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

Theorem round_bounded_small_pos : forall x ex, (ex <= fexp ex)%Z -> (bpow (ex - 1) <= x < bpow ex)%R -> round x = 0%R \/ round x = bpow (fexp ex).