第一次作业请在 3 月 5 日上课前交，逾期不再接收！
Your company is trying to choose between purchasing the Opteron or Itanium 2. You have analyzed your company’s applications, and 60% of the time it will be running applications similar to wupwise, 20% of the time applications similar to ammp, and 20% of the time applications similar to apsi.
a. If you were choosing just based on overall SPEC performance, which would you choose and why?
b. What is the weighted average of execution time ratios for this mix of applications for the Opteron and Itanium 2?
c. What is the speedup of the Opteron over the Itanium 2?
In this exercise, assume that we are considering enhanc- ing a machine by adding vector hardware to it. When a computation is run in vec- tor mode on the vector hardware, it is 10 times faster than the normal mode of execution. We call the percentage of time that could be spent using vector mode the percentage of vectorization. Vectors are discussed in Chapter 4, but you don’t need to know anything about how they work to answer this question!
a. Draw a graph that plots the speedup as a percentage of the compu- tation performed in vector mode. Label the y-axis “Net speedup” and label the x-axis “Percent vectorization.”
b. What percentage of vectorization is needed to achieve a speedup of 2?
c. What percentage of the computation run time is spent in vector mode if a speedup of 2 is achieved?
d. What percentage of vectorization is needed to achieve one-half the maximum speedup attainable from using vector mode?
e. Suppose you have measured the percentage of vectorization of the program to be 70%. The hardware design group estimates it can speed up the vector hardware even more with significant additional investment. You won- der whether the compiler crew could increase the percentage of vectorization, instead. What percentage of vectorization would the compiler team need to achieve in order to equal an addition 2× speedup in the vector unit (beyond the initial 10×)?
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 con- verted to fast mode?
When making changes to optimize part of a processor, it is often the case that speeding up one type of instruction comes at the cost of slow- ing down something else. For example, if we put in a complicated fast floating- point unit, that takes space, and something might have to be moved farther away from the middle to accommodate it, adding an extra cycle in delay to reach that unit. The basic Amdahl’s law equation does not take into account this trade-off.
a. If the new fast floating-point unit speeds up floating-point opera- tions by, on average, 2×, and floating-point operations take 20% of the origi- nal program’s execution time, what is the overall speedup (ignoring the penalty to any other instructions)?
b. Now assume that speeding up the floating-point unit slowed down data cache accesses, resulting in a 1.5× slowdown (or 2/3 speedup). Data cache accesses consume 10% of the execution time. What is the overall speedup now?
c. After implementing the new floating-point operations, what percentage of execution time is spent on floating-point operations? What percentage is spent on data cache accesses?
Your company has just bought a new Intel Core i5 dual-core processor, and you have been tasked with optimizing your software for this processor. You will run two applications on this dual core, but the resource requirements are not equal. The first application requires 80% of the resources, and the other only 20% of the resources. Assume that when you parallelize a por- tion of the program, the speedup for that portion is 2.
a. Given that 40% of the first application is parallelizable, how much speedup would you achieve with that application if run in isolation?
b. Given that 99% of the second application is parallelizable, how much speedup would this application observe if run in isolation?
c. Given that 40% of the first application is parallelizable, how much overall system speedup would you observe if you parallelized it?
d. Given that 99% of the second application is parallelizable, how much overall system speedup would you observe if you parallelized it?
When parallelizing an application, the ideal speedup is speeding up by the number of processors. This is limited by two things: percent- age of the application that can be parallelized and the cost of communication. Amdahl’s law takes into account the former but not the latter.
a. What is the speedup with N processors if 80% of the application is parallelizable, ignoring the cost of communication?
b. What is the speedup with 8 processors if, for every processor added, the communication overhead is 0.5% of the original execution time.
c. What is the speedup with 8 processors if, for every time the number of processors is doubled, the communication overhead is increased by 0.5% of the original execution time?
d. What is the speedup with N processors if, for every time the number of processors is doubled, the communication overhead is increased by 0.5% of the original execution time?
e. Write the general equation that solves this question: What is the number of processors with the highest speedup in an application in which P% of the original execution time is parallelizable, and, for every time the number of processors is doubled, the communication is increased by 0.5% of the original execution time?