1. Dependable Software Systems
4/17/2017
Dependable Software Systems
Topics in
Data-Flow Testing
Material drawn from [Beizer, Mancoridis, Vokolos]
Dependable Software Systems (Data-Flow Testing)

2. Dependable Software Systems (Data-Flow Testing)
Data-flow testing uses the control flowgraph to explore the unreasonable things that can happen to data (i.e., anomalies).
Consideration of data-flow anomalies leads to test path selection strategies that fill the gaps between complete path testing and branch or statement testing.
Dependable Software Systems (Data-Flow Testing)

3. Data-Flow Testing (Cont’d)
Data-flow testing is the name given to a family of test strategies based on selecting paths through the program’s control flow in order to explore sequences of events related to the status of data objects.
E.g., Pick enough paths to assure that:
Every data object has been initialized prior to its use.
All defined objects have been used at least once.
Dependable Software Systems (Data-Flow Testing)

4. Data Object Categories
(d) Defined, Created, Initialized
(k) Killed, Undefined, Released
(u) Used:
(c) Used in a calculation
(p) Used in a predicate
Dependable Software Systems (Data-Flow Testing)

5. Dependable Software Systems (Data-Flow Testing)
(d) Defined Objects
An object (e.g., variable) is defined when it:
appears in a data declaration
is assigned a new value
is a file that has been opened
is dynamically allocated
...
Dependable Software Systems (Data-Flow Testing)

6. Dependable Software Systems (Data-Flow Testing)
(k) Killed Objects
An object is killed when it is:
released (e.g., free) or otherwise made unavailable (e.g., out of scope)
a loop control variable when the loop exits
a file that has been closed
...
Dependable Software Systems (Data-Flow Testing)

7. Dependable Software Systems (Data-Flow Testing)
(u) Used Objects
An object is used when it is part of a computation or a predicate.
A variable is used for a computation (c) when it appears on the RHS (sometimes even the LHS in case of array indices) of an assignment statement.
A variable is used in a predicate (p) when it appears directly in that predicate.
Dependable Software Systems (Data-Flow Testing)

8. Example: Definition and Uses
What are the definitions and uses for the program below?
1. read (x, y);
2. z = x + 2;
3. if (z < y)
4 w = x + 1;
else
5. y = y + 1;
6. print (x, y, w, z);
Dependable Software Systems (Data-Flow Testing)

9. Example: Definition and Uses
C-use
P-use
x, y z x
z, y w y
x, y, w, z
1. read (x, y);
2. z = x + 2;
3. if (z < y)
4 w = x + 1;
else
5. y = y + 1;
6. print (x, y, w, z);
Dependable Software Systems (Data-Flow Testing)

10. Dependable Software Systems (Data-Flow Testing)
Data-Flow Anomalies
A data-flow anomaly is denoted by a two character sequence of actions. E.g.,
ku: Means that an object is killed and then used.
dd: Means that an object is defined twice without an intervening usage.
Dependable Software Systems (Data-Flow Testing)

11. Dependable Software Systems (Data-Flow Testing)
Example
E.g., of a valid (not anomalous) scenario where variable A is a dpd:
A = C + D;
if(A > 0)
X = 1;
else
X = -1;
A = B + C;
Dependable Software Systems (Data-Flow Testing)

12. Two Letter Combinations for d k u
dd: Probably harmless, but suspicious.
dk: Probably a bug.
du: Normal situation.
kd: Normal situation.
kk: Harmless, but probably a bug.
ku: Definitely a bug.
ud: Normal situation (reassignment).
uk: Normal situation.
uu: Normal situation.
Dependable Software Systems (Data-Flow Testing)

13. Single Letter Situations
A leading dash means that nothing of interest (d, k, u) occurs prior to the action noted along the entry-exit path of interest.
A trailing dash means that nothing of interest happens after the point of action until the exit.
Dependable Software Systems (Data-Flow Testing)

14. Single Letter Situations
-k: Possibly anomalous:
Killing a variable that does not exist.
Killing a variable that is global.
-d: Normal situation.
-u: Possibly anomalous, unless variable is global.
k-: Normal situation.
d-: Possibly anomalous, unless variable is global.
u-: Normal situation.
Dependable Software Systems (Data-Flow Testing)

