Section RND_FLT.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable emin prec : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Inductive FLT_format (x : R) : Prop :=
FLT_spec (f : float beta) :
x = F2R f -> (Z.abs (Fnum f) < Zpower beta prec)%Z ->
(emin <= Fexp f)%Z -> FLT_format x.
Definition FLT_exp e := Z.max (e - prec) emin.
(** Properties of the FLT format *)
Global Instance FLT_exp_valid : Valid_exp FLT_exp.

(** Links between FLT and FIX (underflow) *)
Theorem cexp_FLT_FIX :
forall x, x <> 0%R ->
(Rabs x < bpow (emin + prec))%R ->
cexp beta FLT_exp x = cexp beta (FIX_exp emin) x.