Data Flow Coverage Criteria
All-Defs Coverage (ADC): For each
def-path set S = du(n, v), TR contains
at least one path d in S.
All-Uses Coverage (AUC): For each
def-pair set S = du(ni , nj , v), TR
contains at least one path d in S.
All-du-Paths Coverage (ADUPC): For
each def-pair set S = du(ni , nj, v), TR
contains every path d in S.
1
Data Flow Coverage Criteria
All-Defs Coverage requires that each def
reaches at least one use,
All-Uses Coverage requires that each def
reaches all possible uses
All-du-Paths Coverage requires that each def
reaches all possible uses through all possible
du-paths.
The formal definitions of the criteria are simply
appropriate selections from the appropriate set.
2
Differences Among the three Data
Flow Coverage Criteria
The graph has one def, so only one path is
needed to satisfy all-defs.
The def has two uses, so two paths are
needed to satisfy all-uses.
Since two paths go from the def to each use,
four paths are needed to satisfy all-du-paths.
3
Annotated Control Graph
 Nodes 4 and 6 are final
nodes, corresponding to
the return statements.
 Node 2 is introduced to
capture the for loop; it
has no executable
use(3)=
statements.
 DU (def-use) pairs are
shown as a variable
name followed by the def
node, then the use node.
def (5) = { i }
use (5) = { i }
Def -Use Pairs = { (1, 1,x), (1,3,x), (1,3,y), (1, 2,i), (1, 3,i),
(1,5,i), (1,6,i), (5, 2,i), (5, 3,i), ( 5, 6,i), (5, 5,i)}
example of a graph annotated with
defs and uses
5
public static void computeStats (int [ ] numbers)
{
int length = numbers.length;
double med, var, sd, mean, sum, varsum;
sum = 0;
for (int i = 0; i < length; i++)
{
sum += numbers [ i ];
}
med = numbers [ length / 2];
mean = sum / (double) length;
1
2
i=0
3
varsum = 0;
for (int i = 0; i < length; i++)
4
{
5
varsum = varsum + ((numbers [ I ] - mean) * (numbers [ I ] - mean));
i=0
}
var = varsum / ( length - 1.0 );
sd = Math.sqrt ( var );
6
System.out.println ("length:
" + length);
i < length
System.out.println ("mean:
" + mean);
i >= length
System.out.println ("median:
" + med);
7
System.out.println ("variance:
" + var);
8
System.out.println ("standard deviation: " + sd); }
i++
6
CFG for ComputeStats – With Defs & Uses
1
def (1) = { numbers, sum, length }
2
def (2) = { i }
3
use (3, 5) = { i, length }
use (3, 4) = { i, length }
4
def (4) = { sum, i }
use (4) = { sum, numbers, i }
5
6
def (5) = { med, mean, varsum, i }
use (5) = { numbers, length, sum }
use (6, 8) = { i, length }
use (6, 7) = { i, length }
7
def (7) = { varsum, i }
use (7) = { varsum, numbers, i, mean }
8
def (8) = { var, sd }
use (8) = { varsum, length, mean,
med, var, sd }
7
Defs and Uses Tables for ComputeStat
Node
1
2
3
4
5
Def
Use
{ numbers, sum,
length }
{i}
{ numbers }
{ sum, i }
{ med, mean,
varsum, i }
{ numbers, i, sum }
{ numbers, length, sum }
8
{ varsum, i }
{ var, sd }
Use
(1, 2)
(2, 3)
(3, 4)
(4, 3)
{ i, length }
(3, 5)
{ i, length }
(5, 6)
6
7
Edge
{ varsum, numbers, i,
mean }
{ varsum, length, var,
mean, med, var, sd }
(6, 7)
{ i, length }
(7, 6)
(6, 8)
{ i, length }
8
DU Pairs for ComputeStat
variable
DU Pairs Defs come before uses, do not
count as DU pairs
numbers (1, 4) (1, 5) (1, 7)
length
(1, 5) (1, 8) (1, (3,4)) (1, (3,5)) (1, (6,7)) (1, (6,8))
med
var
sd
mean
sum
varsum
i
(5, 8)
defs after use in loop, these
(8, 8)
are valid DU pairs
(8, 8)
(5, 7) (5, 8)
No def-clear path …
(1, 4) (1, 5) (4, 4) (4, 5)
different scope for i
(5, 7) (5, 8) (7, 7) (7, 8)
(2, 4) (2, (3,4)) (2, (3,5)) (2, 7) (2, (6,7)) (2, (6,8))
(4, 4) (4, (3,4)) (4, (3,5)) (4, 7) (4, (6,7)) (4, (6,8))
(5, 7) (5, (6,7)) (5, (6,8))
No path through graph from
(7, 7) (7, (6,7)) (7, (6,8))
nodes 5 and 7 to 4 or 3
9
DU Paths for Stats
variable
numbers
length
med
var
sd
sum
DU Pairs
DU Paths
(1, 4)
(1, 5)
(1, 7)
[ 1, 2, 3, 4 ]
[ 1, 2, 3, 5 ]
[ 1, 2, 3, 5, 6, 7 ]
(1, 5)
(1, 8)
(1, (3,4))
(1, (3,5))
(1, (6,7))
(1, (6,8))
[ 1, 2, 3, 5 ]
[ 1, 2, 3, 5, 6, 8 ]
[ 1, 2, 3, 4 ]
[ 1, 2, 3, 5 ]
[ 1, 2, 3, 5, 6, 7 ]
[ 1, 2, 3, 5, 6, 8 ]
(5, 8)
(8, 8)
(8, 8)
(1, 4)
(1, 5)
(4, 4)
(4, 5)
[ 5, 6, 8 ]
No path needed
No path needed
[ 1, 2, 3, 4 ]
[ 1, 2, 3, 5 ]
[ 4, 3, 4 ]
[ 4, 3, 5 ]
variable
mean
DU Pairs
(5, 7)
(5, 8)
DU Paths
[ 5, 6, 7 ]
[ 5, 6, 8 ]
varsum
(5, 7)
(5, 8)
(7, 7)
(7, 8)
[ 5, 6, 7 ]
[ 5, 6, 8 ]
[ 7, 6, 7 ]
[ 7, 6, 8 ]
i
(2, 4)
(2, (3,4))
(2, (3,5))
(4, 4)
(4, (3,4))
(4, (3,5))
(5, 7)
(5, (6,7))
(5, (6,8))
(7, 7)
(7, (6,7))
(7, (6,8))
[ 2, 3, 4 ]
[ 2, 3, 4 ]
[ 2, 3, 5 ]
[ 4, 3, 4 ]
[ 4, 3, 4 ]
[ 4, 3, 5 ]
[ 5, 6, 7 ]
[ 5, 6, 7 ]
[ 5, 6, 8 ]
[ 7, 6, 7 ]
[ 7, 6, 7 ]
[ 7, 6, 8 ]
10