15. Data-Flow Anomaly State Graph
state of variable
action K k
u,k
anomalous
state d d
d,k U D A u u
k,u,d
Dependable Software Systems (Data-Flow Testing)

16. Data-Flow Anomaly State Graph with Variable Redemptionk k u KU K u k d d k u d u DK D U k d u d u k DD d
Dependable Software Systems (Data-Flow Testing)

17. Static vs Dynamic Anomaly Detection
Static Analysis is analysis done on source code without actually executing it.
E.g., Syntax errors are caught by static analysis.
Dependable Software Systems (Data-Flow Testing)

18. Static vs Dynamic Anomaly Detection (Cont’d)
Dynamic Analysis is analysis done as a program is executing and is based on intermediate values that result from the program’s execution.
E.g., A division by 0 error is caught by dynamic analysis.
If a data-flow anomaly can be detected by static analysis then the anomaly does not concern testing. (Should be handled by the compiler.)
Dependable Software Systems (Data-Flow Testing)

19. Anomaly Detection Using Compilers
Compilers are able to detect several data-flow anomalies using static analysis.
E.g., By forcing declaration before use, a compiler can detect anomalies such as: -u ku
Optimizing compilers are able to detect some dead variables.
Dependable Software Systems (Data-Flow Testing)

20. Is Static Analysis Sufficient?
Questions:
Why isn’t static analysis enough?
Why is testing required?
Could a good compiler detect all data-flow anomalies?
Answer: No. Detecting all data-flow anomalies is provably unsolvable.
Dependable Software Systems (Data-Flow Testing)

21. Static Analysis Deficiencies
Current static analysis methods are inadequate for:
Dead Variables: Detecting unreachable variables is unsolvable in the general case.
Arrays: Dynamically allocated arrays contain garbage unless they are initialized explicitly. (-u anomalies are possible)
Dependable Software Systems (Data-Flow Testing)

22. Static Analysis Deficiencies (Cont’d)
Pointers: Impossible to verify pointer values at compile time.
False Anomalies: Even an obvious bug (e.g., ku) may not be a bug if the path along which the anomaly exists is unachievable. (Determining whether a path is or is not achievable is unsolvable.)
Dependable Software Systems (Data-Flow Testing)

23. Dependable Software Systems (Data-Flow Testing)
Data-Flow Modeling
Data-flow modeling is based on the control flowgraph.
Each link is annotated with:
symbols (e.g., d, k, u, c, p)
sequences of symbols (e.g., dd, du, ddd)
that denote the sequence of data operations on that link with respect to the variable of interest.
Dependable Software Systems (Data-Flow Testing)

24. Control Flowgraph Annotated for X and Y Data Flows
1 INPUT X,Y
Z:= X+Y
Y:= X-Y
3 IF Z>=0 GOTO SAM
4 JOE: Z:=Z-1
5 SAM: Z:=Z+V
U:=0
6 LOOP
B(U),Q(V):=(Z+V)*U
7 IF B(U)=0 GOTO JOE
Z:=Z-1
8 IF Z=0 GOTO ELL
U:=U+1
9 UNTIL U=z
B(U-1):=B(U+1)+Q(V-1)
ELL: B(U+Q(V)):=U+V
11 IF U=V GOTO JOE
12 IF U>V THEN U:=Z
YY:Z:=U
2 END
LOOP
B(U)?
JOE
dcc 1 3 4 5 6 7
SAM Z?
ELL
U,Z? Z? 2 13 12 11 10 9 8
END YY
U,V?
U,V?
Dependable Software Systems (Data-Flow Testing)

25. Control Flowgraph Annotated for Z Data Flows
1 INPUT X,Y
Z:= X+Y
Y:= X-Y
3 IF Z>=0 GOTO SAM
JOE: Z:=Z-1
SAM: Z:=Z+V
U:=0
6 LOOP
B(U),Q(V):=(Z+V)*U
7 IF B(U)=0 GOTO JOE
Z:=Z-1
8 IF Z=0 GOTO ELL
U:=U+1
9 UNTIL U=z
B(U-1):=B(U+1)+Q(V-1)
ELL: B(U+Q(V)):=U+V
11 IF U=V GOTO JOE
12 IF U>V THEN U:=Z
YY:Z:=U
2 END p
LOOP
B(U)?
JOE d 1 3 4 5 6 7 p cd cd c
SAM Z? cd p
ELL d p p c 2 13 12 11 10 9 8 Z?
U,Z?
END YY
U,V?
U,V? p
Dependable Software Systems (Data-Flow Testing)

