathematics. An m × n key insights matrix can encode information about m objects ˽ Randomization isn’t just used to model noise in data; it can be a powerful (each described by n features), or the behavior of a computational resource to develop discretized differential operator on a finite element algorithms with improved running times and stability properties as well as mesh; an n × n positive-definite matrix can encode algorithms that are more interpretable in the correlations between all pairs of n objects, or the downstream data science applications. -
Fair Benchmarking for Cloud Computing Systems
Fair Benchmarking for Cloud Computing Systems Authors: Lee Gillam Bin Li John O’Loughlin Anuz Pranap Singh Tomar March 2012 Contents 1 Introduction .............................................................................................................................................................. 3 2 Background .............................................................................................................................................................. 4 3 Previous work ........................................................................................................................................................... 5 3.1 Literature ........................................................................................................................................................... 5 3.2 Related Resources ............................................................................................................................................. 6 4 Preparation ............................................................................................................................................................... 9 4.1 Cloud Providers................................................................................................................................................. 9 4.2 Cloud APIs ...................................................................................................................................................... 10 4.3 Benchmark selection ...................................................................................................................................... -
Evolving Software Repositories
1 Evolving Software Rep ositories http://www.netli b.org/utk/pro ject s/esr/ Jack Dongarra UniversityofTennessee and Oak Ridge National Lab oratory Ron Boisvert National Institute of Standards and Technology Eric Grosse AT&T Bell Lab oratories 2 Pro ject Fo cus Areas NHSE Overview Resource Cataloging and Distribution System RCDS Safe execution environments for mobile co de Application-l evel and content-oriented to ols Rep ository interop erabili ty Distributed, semantic-based searching 3 NHSE National HPCC Software Exchange NASA plus other agencies funded CRPC pro ject Center for ResearchonParallel Computation CRPC { Argonne National Lab oratory { California Institute of Technology { Rice University { Syracuse University { UniversityofTennessee Uniform interface to distributed HPCC software rep ositories Facilitation of cross-agency and interdisciplinary software reuse Material from ASTA, HPCS, and I ITA comp onents of the HPCC program http://www.netlib.org/nhse/ 4 Goals: Capture, preserve and makeavailable all software and software- related artifacts pro duced by the federal HPCC program. Soft- ware related artifacts include algorithms, sp eci cations, designs, do cumentation, rep ort, ... Promote formation, growth, and interop eration of discipline-oriented rep ositories that organize, evaluate, and add value to individual contributions. Employ and develop where necessary state-of-the-art technologies for assisting users in nding, understanding, and using HPCC software and technologies. 5 Bene ts: 1. Faster development of high-quality software so that scientists can sp end less time writing and debugging programs and more time on research problems. 2. Less duplication of software development e ort by sharing of soft- ware mo dules.