Your company has just bought a new Intel Core i5 dual core p

Your company has just bought a new Intel Core i5 dual- core processor, and you have been tasked with optimizing your software for this processor. You will run two applications on this dual core. but the resource requirements are not equal. The first application requires 80% of the resources. and the other only 20% of the resources. Assume that when you parallelize a portion of the program, the speedup for that portion is 2. Given that 40% of the first application is parallelizable, how much speedup would you achieve with that application if run in isolation? Given that 99% of the second application is parallelizable. how much speedup would this application observe if run in isolation Given that 40% of the first application is parallelizable, how much overall system speedup would you observe if you parallelized it? Given that 99% of the second application is parallelizable, how much overall system speedup would you observe if you parallelized it?

Solution

for this we must know about Amdahl\'s Law , it states that, if x is the fraction of the application that can be parallalized then, then the maximum speedup for that application is given by 1 / ((1-x) + (x/N))

whrere N is the number of processors .

so now we just need to apply the formula for the different portions given .

here N is 2 since it is dual core .

(a) here x = 0.4 since 40% is parallelized.

speedup = 1 / ((1 - 0.4) + (0.4/2)) = 1.25

(b) x = 0.99

speedup = 1 / ((1 - 0.99) + (0.99/2)) = 1.98

(c) let us calculate the sppeed up of the first application running on 80% resources -

speedupF = (1/ ((1-0.4) + (0.4/2)) = 1.25

speedup for second application given 20% resources running only in serial ( put x = 0 in formula)

speedupS = (1/((1 - 0) + (0/2))) = 1

now multiply bby resources available to get the actual excution power like -

overall speedup = 1 / ( 0.2 * sppedupS + 0.8 *speedupF) = 1.19

(d) similar to (c)

overall speedup = 1 / ( 0.8 + 0.2 * ((1 - 0.99) + (0.99/2))) = 1.11

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thank you