(** Hence the number of bits of [a] is [1+log2 a] (see [Pos.size_nat] and [Pos.size]). *)
(** For negative numbers, things are the other ways around: log2 gives the highest zero bit (for numbers below -1). *)

(* Specifications: *)
Lemma bit_log2_neg : forall a, a < -1 -> a.[log2 (P (-a))] = false.
Lemma bits_above_log2_neg : forall a n, a < 0 -> log2 (P (-a)) < n ->
a.[n] = true.