Loop Skewing

• Normalization can change the shape of the iteration space
• It may affect the ability to interchange loops
• Consider following code
  

  for I = 2, n for j = I, n A[I,j] = 0.5 *(A[I,j-1]+A[i-1,j]) endfor endfor

• Using un-normalized iteration vector the dependence distances are (0,1) and (1,0)

Iteration Space of The Loop

• After interchange the code is
  for j = 2, n
  for i = 2, j
  A[I,,j] = 0.5 *(A[I,,j-1]+A[i-1,,j])
  endfor
  endfor