(** 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.

Theorem BofZ_representable:
forall n,
integer_representable n ->
B2R _ _ (BofZ n) = Z2R n
/\ is_finite _ _ (BofZ n) = true
/\ Bsign _ _ (BofZ n) = (n <? 0).