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White-Box Testing

White-Box Testing. Pfleeger, S. Software Engineering Theory and Practice 2 nd Edition. Prentice Hall, 2001. Ghezzi, C. et al., Fundamentals of Software Engineering. Prentice Hall, 2002. Pressman, R., Software Engineering A Practitioner’s Approach, Mc Graw Hill, 2005.

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White-Box Testing

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  1. White-Box Testing Pfleeger, S. Software Engineering Theory and Practice 2nd Edition. Prentice Hall, 2001. Ghezzi, C. et al., Fundamentals of Software Engineering. Prentice Hall, 2002. Pressman, R., Software Engineering A Practitioner’s Approach, Mc Graw Hill, 2005. Hutchinson, Marnie, Software Testing Fundamentals, Wiley, 2003. 0310

  2. Coverage • Statement • Branch • Condition • Path • Def-use • Others

  3. Statement Coverage • Every statement gets executed at least once • Every node in the CFG gets visited at least once

  4. Example (from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 5

  5. Examples: number of paths neededfor Statement Coverage?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 5

  6. Examples: number of paths neededfor Statement Coverage?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 4 1 5 5

  7. Branch coverage • Every decision is made true and false • Every edge in a CFG of the program gets traversed at least once • Also known as • Decision coverage • All edge coverage • Basis path coverage • Branch is finer than statement • C1 is finer than C2 if •  T1C1 T2C2T2  T1

  8. Examples: number of paths neededfor Branch Coverage?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 5

  9. Examples: number of paths neededfor Branch Coverage?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 2 5 5

  10. Condition coverage • Every complex condition is made true and false by every possible combination • E.G., (x and y) • x = true, y = true • x=false, y=true • x = true, y= false • x =false, y = false • There are lots of different types of condition coverage: Condition, multiple condition, condition/decision, modified condition/decision (MCDC), …I’m only covering the simplest. • Condition coverage is not finer than branch coverage • There are pathological cases where you can achieve Condition and not Branch • Under most circumstances, achieving Condition achieves Branch

  11. Condition Coverage: CFGs • One way to determine the number of paths is to break the compound conditional into atomic conditionals • Suppose you were writing the CFG for the assembly language implementation of the control construct If (A AND B) then C Endif (short circuit eval) (no short circuit eval) LD A LD A ; in general, lots of BZ :endif LAND B ; code for A and B LD B BZ :endif BZ :endif JSR C JSR C :endif nop :endif nop

  12. AND Condition 1 • 1.read (a,b); • 2.if (a == 0 && b == 0) then { • 3. c  a + b } • 4. else c  a * b paths: 1, 2A,2B,3, J 1, 2A, 2B, 4, J 1, 2A, 4, J 2A 2B 4 3 Join

  13. OR Condition 1 • 1.read (a,b); • 2.if (a == 0 || b == 0) then } • 3. c  a + b; • 4.while( c < 100) • 5. c  a + b;} • Paths: • 1, 2A, 3, 4, 5, 4 … J • 1, 2A, 3, 4, J • 1, 2A, 2B, 3, 4, 5, 4, … J • 1,2A, 2B, J 2A 3 2B 4 5 Join

  14. Path • A path is a sequence of statements • A path is sequence of branches • A path is a sequence of edges

  15. Examples: number of paths neededfor Path Coverage?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 5

  16. Examples: number of paths neededfor Path Coverage?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 16 5 5

  17. Path Coverage-1 1,2,3 • Every distinct path through code is executed at least once • Example 1. read (x) 2. read (z) 3. if x  0 thenbegin 4. y  x * z; 5. x  z end 6. else print ‘Invalid’ 7.if y > 1 then 8. print y 9. else print ‘Invalid’ • Test Paths: 1, 2, 3, 4, 5, J1, 7, 8, J2 1, 2, 3, 4, 5, J1, 7, 9, J2 1, 2, 3, 6, J1, 7, 8, J2, 1, 2, 3, 6, J1, 7, 9, J2 4,5 6 Join1 7 8 9 Join2

  18. Counting Paths • It is not feasible to calculate the total number of paths

  19. Linearly independent paths • It is feasible to calculate the number of linearly independent paths • The number of linearly independent paths is the number of end-to-end paths required to touch every path segment at least once • A linearly independent path introduces at least one new set of process statements or a new condition

  20. Independent Paths • Consider the following encoding: • Label each edge in the CFG with a positive integer • Describe a path using a vector where each element of the vector is the number of times the edge at that index is traversed: A 2 • The path ABD can be written as • [1, 0, 1, 0] 1 B C 4 3 D

  21. Independent Paths • Consider the following encoding: • Label each edge in the CFG with a positive integer • Describe a path using a vector where each element of the vector is the number of times the edge at that index is traversed: • Paths can be combined by adding or subtracting these path vectors • A basis set is a set of linearly independent paths • Each path in the basis set can not be formed as a combination of other paths in the basis set

