• For statements involving A[i,,j]
  distance vector (0,0)
  direction vector (=,=)
  dependence is loop independent
• For statements involving B[i,,j]
  distance vector (0,1)
  direction vector (=,<)
  dependence is carried by the inner loop
• For statements involving C[i,,j]
  distance vector (1,-1)
  direction vector (<,>)
  dependence is carried by the outer loop

Dependence Level

Loop nest level that carries the data dependence relation

Therefore, for C[i,,j] level is 1 for B[i,,j] level is 2 for A[i,,j] level is

Iteration Vector - Triangular Space

Advantages of normalized iteration vector:

• Later iterations have larger iteration vector
• Adjacent iterations differ by only one
  However, neither of these require first iteration to have vector (0,0, · · ·, 0).

Consider following program: