block scaling

Both formats store the same eight 4-bit values per element. The difference is all in the scale, and the answer shows which of the two scale choices buys more accuracy and what it costs in bits.

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.