26. Definition-Clear Path Segments
A Definition-clear Path Segment (w.r.t. variable X) is a connected sequence of links such that X is defined on the first link and not redefined or killed on any subsequent link of that path segment.
Dependable Software Systems (Data-Flow Testing)

27. Definition-Clear Path Segments for Variable Z (Cont’d)
LOOP
B(), U?
JOE d 1 3 4 5 6 7 p cd cd c
SAM Z? cd p
ELL d p p 2 13 c 12 11 10 9 8 Z?
END YY
U,V?
U,V?
U,Z? p
Dependable Software Systems (Data-Flow Testing)

28. Non Definition-Clear Path Segments for Variable Z (Cont’d)
LOOP
B(), U?
JOE d 1 3 4 5 6 7 p cd cd c
SAM Z? cd p
ELL d p p 2 13 c 12 11 10 9 8 Z?
END YY
U,V?
U,V?
U,Z? p
Dependable Software Systems (Data-Flow Testing)

29. Dependable Software Systems (Data-Flow Testing)
Simple Path Segments
A Simple Path Segment is a path segment in which at most one node is visited twice.
E.g., (7,4,5,6,7) is simple.
Therefore, a simple path may or may not be loop-free.
Dependable Software Systems (Data-Flow Testing)

30. Loop-free Path Segments
A Loop-free Path Segment is a path segment for which every node is visited at most once.
E.g., (4,5,6,7,8,10) is loop-free.
path (10,11,4,5,6,7,8,10,11,12) is not loop-free because nodes 10 and 11 are visited twice.
Dependable Software Systems (Data-Flow Testing)

31. Dependable Software Systems (Data-Flow Testing)
du Path Segments
A du Path is a path segment such that if the last link has a use of X, then the path is simple and definition clear.
Dependable Software Systems (Data-Flow Testing)

32. Dependable Software Systems (Data-Flow Testing)
def-use Associations
A def-use association is a triple (x, d, u,), where: x is a variable, d is a node containing a definition of x, u is either a statement or predicate node containing a use of x, and there is a sub-path in the flow graph from d to u with no other definition of x between d and u.
Dependable Software Systems (Data-Flow Testing)

33. Example: Def-Use Associations1
read (x, y)
Some Def-Use Associations:
(x, 1, 2), (x, 1, 4), …
(y, 1, (3,t)), (y, 1, (3,f)), (y, 1, 5), …
(z, 2, (3,t)),... 2
z = x + 2 3
z < y T F 4 5
y = y + 1
w = x + 1 6
print (x,y,w,z)
Dependable Software Systems (Data-Flow Testing)

34. Example: Def-Use Associations
What are all the def-use associations for the program below?
read (z) x = 0 y = 0 if (z  0) {
x = sqrt (z) if (0  x && x  5) y = f (x) else y = h (z) }
y = g (x, y)
print (y)
Dependable Software Systems (Data-Flow Testing)

35. Example: Def-Use Associations
read (z) x = 0 y = 0 if (z  0) {
x = sqrt (z) if (0  x && x  5) y = f (x) else y = h (z) }
y = g (x, y)
print (y)
def-use associations for variable z.
Dependable Software Systems (Data-Flow Testing)

36. Example: Def-Use Associations
read (z) x = 0 y = 0 if (z  0) {
x = sqrt (z) if (0  x && x  5)
y = f (x) else y = h (z) }
y = g (x, y)
print (y)
def-use associations for variable x.
Dependable Software Systems (Data-Flow Testing)

37. Example: Def-Use Associations
read (z) x = 0 y = 0 if (z  0) {
x = sqrt (z) if (0  x && x  5) y = f (x) else y = h (z) }
y=g (x, y)
print (y)
def-use associations for variable y.
Dependable Software Systems (Data-Flow Testing)

