For the four loop nests shown below, give definitions of the
"iteration space sets" and the flow of information within that
iteration space, both as diagrams (like the circles and arrows I drew
in class last Thursday and today) and as sets defined by constraints
on variables (as I did at the end of class today).

If you can, discuss what this means about the number of processors
that could collaborate productively to solve the problem without
having to communicate information between processors during the
calculation (these loop nests will have simpler patterns than the one
I worked with, so don't worry if your example isn't as complicated as
mine was).


Loop nest #1

     for i = 10 to 19
       A[i] = A[i] * A[i-5]


Loop nest #2

     for i = 2*N to 3*N-1
       A[i] = A[i] * A[i-N]


Loop nest #3

     for i = 1 to N
       row_sum[i] = 0
       for j = 1 to M
         row_sum[i] = row_sum[i] + matrix[i][j]


Loop nest #4

     for i = 1 to N
       for j = 1 to M
         A[i][j] = B[i][j] * C[i][j]