Data dependency vectors in space time mapping

Question

Hello,

in the space time mapping of systolic arrays we determined the data dependency vectors by subtracting the indices of the left hand side of an assignment by the indices of the right hand side. For example the action c[i][j][k+1]  = c[i][j][k] + a[i][k] * b[k][j] has the data dependency vector (i, j, k+1) - (i, j, k) = (0, 0, 1).

Now I was wondering about actions that have multiple dependencies. For example c[i][j][k+1] = c[i][j][k] + c[i][j][k-1]. What would the data dependency vector look like for this action or would this one action have two dependency vectors?

Answer 1

The short answer is that an assignment can produce many dependence vectors. For instance, c[i][j][k+1] = c[i][j][k] + c[i][j][k-1] will produce vectors

    (i,j,k+1) - (i,j,k) = (0,0,1)

    (i,j,k+1) - (i,j,k-1) = (0,0,2)