ilp

Occupancy is how many warps an SM holds against its maximum, and it is a means, not an end. The arithmetic from registers per thread to resident warps, the launch bound that caps registers and the spills that follow, the profiler's occupancy view, and the kernel where halving occupancy doubled speed.

A sum reads every byte once and does one add per element, so the only question is whether you reach the bandwidth ceiling. The ceiling in milliseconds, four versions from an atomic per element to warp shuffles with sixteen loads in flight, and the bytes-in-flight math behind the last jump.