tiling

Trace a two-by-two output-stationary array cycle by cycle. Derive its fill and drain cost without turning a toy schedule into a TPU benchmark.

Calculate the data a kernel could reuse, then test whether it stays in L2. Distinguish capacity, cache-policy hints and measured traffic from a guarantee of residency.

Derive the bank mapping before and after padding, trace a fixed-tile kernel, and measure whether the saved conflict outweighs other resource costs.

Follow an accumulator across K tiles, count reuse at each memory level, and decide whether a tile improves measured GEMM performance.

Follow the running maximum and weighted sum across attention tiles, with executable arithmetic and an honest memory-traffic comparison.

Write and verify tiled NumPy matmul, derive its logical footprint and distinguish a cache model from the causes of measured runtime.