(** ** 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 round_NE_underflows: forall x, (0 <= x <= bpow radix2 (emin - 1))%R -> round radix2 fexp (round_mode mode_NE) x = 0%R.