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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \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) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
Require Import BinPos.
Require Export BinNat.
Require Import NAxioms NProperties.
Local Open Scope N_scope.
(** * [BinNat.N] already implements [NAxiomSig] *)
Module N <: NAxiomsSig := N.
(*
Require Import NDefOps.
Module Import NBinaryDefOpsMod := NdefOpsPropFunct NBinaryAxiomsMod.
(* Some fun comparing the efficiency of the generic log defined
by strong (course-of-value) recursion and the log defined by recursion
on notation *)
Time Eval vm_compute in (log 500000). (* 11 sec *)
Fixpoint binposlog (p : positive) : N :=
match p with
| xH => 0
| xO p' => N.succ (binposlog p')
| xI p' => N.succ (binposlog p')
end.
Definition binlog (n : N) : N :=
match n with
| 0 => 0
| Npos p => binposlog p
end.
Time Eval vm_compute in (binlog 500000). (* 0 sec *)
Time Eval vm_compute in (binlog 1000000000000000000000000000000). (* 0 sec *)
*)
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