(** Rounding to odd the argument of [BofZ]. *)

(* Specifications: *)
Lemma round_odd_flt:
forall prec' emin' x choice,
prec > 1 -> prec' > 1 -> prec' >= prec + 2 -> emin' <= emin - 2 ->
round radix2 fexp (Znearest choice) (round radix2 (FLT_exp emin' prec') Zrnd_odd x) =
round radix2 fexp (Znearest choice) x.
Corollary round_odd_fix:
forall x p choice,
prec > 1 ->
0 <= p ->
(bpow radix2 (prec + p + 1) <= Rabs x)%R ->
round radix2 fexp (Znearest choice) (round radix2 (FIX_exp p) Zrnd_odd x) =
round radix2 fexp (Znearest choice) x.
Lemma round_odd_flt:
forall prec' emin' x choice,
prec > 1 -> prec' > 1 -> prec' >= prec + 2 -> emin' <= emin - 2 ->
round radix2 fexp (Znearest choice) (round radix2 (FLT_exp emin' prec') Zrnd_odd x) =
round radix2 fexp (Znearest choice) x.
Corollary round_odd_fix:
forall x p choice,
prec > 1 ->
0 <= p ->
(bpow radix2 (prec + p + 1) <= Rabs x)%R ->
round radix2 fexp (Znearest choice) (round radix2 (FIX_exp p) Zrnd_odd x) =
round radix2 fexp (Znearest choice) x.