HW2-1 (50 points) Three enhancements with the following speedups are proposed fo

Question

HW2-1 (50 points) Three enhancements with the following speedups are proposed for a new architecture: Speedup-10 Speedup2-5 Speedups- 2 The portions of any program where these enhancements can be used are non-overlapping. (a) Show how to use an extended version of Amdahl's Law for three enhancements to answer the following question. If enhancements 1, 2, and 3 are usable 10%, 30%, and 40% of the time, respectively, what overall speedup is achievable? (b) If only one enhancement can be implemented, which should it be? If two enhancments can be implemented, which should be chosen? Justify your answers

Explanation / Answer

Answer:-------------

a.

By Applying Amdhal's Law to three enhancemenets we fill overall speedup,

====> 1 / [ (1 - FEi ) + ( FEi  / SEi ) ]

====> 1 / [ 1 - ( FE1 + FE2 + FE3 ) + ( ( FE1/ SE1 ) + ( FE2 / SE2 ) + ( FE3 /SE3 ) ) ]

Now by replacing the all values,,

====> 1 / [ 1 - ( 0.1 + 0.3 + 0.4 ) + ( ( 0.1/ 10 ) + ( 0.3 / 5) + ( 0.4 / 2) ) ]

====> 1 / [ 1 - ( 0.8 ) + ( ( 0.01 ) + ( 0.06) + ( 0.2) ) ]

====> 1 / [ 0.2 + ( 0.01 + 0.06 + 0.2 ) ]

====> 1 / [ 0.2 + 0.27 ]

====> 1 / 0.47

====> 2.127

b.

SpeedupE1 =>  1 / [ (1 - FE1) + ( FE1  / SE1) ] => 1 / [ (1 - 0.1) + ( 0.1 / 10) ] => 1 / 0.91 => 1.0989

SpeedupE2 =   1 / [ (1 - FE2) + ( FE2  / SE2) ] => 1 / [ (1 - 0.3) + ( 0.3 / 5) ] => 1 / 0.76 => 1.3157

SpeedupE3 = 1 / [ (1 - FE3) + ( FE3  / SE3) ] => 1 / [ (1 - 0.4) + ( 0.4 / 2) ] => 1 / 0.8 => 1.25

Since, the Speedup provided by enhancement 2 is the highest, then we shall choose it.

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