Fusion preserves effects and numeric contracts

For pure elementwise functions, composing g(f(x)) can let each produced element feed its consumer immediately. A producer with several consumers may instead be recomputed after fusion or require retained shared storage. If an operation reads mutable state, advances a random generator, performs I/O, or has ordering effects, duplicating or moving it can change behavior. Compiler effect interfaces and operation contracts supply information for legality; a graph edge alone is not sufficient proof.

Materialization can also provide a synchronization or layout boundary. A later operation may need results from many producer iterations, not just one corresponding element. Moving that consumer inside a producer loop can read incomplete data unless the schedule and synchronization are transformed correctly. Conversely, a legal fused region can still use temporary storage internally. A dump containing one fusion operation does not guarantee zero buffers or one specific hardware implementation; inspect the selected lowering and target behavior.

Reassociating a reduction or contracting multiply-plus-add into a fused operation can change rounding. NaNs, infinities, signed zero, exception behavior, and precision conversions add further constraints. LLVM 20.1.0 spells out fast-math flags rather than declaring all floating operations algebraic real numbers. A pipeline must preserve the source contract or carry explicit permissions for the particular transformation. A tolerance accepted by a model benchmark is not itself permission to silently change unrelated users' numerical semantics.

Fusion that preserves the original operation sequence and required rounding can be legal even when reassociation is not. Distinguish avoiding a memory write from removing a semantic conversion or rounding point. A producer returning a narrower dtype may require that narrowing before its consumer, even if the fused hardware prefers a wider register. Correctness tests should include cancellation and boundary values, while legality follows the documented source and IR contracts rather than only observed error on a convenient input.

Count the actual intermediate reads and writes removed at a named memory boundary. A value already retained in cache may contribute less main-memory traffic than its logical buffer size suggests. Fusion can increase register pressure, spill, reduce occupancy, or duplicate expensive producer work for multiple consumers. It can also prevent a tuned library call. Compare end-to-end latency and resource use after checking every consumer's values; smaller IR and fewer launches are intermediate observations, not the final outcome.

The Roofline lab supplies a synthetic traffic-bound exercise. Reset and set both I=4 FLOP/byte, B=80 GB/s, predict 320 GFLOP/s. Reset and re-set I=8, B=80, predicting 640 GFLOP/s under its fixed 1000 GFLOP/s compute ceiling; Play traces the roof without changing kernel parameters. The doubled intensity could represent halved boundary traffic only if counted work stays fixed. The instrument does not fuse operations, model spills, or prove the measured speedup of any compiler transformation.