hw1_sol2.docx - CSCE 614: Computer Architecture Spring 2019...

CSCE 614: Computer Architecture
Spring 2019
Homework 1
Assigned: Jan 24
Due in class Feb/07
Total points: 50
Name:
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?
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?

Speedup for two enhancements = [ 1 – (FE
1
+ FE
2
) + ( (FE
1
/SE
1
) + (FE
2
/SE
2
) ) ] -1
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