Glossary

Tiling (folding)

Beginner

Cutting a big job into pieces the size of the grid and running them one after another.

Novice

Splitting a matrix multiplication that is bigger than the array into blocks (tiles) that fit, running each, and combining the results. Edge tiles may only partly fill the array.

Expert

A GEMM mapped onto an R×CR \times C array needs ⌈SR/R⌉×⌈SC/C⌉\lceil S_R/R \rceil \times \lceil S_C/C \rceil folds. Tile order sets how often each operand is re-read from the buffer; tile size relative to the matrix sets the fragmentation loss.

Explained in Systolic arrays (Architectures).

See also: Array utilization.

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