Section RND_FLX.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable prec : Z.
Class Prec_gt_0 :=
prec_gt_0 : (0 < prec)%Z.
Context { prec_gt_0_ : Prec_gt_0 }.
Inductive FLX_format (x : R) : Prop :=
FLX_spec (f : float beta) :
x = F2R f -> (Z.abs (Fnum f) < Zpower beta prec)%Z -> FLX_format x.
Definition FLX_exp (e : Z) := (e - prec)%Z.
(** Properties of the FLX format *)
Global Instance FLX_exp_valid : Valid_exp FLX_exp.

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