[tryfinally]

You can store it and move it around, but arithmetic operations are prohibitively expensive without hardware acceleration.

(Note that bfloat16 has a different range than float16, so you can't interpret one as the other)

[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.