1. “White box” or “glass box” tests

2. Basic goal of white box testing
developer
client
user
Test planning
White box testing--”lowest level”:
Part of a comprehensive test plan—see fig in text
Unit tests
User
test
activities
Client
test
activities
Integration
tests
Structure tests
Functional
tests
Performance
tests

3. General method 1: Path testing or basis path testing
basic goal: make sure all paths in the control structure of a unit are tested at least once
why?
1. "bad code" is more likely in rarely executed paths
2. what we think is a "rare" path may turn out to be taken a lot
3. syntax errors can occur anywhere

4. White box testing--example
integer a,b,count=0;
input a,b;
if (a == 0)
while (b > 0)
{b = b-1; count++;}
else if (a > 0)
while (b < 0)
{b = b+1; count--;}
else
a = b;
output a,b,count;
What (minimal) set of tests would make sure that all paths are tested in this code?
Are there other test cases that would be advisable?

5. White box testing requirements
what needs to be tested:
1. all independent paths must be followed at least once
2. all logical decisions must have both true and false input
3. all loops must be executed at boundaries and within their bounds
4. all internal data structures must be used

6. node represents one or more statements
Basis path method
This method guarantees that every statement will be executed at least once
Flow graph:
node represents one or more statements
edges represent control flow, as in flowcharts
Example: flow graphs for control structures:
Until
Sequential If
Case
While

7. Basis path method (continued)
Determine number of tests needed:
develop a "flow graph" G
--make graph for basic control structure
--sequential statements with no branches in or out can be merged into one statement
compute the "cyclotomic complexity”:
V(G) = E - N + 2, where E = #edges, N = #nodes
or V(G) = number of planar regions defined by the graph
V(G) is an upper bound on the number of "independent" paths through the code which must be followed through an appropriate choice of test cases in order to execute every statement at least once
NOTE: this gives the number of paths for the GRAPH; program structure may mean a smaller number of paths is actually needed

8. Basis path method--example
Flow chart: 1
Example: 2
integer a,b,count=0; //1
input a,b; //2
if (a == 0) //3
while (b > 0) //4
{b = b-1; //5
count++;} //6
else if (a > 0) //7
while (b < 0) //8
{b = b+1; //9
count--;} //10
else //11
a = b; //12
output a,b,count; //13 3 4 7
Flow graph: 5 6 8 11
E=11,N=8;
E-N+2=5
5 paths 9 12 10
1,2,3 * * 4 7 13 *
11,12
5,6
9,10 8
Tests:
a b
0 2: path 1-3,4,5-6,4
0 -1: path 1-3,4,13
1 -1: path 1-3,7,8,9-10,8
1 2: path 1-3,7,8,13
-1 -1: path 1-3,11-12,13 13
* 1 edge,
multiple paths

9. Basis path method—6 steps
2. Construct flow chart: 1
1. Number lines of executable code:
integer a,b,count=0; //1
input a,b; //2
if (a == 0) //3
while (b > 0) //4
{b = b-1; //5
count++;} //6
else if (a > 0) //7
while (b < 0) //8
{b = b+1; //9
count--;} //10
else //11
a = b; //12
output a,b,count; //13 2 3 4 7 5 6 8 11 9 12
3. Construct flow graph: 10
11,12
1,2,3
5,6 4 13 7 13
5. Determine tests, paths (paths: see previous slide): a b
9,10 8
Note; treat a function call (including a recursive call) as ONE statement, don’t expand
4. Compute upper bound on number of paths:
E=11,N=8; E-N+2=5;
5 paths
6. Add additional tests
(e.g., let b=0)

10. Basis path method--augmentations
Basis path method can also be used with a “graph matrix” to automate the generation of test cases (Beizer, Software Testing Techniques, 1990):
Example: use the flow graph to define a graph matrix:
Entries can be, for example:
--Edges (1 or 0)
--Probability of execution
--Time to traverse an edge
--Memory needed to traverse edge
--Resources needed to traverse edge
Values can be used to determine what
test cases should be run 1 1 2 3 4 5 5 2 3 4

