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Software Testing
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could have that combination of T and F for the decisions in the program. It can be exceedingly hard to determine if a path is infeasible or if it is just hard to nd a test case that executes that path. Most programs with loops will have an in nite number of paths. In general, every-path testing is not reasonable.
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EXAMPLE 10.5
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The following table shows the eight feasible paths in the triangle pseudocode from Example 10.3.
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Path ABCEGIK ABCEGHIK ABCEGHIJK ABCDEGIK ABCDEGHIK ABCDEGHIJK ABCDEFGIK ABCDEFGHIJK
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T/F FFFF FFTF FFTT TFFF TFTF TFTT TTFF TTTT
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Test Case 3,4,5 3,4,8 0,5,6 5,8,5 3,8,3 0,4,0 3,3,3 0,0,0
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Output Scalene Not a triangle Bad inputs Isosceles Not a triangle Bad inputs Equilateral Bad inputs
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Multiple-Condition Coverage
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A multiple-condition testing criterion requires that each primitive relation condition is evaluated both true and false. Additionally, all combinations of T/F for the primitive relations in a condition must be tried. Note that lazy evaluation3 of expressions will eliminate some combinations. For example, in an and of two primitive relations, the second will not be evaluated if the rst one is false.
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EXAMPLE 10.6
In the pseudocode in Example 10.3, there are multiple conditions in each decision statement. Primitives that are not executed because of lazy evaluation are shown with an X .
A compiler does lazy evaluation when it does not generate code for tests that are not needed. For example, if the rst condition of an or expression is true, the second condition does not need to be tested.
if(a==b||b==c||a==c) Combination TXX FTX FFT FFF
CHAPTER 10 Software Testing
Possible Test Case 3,3,4 4,3,3 3,4,3 3,4,5
Branch ABC-D ABC-D ABC-D ABC-E
if(a==b&&b==c) Combination TT TF FX Possible Test Case 3,3,3 3,3,4 4,3,3 Branch E-F E-G E-G
if(a>=b+c||b>=a+c||c>=a+b) Combination TXX FTX FFT FFF Possible Test Case 8,4,3 4,8,3 4,3,8 3,3,3 Branch G-H G-H G-H G-I
if(a<=0||b<=0||c<=0) Combination TXX FTX FFT FFF Possible Test Case 0,4,5 4, 2, 2 5,4, 3 3,3,3 Branch I-J I-J I-J I-K
Software Testing
Subdomain Testing
Subdomain testing is the idea of partitioning the input domain into mutually exclusive subdomains and requiring an equal number of test cases from each subdomain. This was basically the idea behind the test matrix. Subdomain testing is more general in that it does not restrict how the subdomains are selected. Generally, if there is a good reason for picking the subdomains, then they may be useful for testing. Additionally, the subdomains from other approaches might be subdivided into smaller subdomains. Theoretical work has shown that subdividing subdomains is only e ective if it tends to isolate potential errors into individual subdomains. Every-statement coverage and every-branch coverage are not subdomain tests. There are not mutually exclusive subdomains related to the execution of di erent statements or branches. Every-path coverage is a subdomain coverage, since the subdomain of test cases that execute a particular path through a program is mutually exclusive with the subdomain for any other path.
EXAMPLE 10.7
For the triangle problem, we might start with a subdomain for each output. These might be further subdivided into new subdomains based on whether the largest or the bad element is in the first position, second position, or third position (when appropriate).
Subdomain Equilateral Isos rst Isos sec Isos third Scalene rst Scalene sec Scalene third
Possible Test Case 3,3,3 8,5,5
Subdomain Not triangle rst Not triangle sec Not triangle third
Possible Test Case 8,3,3 3,8,4 4,3,8 0,3,4 3,0,4 3,4,0
5,8,5 Bad input rst 5,5,8 5,4,3 4,5,3 3,4,5 Bad input sec Bad input third
10.3.4.6 C1 Subsumes C0
CHAPTER 10 Software Testing
EXAMPLE 10.8 C1 Subsumes C0
For the triangle problem, in Example 10.3 we selected good test cases until we achieved the C0 coverage. The test cases were (3,4,5 scalene), (3,5,3 isosceles), (0,1,0 bad inputs), and (4,4,4 equilateral). These tests also covered four out the five possible outputs. However, we can achieve C1 coverage with two test cases: (3,4,5 scalene) and (0,0,0 bad inputs). This test is probably not as good as the first test set. However, it achieves C1 coverage and it also achieves C0 coverage.
Data Flow Testing
Data ow testing is testing based on the ow of data through a program. Data ows from where it is de ned to where it is used. A de nition of data, or def, is when a value is assigned to a variable. Two di erent kinds of use have been identi ed. The computation use, or c-use, is when the variable appears on the right-hand side of an assignment statement. A c-use is said to occur on the assignment statement. The predicate use, or p-use, is when the variable is used in the condition of a decision statement. A p-use is assigned to both branches out of the decision statement. A de nition free path, or def-free, is a path from a de nition of a variable to a use of that variable that does not include another de nition of the variable.
EXAMPLE 10.9 Control Flow Graph of Triangle Problem (Example 10.3)
The control flow graph in Fig. 10-2 is annotated with the definitions and uses of the variables a,b, and c.
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