38. Definition-Clear Paths
A path (i, n1, ..., nm, j) is called a definition-clear path with respect to x from node i to node j if it contains no definitions of variable x in nodes (n1, ..., nm , j) .
The family of data flow criteria requires that the test data execute definition-clear paths from each node containing a definition of a variable to specified nodes containing c-use and edges containing p-use of that variable.
Dependable Software Systems (Data-Flow Testing)

39. Data-Flow Testing Strategies
All du Paths (ADUP)
All Uses (AU)
All p-uses/some c-uses (APU+C)
All c-uses/some p-uses (ACU+P)
All Definitions (AD)
All p-uses (APU)
All c-uses (ACU)
Dependable Software Systems (Data-Flow Testing)

40. All du Paths Strategy (ADUP)
ADUP is one of the strongest data-flow testing strategies.
ADUP requires that every du path from every definition of every variable to every use of that definition be exercised under some test All du Paths Strategy (ADUP).
Dependable Software Systems (Data-Flow Testing)

41. Dependable Software Systems (Data-Flow Testing)
Example: pow(x,y) b g a f i d 1 5 8 9 14 16 17 c h e
Dependable Software Systems (Data-Flow Testing)

42. Example: pow(x,y) du-Path for Variable x
This program computes x to the power of y, where x and y are integers.
INPUT: The x and y values.
OUTPUT: x raised to the power of y is printed to stdout. */ 1
void pow (int x, y) 2 { 3
float z; 4
int p; b g 5
if (y < 0) 6
p = 0 – y; a f i d 7
else p = y; 1 5 8 9 14 16 17 8
z = 1.0; 9
while (p != 0) c h 10 { e 11
z = z * x; 12
p = p – 1; 13 } 14
if (y < 0) 15
z = 1.0 / z; 16
printf(z); 17 }
Dependable Software Systems (Data-Flow Testing)

43. Example: pow(x,y) du-Path for Variable x
This program computes x to the power of y, where x and y are integers.
INPUT: The x and y values.
OUTPUT: x raised to the power of y is printed to stdout. */ 1
void pow (int x, y) 2 { 3
float z; 4
int p; b g 5
if (y < 0) 6
p = 0 – y; a f i d 7
else p = y; 1 5 8 9 14 16 17 8
z = 1.0; 9
while (p != 0) c h 10 { e 11
z = z * x; 12
p = p – 1; 13 } 14
if (y < 0) 15
z = 1.0 / z; 16
printf(z); 17 }
Dependable Software Systems (Data-Flow Testing)

44. Example: pow(x,y) du-Path for Variable y
This program computes x to the power of y, where x and y are integers.
INPUT: The x and y values.
OUTPUT: x raised to the power of y is printed to stdout. */ 1
void pow (int x, y) 2 { 3
float z; 4
int p; b g 5
if (y < 0) 6
p = 0 – y; a f i d 7
else p = y; 1 5 8 9 14 16 17 8
z = 1.0; 9
while (p != 0) c h 10 { e 11
z = z * x; 12
p = p – 1; 13 } 14
if (y < 0) 15
z = 1.0 / z; 16
printf(z); 17 }
Dependable Software Systems (Data-Flow Testing)

45. Example: pow(x,y) du-Path for Variable y
This program computes x to the power of y, where x and y are integers.
INPUT: The x and y values.
OUTPUT: x raised to the power of y is printed to stdout. */ 1
void pow (int x, y) 2 { 3
float z; 4
int p; b g 5
if (y < 0) 6
p = 0 – y; a f i d 7
else p = y; 1 5 8 9 14 16 17 8
z = 1.0; 9
while (p != 0) c h 10 { e 11
z = z * x; 12
p = p – 1; 13 } 14
if (y < 0) 15
z = 1.0 / z; 16
printf(z); 17 }
Dependable Software Systems (Data-Flow Testing)

46. Example: pow(x,y) du-Path for Variable y
This program computes x to the power of y, where x and y are integers.
INPUT: The x and y values.
OUTPUT: x raised to the power of y is printed to stdout. */ 1
void pow (int x, y) 2 { 3
float z; 4
int p; b g 5
if (y < 0) 6
p = 0 – y; a f i d 7
else p = y; 1 5 8 9 14 16 17 8
z = 1.0; 9
while (p != 0) c h 10 { e 11
z = z * x; 12
p = p – 1; 13 } 14
if (y < 0) 15
z = 1.0 / z; 16
printf(z); 17 }
Dependable Software Systems (Data-Flow Testing)

