Path testing

1
Path testing

• Path testing is a design structural testing in
  that it is based on the source code of the
  program to be tested.
• The methodology uses the graphical representation
  of the source code
• Thus it is very much control flow or path
  oriented
• This methodology has been available since the
  mid-1970s

2
Path Analysis

• Why path analysis for test case design?
• Provides a systematic methodology of White Box
  testing.
• Reproducible
• Traceable
• Countable
• What is path analysis?
• Analyzes the number of paths that exist in the
  system
• Facilitates the decision process of how many
  paths to include in the test

3
Linearly Independent Path

• A path through the system is Linearly
  Independent from other paths only if it
  includes some segment or edge that is not
  covered in the other path.

S1
- The statements are represented by the
rectangular and diamond blocks. - The segments
between the blocks are labeled with numbered
circles.
1
2
C1
Path1 S1 C1 S3 Path2 S1 C1 S2 S3
OR Path1 edges (1,4) Path2 edges (1,2,3)
S2
4
3
S3
Path1 and Path2 are linearly independent because
each includes some edges that is not included in
the other. This definition will require more
explanation later.
4
Another Example of Linearly Independent Paths
S1
1
S2
8
C1
2
Path1 edges (1,2,8) Path2 edges
(1,5,3,9) Path3 edges (1,5,6,4,10) Path4
edges (1,5,6,7) Note that these are all
linearly independent
5
S3
C2
3
9
6
C3
4
10
S4
7
S5
5
Statement Coverage Method

• Count all the linearly independent paths
• Pick the minimum number of linearly independent
  paths that will include all the statements (Ss
  and Cs in the diagram)

S1
Path1 S1 C1 S3 Path2 S1 C1 S2 S3
1
2
C1
S2
4
3
S3
Do we need Path1 and Path2 to cover all the
statements (S1,C1,S2,S3) ?
6
Another Example of Statement Coverage
S1
1
S2
8
C1
2
The 4 Linearly Independent Paths Covers Path1
includes S1-C1-S2-S5 Path2 includes
S1-C1-C2-S3-S5 Path3 includes
S1-C1-C2-C3-S4-S5 Path4 includes S1-C1-C2-C3-S5
5
S3
C2
3
9
6
C3
4
10
S4
7
S5
For 100 Statement Coverage, all we need are 3
paths Path1, Path2, and Path3 to cover all the
statements (S1,C1,S2,C2,S3,C3,S4,S5) - - -
no need for Path4 - - - - !!
7
Statement Coverage
What do you think about a Software Company who
states that they care about quality and executes
every line of code in their testing?!
8
Branch Coverage Method(also known as
decision-decision, or dd, path)

• Identify all the decisions
• Count all the branches from the each of the
  decisions
• Pick the minimum number of paths that will cover
  all the branches from the decisions.

9
Branch Coverage Method
S1
Decision C1 B1 Path1 C1 S3
B2 Path2 C1 S2 S3
1
C1
Branch 1
Branch 2
2
S2
4
3
S3
Path1 and Path2 are needed to cover both branches
from C1.
10
Another Example of Branch Coverage
The 3 Decisions C1 - B1 C1-
S2 - B2 C1- C2 C2 -
B3 C2 S3 - B4 C2 C3 C3
- B5 C3 S4 - B6 C3 S5
S1
1
S2
8
C1
2
5
S3
C2
3
9
6
C3
4
10
S4
The 4 Linearly Independent Paths Covers Path1
includes S1-C1-S2-S5 Path2 includes
S1-C1-C2-S3-S5 Path3 includes
S1-C1-C2-C3-S4-S5 Path4 includes S1-C1-C2-C3-S5
7
S5
We need Path1 to cover B1,
Path2 to cover B2 and B3,
Path3 to cover B4 and B5,
Path4 to cover B6
11
Branch Coverage
What do you think about a Software Company who
states that they care about quality and executes
every branch in their testing?!
12
McCabes Cyclomatic Number

• Is there a way to know how many linearly
  independent paths exist?
• McCabes Cyclomatic number used to study program
  complexity may be applied. There are 3 ways to
  get the Cyclomatic Complexity number from a flow
  diagram.
• of binary decisions 1
• of edges - of nodes 2
• of closed regions 1

13
McCabes Cyclomatic Complexity NumberEarlier
Example
We know there are 2 linearly independent paths
from before Path1 C1 S3
Path2 C1 S2 S3
S1
1

• McCabes Cyclomatic Number
• a) of binary decisions 1 1 1 2
• b) of edges - of nodes 2 4-42 2
• c) of closed regions 1 1 1 2

C1
2
S2
4
Closed region
3
S3
14
McCabes Cyclomatic Complexity NumberAnother
Example

