(** ** Decidable equality *)
Definition Beq_dec: forall (f1 f2: binary_float), {f1 = f2} + {f1 <> f2}.

Lemma round_int_no_overflow:
forall n,
Z.abs n <= 2^emax - 2^(emax-prec) ->
(Rabs (round radix2 fexp (round_mode mode_NE) (Z2R n)) < bpow radix2 emax)%R.