Tiling - 2023.2 English

Vitis Libraries

Release Date
2023-12-20
Version
2023.2 English

Input matrices are processed in distinct blocks. Matrix elements must be rearranged into a specific pattern.

The following table demonstrates how a 16x16 input matrix should be rearranged into a 4x4 tiling pattern.

Note

Indices are quoted assuming a row major matrix. A column major matrix would be the transpose of the table below.

Table 53 Matrix Multiply 4x4 tiling pattern
  Tile Col 0 Tile Col 1 Tile Col 2 Tile Col 3
Tile Row 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
Tile Row 1 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111
112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127
Tile Row 2 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159
160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175
176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191
Tile Row 3 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207
208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223
224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239
240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

This is stored contiguously in memory like:

0, 1, 2, 3, 16, 17, 18, 19, 32, 33, 34, 35, 48, 49, 50, 51, 4, 5, 6, 7, 20, 21, 22, 23, 36, 37, 38, 39, 52, 53, 54, 55, 8, 9, 10, 11, 24, 25, 26, 27, 40, 41, 42, 43, 56, 57, 58, 59, 12, 13, 14, 15, 28, 29, 30, 31, 44, 45, 46, 47, 60, 61, 62, 63, 64, 65, 66, 67, 80, 81, 82, 83, 96, 97, 98, 99, 112, 113, 114, 115, … , 204, 205, 206, 207, 220, 221, 222, 223, 236, 237, 238, 239, 252, 253, 254, 255

The following table demonstrates how a 16x16 input matrix should be rearranged into a 4x2 tiling pattern.

Table 54 Matrix Multiply 4x2 tiling pattern
  Tile Col 0 Tile Col 1 Tile Col 2 Tile Col 3 Tile Col 4 Tile Col 5 Tile Col 6 Tile Col 7
Tile Row 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
Tile Row 1 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111
112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127
Tile Row 2 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159
160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175
176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191
Tile Row 3 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207
208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223
224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239
240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

This is stored contiguously in memory like:

0, 1, 16, 17, 32, 33, 48, 49, 2, 3, 18, 19, 34, 35, 50, 51, …, 206, 207, 222, 223, 238, 239, 254, 255

Multiplying a 16x16 matrix (with 4x4 tiling) with a 16x16 matrix (with 4x2 tiling) will result in a 16x16 matrix with 4x2 tiling.