Require Bvector.  (* stdlib uses LSB first (little-endian) representation *)
Require Vector.
Require List.

(* Convert a nat list to a bitvector. Non-zero values are considered true *)
Fixpoint list2Bvec_aux (l:list nat) : Bvector.Bvector (List.length l) :=
  match l return Bvector.Bvector (List.length l) with
  | List.cons O xs =>
      Bvector.Bcons false _ (list2Bvec_aux xs)
  | List.cons _ xs =>
      Bvector.Bcons true _ (list2Bvec_aux xs)
  | List.nil => Bvector.Bnil
  end.
Definition list2Bvec (l:list nat) : Bvector.Bvector (List.length (List.rev l)) :=
  list2Bvec_aux (List.rev l).

(* Convert a bitvector to nat. Little-endian representation assumed *)
Fixpoint bvec2nat_aux {n:nat} (cur:nat) (bv:Bvector.Bvector n): nat :=
  match bv with
  | Vector.cons _ x _ xs =>
      if x then (Nat.pow 2 cur) + bvec2nat_aux (S cur) xs
      else bvec2nat_aux (S cur) xs
  | Vector.nil _ => 0
  end.
Definition bvec2nat {n:nat} (bv:Bvector.Bvector n): nat := bvec2nat_aux 0 bv.

(* Find nth bit of a bitvector *)
Definition Bnth {z i:nat} (bv: Bvector.Bvector z) (pf:i<z): bool :=
  Vector.nth_order bv pf.

(* Find list of set bits in a bitvector *)
Fixpoint find_set_bits {z:nat} (bv: Bvector.Bvector z) : list nat :=
  match bv with
  | Vector.cons _ x _ xs =>
      if x then List.cons (z-1) (find_set_bits xs)
      else (find_set_bits xs)
  | Vector.nil _ => List.nil
  end.



Require Import List. 
Import ListNotations. 
Compute list2Bvec [0;0;1;0].  (* 0100₂ ie, 4₁₀ *)
Check Bvector.BshiftL _ (list2Bvec [0;0;1;0]) false.

Check Vector.shiftrepeat (Vector.cons _ 0 _ (Vector.nil _)).

Require Import Vector. 


Import VectorNotations. 
Compute Bvector.BshiftL 1 (list2Bvec [0;0;1;0]) false.
(*
= [false; false; true; false]
     : Bvector (length [0; 0; 1; 0])
*)
Compute bvec2nat (list2Bvec [0;0;1;0]).
(* = 2 : nat *)
Compute bvec2nat (list2Bvec [0;1;0;0]).
(* = 4 : nat *)

Compute Bnth (list2Bvec [0;0;1;0]) (_:2<_).
(* = true : bool *)
Compute Bnth (list2Bvec [0;0;1;0]) (_:1<_).
(* = false : bool *)


Compute find_set_bits (list2Bvec [0;0;1;0]).  (* [2] : list nat *)
Compute find_set_bits (list2Bvec [1;0;1;0]).  (* [2; 0] : list nat *)

Check Bvector.BshiftL .

Check Bcons.

Check Nat.pow.
Compute Nat.pow 2 3.
Check Vector.nth_order.
Check Vector.nth_order (list2Bvec [0;0;1;0]).
Compute Vector.nth_order (list2Bvec [0;0;1;0]) (_:0<_).