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computational force, mass, and energy

INTERNATIONAL JOURNAL OF MODERN PHYSICS C 1997年第3期8卷 437-457页

作者： Numrich, RW Cray Research A Silicon Graphics Company 655 Lone Oak Dr. Eagan MN 55121 U.S.A

This paper describes a correspondence between computational quantities commonly used to report computer performance measurements and mechanical quantities from classical Newtonian mechanics. It defines a set of three fundamental computational quantities that are sufficient to establish a system of computational measurement. From these quantities, it defines derived computational quantities that have analogous physical counterparts. These computational quantities obey three laws of motion in computational space. The solutions to the equations of motion, with appropriate boundary conditions, determine the computational mass of the computer. computational forces, with magnitudes specific to each instruction and to each computer, overcome the inertia represented by this mass. The paper suggests normalizing the computational mass scale by picking the mass of a register on the CRAY-1 as the standard unit of mass.

关键词： binary operations computational force computational mass computational power machine instructions

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Hopping-Pong: Changing Trajectory of Moving Object Using computational Ultrasound force 19

Hopping-Pong: Changing Trajectory of Moving Object Using Com...

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14th ACM International Conference on Interactive Surfaces and Spaces (ISS)

作者： Morisaki, Tao Mori, Ryoma Mori, Ryosuke Makino, Yasutoshi Itoh, Yuta Yamakawa, Yuji Shinoda, Hiroyuki Univ Tokyo Kasiwa Japan Univ Tokyo Meguro Ku Kasiwa Japan Tokyo Inst Technol Yokohama Kanagawa Japan JST PREST Kasiwa Japan JST PREST Yokohama Kanagawa Japan JST PREST Meguro Ku Yokohama Kanagawa Japan

ISBN: (纸本)9781450368919

Physically moving real objects via a computational force connects computers and the real world and has been applied to tangible interfaces and mid-air display. Many researchers have controlled only a stationary real object by computational force. On the other hand, controlling a moving object can expand the real space that is controllable by the computer. In this paper, we explore the potential of computational force from the viewpoint of changing the trajectory of a moving object. Changing the trajectory is the primitive model to control a moving object, and it is the technological challenge requiring high-speed measurement and non-contact force with high-spatial resolution. As a proof-of-concept, we introduce Hopping-Pong changing the trajectory of a flying Ping-Pong Ball (PPB) using ultrasound force. The result shows that Hopping-Pong changes the trajectory of a PPB 344 mm. We conclude that a computational force is capable of controlling a moving object in the real world. This research contributes to expanding the computationally controlled space with applications for augmented sports, HCI and factory automation.

关键词： Controlling Moving Object computational force Ultrasound Augmented Ping-Pong

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computational forces in the Linpack benchmark

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2008年第9期68卷 1283-1290页

作者： Numrich, Robert W. Univ Minnesota Minnesota Supercomp Inst Minneapolis MN 55455 USA

Dimensional analysis reduces a complicated ten-parameter formula for the execution time of the Linpack benchmark to a simpler two-parameter formula. These two parameters are ratios of software forces and hardware forces that determine a self-similarity Surface. Machines move along paths on this surface as the problem size and the number of processors change. Two machines scale the same way, they move along the same path, if they have the same hardware forces. To design efficient algorithms, the programmer must produce software forces large enough to overcome the hardware forces. Modern machines have larger hardware forces than older machines and are harder to program. (C) 2008 Elsevier Inc. All rights reserved.

