Design Space Exploration of Deeply Nested Loop 2D Filtering and 6 Level FSBM Algorithm Mapped onto Systolic Array

Listing 3

URE algorithm for 2D filtering.

 For 𝑖 = 1 to 𝑘₁

 For 𝑗 = 1 to 𝑘₂

For 𝑘 = 1 to 4 //window size = 4 × 3

             For 𝑙 = 1 to 3

            If (𝑖 == 1 && 𝑗 == 1)

                 𝑤(𝑖,𝑗,𝑘,𝑙)= 𝑊_new

            Else if(𝑗 == 𝑘₂)

                 𝑤(𝑖,𝑗,𝑘,𝑙) = 𝑤(𝑖−1,𝑗,𝑘,𝑙);//next 𝑖

            //[Dvw1 = 1 0 0 0]

            Else

            𝑤(𝑖,𝑗,𝑘,𝑙)=𝑤(𝑖,𝑗−1,𝑘,𝑙);

            // next 𝑗 [Dvw2 = 0 1 0 0]

            End if

  If (𝑖 == 1 && 𝑗 == 1)

  𝐼(𝑖,𝑗,𝑘,𝑙)=𝐼_new;

  Else if(𝑖 == 1 && 𝑗 > 1) // first row—second window calculation

  𝐼(𝑖,𝑗,𝑘,𝑙)=𝐼(𝑖,𝑗+1,𝑘,𝑙+1); move to the next 𝑗 pixel –𝑗 + 1; pixel data—reads in next column of pixel and

  old data is moved in the (𝑘,𝑙) plane-PE_array from (𝑘,𝑙) to (𝑘,𝑙 + 1);//[ 𝐃𝐕_𝐱𝟐 = 0 1 0 1]

  Else if (j==k 𝟐 )    // for next 𝑖

  𝐼(𝑖,𝑗,𝑘,𝑙)=𝐼(𝑖+1,𝑗,𝑘+1,𝑙); // move to the next 𝑖 pixel 𝑖 + 1; pixel data—reads in next row of

  // pixel and old data is moved in the (𝑘,𝑙) plane-PE_array from (𝑘,𝑙) to (𝑘+1,𝑙)

  //[ 𝐃𝐕_𝐱𝟏 = 1 0 1 0]

  End if

  If (𝑙 ==1 && 𝑘 == 1)

  𝑂(𝑖,𝑗,𝑘,𝑙) = 0;

  Else if (k < 3)

  𝑂(𝑖,𝑗,𝑘,𝑙)=𝑂(𝑖,𝑗,𝑘,𝑙−1)+𝐼(𝑖,𝑗,𝑘,𝑙)∗𝑊(𝐼,𝑗,𝑘,𝑙);

  Else

  𝑂(𝑖,𝑗,𝑘,𝑙)=𝑂(𝑖,𝑗,𝑘−1,𝑙)+𝐼(𝑖,𝑗,𝑘,𝑙)∗𝑊(𝐼,𝑗,𝑘,𝑙);

  End;

End For 𝑙,𝑘,𝑗,𝑖;