Question: Problem 1. Consider the following instructions of a sequential program: I1 : z = (b * d) / (b + d) I2 : x =

Problem 1. Consider the following instructions of a sequential program: I1 : z = (b * d) / (b + d) I2 : x = z*z + (c * a) I3 : y = (e + a) * d

I4: z = x + d / (b + c)

Which pairs of instructions (I1-i2, I1-I3, I1-I4, I2-I3, I2-I4, I3-I4) can be parallelized? Use the data dependency conditions to decide which instructions can be executed in parallel.
Can all four I1-I2-I3-I4 be parallelized?

SHOW THE WORK.

Problem 2. [ 2 points] Consider the following sequential program:

x[0] = 1 x[1] = x[0] + 2 x[2] = x[1] + 3 x[3] = 3 x[4] = x[2] + 3 x[5] = x[1] + 2 The fastest execution time of this portion of the program can be obtained by executing this code in parallel. What is the number of processors that can be used to execute this code in parallel and obtain the minimum execution time? You do not need to use Amdahls law. Justify your answer. [2 points]

Problem 3.

.The Amdahl's law computes the speedup in execution time for a program executed on P processors but for which the input size is fixed. If the input size increases proportionally to the number of processors, then Gustafson law is used to calculate the speedup. Give two examples of problems and/or situations in which Gustafson law should be applied instead of Amdahl's law.

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