(** 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).