(** 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 generic_format_truncate :
forall m e l,
(0 <= m)%Z ->
let '(m', e', l') := truncate (m, e, l) in
format (F2R (Float beta m' e')).