47. Example: Using du-Path Testing to Test Program COUNT
Consider the following program:
/* COUNT
This program counts the number of characters and lines in a text file.
INPUT: Text File
OUTPUT: Number of characters and number of lines. */
1                  main(int argc, char *argv[])
2                  {
3                  int numChars = 0;
4                  int numLines = 0;
5                  char chr;
6                  FILE *fp = NULL;
7                 
Dependable Software Systems (Data-Flow Testing)

48. Program COUNT (Cont’d)
8                  if (argc < 2)
9                  {
10              printf(“\nUsage: %s <filename>”, argv[0]);
11              return (-1);
12              }
13              fp = fopen(argv[1], “r”);
14              if (fp == NULL)
15              {
16              perror(argv[1]); /* display error message */
17              return (-2);
18              }
Dependable Software Systems (Data-Flow Testing)

49. Program COUNT (Cont’d)
while (!feof(fp))
20              {
21              chr = getc(fp); /* read character */
22              if (chr == ‘\n’) /* if carriage return */
23              numLines;
24              else
25              numChars;
26              }
27              printf(“\nNumber of characters = %d”, numChars);
28              printf(“\nNumber of lines = %d”, numLines);
29              }
Dependable Software Systems (Data-Flow Testing)

50. The Flowgraph for COUNT
The junction at line 12 and line 18 are not needed because if you are at these lines then you must also be at line 14 and 19 respectively.
Dependable Software Systems (Data-Flow Testing)

51. Dependable Software Systems (Data-Flow Testing)
du-Path for argc
Dependable Software Systems (Data-Flow Testing)

52. Dependable Software Systems (Data-Flow Testing)
du-Path for argc
Dependable Software Systems (Data-Flow Testing)

53. Dependable Software Systems (Data-Flow Testing)
du-Path for argv[]
Dependable Software Systems (Data-Flow Testing)

54. Dependable Software Systems (Data-Flow Testing)
du-Path for argv[]
Dependable Software Systems (Data-Flow Testing)

55. Dependable Software Systems (Data-Flow Testing)
du-Path for numChars
Dependable Software Systems (Data-Flow Testing)

56. Dependable Software Systems (Data-Flow Testing)
du-Path for numChars
Dependable Software Systems (Data-Flow Testing)

57. Dependable Software Systems (Data-Flow Testing)
du-Path for numChars
Dependable Software Systems (Data-Flow Testing)

58. Dependable Software Systems (Data-Flow Testing)
du-Path for numLines
Dependable Software Systems (Data-Flow Testing)

59. Dependable Software Systems (Data-Flow Testing)
du-Path for numLines
Dependable Software Systems (Data-Flow Testing)

60. Dependable Software Systems (Data-Flow Testing)
du-Path for numLines
Dependable Software Systems (Data-Flow Testing)

61. Dependable Software Systems (Data-Flow Testing)
du-Path for chr
Dependable Software Systems (Data-Flow Testing)

62. Dependable Software Systems (Data-Flow Testing)
du-Path for chr
Dependable Software Systems (Data-Flow Testing)

63. Dependable Software Systems (Data-Flow Testing)
du-Path for fp
Dependable Software Systems (Data-Flow Testing)

64. Dependable Software Systems (Data-Flow Testing)
du-Path for fp
Dependable Software Systems (Data-Flow Testing)

65. Dependable Software Systems (Data-Flow Testing)
du-Path for fp
Dependable Software Systems (Data-Flow Testing)

66. Dependable Software Systems (Data-Flow Testing)
All Uses Strategy (AU)
AU requires that at least one path from every definition of every variable to every use of that definition be exercised under some test.
Hence, at least one definition-clear path from every definition of every variable to every use of that definition be exercised under some test.
Clearly, AU < ADUP.
Dependable Software Systems (Data-Flow Testing)

