A.3 Input and Output Sets

To determine data dependence, it is necessary to form the input and output sets for the given statements.

IN(S1) denotes the set of input items of S1 (items whose values may be read by S1 ). OUT(S1) denotes the set of output items (scalar variables or array elements) of statement S1 (items whose values may be changed by S1 ).

The following example shows the IN and OUT sets for the assignment statement in the loop:

 for (i=1; i<=10; i++)
   S1:  x[i] = a[i+1] * b;

   IN[S1] = {a[2], a[3], a[4], ..., a[11], b}

   OUT[S1] = {x[1], x[2], x[3], ..., x[10]}

In practice, KAP often approximates the IN and OUT sets because the actual loop bounds are frequently unknown at compile time.