2. Performance Measurement

3. Performance Analysis Paper and pencil. Don’t need a working computer program or even a computer.

4. 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(n 2 )

5. Limitations of Analysis Doesn’t account for constant factors. but constant factor may dominate 1000n vs n 2 and we are interested only in n < 1000

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

7. Memory Hierarchy R L1 L2 MAIN ALU 8-3232KB512KB512MB 1C2C10C100C

8. 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.

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

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

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

12. Timing In C clock_t start, stop; start = clock(); /* set start to current time in hundredths of a second */ /* code to be timed comes here */ stop = clock(); /* set stop to current time */ runTime = (double) (stop – start)/ CLOCKS_PER_SEC;

13. Shortcoming Clock accuracy assume 100 ticks Repeat work many times to bring total time to be >= 1000 ticks

14. Accurate Timing start = clock(); counter = 0; do { counter++; doSomething(); } while (clock() - start < 1000) elapsedTime = (double) (clock() – start)/ CLOCKS_PER_SEC ; timeForTask = elapsedTime/counter;

15. Accuracy Now accuracy is 10%. first reading may be just about to change to start + 100 second reading may have just changed to stop so stop - start is off by 100 ticks

16. Accuracy first reading may have just changed to start second reading may be about to change to stop + 100 so stop - start is off by 100 ticks

17. Accuracy Examining remaining cases, we get trueElapsedTime = stop - start +- 100 To ensure 10% accuracy, require elapsedTime = stop – start >= 1000

18. What Went Wrong? start = clock(); counter = 0; do { counter++; insertionSort(a,n); } while (clock() - start < 1000) elapsedTime = (double)(clock() – start)/ CLOCKS_PER_SEC ; timeToSort = elapsedTime/counter;

19. The Fix start = clock(); counter = 0; do { counter++; /* put code to initialize a here */ insertionSort(a,n); } while (clock() - start < 1000)

20. Bad Way To Time do { counter++; start = clock(); doSomething(); stop = clock(); elapsedTime += stop - start; } while (elapsedTime < 1000)