(** 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.