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# partimes - Amdahl Parallel Performance Mohamed Iskandarani...

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Amdahl Parallel Performance Mohamed Iskandarani December 2, 2008

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Amdahl Outline Amdahl
Amdahl Amdahl’s law Definitions: t s ( P ) execution time of serial portion on P processors t p ( P ) execution time of parallel portion on P processors Speedup = time on 1 processors time on P processors = t s ( 1 ) + t p ( 1 ) t s ( P ) + t p ( P ) Assumptions 1. uniform serial time: t s ( 1 ) = t s ( P ) = t s . 2. parallel overhead is negligeable: t 1 ( P ) = Pt p ( P )

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Amdahl Amdahl’s law S = t s + t p ( 1 ) t s + t p ( 1 ) P = 1 t s t s + t 1 ( p ) + t p ( 1 ) P [ t s + t p ( 1 )] (1) = 1 β A + 1 - β A P (2) β A = t s t s + t 1 ( P ) = serial fraction (3)
Amdahl Amdahl’s law for fixed β A 0 200 400 600 800 1000 1200 0 10 20 30 40 50 60 70 80 90 100 β A =0.01 β A =0.10 β A =0.50 S P

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Amdahl Amdahl’s law for fixed P 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 β S max /P P=128 P=256 P=512 P=1024
Amdahl Gustafson’s law S = t s + Pt p ( P ) t s + t p ( P ) = t s t s + t p ( P ) + P t p ( P ) t s + t p ( p ) = β G + P ( 1 - β G ) β G = t s t s + t p ( P ) = scaled serial fraction

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Amdahl Amdahl-Gustafson’s equivalence ( 1 - β A ) t s = β A t p ( 1 ) ( 1 - β G ) t s = β G t p ( P ) ( 1 - β A ) ( 1 - β G ) = P β A β G
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