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  • 1
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    NAS Parallel Benchmark Results 11-96 (1997)
    In:  CASI
    Details
    Publication Date: 2019-07-10
    Description: The NAS Parallel Benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a "pencil and paper" fashion. In other words, the complete details of the problem to be solved are given in a technical document, and except for a few restrictions, benchmarkers are free to select the language constructs and implementation techniques best suited for a particular system. These results represent the best results that have been reported to us by the vendors for the specific 3 systems listed. In this report, we present new NPB (Version 1.0) performance results for the following systems: DEC Alpha Server 8400 5/440, Fujitsu VPP Series (VX, VPP300, and VPP700), HP/Convex Exemplar SPP2000, IBM RS/6000 SP P2SC node (120 MHz), NEC SX-4/32, SGI/CRAY T3E, SGI Origin200, and SGI Origin2000. We also report High Performance Fortran (HPF) based NPB results for IBM SP2 Wide Nodes, HP/Convex Exemplar SPP2000, and SGI/CRAY T3D. These results have been submitted by Applied Parallel Research (APR) and Portland Group Inc. (PGI). We also present sustained performance per dollar for Class B LU, SP and BT benchmarks.
    Keywords: Computer Systems
    Type: NAS-96-18
    Format: text
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    NASA TECHNICAL REPORTS
  • 2
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    The Quest for Pi (1996)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: This article gives a brief history of the analysis and computation of the mathematical constant Pi=3.14159 ..., including a number of the formulas that have been used to compute Pi through the ages. Recent developments in this area are then discussed in some detail, including the recent computation of Pi to over six billion decimal digits using high-order convergent algorithms, and a newly discovered scheme that permits arbitrary individual hexadecimal digits of Pi to be computed.
    Keywords: Numerical Analysis
    Type: NASA-TM-112037 , NAS 1.15:112037 , NAS-96-015
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 3
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    On the Rapid Computation of Various Polylogarithmic Constants (1996)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: We give algorithms for the computation of the d-th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of log(2) or pi on a modest workstation in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of pi, the billionth hexadecimal digits of pi-squared, log(2) and log-squared(2), and the ten billionth decimal digit of log(9/10). These calculations rest on the observation that very special types of identities exist for certain numbers like pi, pi-squared, log(2) and log-squared(2). These are essentially polylogarithmic ladders in an integer base. A number of these identities that we derive in this work appear to be new, for example a critical identity for pi.
    Keywords: Numerical Analysis
    Type: NASA-TM-112039 , NAS 1.15:112039 , NAS-96-016
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    NASA TECHNICAL REPORTS
  • 4
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    Automated Generation of Message-Passing Programs: An Evaluation of CAPTools using NAS Benchmarks (1998)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: Scientists at NASA Ames Research Center have been developing computational aeroscience applications on highly parallel architectures over the past ten years. During the same time period, a steady transition of hardware and system software also occurred, forcing us to expand great efforts into migrating and receding our applications. As applications and machine architectures continue to become increasingly complex, the cost and time required for this process will become prohibitive. Various attempts to exploit software tools to assist and automate the parallelization process have not produced favorable results. In this paper, we evaluate an interactive parallelization tool, CAPTools, for parallelizing serial versions of the NAB Parallel Benchmarks. Finally, we compare the performance of the resulting CAPTools generated code to the hand-coded benchmarks on the Origin 2000 and IBM SP2. Based on these results, a discussion on the feasibility of automated parallelization of aerospace applications is presented along with suggestions for future work.
    Keywords: Computer Systems
    Type: ACM International Conference on Supercomputing; Jul 13, 1998 - Jul 17, 1998; Melbourne; Australia
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  • 5
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    Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations (1998)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.
    Keywords: Numerical Analysis
    Type: 10th Conference on Finite Element Methods in Fluids; Jan 08, 1998; Tucson, AZ; United States
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  • 6
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    Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes (1998)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.
