Loop Interchange and Subscripts: Matrix Multiply

Matrix multiplication is commonly written as shown in the following example.

DO I=1, N
DO J=1, N
DO K=1, N
C(I,J) = C(I,J) + A(I,K)*B(K,J)
END DO
END DO
END DO

The use of B(K,J), is not a stride-1 reference and therefore will not normally be vectorizable. If the loops are interchanged, however, all the references will become stride-1 as in the Matrix Multiplication with Stride-1 example that follows.

Note
Interchanging is not always possible because of dependencies, which can lead to different results.

Matrix Multiplication with Stride-1

DO J=1,N
DO K=1,N
DO I=1,N
C(I,J) = C(I,J) + A(I,K)*B(K,J)
ENDDO
ENDDO
ENDDO

For additional information, see Publications on Compiler Optimizations.