Notation bpow e := (bpow beta e).(* floating-point format with gradual underflow *)
Definition FLT_format (x : R) :=
  exists f : float beta,
  x = F2R f /\ (Zabs (Fnum f) < Zpower beta prec)%Z /\ (emin <= Fexp f)%Z.Definition FLT_exp e := Zmax (e - prec) emin.(** Properties of the FLT format *)
Global Instance FLT_exp_valid : Valid_exp FLT_exp.

Theorem round_FLT_FLX : forall rnd x, (bpow (emin + prec - 1) <= Rabs x)%R -> round beta FLT_exp rnd x = round beta (FLX_exp prec) rnd x.