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CHAPTER 10 Software Testing
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This list of subdomains could be increased to distinguish other subdomains that might be considered significant. For example, in scalene subdomains, there are actually six different orderings, but the placement of the largest might be the most significant based on possible mistakes in programming.
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Note that one test case in each subdomain is usually considered minimal but acceptable.
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TEST MATRICES
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A way to formalize this identi cation of subdomains is to build a matrix using the conditions that we can identify from the speci cation and then to systematically identify all combinations of these conditions as being true or false.
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EXAMPLE 10.2
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The conditions in the triangle problem might be (1) a b or a c or b c, (2) a b and b c, (3) a < b c and b < a c and c < a b, and (4) a > 0 and b > 0 and c > 0. These four conditions can be put on the rows of a matrix. The columns of the matrix will each be a subdomain. For each subdomain, a T will be placed in each row whose condition is true and an F when the condition is false. All
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Conditions a b or a c or b c a b and b c a < b c or b < a c or c < a b a > 0 or b > 0 or c > 0 Sample test case Expected output
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AM FL Y
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0,0,0
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3,3,3
0,4,0
3,8,3
5,8,5
0,5,6
3,4,8
3,4,5
Bad inputs
Equilateral
Bad inputs
Not triangle
Isosceles
Bad inputs
Not triangle
Scalene
Software Testing
valid combinations of T and F will be used. If there are three conditions, there may be 23 8 subdomains (columns). Additional rows will be used for values of a, b, and c and for the expected output for each subdomain.
10.3.4 STRUCTURAL TESTING
Structural testing is based on the structure of the source code. The simplest structural testing criterion is every statement coverage, often called C0 coverage.2
C0 Every Statement Coverage
This criterion is that every statement of the source code should be executed by some test case. The normal approach to achieving C0 coverage is to select test cases until a coverage tool indicates that all statements in the code have been executed.
EXAMPLE 10.3
The following pseudocode implements the triangle problem. The matrix shows which lines are executed by which test cases. Note that the first three statements (A, B, and C) can be considered parts of the same node. Node A B C D E F G H I J K Source Line read a,b,c type= scalene if(a==b||b==c||a==c) type= isosceles if(a==b&&b==c) type= equilateral if(a>=b+c||b>=a+c||c>=a+b) type= not a triangle if(a<=0||b<=0||c<=0) type= bad inputs print type * * * * * * * * * * * * * * 3,4,5 * * * 3,5,3 * * * * * 0,1,0 * * * * * 4,4,4 * * * * * * *
E. F. Miller developed the C0 and C1 naming system. His work contains many other criteria.
CHAPTER 10 Software Testing
By the fourth test case, every statement has been executed. This set of test cases is not the smallest set that would cover every statement. However, finding the smallest test set would often not find a good test set.
C1 Every-Branch Testing
A more thorough test criterion is every-branch testing, which is often called C1 test coverage. In this criterion, the goal is to go both ways out of every decision.
EXAMPLE 10.4
If we model the program of Example 10.3 as a control flow graph (see 2), this coverage criterion requires covering every arc in the control flow diagram. See Fig. 10-1. Arcs ABC D ABC E
A,B,C D E F G H I J K
3,4,5
3,5,3 *
0,1,0 *
4,4,4 *
* * * * * * * * * * * * * * * * * * *
D E E F E G F G G H G I H I I J I K J K
Fig. 10-1. Control ow graph for Example 10.3.
Every-Path Testing
Even more thorough is the every-path testing criterion. A path is a unique sequence of program nodes that are executed by a test case. In the testing matrix (Example 10.2) above, there were eight subdomains. Each of these just happens to be a path. In that example, there are sixteen di erent combinations of T and F. However, eight of those combinations are infeasible paths. That is, there is no test case that
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