1. How does the complexity of the flow of control affect test cases?
Testing and Flow
How does the complexity of the flow of control affect test cases?
This should follow the Flow Graph presentation
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2. Introduction This considers again white box testing
Since the focus is on testing flow of control we have to digress into several topics
Flow Charts
Flow Graphs
Graph theory
We are going to have some fun!
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3. Cyclomatic Complexity
AKA McCabe essential complexity
A metric that measures flow complexity
Gives an upper bound on independent paths in a set the covers the code
The formula for Cyclomatic Complexity is defined as: M = E – N + 2P where
E is number of edges (arrows)
N is number of nodes
P is number of connected components
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4. Connectivity
If the item in question is a function or a program, then it is connected and P=1
Formula become M = E – N + 2
If the item in question is a class, then all of its methods may be disconnected with P>1
More likely some methods will call others
We will see some disconnected components and some weakly connected components
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5. Notes This metric only works on structured programs
Not usually a problem today
Besides the usual such as if and while, do not forget the stealth flow statements:
Return
Break
Continue
These have no predicates
Compound conditions with short circuit evaluation may add others
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6. Consider this code
int f1, f2, total=0, counter=1; while(!infile){ cin >> f1 >> f2 if(f1==0){ total+=f1; counter++; } else if(f2 == 0){ cout << total<<counter; counter = 0; } else total -= f2;
cout << f1 << f2;
} // end while
cout << counter;
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7. Flow Graph N = 9 E = 11 9 1 P = 1 M = E – N + 2P M = 11 – 9 + 2 M = 43
Independent Paths
1, 9
1, 2, 3, 8, 1, 9
1, 2, 4, 5, 7, 8, 1, 9
1, 2, 4, 6, 7, 8, 1, 9
The first could be left out, it is covered by the others 5 6
From Pressman 7 8
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8. Basis Path Testing
The Cyclomatic Complexity number gives an upper bound of linearly independent paths
Notice that we could have left the first path out
Basis Path Testing uses this upper bound to find a set of test cases that covers every node and every edge
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9. First Alternative Calculation
It is possible to count regions in the graph to compute Cyclomatic Complexity as well
A region is any enclosed by edges
This includes the surrounding region as well
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10. Region Counting 11 1 Four regions, Cylomatic Complexity must be four B
2,3 B A 6
4,5 7 D 8 C
From Pressman 9 10
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11. Second Alternative Calculation
Predicate nodes plus one
M = π + 1
A predicate node is any node with outdegree greater than 1
A compound condition, such as (X || Y) adds an additional predicate node
If X is true, we do not evaluate Y
Similarly with False AND Y
With a switch the case is the predicate
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12. Predicate Nodes 11 1
Three predicate nodes, Cylomatic Complexity must be four
2,3 6
4,5 7 8
From Pressman 9 10
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13. Commentary
The counting of predicate node is particularly easy for programs to compute
Scan the source and look only for flow constructs
No need to construct the flow graph
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14. Compound Conditions
The process dictates that we consider a compound predicate as two:
(x>y || x == 5)
At the machine level this makes sense
The real problem is if there are function calls that may or may not be executed
(x>z(y+1) && boolfun(y))
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15. Non-Structured Constructs
A function or program with multiple exits violates the structured programming tenets
Although it is not always a bad thing
We may adjust the formula for multiple exits, s M = π – S + 2
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16. Generating Test Cases Simple, but not necessarily easy, procedure
Create a flow graph
Determine the Cyclomatic Complexity
Determine the basis set of paths
Prepare one test case for each path
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17. Black ≠ White Black box testing and white box testing are not the same
Duh!
The upper bound for the number of test cases might not satisfy the demands of black box testing
Or it might
White box testing cannot detect a left out case
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18. Development We usually connect Cyclomatic Complexity with testing
We may also use it as an aid to development
Routines which have high Cyclomatic Complexity measures are candidates for refactoring
There may be a group policy mandating dividing complicated routines
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19. Paths This graph has M = 3 Two paths provide a basis path set
1, 2, 4, 5, 7
1, 3, 4, 6, 7
Yet if 3 and 5 have some kind of interaction, this may not be enough
There are four distinct paths through this 1 3 2 4 6 5 7
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20. Cyclomatic number again
We know that the Cyclomatic Complexity meaure provides an upper bound for every statement testing
It also provides a lower bound for every path testing
Thus every stmt ≤ cyclomatic ≤ every path
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21. Problems Not everyone is happy with this metric
Some claim that it is no better than LOC for any prediction
Almost everyone agrees that if two codes with the same function have approximately the same LOC and much different Cyclomatic Complexity (M), then the smaller M code is preferred
In general we expect M and LOC to correlate
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22. False Complexity
What we expect is that higher value will occur with higher complexity
This implies lower readability and higher costs to maintain
Switches tend to be easy to read but add one for each case
Thus larger values even though readability/maintainability does not suffer
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23. Nesting
We generally agree that nesting is less desirable with respect to complexity
Two loops nested is harder to understand than if they are sequentially encountered
Yet they both have the same Cyclomatic Complexity
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24. Automatic Metrics
There is some disagreement between automated measures
These are often in the area of whether to increase the number for a compound condition or to treat compound conditions with side effects differently than those without
Moral: only use one automated measure and then determine what is the threshold of a too complex
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25. Results
The conclusion is that this and every other metric is imperfect
We take its value as advice, but not as law
We still believe that a lower metric is better
But we also believe that the opinion of a real developer is better still
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26. An Exercise On the next two screens is a function and then a method
We will examine these
We will:
Construct a flow graph
Count regions
Count predicates
Compute Cyclomatic Complexity in several ways
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27. Insertion Sort void insertion(int ar[], unsigned int max) {
unsigned int cur;
int temp,i;
for(cur=0;cur<max;cur++) {
temp = ar[cur]; // cur is now free
for(i=cur-1;i>=0 && ar[i] > temp;i--)
ar[i+1]=ar[i];
ar[i+1] = temp; }
return;
} // end of insertion
M = E – N + 2P
M = π + 1
Regions
Predicates
Copyright © Curt Hill

28. Cache::IsPresent bool Cache::IsPresent(int k, char * & vp){ int i;
reads++;
clock++;
vp = NULL;
for(i=0;i<size;i++) {
if(k == item[i].key) {
if(item[i].ptr == NULL)
return false;
if(lru)
item[i].value = clock;
else
item[i].value++;
vp = item[i].ptr;
hits++;
return true;
} // end of if
} // end of for }
M = E – N + 2P
M = π + 1
Regions
Predicates
Copyright © Curt Hill

29. Finally Ready to try this yourself?
Let’s do a couple of assignments to make this more familiar
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