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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sun-Ni law ： ウィキペディア英語版 Sun-Ni law Sun-Ni's Law (or Sun and Ni's Law, also known as memory-bounded speedup), is a memory-bounded speedup model which states that as computing power increases the corresponding increase in problem size is constrained by the system’s memory capacity. In general, as a system grows in computational power, the problems run on the system increase in size. Analogous to Amdahl's law, which says that the problem size remains constant as system sizes grow, and Gustafson's law, which proposes that the problem size should scale but be bound by a fixed amount of time, Sun-Ni's Law states the problem size should scale but be bound by the memory capacity of the system. Sun-Ni's Law 〔() Another View on Parallel Speedup, Xian-He Sun and Lionel Ni, Proceedings of IEEE Supercomputing Conference '90.〕〔() Scalable Problems and Memory-Bounded Speedup, X.H. Sun, and L. Ni, Journal of Parallel and Distributed Computing, Vol. 19, p.27-37, Sept.1993.〕 was initially proposed by Xian-He Sun and Lionel Ni at the Proceedings of IEEE Supercomputing Conference 1990. With the increasing disparity between CPU speed and memory data access latency, application execution time often depends on the memory speed of the system.〔() Hitting the Memory Wall:Implications of the Obvious, Wm.A. Wulf and Sally A. McKee, ACM SIGARCH Computer Architecture News Vol. 23 p. 20–24 March 1995.〕 As predicted by Sun and Ni, data access has become the premier performance bottleneck for high-end computing. From this fact one can see the intuition behind Sun-Ni's Law, as system resources increase, applications are often bottlenecked by memory speed and bandwidth, thus an application can achieve a larger speedup by utilizing all the memory capacity in the system. Sun-Ni's Law can be applied to different layers of a memory hierarchy system, from L1 cache to main memory. Through its memory-bounded function,''W=G(M)'', it reveals the trade-off between computing and memory in algorithm and system architecture design. All three speedup models, Sun-Ni, Gustafson, and Amdahl, provide a metric to analyze speedup for Parallel computing. Amdahl’s law focuses on the time reduction for a given fixed-size problem. Amdahl’s law states that the sequential portion of the problem (algorithm) limits the total speedup that can be achieved as system resources increase. Gustafson’s law suggests that it is beneficial to build a large-scale parallel system as the speedup can grow linearly with the system size if the problem size is scaled up to maintain a fixed execution time.〔() Reevaluating Amdahl's Law in the Multicore Era, Xian-He Sun and Yong Chen, Journal of Parallel and Distributed Computing, Vol. 70 p.183-188, February 2010.〕 Yet as memory access latency often becomes the dominant factor in an application’s execution time,〔() Scaling the Bandwidth Wall:Challenges in and Avenues for CMP Scaling, Brian M. Rogers, Anil Krishna, Gorden B. Bell, Ken Vu, Xiaowei Jiang, and Yan Solihin, ACM SIGARCH Computer Architecture News, Vol. 37 p.371-382, June 2009〕 applications may not scale up to meet the time bound constraint.〔〔 Sun-Ni's Law, instead of constraining the problem size by time, constrains the problem by the memory capacity of the system, or in other words bounds based on memory. Sun-Ni's Law is a generalization of Amdahl's Law and Gustafson's Law. When the memory-bounded function ''G(M)=1'', it resolves to Amdahl's law, when the memory-bounded function ''G(M)=m'',the number of processors, it resolves to Gustafson's Law. ==Derivation of Sun-Ni's Law== Let $\backslash textstyle\; W^$ be the scaled workload under a memory space constraint. The memory bounded speedup can be defined as: ''Sequential Time to Solve W */Parallel Time to Solve W *'' Suppose $\backslash textstyle\; f$ is the portion of the workload that can be parallelized and $\backslash textstyle(1-f)$ is the sequential portion of the workload. Let $\backslash textstyle\; y\; =\; g(x)$ be the function that reflects the parallel workload increase factor as the memory capacity increases m times. Let: $\backslash textstyle\; W\; =\; g(M)$ and: $\backslash textstyle\; W^\; =\; g(m\backslash cdot\; M)$ where $\backslash textstyle\; M$ is the memory capacity of one node. Thus, $W^\; =\; g(m\backslash cdot\; g^(W))$ The memory bounded speedup is then: $\backslash frac\}$ For any power function $\backslash textstyle\; g(x)\; =\; ax^$ and for any rational numbers ''a'' and ''b'', we have: $g(mx)\; =\; a(mx)^\; =\; m^\backslash cdot\; ax^\; =\; m^g(x)\; =\; \backslash bar(m)g(x)$ where $\backslash textstyle\; \backslash bar(m)$ is the power function with the coefficient as 1. Thus by taking the highest degree term to determine the complexity of the algorithm, we can rewrite memory bounded speedup as: $\backslash frac\}\; =\; \backslash frac\}$ In this equation, $\backslash textstyle\; \backslash bar(m)$ represents the influence of memory change on the change in problem size. Suppose $\backslash textstyle\; \backslash bar(m)\; =1$, Then the memory-bounded speedup model reduces to Amdahl's law, since problem size is fixed or independent of resource increase. Suppose $\backslash textstyle\; \backslash bar(m)=m$, Then the memory-bounded speedup model reduces to Gustafson's law, which means when memory capacity increases ''m'' times and the workload also increases ''m'' times all the data needed is local to every node in the system. Often, for simplicity and for matching the notation of Amdahl's Law and Gustafson's Law, the letter ''G'' is used to represent the memory bound function $\backslash textstyle\; \backslash bar(m)$, and ''n'' replaces ''m''. Using this notation we get: $Speedup\_\backslash text\; =\; \backslash frac\}$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sun-Ni law」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.