Roofline and Tuning · arch

Computer Architecture · All levels

Roofline bounds kernel throughput by compute peak and memory bandwidth. Arithmetic intensity decides which roof binds, and tuning moves the point.

Roofline sketch with a memory-bound dot product and a compute-bound tiled GEMM.

The roofline plot: a bandwidth slope up to the ridge point, then a flat compute roof.

Lesson	What it covers
Roofline foundations	Intensity, the min bound, the ridge point and sustained ceilings.
Placing kernels	Three worked placements, per-level ceilings and a calculator model.
Tiling moves points	Reuse shifts intensity right, with a worked tiling example.
Roofline limits and Amdahl	Latency gaps, contention, power caps and Amdahl's law.

Check yourself A kernel reports high compute utilization yet runs far below peak. Which roofline question do you ask first?

Ask for its arithmetic intensity at the DRAM boundary. High ALU activity with low intensity means the DRAM slope binds, not the compute roof.