1. Amdahl’s Law by Amdahl, G: “Validity of the single-
“When the fraction of serial work in a given problem is small, say s, the maximum speedup obtainable (from an even infinit # of processors) is only 1/s.”
by Amdahl, G: “Validity of the single-
processor approach to achieve large-
scale computer capabilities” AFIPS Conf.
Proceedings 30, 1967, pp
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2. For a Fixed Problem Size:
Time = 1
Run on Parallel Processor
Run on Serial Processor
Time = S + P/N 1
S + P/N
Speedup =
= S + P
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3. “unforgivingly deepness”
1% % % %
91x
48x
31x
24x S
Serial fraction
Speed up
1024
“unforgivingly deepness”
- S. Gustafson
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4. A different view of Amdahl’s Law
Problem size scale with the # of PEs :
and “As a first approximation, we have found that it is the parallel or vector part of a program that scales with the problem size. Time for vector start-up, program loading, serial bottlenecks, and I/O that make up the s component of the run do not grow as rapid as with problem size.”
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5. Scaled-Sized Model for Speedup = s + Np
Time = 1
Run on Parallel Processor
Run on Serial Processor
Time = S + P/N
Time = s + Np
Hypothetical run on serial processor 1 N S P
Run on Parallel Processor
Scaled speedup = (s + p x N)/(s + p)
= s + p x N
Time = 1
Scaled-Sized Model for Speedup = s + Np
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