(** 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_finite:
forall n,
Z.abs n <= 2^emax - 2^(emax-prec) ->
B2R _ _ (BofZ n) = round radix2 fexp (round_mode mode_NE) (Z2R n)
/\ is_finite _ _ (BofZ n) = true
/\ Bsign _ _ (BofZ n) = Z.ltb n 0%Z.