Description

P1) Assume that we are considering enhancing a quad-core machine by adding encryption hardware to it. When computing encryption operations, it is 20 times faster than the normal mode of execution. We will define percentage of encryption as the percentage of time in the original execution that is spent performing encryption operations. The specialized hardware increases power consumption by 2%.

a. Draw a graph that plots the speedup as a percentage of the computation spent performing encryption. Label the y-axis “Net speedup” and label the x-axis “Percent encryption.”

b. With what percentage of encryption will adding encryption hardware result in a speedup of 2?

c. What percentage of time in the new execution will be spent on encryption operations if a speedup of 2 is achieved?

d. Suppose you have measured the percentage of encryption to be50%. The hardware design group estimates it can speed up the encryption hardware even more with significant additional investment. You wonder whether adding a second unit in order to support parallel encryption operations would be more useful. Imagine that in the original program, 90% of the encryption operations could be performed in parallel. What is the speedup of providing two or four encryption units, assuming that the parallelization allowed is limited to the number of encryption units?

P2) Assume that we make an enhancement to a computer that improves some mode of execution by a factor of 10. Enhanced mode is used 50% of the time, measured as a percentage of the execution time when the enhanced mode is in use. Recall that Amdahl’s Law depends on the fraction of the original, unenhanced execution time that could make use of enhanced mode. Thus, we cannot directly use this 50% measurement to compute speedup with Amdahl’s Law.

a. What is the speedup we have obtained from fast mode?

b. What percentage of the original execution time has been converted to fast mode?

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