• McCabes Cyclomatic Number
• a) of binary decisions 1 2 1 3
• b) of edges - of nodes 2 7-62 3
• c) of closed regions 1 2 1 3

S1
1
4
C1
2
C2
5
S2
There are 3 Linearly Independent Paths
Closed Region
Closed Region
S4
7
3
6
S3
15
An example of 2n total path
Since for each binary decision, there are 2 paths
and there are 3 in sequence, there are 23 8
total logical paths path1
S1-C1-S2-C2-C3-S4 path2 S1-C1-S2-C2-C3-S5
path3 S1-C1-S2-C2-S3-C3-S4 path4
S1-C1-S2-C2-S3-C3-S5 path5 S1-C1-C2-C3-S4
path6 S1-C1-C2-C3-S5 path7
S1-C1-C2-S3-C3-S4 path8 S1-C1-C2-S3-C3-S5
S1
1
C1
2
3
S2
4
C2
5
6
S3
How many Linearly Independent paths are
there? Using Cyclomatic number 3 decisions 1
4 One set would be path1 includes edges
(1,2,4,6,9) path2 includes edges (1,2,4,6,8)
path3 includes edges (1,2,4,5,7,9) path5
includes edges (1,3,6,9)
7
C3
9
8
S4
S5
Note 1 with just 2 paths ( Path1 and Path8) all
the statements are covered. Note2 with just 2
paths ( Path1 and Path8) all the branches are
covered.
16
Example with a Loop
Total number of paths may be infinite (very
large) because of the loop
S1
1
Linearly Independent Paths 1 decision 1 2
path1 S1-C1-S3 (segments 1,4) path2
S1-C1-S2-C1-S3 (segments 1,2,3,4)
C1
4
S3
2
One path will cover all statements path2
(S1,C1,S2, S3)
S2
3
One path will cover all branches path2
S1-C1-S2-C1-S3
branch1 (C1-S2) and branch 2
(C1-S3)
17
More on Linearly Independent Paths

• In discussing dimensionality, we talks about
  orthogonal vectors (or basis of vector space) .
  
• Two dimensional space has two orthogonal vector
  from which all the other vectors in two dimension
  can be obtained via linear combination of these
  vectors
• 1,0
• 0,1

e.g. 2,4 21,0 40,1
2,4
1,0
0,1
18
More on Linearly Independent Paths

• A set of paths is considered to be a Linearly
  Independent Set if every path may be constructed
  as a linear combination of paths from the
  linearly independent set. For example

We already know a) there are a total of 224
logical paths. b)
2 paths that will cover all statements
and all branches.
c) 2 branches 1 3
linearly independent paths.
C1
2
1
S1
1
2
3
4
5
6
3
We pick path1, path2 and path3 as The Linearly
Independent Set
1
path1
1
1
C2
5
path2
1
1
4
path3
1
1
1
S1
path4
1
1
1
1
6
path 4 path3 path1 path2
(0,1,1,1,0,0)(1,0,0,0,1,1)- (1,0,0,1,0,0)

(1,1,1,1,1,1) - (1,0,0,1,0,0)

(0,1,1,0,1,1)
19
More on Linearly Independent Paths
We already know a) there are a total of 224
logical paths. b)
2 paths that will cover all statements
and all branches.
c) 2 branches 1 3
linearly independent paths.
C1
2
1
S1
1
2
3
4
5
6
3
1
path1
1
1
C2
5
path2
1
1
4
path3
1
1
1
S1
path4
1
1
1
1
6
Although path1 and path3 are linearly
independent, they do NOT form a Linearly
Independent Set because no linear combination of
path1 and path3 can get , say, path4.
20
More on Linearly Independent Paths

• Because the Linearly Independent Set of paths
  display the same characteristics as the
  mathematical concept of basis in n-dimensional
  vector space, the testing using the Linearly
  Independent Set of paths is sometimes called the
  basis testing.
• The main notion is that since the linear
  independent set of paths as a set can span all
  the paths for the design/code construct, then
  basis testing covers the essence of the whole
  structure.

21
Total Possible Logical Paths can be Big!
s1
There are 5 choices each time we process
through this loop. For passing through the loop
n times we have 5n possibilities of logical
paths. If we go through the loop just 3 times,
we have (5)3 125 possible paths!
c1
1
c3
c2
4
2
s2
5
3
s3
c4
s4
22
Paths Analysis

• Interested in total number of all possible
  combinations of logical paths
• Interested in Linearly Independent paths
• Interest in Branch coverage or DD-path
• Interested in Statement coverage

Which one do you think is the largest set, next
largest, - - - , etc.?