01 Chapter 2 · pack
Pack
An 8-wide row-major panel stores a 4-wide chunk contiguously in its row and four addresses away on the next row. Pack copies each 4×4 tile into one run.
source address = row·8 + col
pack 4×4 tile → 16 contiguous addressesThe number in each cell is the source address, row·8 + col. Four tiles cover the 8×8 panel. Each packed tile is 16 contiguous addresses. Inside a row the four values are adjacent; the next row of the same tile starts eight addresses later in the panel and only four later in the packed run.
row-major · address = row·8 + col
packed · four tiles, 16 addresses each
pack · strided source, contiguous run
Four tiles. Play, and watch a chunk of four move.
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Reading the picture
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The next row skips
Inside a row the four values are adjacent. The next row of the same tile starts eight addresses later in the panel and only four later in the packed run, so the source skips four addresses and the packed side skips none.
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Unit stride is the point
A microkernel wants a contiguous vector load. Pack pays the strided reads once, then every k step is a unit-stride load. The copy is the layout fix, not the arithmetic.
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The same habit in front of QKᵀ and PV
The GEMM microkernel packs A and B before the K loop. Attention's two matrix multiplies want the same panels. Memory in flight is what happens to those bytes after they are packed. Open the microkernel Open memory in flight Open attention
Each cell shows its source address. Packed addresses run 0–63, tile by tile.