Loop distribution for nested Loops.

[Ajit Kumar Agarwal <ajit dot kumar dot agarwal at xilinx dot com>]

All:

For the Loop given in Fig(1), there is no possibility of loop distribution because of the dependency of S1 and S2 on the outerloop index k.
Due to the dependency the Loop cannot be distributed. 

The Loop can be distributed with the transformation given in Fig(2) where the loop given in Fig(1) is distributed due to the dependency
Hoisting transformation. The Dependency hoisting transformation where the dependency is shifted to insertion of new outer Loop and the 
Dependency is based on the inserted outerloop.  This makes the loop k(S1) and j(S2) distributed with the insertion of new outerloop and transfer 
The dependency  of S1  and S2 to the inserted outer loop. 

Do k = 1, n-1
  Do I = k+1, n

S1:  a(I,k) = a(I,k)/a(k,k)

  Enddo
  Do j = k+1,n
     Do I = k+1,n
  S2:  a(I,j) = a(I,j) - a(I,k) *a(k,j);
     Enddo
   Enddo
Enddo

Fig(1)

Do x = 1, n
   Do k = 1, x-1
      Do I = k+1, n

S2:     a(I,x) = a(I,x) - a(I,k) * a(k,x)

      Enddo
   enddo
  Do i = x+1,n
     S1:  a(I,x) = a(I,x)/a(x,x);
   Enddo
Enddo

Fig(2).

The above transformation looks interesting making the candidate of loop distribution of nested loops with the presence of dependency by
Shifting the dependency to new inserted outer loop.

It is useful to have dependency hoisting transformation that makes the loop distribution possible for nested loops

My question is  the partitioning based Loop distributed transformation does the distribution of the nested Loops?  

Thanks & Regards
Ajit