The direction vector is defined as a sequence of direction vector elements (one element for each loop enclosing both statements involved in the dependence arc). The following symbols are direction vector elements: <, =, >, <, >, /, or *. Refer to the following loop:
Loops Line
+--------- 10 for ( i=1; i<n ; i++) {
| 11 a[i] = b[i] + c[i];
| 12 c[i] = a[i-1] - 1;
|_________ 13 }
If line 12 in iteration I" depends on line 11 in
iteration I' , the element of the direction vector
for loop I is as follows:
direction vector element when < I' must be < I" = I' must be = I" > I' must be > I" <= I' must be < or = I" >= I' must be > or = I" / I' must not = I" * no relation between I' and I" can be proven
In the previous example, the dependence for variable a has a
direction vector of < , because the dependence flows
from iteration I' to iteration I'+1
and I' < I'+1 . For example, the dependence on
a[1] flows from iteration 1 to iteration 2, and
1 < 2. The data dependence for the variable
c has a direction vector of = because the
dependence stays in the same iteration of the loop (from iteration
I' to iteration I' ).