Roofline Classifier

Prompt

You are given measurements from three kernels on a GPU with:

peak compute: 120 TFLOP/s
peak memory bandwidth: 3,000 GB/s
typical launch overhead: 8 us

Measurements:

kernel	flops	bytes moved	measured time
A	2.1e9	8.6e9	3.2 ms
B	9.0e12	1.2e11	82 ms
C	1.0e6	1.0e6	12 us

Deliverable

For each kernel:

1. Compute arithmetic intensity.
2. Compute achieved TFLOP/s.
3. Compute achieved GB/s.
4. Classify the limiting regime: memory-bound, compute-bound, or overhead-bound.
5. Pick one optimization lever and one lever that would probably waste time.

Hints

Arithmetic intensity:

flops / bytes_moved

Rough roofline threshold:

peak_flops / peak_bandwidth

If a kernel runs in roughly launch-overhead time and barely does work, it is not meaningfully memory-bound or compute-bound yet. It is too small.

Acceptance criteria

The answer should not just label kernels. It should connect each label to action:

1. Memory-bound: reduce bytes, improve locality, fuse away intermediates.
2. Compute-bound: use faster math paths, better tiling, tensor cores, lower precision when valid.
3. Overhead-bound: batch more work, fuse, compile, use CUDA graphs, or move the loop.

Stretch

Add a fourth row for a real measurement from your machine and classify it with the same method.

Debrief

The roofline model is not a perfect oracle. It is a guardrail against optimizing the wrong scarce resource.