(** Conversion from an integer.  Round to nearest. *)
Definition BofZ (n: Z) : binary_float :=
binary_normalize prec emax prec_gt_0_ Hmax mode_NE n 0 false.

Lemma BofZ_finite_pos0:
forall n,
Z.abs n <= 2^emax - 2^(emax-prec) -> is_finite_pos0 (BofZ n) = true.