VLSI Design

Research Article

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

Listing 1

𝑛 -D multidimensional algorithm in URE form.
Do 𝑖 1 = 1 to π‘˜ 1 ;
    Do 𝑖 2 = 1 to π‘˜ 2 ;
      Do 𝑖 3 = 1 to π‘˜ 3 ;
    𝐴 1 ( 𝑖 1 , 𝐼 2 , 𝑖 3 , . . . , 𝑖 𝑛 )     = 𝐴 1 ( 𝑖 1 , 𝐼 2 , 𝑖 3 βˆ’ 1 , . . . , 𝑖 𝑛 ) ;//broadcast in 𝑖 2 direction
                                            (1a)
    𝐴 2 ( 𝑖 1 , 𝑖 2 , 𝐼 3 , . . . , 𝑖 𝑛 )     = 𝐴 2 ( 𝑖 1 βˆ’ 1 , 𝑖 2 , 𝐼 3 , . . . , 𝑖 𝑛 ) ;//broadcast in 𝑖 1 direction
    𝐴 3 ( 𝐼 1 , 𝑖 2 , 𝑖 3 , . . . , 𝑖 𝑛 ) = 𝐴 3 ( 𝐼 1 , 𝑖 2 , 𝑖 3 βˆ’ 1 , . . . , 𝑖 𝑛 ) broadcast in 𝑖 3 direction
    𝐴 𝑛 βˆ’ 1 ( 𝑖 1 , 𝑖 2 , 𝑖 3 , 𝐼 4 , . . . , 𝑖 𝑛 ) = 𝐴 𝑛 βˆ’ 1 ( 𝑖 1 , 𝑖 2 , 𝑖 3 βˆ’ 1 , 𝐼 4 , . . . , 𝑖 𝑛 ) ;
         𝐢 [ β†’ 𝐈 ] = 𝑓 2 (C[ β†’ 𝐈 βˆ’ β†’ 𝐝 ], 𝑓 1 ( 𝐴 1 𝐴 2 [ β†’ 𝐈 ] ))          (2)
        or
         𝐢 [ 𝑖 1 , 𝑖 2 , 𝑖 3 , . . . , 𝑖 𝑛 ] = 𝐢 [ 𝐼 1 , 𝐼 2 , 𝑖 3 , . . . , 𝑖 𝑛 βˆ’ 1 ]+ 𝐴 1 ( 𝑖 1 , 𝐼 2 , 𝑖 3 , . . . , 𝑖 𝑛 ) Γ— 𝐴 2 ( 𝐼 1 , 𝑖 2 , 𝑖 3 , . . . , 𝑖 𝑛 )
                                           (3)
        End Do 𝑖 𝑛 ;  … .;
        End Do   𝑖 2 ;
    End Do   𝑖 1 ;