(** Given a triple (mantissa, exponent, position), this function
    computes a triple with a canonic exponent, assuming the
    original triple had enough precision. *)

Definition truncate t :=
  let '(m, e, l) := t in
  let k := (fexp (Zdigits beta m + e) - e)%Z in
  if Zlt_bool 0 k then truncate_aux t k
  else t.

Theorem truncate_0 : forall e l, let '(m', e', l') := truncate (0, e, l)%Z in m' = Z0.