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fa09_cs433_hw1_sol

# fa09_cs433_hw1_sol - CS433 Computer Systems Organization...

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CS433: Computer Systems Organization Fall 2009 Homework 1 Assigned: Sept/1 Due in class Sept/15 Total points: 40 for undergraduate students, 54 for graduate students. Instructions: Please write your name, NetID and an alias on your homework submissions for posting grades (If you don’t want your grades posted, then don’t write an alias). We will use this alias throughout the semester. Homeworks are due in class on the date posted. 1. Amdahl’s law [8 points] Three enhancements with the following speedups are proposed for a new architecture: Speedup 1 = 30 Speedup 2 = 20 Speedup 3 = 10 Only one enhancement is usable at a time. a) [4 points] If enhancements 1 and 2 are each usable for 30% of the time, what fraction of the time must enhancement 3 be used to achieve an overall speedup of 10? Solution: To solve this problem, we first need to develop a new and improved form of Amdahl’s Law that can handle multiple enhancements where only one enhancement is usable at a time. We simply change the terms involving the fraction of time an enhancement can be used into summations: Speedup = [ 1 – (FE 1 + FE 2 + FE 3 ) + ( (FE 1 /SE 1 ) + (FE 2 /SE 2 ) + (FE 3 /SE 3 ) ) ] -1 If we plug in the numbers, we get: 10 = [ 1 – (0.30 + 0.30 + FE 3 ) + ( (0.30/30) + (0.30/20) + (FE 3 /10) ) ] -1 FE 3 = 0.36 Therefore, the third enhancement must be usable in the enhanced system 36% of the time to achieve an overall speedup of 10. Grading: 3. points for correctly setting up the equation 1. points for the correct values in the equation and get the final answer. b) [4 points] Assume for some benchmark, the fraction of use is 15% for each of enhancements 1 and 2 and 70% for enhancement 3. We want to maximize performance. If only one enhancement can be implemented, which should it be? If two enhancements can be implemented, which should be chosen? Solution: Here we will again use Amdahl’s law to compute speedups. Speedup for one enhancement only = [ 1 – FE 1 + (FE 1 /SE 1 ) ] -1 Speedup for two enhancements = [ 1 – (FE 1 + FE 2 ) + ( (FE 1 /SE 1 ) + (FE 2 /SE 2 ) ) ] -1

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If we plug in the numbers, we get: Speedup 1 = (1 – 0.15 + 0.15/30) -1 = 1.169 Speedup 2 = (1 – 0.15 + 0.15/20) -1 = 1.166 Speedup 3 = (1 – 0.70 + 0.70/10) -1 = 2.703 Therefore, if we are allowed to select a single enhancement, we would choose E 3 Speedup 12 = [(1 - 0.15 - 0.15) + (0.15/30 + 0.15/20)] -1 = 1.4035 Speedup 13 = [(1 - 0.15 - 0.70) + (0.15/30 + 0.70/10)] -1 = 4.4444 Speedup 23 = [(1 - 0.15 - 0.70) + (0.15/20 + 0.70/10)] -1 = 4.3956 Therefore, if two enhancements can be implemented, we would choose E 1 and E 3. Grading: 2 points for correctly calculating one enhancement speedups 2 points for the correctly calculating two enhancement speedups
2. Measuring processor’s time [8 points] After graduating, you are asked to become the lead computer designer at Hyper Computer, Inc. Your study of usage of high-level language constructs suggests that procedure calls are one of the most expensive operations. You have invented a new architecture with an ISA that reduces the loads and stores normally associated with procedure calls and returns. The first thing you do is run some experiments with and without this optimization. Your experiments use the same state-of-the-art optimizing compiler that will be used with either version of the computer.

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