Consider a multicore processor with four heterogeneous cores labeled A, B, C, an

Question

Consider a multicore processor with four heterogeneous cores labeled A, B, C, and D. Assume cores A and D have the same speed. Core B runs twice as fast as core A, and core C runs three times faster than core A. Assume that all four cores start executing the following application at the same time and no cache misses are encountered in all core operations. Suppose an application needs to compute the square of each element of an array of 256 elements. Assume 1 unit time for core A or D to compute the square of an element. Thus, core B takes ½ unit time and core C takes 1/3unit time to compute the square of an element. Given the following division of labor in four cores: Core A - 32 elements Core B - 128 elements Core C - 64 elements Core D - 32 elements
a. Compute the total execution time (in time units) for using the four-core processor to compute the squares of 256 elements in parallel. The four cores have different speeds. Some faster cores finish the job and may become idle, while others are still busy computing until all squares are computed.
b. Calculate the processor utilization rate, which is the total amount of time the cores are busy (not idle) divided by the total execution time they are using all cores in the processor to execute the above application.
Consider a multicore processor with four heterogeneous cores labeled A, B, C, and D. Assume cores A and D have the same speed. Core B runs twice as fast as core A, and core C runs three times faster than core A. Assume that all four cores start executing the following application at the same time and no cache misses are encountered in all core operations. Suppose an application needs to compute the square of each element of an array of 256 elements. Assume 1 unit time for core A or D to compute the square of an element. Thus, core B takes ½ unit time and core C takes 1/3unit time to compute the square of an element. Given the following division of labor in four cores: Core A - 32 elements Core B - 128 elements Core C - 64 elements Core D - 32 elements
a. Compute the total execution time (in time units) for using the four-core processor to compute the squares of 256 elements in parallel. The four cores have different speeds. Some faster cores finish the job and may become idle, while others are still busy computing until all squares are computed.
b. Calculate the processor utilization rate, which is the total amount of time the cores are busy (not idle) divided by the total execution time they are using all cores in the processor to execute the above application.
Consider a multicore processor with four heterogeneous cores labeled A, B, C, and D. Assume cores A and D have the same speed. Core B runs twice as fast as core A, and core C runs three times faster than core A. Assume that all four cores start executing the following application at the same time and no cache misses are encountered in all core operations. Suppose an application needs to compute the square of each element of an array of 256 elements. Assume 1 unit time for core A or D to compute the square of an element. Thus, core B takes ½ unit time and core C takes 1/3unit time to compute the square of an element. Given the following division of labor in four cores: Core A - 32 elements Core B - 128 elements Core C - 64 elements Core D - 32 elements
a. Compute the total execution time (in time units) for using the four-core processor to compute the squares of 256 elements in parallel. The four cores have different speeds. Some faster cores finish the job and may become idle, while others are still busy computing until all squares are computed.
b. Calculate the processor utilization rate, which is the total amount of time the cores are busy (not idle) divided by the total execution time they are using all cores in the processor to execute the above application.

Explanation / Answer

consider a multiple processorwith four hetorogeneos cores labelled A,B,C,D

(a)

For A and D.....>1 unit time

For B .....>12 unit time

For C.....>13 unit time

so given core A has 32 elements and core D has 32elements.

So totally....>64 units

For coreB has 128 elements....>128X12=1536 unit time.

For corec has 64 elements....>164x13=832 unit time.

So total execution time=64+1536+832=2432 unit ties.

(b)

Processor utilization time for core A=32/2432=1%

Processor utilization time for core A=1536/2432=63.8%

Processor utilization time for core A=832/2432=34.2%

Processor utilization time for core A=32/2432=1%

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