(** IEEE-754 roundings: up, down and to zero *)

Global Instance valid_rnd_DN : Valid_rnd Zfloor.Global Instance valid_rnd_UP : Valid_rnd Zceil.Global Instance valid_rnd_ZR : Valid_rnd Ztrunc.Global Instance valid_rnd_AW : Valid_rnd Zaway.

Theorem round_bounded_large : forall rnd {Hr : Valid_rnd rnd} x ex, (fexp ex < ex)%Z -> (bpow (ex - 1) <= Rabs x < bpow ex)%R -> (bpow (ex - 1) <= Rabs (round rnd x) <= bpow ex)%R.