Section RND_FTZ.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable emin prec : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Inductive FTZ_format (x : R) : Prop :=
FTZ_spec (f : float beta) :
x = F2R f ->
(x <> 0%R -> Zpower beta (prec - 1) <= Z.abs (Fnum f) < Zpower beta prec)%Z ->
(emin <= Fexp f)%Z ->
FTZ_format x.
Definition FTZ_exp e := if Zlt_bool (e - prec) emin then (emin + prec - 1)%Z else (e - prec)%Z.
(** Properties of the FTZ format *)
Global Instance FTZ_exp_valid : Valid_exp FTZ_exp.

Theorem FTZ_format_FLXN :
forall x : R,
(bpow (emin + prec - 1) <= Rabs x)%R ->
FLXN_format beta prec x -> FTZ_format x.