• Interchange jt loop with I loop
• Compiler finds the new lower limits for jt
  

  For It = -15, 45, 20 for jt = max(-15,it), 45, 20 for i = max(I,it), min(50,it+19) for j=max(I,jt), min(60, jt+19) A[I,j] = A[I,j]+1 endfor endfor endfor endfor

Circular Loop skewing

• A variation of loop skewing
• Skew the inner loop iterations such that they wrap around a cylinder
• The shape of the iteration space does not change but the relative positions change
• Backward dependencies with large distances make tiling unprofitable
• Circular loop skewing shortens backward dependencies

For I = 0, n-1 for j = 0, n-1 A[i] = A[i] + B[i] * C[i] endfor endfor
The circular loop skewing does not change the shape of the iteration space. It changes the iterations computed at each point.