Loop Interchange and Subscripts: Matrix Multiply

Matrix multiplication is commonly written as shown in the example below:

Typical Matrix Multiplication

for (i = 0; i < N; i++)

{

for (j = 0; j < n; j++)

{

for (k = 0; k < n; k++)

{

c[i][j] = c[i][j] + a[i][k] * b[k][j];

}

}

}

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 shown in the "Matrix Multiplication With Stride-1" example.

Caution

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

Matrix Multiplication With Stride-1

for (i = 0; i < N; i++)

{

for (k = 0; k < n; k++)

{

for (j = 0; j < n; j++)

{

c[i][j] = c[i][j] + a[i][k] * b[k][j];

}

}

}