(** A variant of [ZofB] that bounds the range of representable integers. *)
Definition ZofB_range (f: binary_float) (zmin zmax: Z): option Z :=
match ZofB f with
| None => None
| Some z => if Z.leb zmin z && Z.leb z zmax then Some z else None
end.

Theorem ZofB_range_correct:
forall f min max,
let n := Ztrunc (B2R _ _ f) in
ZofB_range f min max =
if is_finite _ _ f && Z.leb min n && Z.leb n max then Some n else None.