A circuit computing a*a can be constructed that is far more efficient than a generic multiplier by exploiting correlation in the partial product array. For example:

%0:4 = datapath.partial_product %a, %a : (i4, i4) -> (i4, i4, i4, i4)

Corresponds to a partial product array that can be simplified without using any logic to construct an upper-triangular partial product array as shown below (where we show the whole array before truncating to 4-bit rows):

   0    0    0 a0a3 a0a2 a0a1 a0a0
   0    0 a1a3 a1a2 a1a1 a1a0    0
   0 a2a3 a2a2 a2a1 a2a0    0    0 
a3a3 a3a2 a3a1 a3a0    0    0    0  

   0    0 a0a3 a0a2 a0a1    0   a0
   0 a1a3 a1a2    0   a1    0    0
a2a3    0   a2    0    0    0    0 
  a3    0    0    0    0    0    0