11. General method 2: based on definition / redefinition of variables:
Data flow testing
General method 2: based on definition / redefinition of variables:
data flow testing: focuses on program variables x---e.g., require that every definition use chain (DU) be covered at least once
DU chains:for each program statement S
def(S)={x|x defined in S} and use(S)={x|x is used in S}
example: if S is the statement a = b + c then
def(S) = {a}; use(S) = {b,c}
x at S is live at S':there is a path from S to S' in which x is not redefined

12. def(S) = {b}; def(S') = {c}; def(S'') = {a}; def (S''') = {d}
Def{S}, use{S}
Example:
b = 3; //S
c = 4; //S'
a = b + c; //S''
d = a + b; //S'''
def(S) = {b}; def(S') = {c}; def(S'') = {a}; def (S''') = {d}
use(S) = f; use(S') = f; use(S'')= {b,c}; use(S''')={a,b}
a at S'' is live at S'''; b at S is live at S',S'', and S''';
c at S' is live at S'';

13. definition use chain (DU) of x is [x,S,S']
DU chains
definition use chain (DU) of x is [x,S,S']
where x is in def(S) and use(S') and def. of x in S is live at S'
so in this example:
b = 3; //S
c = 4; //S'
a = b + c; //S''
d = a + b; //S'''
DU chains are:
a: [a, S'', S'''] b: [b, S,S''] and [b,S,S'''] c: [c, S', S'']
testing: must cover every DU chain at least once

14. another simple example: 0. input j,k; 1. x = j; y = k;
DU chains--example
another simple example:
0. input j,k;
1. x = j; y = k;
2. if (x > 0)
y = y + 2;
x = x + 5;
5. endif
6. z = x + y + 4;
DU chains:
1-[j,0,1]; 2-[k,0,1]; 3-[x,1,2],4-[x,1,4],5-[x,1,6],6-[x,4,6]
7-[y,1,3],8-[y,1,6],9-[y,3,6]
test cases:
j = 4, k = 5;--covers 1,2,3,4,5,7,8 and j = -4, k = 5;--covers 6,9

15. General method 3: state-based testing (text, p. 461):
Works well for object-oriented designs
Derives tests from component’s associated state machine diagram
Each transition in the diagram must be traversed at least once

16. UnitControl process using a state machine
State-based testing (continued)
Example: Finite-state machine (FSM) model—what state transitions must be tested?
Idle
GoingUp
req > floor
req < floor
!(req > floor)
!(timer < 10)
DoorOpen
GoingDn
u,d,o, t = 1,0,0,0
u,d,o,t = 0,0,1,0
u,d,o,t = 0,1,0,0
u,d,o,t = 0,0,1,1
u is up, d is down, o is open
req == floor
!(req<floor)
timer < 10
t is timer_start
UnitControl process using a state machine
From Vahid/Grivargis, Embedded System Design, 2000

17. Polymorphism testing
Polymorphism testing: Must be sure to identify and test all possible bindings, static and dynamic
Example: fig
Network interface
Ethernet
WaveLAN
UMTS

18. Additional white box testing
some methods to broaden the test coverage:
condition testing: add tests for each value of a given condition (e.g., if (a == c and b == d) )
domain testing: for each relational expression (a relational-operator b) generate tests for cases: a < b, a = b, a > b
loop testing: simple loops (max # of iterations = n):
skip it
one pass
two passes
m passes, m < n
n-1, n, n+1 passes
(8 <= # passes <= 4n+8)

19. Additional white box testing (continued)
nested loops: tests can grow geometrically (= Q (n2))
some reductions may be used (see p. 458, Pressman)
concatenated loops:
if loops are not independent, should treat as nested loops
unstructured loops: avoid these in your design and code
Unstructured loops (to be avoided)
Nested loops
Concatenated loops