Example: 2D Gaussian Elimination

Consider the Gaussian Elimination kernel:

     ...
    DO j = i+1, n
     A(j,i) = A(j,i)/Swap(i)
     A(j,i+1:n) = A(j,i+1:n) - A(j,i)*Swap(i+1:n)
     Y(j) = Y(j) - A(j,i)*Temp
    END DO

Want to minimise communications in loop.

Y(k) is always used in the same statement as A(k,i). This implies that Y should be aligned with the first dimension of A. In order that the value of i is unimportant Y(k) should be local to A(k,:) in other words a copy of Y should be aligned to every column of A.

!HPF$ ALIGN Y(:) WITH A(:,*)
      ! Y aligned with each col of A

A similar argument to above except that SWAP(k) should be local to A(i,k), ie SWAP should be aligned with the second dimension of A. In order that the value of i is unimportant SWAP(k) should be local to A(:,k), in other words a copy of Y should be aligned to every row of A.

!HPF$ ALIGN Swap(:) WITH A(*,:)
      ! Swap aligned with each row of A

There is no advantage in using BLOCK distribution, calculation of a particular element does not use that elements neighbours in the calculation, it is therefore safe to balance the load by using CYCLIC distribution.

!HPF$ DISTRIBUTE A(CYCLIC,CYCLIC) ! onto default grid

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See Figure 48 for a visualisation of the relative alignments.

  
Figure 48: Visualisation of 2D Gaussian Elimination

Now try this question

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