[tomtom1337]

Oh, I should have clarified - could one start with a bfloat16 on software-side, convert to float16 (so that e.g a 3.4E38 float16 becomes a 65504 float16), then do any "heavy math" in fast hardware float16 instructions, and then convert back at the end?

[sapiogram]

Nothing necessarily wrong with that code, but it also kinda smells. Why even store it as bfloat16 at all? You risk getting the numerical disadvantages of both float16-representation, and none of the advantages.