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Tuesday february 14 12 the experimentally determined

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Unformatted text preview: andates measuring at a given processor count • This is because communication cost is a function of theoretical limits and implementation. Tuesday, February 14, 12 The experimentally determined serial fraction e of the parallel computation is e = (σ(n) + κ(n,p))/T(n,1) e⋅T(n,1) = σ(n) + κ(n,p) Deriving the K-F Metric The parallel execution time T(n,p) = σ(n) + ϕ(n)/p + κ(n,p) can now be rewritten as T(n,p) = T(n,1)⋅e + T(n,1)(1 - e)/p Let ψ represent ψ(n,p), and fraction of time that ψ = T(n,1)/T(n,p) is parallel * total time is then parallel time - a good T(n,1) = T(n, p)ψ. approximation of ϕ(n) Therefore T(n,p) = T(n,p)ψe + T(n,p)ψ(1-e)/p Tuesday, February 14, 12 The experimentally determined serial fraction e of the parallel computation is e = (σ(n) + κ(n,p))/T(n,1) e⋅T(n,1) = σ(n) + κ(n,p) Deriving the K-F Metric Divide Tuesday, February 14, 12 The parallel execution time T(n,p) = σ(n) + ϕ(n)/p + κ(n,p) can now be rewritten as T(n,p) = T(n,1)⋅e + T(n,1)(1 - e)/p Let ψ represent ψ(n,p), and The ψ = T(n,1)/T(n,p) standard formula then T(n,1) = T(n, p)ψ. Therefore T(n,p) = T(n,p)ψe + T(n,p)ψ(1-e)/p The experimentally determined serial fraction e of the parallel computation is e = (σ(n) + κ(n,p))/T(n,1) Total e⋅T(n,1) = σ(n) + κ(n,p) execution time Deriving the K-F Metric Total time * serial fraction is the serial time Tuesday, February 14, 12 The parallel execution time T(n,p) = σ(n) + ϕ(n)/p + κ(n,p) can now be rewritten as T(n,p) = T(n,1)⋅e + T(n,1)(1 - e)/p Let ψ represent ψ(n,p), and Experimentally ψ = T(n,1)/T(n,p) determined serial then fraction T(n,1) = T(n, p)ψ. Therefore T(n,p) = T(n,p)ψe + T(n,p)ψ(1-e)/p The experimentally determined serial fraction e of the parallel computation is e = (σ(n) + κ(n,p))/T(n,1) Total e⋅T(n,1) = σ(n) + κ(n,p) execution time Deriving the K-F Metric (Total time * parallel part)/p is the parallel time Tuesday, February 14, 12 The parallel execution time T(n,p) = σ(n) + ϕ(n)/p + κ(n,p) can now be rewritten as T(n,p) = T(n,1)⋅e + T(n,1)(1 - e)/p Let ψ represent ψ(n,p), and fraction of ψ = T(n,1)/T(n,p) time that is then parallel T(n,1) = T(n, p)ψ. Therefore T(n,p) = T(n,p)ψe + T(n,p)ψ(1-e)/p Karp-Flatt Metric T(n,p) = T(n,p)ψe + T(n,p)ψ(1-e)/p ⇒ 1 = ψe + ψ(1-e)/p ⇒ 1/ψ = e + (1-e)/p ⇒ 1/ψ = e + 1/p - e/p ⇒ 1/ψ = e(1-1/p) +1/p ⇒ Tuesday, February 14, 12 What is it good for? account the parallel overhead • Takes intoAmdahl’s Law and Gustafson-Barsis. (κ(n,p)) ignored by • Helps us to detect other sources of inefficiency ignored in these (sometimes too simple) models of execution time ϕ(n)/p may not be accurate because of load balance issues or work not dividing evenly into c⋅p chunks. other interactions with the system may be causing problems Can determine if the efficiency drop with increasing p for a fixed size problem is a. because of limited parallelism b. because of increases in algorithmic or architectural overhe...
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This note was uploaded on 02/19/2012 for the course ECE 563 taught by Professor Staff during the Spring '08 term at Purdue.

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