Speed up

Question

Consider 3 enhancements EA, EB, and EC with speedup 30, 20, 15 respectively are applied to old system to make a new system. If enhancements EA and EB are usable for 25% of the time, then the fraction (in %) of the time must EC be used to achieve an overall speed-up of 10 is ________. (in integer form)

Comments

Can you please explain the above equation how you got???

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denominator is the time taken after enhancement.

if x% of the code are enhanced with speedup k, then the new time taken would be x%/k.

applying this formula, you will get the below denominator.

and we know the formula for speedup.

put everything in right place with right values, you will get the answer.

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This is given by Amdahl's law - you can Google it to understand what it is about.

Answer 1

Suppose there are 4 types of instructions A, B, C, and D and there are 100 units of time taken by them.

It is given that 25 units of time is taken by type A, 25 units of time is taken by type B, x units of time is taken by type C, and the rest(= 50-x) unit of time is taken by type D.

 

Now, when partial speed ups are applied time taken by type A instructions = 25/30 (Since the speed up is of 30)

time taken by type B = 25/20

time taken by type C = x/15

time taken by type D = (50-x)/1 = 50-x

Total time taken now = 25/30 + 25/20 + x/15 + 50-x

 

Speedup = (former time)/(new time) = 100/ (25/30 + 25/20 + x/15 + 50-x) = 10. (Solving this x comes out to be 45, which is 45% of 100).

 

Getting to Amdahl's law:

Speed up = 1/ ( (Sum of fractional speedup) + (1-fractions of given instructions) )    

[This equation is equivalent to above if we had assumed 1 instruction instead of 100]

Sorry for the bad formatting. Please let me know if this is unclear.