关键词： scalability dimensional analysis performance analysis computational intensity computational force parallel numerical algorithms Linpack benchmark

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computational forces in the SAGE benchmark

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2009年第3期69卷 315-325页

作者： Numrich, Robert W. Univ Minnesota Minnesota Supercomp Inst Minneapolis MN 55455 USA

Dimensional analysis applied to a complicated timing formula for the SAGE benchmark yields new insight into the limits to scalability. A single surface, defined by two curvilinear coordinates, describes the parallel efficiency of the benchmark. Each machine, as a function of the number of processors, follows its own path on the surface determined by dimensionless ratios of hardware forces to software forces. Two machines with the same ratios follow the same path and are self-similar, even though the numerical value of each individual force may be different. For this benchmark, latency effects are unimportant relative to bandwidth effects because of the slab decomposition used to distribute the problem across processors. To a good first-order approximation, a single force ratio describes the efficiency as a function of the number of processors. A simpler model, with a single dimensionless exponent, describes the first-order behavior of the computational power as a function of the number of processors. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Parallel algorithms Benchmark analysis computational intensity computational force Dimensional analysis Self-similarity Scaling

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PARALLEL COMPUTING 2011年第2期37卷 69-84页

作者： Numrich, Robert W. Heroux, Michael A. Univ Minnesota Minnesota Supercomp Inst Minneapolis MN 55455 USA Sandia Natl Labs Albuquerque NM 87185 USA St Johns Univ Collegeville MN 56321 USA

Self-similarity is a property of physical systems that describes how to scale parameters such that dissimilar systems appear to be similar. Computer systems are self-similar if certain ratios of computational forces, also known as computational intensities, are equal. Two machines with different computational power, different network bandwidth and different inter-processor latency behave the same way if they have the same ratios of forces. For the parallel conjugate gradient algorithm studied in this paper, two machines are self-similar if and only if the ratio of one force describing latency effects to another force describing bandwidth effects is the same for both machines. For the two machines studied in this paper, this ratio, which we call the mixing coefficient, is invariant as problem size and processor count change. The two machines have the same mixing coefficient and belong to the same equivalence class. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Parallel algorithms Benchmark analysis computational intensity computational force Dimensional analysis Equivalence class Self-similarity Scaling Mixing coefficient

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Computer performance analysis and the Pi Theorem

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COMPUTER SCIENCE-RESEARCH AND DEVELOPMENT 2014年第1期29卷 45-71页

作者： Numrich, Robert W. Univ Minnesota Minnesota Supercomp Inst Minneapolis MN 55455 USA

This paper applies the Pi Theorem of dimensional analysis to a representative set of examples from computer performance analysis. It is a survey paper that takes a different look at problems involving latency, bandwidth, cachemiss ratios, and the efficiency of parallel numerical algorithms. The Pi Theorem is the fundamental tool of dimensional analysis, and it applies to problems in computer performance analysis just as well as it does to problems in other sciences. Applying it requires the definition of a system of measurement appropriate for computer performance analysis with a consistent set of units and dimensions. Then a straightforward recipe for each specific problem reduces the number of independent variables to a smaller number of dimensionless parameters. Two machines with the same values of these parameters are self-similar and behave the same way. Self-similarity relationships emphasize how machines are the same rather than how they are different. The Pi Theorem is simple to state and simple to prove, using purely algebraic methods, but the results that follow from it are often surprising and not simple at all. The results are often unexpected but they almost always reveal something new about the problem at hand.

关键词： Performance analysis Dimensional analysis Scaling Pi Theorem Cache behavior Parallel algorithms Performance metrics Latency Bandwidth computational force computational intensity

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Dimensional analysis applied to a parallel QR algorithm

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7th International Conference on Parallel Processing and Applied Mathematics

作者： Numrich, Robert W. Univ Minnesota Minnesota Supercomp Inst Minneapolis MN 55455 USA

ISBN: (纸本)9783540681052

We apply dimensional analysis to a formula for execution time for a QR algorithm from a paper by Henry and van de Geijn. We define a single efficiency surface that reduces performance analysis for this algorithm to an exercise in differential geometry. As the problem size and the number of processors change, different machines move along different paths on the surface determined by two computational forces specific to each machine. We show that computational force, also called computational intensity, is a unifying concept for understanding the performance of parallel numerical algorithms.

关键词： scalability performance analysis computational intensity computational force parallel numerical algorithms dimensional analysis

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