Definition binary_round m sx mx ex :=
  let '(mz, ez) := shl_align_fexp mx ex in binary_round_aux m sx mz ez loc_Exact.

Theorem binary_round_correct : forall m sx mx ex, let z := binary_round m sx mx ex in valid_binary z = true /\ let x := F2R (Float radix2 (cond_Zopp sx (Zpos mx)) ex) in if Rlt_bool (Rabs (round radix2 fexp (round_mode m) x)) (bpow radix2 emax) then FF2R radix2 z = round radix2 fexp (round_mode m) x /\ is_finite_FF z = true /\ sign_FF z = sx else z = binary_overflow m sx.