Consider a multi - core processor with heterogeneous cores: A, B, C and D where

Question

Consider a multi - core processor with heterogeneous cores: A, B, C and D where core B runs twice as fast as A, core C runs three times as fast as A and cores D and A run at the same speed (ie have the same processor frequency, micro architecture etc). Suppose an application needs to compute the square of each element in an array of 256 elements. Consider the following two divisions of labor: Compute (1) the total execution time taken in the two cases and (2) cumulative processor utilization (Amount of total time processors are not idle divided by the total execution time). For case (b), if you do not consider Core D in cumulative processor utilization (assuming we have another application to run on Core D), how would it change? Ignore cache effects by assuming that a perfect prefetcher is in operation.

Explanation / Answer

a) first derivative test
dA/dq = - km/q^2 + h/2 = 0

km/q^2 = h/2
q = sqrt( 2 k m/h)

second derivative
A'' = 2 k m/q^3 >0 so it is minimum

b) A = ( k + bq) m/q + cm + hq /2
A = k m/q + bm + cm + hq/2
first derivative test
A'= -km/q^2 + h/2
so same min
q = sqrt(2km/h)

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