Notation bpow e := (bpow beta e).Class Prec_gt_0 :=
  prec_gt_0 : (0 < prec)%Z.Class Prec_gt_0 :=
  prec_gt_0 : (0 < prec)%Z.(* unbounded floating-point format *)
Definition FLX_format (x : R) :=
  exists f : float beta,
  x = F2R f /\ (Zabs (Fnum f) < Zpower beta prec)%Z.Definition FLX_exp (e : Z) := (e - prec)%Z.(** Properties of the FLX format *)

Global Instance FLX_exp_valid : Valid_exp FLX_exp.

Theorem FLX_format_FIX : forall x e, (bpow (e - 1) <= Rabs x <= bpow e)%R -> FIX_format beta (e - prec) x -> FLX_format x.