(** Definition and basic properties about the ulp *)
(** Now includes a nice ulp(0): ulp(0) is now 0 when there is no minimal
   exponent, such as in FLX, and beta^(fexp n) when there is a n such
   that n <= fexp n. For instance, the value of ulp(O) is then
   beta^emin in FIX and FLT. The main lemma to use is ulp_neq_0 that
   is equivalent to the previous "unfold ulp" provided the value is
   not zero. *)

Definition ulp x := match Req_bool x 0 with
  | true   => match negligible_exp with
            | Some n => bpow (fexp n)
            | None => 0%R
            end
  | false  => bpow (canonic_exp beta fexp x)
 end.

Lemma ulp_neq_0 : forall x:R, (x <> 0)%R -> ulp x = bpow (canonic_exp beta fexp x).