simd-anim
All kernels

01 SME · GEMM microkernel

Microkernel

One kernel, three moves: pack fixes the layout, the K loop does ldr + fmopa, the store writes C out. Follow where each value goes.

Instruction
pack   ld1w / ldnt1w → st1w  (A and B into packed panels)
loop   ldr zA, [pa, #k, mul vl] ; ldr zB, [pb, #k, mul vl]
       fmopa za0.s, p0/m, p0/m, zA.s, zB.s
       prfm pldl2keep, [pb] ; prfm pldl1strm, [pc]
store  st1w { za0h.s[w12, 0] }, p0, [pc] → stnt1w

Types: everything is f32. Deliberately small: C is one 4 × 4 ZA tile, A is 4 × 2, B is 2 × 4, K = 2 groups. The real kernel is the same choreography at 32 × 32 with a 2 × 2 tile grid, four load slots, and K_BLK = 512.

Pack · once per K blockchanges with the layout

A source · M×K row-major

A panel · one column per k

ld1w → ZA → st1w (transpose route)

B source · K×N row-major

B panel · one column per k

ldnt1w → st1w (straight copy)

Main loop · per k groupthe core · identical in all four states

Load slots

zA.s
zB.s

C · one 4 × 4 ZA tile

za0

C in memory · one slice per row

C = A × B · 4 × 4 · K accumulation

Ready. Pick the A and B layouts, then play: pack, K loop, store.

Arrow keys step, space plays or pauses.

Reading the picture

  1. The smallest honest picture

    The real kernel runs a 2 × 2 grid of tiles covering 32 × 32, four FMOPAs per k group, four load slots. Everything here is the same choreography, scaled down — one 4 × 4 tile, two k groups — so you can follow every single value. One shortcut is worth naming: the drawn tile starts at zero, so the loop only accumulates — a real kernel must clear ZA first (zero {za}) before its first FMOPA.

  2. Transpose is absorbed by pack

    Only the highlighted read pattern changes: gather takes one element per source row (row-strided ld1w, transposed in the ZA), copy takes one contiguous run (ldnt1w). Both produce the same panels, so the tagged core — the loop — never learns which layout you chose.

  3. Software pipelining

    Each load slot carries one k group; in the real kernel there are four, with pldl2keep pulling B into L2 and pldl1strm streaming C. A leftover K tail runs its own small ldr + fmopa loop, and C leaves through st1w slices plus a non-temporal stnt1w flush.

  4. Words this page borrows

    rank-1 layer — one outer product: a single A column times a single B row, one k's contribution added to every cell of C at once. k-major — K runs contiguously, one k per drawn panel column. mul vl — the byte length of one scalable vector at the current SVL (16 B here), so [pa, #1, mul vl] is the next vector along. non-temporal — a store that goes straight to memory without first fetching the line it overwrites (no read-for-ownership). w12 picks the ZA row a store cuts out; p0 is the predicate saying which of its four words are written.

A and B hold small integers; C = A × B.