Notation bpow e := (bpow beta e).

Theorem relative_error_N_round : (0 < p)%Z -> forall x, (bpow emin <= Rabs x)%R -> (Rabs (round beta fexp (Znearest choice) x - x) <= /2 * bpow (-p + 1) * Rabs (round beta fexp (Znearest choice) x))%R.