1. CS 584

2. Logic
The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding.
The basis of logic is the syllogism, consisting of a major and minor premise and a conclusion.

3. Example
Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a post-hole in sixty seconds.
Conclusion: Sixty men can dig a post-hole in one second.

4. Performance Analysis: "Tar Baby"
Ask the right questions
Questions to consider
What is time?
What is work?
Objectivity is the key
Take a step back from your program

5. Performance Analysis Statements
There is always a trade-off between time and solution quality.
We should compare the quality of the answer for a given execution time.
For any performance reporting, find and clearly state the quality measure.

6. Efficiency Efficiency is defined as speedup/P
With superlinear speedup efficiency > 1
Does cache make a processor work at 110%?
Why is communication not considered work but rather overhead?

7. Speedup
Conventional speedup is defined as the reduction in execution time.
Consider running a problem on a slow parallel computer and on a faster one.
Same serial component
Speedup will be lower on the faster computer.

8. Speedup and Amdahl's Law
Conventional speedup penalizes faster absolute speed.
Assumption that task size is constant as the computing power increases results in an exaggeration of task overhead.
Scaling the problem size reduces these distortion effects.

9. Solution Gustafson introduces scaled speedup.
Scale the problem size as you increase the number of processors.
Calculated in two ways
Experimentally
Analytical models

10. Traditional Speedup C ( N ) = Speedup C ( N )1 C ( N ) P
C1 is complexity (time) taken on a single processor
CP is complexity (time) taken on P processors

11. Scaled Speedup ) ( PN C Speedup =1 PN C
Speedup P =
C1 is complexity (time) taken on a single processor
CP is complexity (time) taken on P processors

12. Experimental Scaled Speedup
Keep the ratio N/P constant between single processor case and many processor case when testing
Example:Calculate the speedup for 8, and 16 processors.
N/P = 256
How big should the problem be?

13. Using analytical models
Examine the control flow of the algorithm
Find a general algebraic form for the complexity (execution time).
Fit the curve with experimental data.
If the fit is poor, find the missing terms and repeat.
Calculate the scaled speedup using formula.

14. Example Serial Time = 2 + 12 N seconds
Parallel Time = N/P + 5P seconds
Let N/P = 128
Scaled Speedup for 4 processors is: ) ( 1 = PN C P ) 4 ( 5 /
128 12 )) 2 = + 93 . 3
1560
6146 =

15. Traditional Speedup
ideal
Speedup
measured
Number of Processors

16. Scaled Speedup Large Problem ideal Speedup Medium problem
Small problem
Number of Processors

17. Assignment Problems on the web Create a model for your program
Use the model to calculate
traditional speedup
scaled speedup
Experimentally calculate the values
Compare the results.