A.5 Data Dependence Direction Vectors

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' ).

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