(** ** Conversion from scientific notation *)

(** Russian peasant exponentiation *)

Fixpoint pos_pow (x y: positive) : positive :=
  match y with
  | xH => x
  | xO y => Pos.square (pos_pow x y)
  | xI y => Pos.mul x (Pos.square (pos_pow x y))
  end.

Lemma Zpower_log: forall (base: radix) n, 0 < n -> 2 ^ (n * Z.log2 base) <= base ^ n <= 2 ^ (n * Z.log2_up base).