hopper

FlashAttention-2 reaches well under half of an H100's BF16 peak. The answer explains why in one ratio, exponentials against matmuls, and maps each FA3 technique to the stall it hides.

Occupancy is the minimum of four separate budgets, and candidates usually compute one of them. The answer works all four for an H100, finds which one binds, and then asks whether raising occupancy would help at all.

Every dimension of a GEMM tile is pinned by a different piece of hardware. The answer derives the reuse that sets the M and N sides, the swizzle row that sets K, and the register and shared-memory budgets that stop the tile growing.

Eight tiles too many turns a one-wave GEMM into two. The answer prices the waste in microseconds for a real prefill shape, then compares the three fixes, including the one that lives in the scheduler, not the kernel.

Both changes move work off the threads: one takes over address generation, the other takes over operand staging. The answer counts the instructions each one removes and shows why a Hopper kernel is organized around barriers instead of thread blocks that do everything.

Fine-grained scales let E4M3 carry every tensor, but they change along the reduction axis, so the tensor cores cannot apply them. The answer walks the main loop where they do get applied, prices that work against the MMA, and explains what Blackwell moves into hardware.