(** 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_minus:
forall minus_nan m f p q,
ZofB_range f 0 (2 * q - 1) = Some p -> q <= 2^prec -> (Z2R q <= B2R _ _ f)%R ->
ZofB_range (Bminus _ _ _ Hmax minus_nan m f (BofZ q)) (-q) (q - 1) = Some (p - q).