A single moderately complex shader. Compiled to multiple targets by the harness (same source, varying -target) to isolate generateOutput cost. ``n`` scales the amount of straight-line math the backend must emit. Scaling null: n scales op count and the emitted output is O(n); ideal codegen cost is O(n).
bucket: codegen · mode: target · flags: -target spirv -emit-spirv-directly
compileInner split into phase buckets (named leaves + (self) residuals) stacked across the sweep sizes — the top edge is compileInner, so you can see which phase drives the scaling.
floor-subtracted power-law fit (t − floor) = a·Nk; floor = the minimal workload (fixed per-compile cost), k the global exponent, top-2× the local high-end doubling ratio.
| N range | floor (ms) | k (work) | fit R² | t(Nmin) | t(Nmax) | top-2× |
|---|---|---|---|---|---|---|
| 100–800 | 11 | 1.65 | 0.991 | 53 | 1295 | 3.76× |
compileInner grows by 1242 ms across the sweep; the mutually-exclusive phase buckets below partition that growth exactly (no nested-timer double counting). × lin is the same metric as the top-level panels, per bucket: the end point vs a linear expectation anchored to the bucket's share of the minimal floor and fitted on the low-N half — 1.0 = grew exactly linearly, >1 bends up. The super-linearity lives where × lin (and k) are red.
| bucket | t@N=100 | t@N=800 | Δ ms | share | × lin | ∝Nk |
|---|---|---|---|---|---|---|
| linkAndOptimizeIR (self) | 8 | 498 | +490 | 39% | 5.50× | 2.03 |
| legalizeExistentialTypeLayout | 4 | 309 | +305 | 25% | 5.84× | 2.12 |
| legalizeResourceTypes | 4 | 304 | +301 | 24% | 5.77× | 2.11 |
| SemanticChecking | 15 | 61 | +46 | 4% | 0.86× | 0.86 |
| generateOutput (self) | 7 | 44 | +36 | 3% | 1.04× | 1.02 |
Near-constant (≤2% of growth each): specializeModule (4→28 ms), simplifyIR (3→28 ms), generateIR (5→16 ms), linkIR (1→2 ms), parseTranslationUnit (0→2 ms), compileInner (self) (1→1 ms), performForceInlining (0→1 ms), performMandatoryEarlyInlining (0→1 ms), frontEndExecute (self) (0→0 ms), unrollLoopsInModule (0→0 ms).
| N | compileInner | generateOutput |
|---|---|---|
| 100 | 53 | 32 |
| 200 | 111 | 82 |
| 400 | 344 | 299 |
| 800 | 1295 | 1215 |