(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
(** Base-2 Logarithm *)
(** Interface of a log2 function, then its specification on naturals *)
Module Type Log2 (Import A : Typ).
Parameter Inline log2 : t -> t.
End Log2.
Module Type NZLog2Spec (A : NZOrdAxiomsSig')(B : Pow' A)(C : Log2 A).

(* Specifications: *)
Axiom log2_spec : forall a, 0<a -> 2^(log2 a) <= a < 2^(S (log2 a)).
Axiom log2_nonpos : forall a, a<=0 -> log2 a == 0.
End NZLog2Spec.