Research Article

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

Table 4

(a) Heuristic search results for 2D filtering

NPENcyc 𝑀 -matrixReg. cost

12121 0 1 3
001 1 1 2 10
12141 0 1 3
001 1 1 414
12181 0 1 3
001 1 1 312
1216 1 0 1 3
00 1 1 1 18
12121 0 1 3
001 1 2 1 10
12151 0 1 3
001 1 2 212
12171 0 1 3
001 1 2 08
1213 1 0 1 3
001 1 2 416
12211 0 1 3
001 1 2 3 14
12191 0 1 3
001 1 2 110
12151 0 1 3
00 1 1 0 412
12151 0 1 3
001 1 0 310
12131 0 1 3
001 1 4 1 14
12211 0 1 3
001 1 4 216
12231 0 1 3
001 1 4 012
12191 0 1 3
001 1 4 420
12271 0 1 3
001 1 4 318
12251 0 1 3
001 1 4 1 14
12211 0 1 3
00 1 1 3 112

(b) Mapping results using the modified heuristic search results process 2D filtering

Window size = 3 × 3; 2D result arrived by using Step 11Window size = 4 × 3
[pe_arr, Ncyc_arr, 𝑀 or Tmat] [pe_arr Ncyc_arr 𝑀 or Tmat]
NPENcyc 𝑀 matrix = [ 𝑃 ; 𝑆 ]NPENCYC 𝑀 matrix = [ 𝑃 ; 𝑆 ]

991 0 0 4; 1 1 2 112121 0 1 4; 1 1 3 1
991 0 0 4; 1 3 0 4 12121 0 1 4; 1 3 1 4
991 0 0 4; 1 3 2 112121 0 1 4; 1 3 3 1
991 0 0 4; 1 2 0 4 12121 0 1 4; 1 2 1 4
991 0 0 4; 1 2 2 112121 0 1 4; 1 2 3 1
991 0 0 4; 1 4 0 412121 0 1 4; 1 4 1 4
991 0 0 4; 1 4 2 112121 0 1 4; 1 4 3 1
991 0 0 4; 1 1 0 4 12121 0 1 4; 1 1 1 4
991 0 0 4; 1 1 2 112121 0 1 4; 1 1 3 1
991 0 0 4; 0 1 0 4 12121 0 1 4; 0 1 1 4
991 0 0 4; 0 1 2 112121 0 1 4; 0 1 3 1
991 0 0 4; 0 3 0 4 12121 0 1 4; 0 3 1 4
991 0 0 4; 0 3 2 112121 0 1 4; −0 3 3 1
991 0 0 4; 0 2 0 4 12121 0 1 4; 0 2 1 4
991 0 0 4; 0 2 2 112121 0 1 4; 0 2 3 1
991 0 0 4; 0 4 0 4 12121 0 1 4; 0 4 1 4
991 0 0 4; 0 4 2 112121 0 1 4; 0 4 3 1
991 0 0 4; 0 1 0 4
991 0 0 4; 0 1 2 1
991 0 0 4; 2 1 0 4
991 0 0 4; 2 1 2 1

*Search space for 𝑀 matrix without the use of the scheduling vector 𝑠 𝑑 ; the execution time takes more execution time to obtain Table 4(a), than the search time which uses the 𝑠 𝑑 as the projection direction for reassignment of PE plane used to obtain Table 4(b).