(** the most useful one: R -> F *)
Definition round x :=
  F2R (Float beta (rnd (scaled_mantissa x)) (canonic_exp x)).

Theorem round_bounded_large_pos : forall x ex, (fexp ex < ex)%Z -> (bpow (ex - 1) <= x < bpow ex)%R -> (bpow (ex - 1) <= round x <= bpow ex)%R.