(** 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_correct:
forall n,
if Rlt_bool (Rabs (round radix2 fexp (round_mode mode_NE) (Z2R n))) (bpow radix2 emax)
then
B2R prec emax (BofZ n) = round radix2 fexp (round_mode mode_NE) (Z2R n) /\
is_finite _ _ (BofZ n) = true /\
Bsign prec emax (BofZ n) = Z.ltb n 0
else
B2FF prec emax (BofZ n) = binary_overflow prec emax mode_NE (Z.ltb n 0).