67. All p-uses/Some c-uses Strategy (APU+C)
APU+C requires that for every variable and every definition of that variable include at least one definition-free path from the definition to every predicate use.
If there are definitions of the variable that are not covered by the above prescription, then add computational-use test cases to cover every definition.
Dependable Software Systems (Data-Flow Testing)

68. All c-uses/Some p-uses Strategy (ACU+P)
ACU+P requires that for every variable and every definition of that variable include at least one definition-free path from the definition to every computational use.
If there are definitions of the variable that are not covered by the above prescription, then add predicate-use test cases to cover every definition.
Dependable Software Systems (Data-Flow Testing)

69. All Definitions Strategy (AD)
AD requires that for every variable and every definition of that variable include at least one definition-free path from the definition to a computational or predicate use.
AD < ACU+P and AD < APU+C.
Dependable Software Systems (Data-Flow Testing)

70. All p-uses (APU) All c-uses (ACU)
APU is the same as APU+C without the C requirement.
APU < APU+C.
ACU is the same as ACU+P without the P requirement.
ACU < ACU+P.
Dependable Software Systems (Data-Flow Testing)

71. Relationship among DF criteria
ALL-PATHS
ALL-DU-PATHS
ALL-USES
ALL-P-USES/SOME-C-USES
ALL-C-USES/SOME-P-USES
ALL-P-USES
ALL-C-USES
ALL-DEFS
ALL-EDGES
ALL-NODES
Dependable Software Systems (Data-Flow Testing)

72. Feasible Data Flow Criteria
What happens if we eliminate all un-executable associations from consideration?
If we eliminate all un-executable associations from consideration, then there are significant differences between the Data Flow criteria and the Feasible Data Flow criteria.
For a large class of “well behaved programs”, the Feasible DF criteria All-p-uses, All-p-uses/some-c-uses, and All-uses bridge the gap between All-edges and All-paths.
However, for certain programs with anomalies there are tests which satisfy All-p-uses without satisfying All-edges.
Dependable Software Systems (Data-Flow Testing)

73. Dependable Software Systems (Data-Flow Testing)
An Example 1
read (x) 6 2 T F
x = sqrt(x) 7 8 3
x < 0 9 T F 4 5
read (y)
Node 4 is un-executable; y is un-initialized.
Essentially, only def-use of concern is (x, 2, 3)
Outcome of node 6 can be either T or F.
All-p-uses satisfied, but not all-edges. 6
y  0 F T
Dependable Software Systems (Data-Flow Testing)

74. Effectiveness of Strategies
Ntafos compared Random, Branch, and All uses testing strategies on 14 Kernighan and Plauger programs.
Kernighan and Plauger programs are a set of mathematical programs with known bugs that are often used to evaluate test strategies.
Ntafos conducted two experiments:
Dependable Software Systems (Data-Flow Testing)

75. Results of 2 of the 14 Ntafos Experiments
Mean Number
of Test Cases
Percentage of
Bugs Found
Strategy
Random
Branch
All Uses 35
3.8
11.3
93.7
91.6
96.3
Mean Number
of Test Cases
Percentage of
Bugs Found
Strategy
Random
Branch
All Uses
100 34 84
79.5
85.5
90.0
Dependable Software Systems (Data-Flow Testing)

76. Data-Flow Testing Tips
Resolve all data-flow anomalies.
Try to do all data-flow operations on a variable within the same routine (i.e., avoid integration problems).
Use strong typing and user defined types when possible.
Dependable Software Systems (Data-Flow Testing)

77. Data-Flow Testing Tips (Cont’d)
Use explicit (rather than implicit) declarations of data when possible.
Put data declarations at the top of the routine and return data objects at the bottom of the routine.
Dependable Software Systems (Data-Flow Testing)

78. Dependable Software Systems (Data-Flow Testing)
Summary
Data are as important as code.
Define what you consider to be a data-flow anomaly.
Data-flow testing strategies span the gap between all paths and branch testing.
Dependable Software Systems (Data-Flow Testing)

79. Dependable Software Systems (Data-Flow Testing)
Summary
AU has the best payoff for the money. It seems to be no worse than twice the number of required test cases for branch testing, but the results are much better.
Path testing with Branch Coverage and Data-flow testing with AU is a very good combination.
Dependable Software Systems (Data-Flow Testing)