    Keywords: Numerical Analysis
    Type: 5th International Symposium on Solving Irregularly Structured Problems in Parallel; Aug 09, 1998 - Aug 11, 1998; Berkley, CA; United States
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  • 7
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    The Automated Instrumentation and Monitoring System (AIMS): Design and Architecture (1997)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: Whether a researcher is designing the 'next parallel programming paradigm', another 'scalable multiprocessor' or investigating resource allocation algorithms for multiprocessors, a facility that enables parallel program execution to be captured and displayed is invaluable. Careful analysis of such information can help computer and software architects to capture, and therefore, exploit behavioral variations among/within various parallel programs to take advantage of specific hardware characteristics. A software tool-set that facilitates performance evaluation of parallel applications on multiprocessors has been put together at NASA Ames Research Center under the sponsorship of NASA's High Performance Computing and Communications Program over the past five years. The Automated Instrumentation and Monitoring Systematic has three major software components: a source code instrumentor which automatically inserts active event recorders into program source code before compilation; a run-time performance monitoring library which collects performance data; and a visualization tool-set which reconstructs program execution based on the data collected. Besides being used as a prototype for developing new techniques for instrumenting, monitoring and presenting parallel program execution, AIMS is also being incorporated into the run-time environments of various hardware testbeds to evaluate their impact on user productivity. Currently, the execution of FORTRAN and C programs on the Intel Paragon and PALM workstations can be automatically instrumented and monitored. Performance data thus collected can be displayed graphically on various workstations. The process of performance tuning with AIMS will be illustrated using various NAB Parallel Benchmarks. This report includes a description of the internal architecture of AIMS and a listing of the source code.
    Keywords: Computer Systems
    Type: NAS-97-001
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  • 8
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    Finding New Math Identities by Computer (1996)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.
    Keywords: Numerical Analysis
    Type: Jan 29, 1997; Portland, OR; United States
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  • 9
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    Methodologies and Tools for Tuning Parallel Programs: 80% Art, 20% Science, and 10% Luck (1996)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: The need for computing power has forced a migration from serial computation on a single processor to parallel processing on multiprocessors. However, without effective means to monitor (and analyze) program execution, tuning the performance of parallel programs becomes exponentially difficult as program complexity and machine size increase. In the past few years, the ubiquitous introduction of performance tuning tools from various supercomputer vendors (Intel's ParAide, TMC's PRISM, CRI's Apprentice, and Convex's CXtrace) seems to indicate the maturity of performance instrumentation/monitor/tuning technologies and vendors'/customers' recognition of their importance. However, a few important questions remain: What kind of performance bottlenecks can these tools detect (or correct)? How time consuming is the performance tuning process? What are some important technical issues that remain to be tackled in this area? This workshop reviews the fundamental concepts involved in analyzing and improving the performance of parallel and heterogeneous message-passing programs. Several alternative strategies will be contrasted, and for each we will describe how currently available tuning tools (e.g. AIMS, ParAide, PRISM, Apprentice, CXtrace, ATExpert, Pablo, IPS-2) can be used to facilitate the process. We will characterize the effectiveness of the tools and methodologies based on actual user experiences at NASA Ames Research Center. Finally, we will discuss their limitations and outline recent approaches taken by vendors and the research community to address them.
    Keywords: Computer Systems
    Type: European Parallel Tools Meeting; Oct 23, 1996 - Oct 25, 1996; Chatillon; France
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  • 10
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    NAS Parallel Benchmarks Results (1995)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: The NAS Parallel Benchmarks (NPB) were developed in 1991 at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a pencil and paper fashion i.e. the complete details of the problem to be solved are given in a technical document, and except for a few restrictions, benchmarkers are free to select the language constructs and implementation techniques best suited for a particular system. In this paper, we present new NPB performance results for the following systems: (a) Parallel-Vector Processors: Cray C90, Cray T'90 and Fujitsu VPP500; (b) Highly Parallel Processors: Cray T3D, IBM SP2 and IBM SP-TN2 (Thin Nodes 2); (c) Symmetric Multiprocessing Processors: Convex Exemplar SPP1000, Cray J90, DEC Alpha Server 8400 5/300, and SGI Power Challenge XL. We also present sustained performance per dollar for Class B LU, SP and BT benchmarks. We also mention NAS future plans of NPB.
    Keywords: Computer Systems
    Type: Supercomputing 1995; Dec 04, 1995 - Dec 08, 1995; San Diego, CA; United States
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