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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 KF
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(1e)/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 KF
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(1e)/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 KF
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(1e)/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 KF
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(1e)/p KarpFlatt Metric
T(n,p) = T(n,p)ψe + T(n,p)ψ(1e)/p ⇒
1 = ψe + ψ(1e)/p ⇒
1/ψ = e + (1e)/p ⇒
1/ψ = e + 1/p  e/p ⇒
1/ψ = e(11/p) +1/p ⇒ Tuesday, February 14, 12 What is it good for?
account the parallel overhead
• Takes intoAmdahl’s Law and GustafsonBarsis. (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.
 Spring '08
 Staff

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