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

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