speedupBasic

Tuesday february 14 12 gene amdahl worked on ibm 704

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Unformatted text preview: sizes of machines, and to derive other useful relations. Tuesday, February 14, 12 Gene Amdahl • Worked on IBM 704, 709, Stretch and 7030 machines • Stretch was first transistorized computer, fastest from 1961 until CDC 6600 in 1964, 1.2 MIPS • • • • Multiprogramming, memory protection, generalized interrupts, the 8-bit byte, Instruction pipelining, prefetch and decoding introduced in this machine Worked on IBM System 360 In technical disagreement with IBM, set up Amdahl Computers to build plug-compatible machines -- later acquired by Hitachi Amdahl's law came from discussions with Dan Slotnick (Illiac IV architect at UIUC) and others about future of parallel processing Tuesday, February 14, 12 Amdahl’s law - key insight With perfect utilization of parallelism on the parallel part of the job, must take at least Tserial time to execute. This observation forms the motivation for Amdahl’s law ψ(p): speedup with p processors Tuesday, February 14, 12 As p ⇒ ∞, Tparallel ⇒ 0 and ψ(∞) ⇒ (Ttotal work)/Tserial. Thus, ψ is limited by the serial part of the program. Two measures of speedup Takes into account communication cost. • σ(n) and ϕ(n) are arguably fundamental properties of a program • κ(n,p) is a property of both the program, the hardware, and the library implementations -- arguably a less fundamental concept. • Can formulate a meaningfully approximation to the speedup without κ(n,p) Tuesday, February 14, 12 Speedup in terms of the serial fraction of a program Given this formulation, the fraction of the program that is serial is simply Speedup can be rewritten in terms of f: This gives us Amdahl’s Law. Tuesday, February 14, 12 Amdahl's Law ⟹ speedup Tuesday, February 14, 12 Example of using Amdahl’s Law A program is 90% parallel. What speedup can be expected when running on four, eight and 16 processors? Tuesday, February 14, 12 What is the efficiency of this program? A 2X increase in machine cost gives you a 1.4X increase in performance. And this is optimistic since communication costs are not considered. Tuesday, February 14, 12 Another Amdahl’s Law example A program is 20% inherently serial. Given 2, 16 and infinite processors, how much speedup can we get? Tuesday, February 14, 12 Limitation of Amdahl’s Law This result is a limit, not a realistic number. The problem is that communication costs (κ(n,p)) are ignored, and this is an overhead that is worse than fixed (which f is), but actually grows with the number of processors. Amdahl’s Law is too optimistic and may target the wrong problem Tuesday, February 14, 12 No communication overhead execution time speedup = 1 maximum speedup number of processors Tuesday, February 14, 12 O(Log2P) communication costs execution time speedup = 1 maximum speedup number of processors Tuesday, February 14, 12 O(P) Communication Costs execution time speedup = 1 maximum speedup number of processors Tuesday, February 14, 12 Amdahl Effect • Complexity of ϕ(n) usually higher than complexity of κ(...
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