  22. Basis Set • A basis set: • p13: [1,0,1,0] • p14: [1,0,0,1] • p23: [0,1,1,0] • The path 24 can be constructed by p23+p14-p13 [0,1,1,0] + [1,0,0,1] – [1,0,1,0] = [0,1,0,1] • p13, p24 is not a basis set • p13: [1,0,1,0] • p24: [0,1,0,1] • (No way to construct [1,0,0,1]) • Another basis set: • p13: [1,0,1,0] • p14: [1,0,0,1] • p23: [0,1,0,1] A 1 2 B 4 3 D

  23. Examples: number of linearly independent paths?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 5

  24. Examples: number of linearly independent paths?(from Hutchinson, Software Testing Fundamentals, Wiley, 2003) 1 6 1 6 2 7 2 7 3 8 3 8 4 9 4 9 5 5 5 5

  25. Cyclomatic Complexity • Software metric for the logical complexity of a program. • Defines the number of independent paths in the basis set of a program • Provides the upper bound for the number of tests that must be conducted to ensure that all statements been have executed at least once • For Edges (E) and Nodes (N) V(G) = E – N + 2

  26. Independent Path Coverage Basis set does not yield minimal test set Example 1. read (x) 2. read (z) 3. if x  0 thenbegin 4. y  x * z; 5. x  z end 6. else print ‘Invalid’ 7.if y > 1 then 8. print y 9. else print ‘Invalid’ Cyclomatic complexity: 3 Test Paths: 1, 2, 3, 4, 5, J1, 7, 8, J2 1, 2, 3, 4, 5, J1, 7, 9, J2 1, 2, 3, 6, J1, 7, 8, J2, 1,2,3 4,5 6 Join1 7 8 9 Join2

  27. Def-Use Coverage Def: x, z Use: x 1,2,3 • Def-use coverage: every path from every definition of every variable to every use of that definition is exercised in some test. • Example 1. read (x) 2. read (z) 3. if x  0 thenbegin 4. y  x * z; 5. x  z end 6. else print ‘Invalid’ 7.if y > 1 then 8. print y 9. else print ‘Invalid’ 4,5 Def: y, x Use: x, z 6 Use: none Join 7 Use: y 8 Use: none 9 Use: y • Test Path: 1, 2, 3, 4, 5, 7, 8, J Join

  28. Strength of Coverage Statement Arrows point from weaker to stronger coverage. Stronger coverage requires more test cases. Branch Def-Use Condition Path

  29. Groups: A A is read(x, y, z) B is if ((x>10) && (y<20)) D is if (z >10) E is repeat until g = 5 B D D1 D2 B1 Show me different minimal test sets that satisfy the 4 criteria E C

  30. Statement: A is read(x, y, z) B is if ((x>10) && (y<20)) D is if (z >10) E is repeat until g = 5 A B D • A,B,B1,E C: x(A) = 0; g (E) =5 • A, B,D,D1,E C: x(A)=11, y(A) = 11, z(A)=11, g(E)=5 • A, B, D, D2, E, C: x(A)=11, y(A) = 11, z(A)=9, g(E)=5 D1 D2 B1 E C

  31. Branch: A is read(x, y, z) B is if ((x>10) && (y<20)) D is if (z >10) E is repeat until g = 5 A B • A,B,B1,E C: x(A) = 0; g (E) =5 • A, B,D,D1,E C: x(A)=11, y(A) = 11, z(A)=11, g(E)=5 • A, B, D, D2, E, C: x(A)=11, y(A) = 11, z(A)=9, g(E)=5 • A,B,B1,E,A …:x(A) = 0; g (E) =4 D D1 D2 B1 E C

  32. Condition: A is read(x, y, z) B is if ((x>10) && (y<20)) D is if (z >10) E is repeat until g = 5 A B • A,B,B1,E C: x(A) = 0; g (E) =5 • A,B,B1,E C: x(A) = 11; y(A) = 22; g (E) =5 • A,B,B1,E C: x(A) = 0; y(A) = 22; g (E) =5 • A, B,D,D1,E C: x(A)=11, y(A) = 11, z(A)=11, g(E)=5 • A, B, D, D2, E, C: x(A)=11, y(A) = 11, z(A)=9, g(E)=5 • A,B,B1,E,A …:x(A) = 0; g (E) =4 D D1 D2 B1 E C

  33. Independent Paths: A is read(x, y, z) B is if ((x>10) && (y<20)) D is if (z >10) E is repeat until g = 5 A B • A,B,B1,E C: x(A) = 0; g (E) =5 • A, B,D,D1,E C: x(A)=11, y(A) = 11, z(A)=11, g(E)=5 • A, B, D, D2, E, C: x(A)=11, y(A) = 11, z(A)=9, g(E)=5 • A,B,B1,E,A,B,B1,E,C: x(A) = 0; g (E) =4 D D1 D2 B1 E C

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