1. Performance Measurement

2. Performance Analysis Paper and pencil.
Don’t need a working computer program or even a computer.
These could be considered some of the advantages of performance analysis over performance measurement.

3. Some Uses Of Performance Analysis
determine practicality of algorithm
predict run time on large instance
compare 2 algorithms that have different asymptotic complexity
e.g., O(n) and O(n2)
If the complexity is O(n2), we may consider the algorithm practical even for large n.
An O(2n) algorithm is practical only for small n, say n < 40.
The worst-case run time of an O(n2) algorithm will quadruple with each doubling of n. So if the worst-case time is 10 sec when n = 100, it will be approximately 40 sec when n = 200.

4. Limitations of Analysis
Doesn’t account for constant factors.
but constant factor may dominate
1000n vs n2
and we are interested only in
n < 1000

5. Limitations of Analysis
Modern computers have a hierarchical memory organization with different access time for memory at different levels of the hierarchy.

6. Memory Hierarchy MAIN L2 L1 ALU R 8-32 32KB 512KB 512MB 1C 2C 10C 100C
1 cycle to add data that are in the registers
2 cycles to copy data from L1 cache to a register
10 cycles to copy from L2 to L1 and register L1
ALU R
8-32
32KB
512KB
512MB 1C 2C
10C
100C

7. Limitations of Analysis
Our analysis doesn’t account for this difference in memory access times.
Programs that do more work may take less time than those that do less work.
A program that does 100 operations on the same data would take less time than a program that performs a single operation on say 50 different pieces of data (assuming, in a simple model) that each time data is fetched from main memory, only one piece of data is fetched. The first program would make one fetch at a cost of 100 cycles and perform 100 operations at a cost of 1 cycle each for a total of 200 cycles. The second program would need 50 * 100 cycles just to fetch the data.

8. Performance Measurement
Measure actual time on an actual computer.
What do we need?

9. Performance Measurement Needs
programming language
working program
computer
compiler and options to use

10. Performance Measurement Needs
data to use for measurement
worst-case data
best-case data
average-case data
timing mechanism --- clock

11. Timing In C++ long start, stop;
time(start); // set start to current time in
// hundredths of a second
// code to be timed comes here
time(stop); // set stop to current time
long runTime – stop – start;
runTime is in hundredths of a second

12. Shortcoming Clock accuracy assume 1/100 second
Repeat work many times to bring total time to be >= 1/10 second
Preceding measurement code is acceptable only when the elapsed time is large relative to the accuracy of the clock.

13. Accurate Timing time(start); long counter; do { counter++;
doSomething();
time(stop);
} while (stop - start < 10)
double elapsedTime = stop - start;
double timeForTask = elapsedTime/counter;

14. Accuracy Now accuracy is 10%.
first reading may be just about to change to start + 1
second reading may have just changed to stop
so stop - start is off by 1 unit
1 unit = 1/100 sec

15. Accuracy first reading may have just changed to start
second reading may be about to change to stop + 1
so stop - start is off by 1 unit

16. Accuracy Examining remaining cases, we get
trueElapsedTime = stop - start +- 1
To ensure 10% accuracy, require
elapsedTime = stop – start
>= 10

17. What Went Wrong? time(start); long counter; do { counter++;
insertionSort(a,n);
time(stop);
} while (stop - start < 10)
double elapsedTime = (stop – start);
double timeToSort = elapsedTime/counter;
Suppose we are measuring worst-case run time. The array a initially is in descending order. After the first iteration, the data is sorted. Subsequent iterations no longer start with worst-case data. So the measured time is for one worst-case sort plus counter-1 best-case sorts!

18. The Fix time(start); long counter; do { counter++;
// put code to initialize a here
insertionSort(a,n);
time(stop);
} while (stop - start < 10)
Now the measured time is for counter number of worst-case sorts plus counter number of initializes. We can measure the time to initialize separately and subtract. Or, if we are to compare with other sort methods, we could ignore the initialize time as it is there in the measurements for all sort methods. Or we could argue that for large n the worst case time to sort using insertion sort (O(n2)) overshadows the initialize time, which is O(n), and so we may ignore the initialize time.

19. Bad Way To Time elapsedTime += stop - start; do { counter++;
time(start);
doSomething();
time(stop)
elapsedTime += stop - start;
} while (elapsedTime < 10)
Suppose the clock is updated every 1/100 sec and doSomething takes 1/99 sec and it takes another 1/100 sec to do everything else in the loop. If the clock is updated exactly at the start of the loop then it is not updated between the start = and elapsedTime += statements. So elapsedTime is always 0.