• Values written during one iteration of the outer loop is read during some iteration of outer loop
• Dependence disappears if outer loop is kept fixed and inner loop runs free
• Therefore, the dependence is carried by the outer loop and label the dependence with 1
• Parallel code:
  for I=1,N
  X[I,1..M]=X[I-1,1..M]
  endfor

Example for I=1,100 for J=1,100 X[I,J]=X[I,J-1] endfor endfor
dependence is carried by the inner loop Parallelization requires loop interchange

Loop Interchange

• The most important loop restructuring transformation
• It was developed for automatic parallelization of loops
• If a loop carried all the dependence then it would be brought to the outermost position
• Rest of the loops which did not carry dependence will be executed in parallel
• It can be done if there are no dependence cycles
• If outer loop iterates many times and inner loop only a few times then loop startup overhead is high
• Interchanging loops will improve performance
• Interchange can lead to spatial locality (remember matrix multiplication?)