Definition Zrnd_FTZ x :=
  if Rle_bool 1 (Rabs x) then rnd x else Z0.Global Instance valid_rnd_FTZ : Valid_rnd Zrnd_FTZ.

Theorem round_FTZ_small : forall x : R, (Rabs x < bpow (emin + prec - 1))%R -> round beta FTZ_exp Zrnd_FTZ x = R0.