Math

NAME (Required): _____________________________

Please show all work details with answers, insert the graph, and provide answers to all of the critical thinking questions on this document. Upload this modified Answer Form to the Intellipath Unit 3 Submission lesson. Make sure you submit your work in a modified MS Word document; hand-written work will not be accepted. If you need assistance, please contact your course instructor.

In 1967, Dr. Gene Amdahl developed Amdahl’s law for predicting speedup gained using multiple processors in parallel while executing a computer program. One version of Amdahl’s law states that the speedup (or efficiency) of using multiple parallel processors can be calculated approximately using the following rational function:

Here, is the number of processors used, and is the decimal equivalent of the percent of the program that must be run sequentially.

For each question, be sure to show all your work details for full credit. Round all value answers to 3 decimal places.

1. Based on the first letter of your last name, in the table below, choose a percent of a program that must be run sequentially. If your choice is not a whole number percent, then use at most 2 decimal places. Using the decimal equivalent for your chosen value of , write your version of this speedup rational function, , below. (20 points)

Explain your answer here:

2. Calculate the corresponding values of for each -value in the table below, and then complete the table. (See part 5 below for the reason why one -value has to be 20.) To receive full credit, be sure to show all of your calculation details. Show calculation details for and one other -value only. (20 points)

Explain your answer here:

3. Graph your speedup function, , using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Microsoft’s Mathematics 4.0, online utilities like desmos.com, and many others.) Insert both the function and the graph into the Word document containing your answers and work details. Be sure to label and number the axes appropriately so that the graph matches the calculated values in part 2 above. (20 points)

Insert both your graph and function here:

4. Given a computer program with your chosen value of , the graph shows the relation between the number of parallel processors used and the efficiency obtained by using multiple processors. Looking at your graph, what appears to be the maximum possible speedup? How did you arrive at this conclusion? (20 points)

Explain your answer here:

5. Suppose the amount of the program that must be completed sequentially could be reduced by 3% (i.e., your value of – ). What would be the new speedup for parallel processors? Because the function, represents how many times faster a program will run when parallel processors are executing portions of the program at exactly the same time, what is the impact on the execution time of reducing the amount of code that must be executed sequentially by 3%? (20 points)

Explain your answer here:

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