Definition int_round_odd (x: Z) (p: Z) :=
(if Z.eqb (x mod 2^p) 0 || Z.odd (x / 2^p) then x / 2^p else x / 2^p + 1) * 2^p.

Lemma Zrnd_odd_int:
forall n p, 0 <= p ->
Zrnd_odd (Z2R n * bpow radix2 (-p)) * 2^p =
int_round_odd n p.