speedupBasic

# Tuesday february 14 12 the experimentally determined

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 02/19/2012 for the course ECE 563 taught by Professor Staff during the Spring '08 term at Purdue.

Ask a homework question - tutors are online