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Source file sva_sentinel.ml

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(**************************************************************************)
(*  This file is part of the Codex semantics library.                     *)
(*                                                                        *)
(*  Copyright (C) 2013-2025                                               *)
(*    CEA (Commissariat à l'énergie atomique et aux énergies              *)
(*         alternatives)                                                  *)
(*                                                                        *)
(*  you can redistribute it and/or modify it under the terms of the GNU   *)
(*  Lesser General Public License as published by the Free Software       *)
(*  Foundation, version 2.1.                                              *)
(*                                                                        *)
(*  It is distributed in the hope that it will be useful,                 *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *)
(*  GNU Lesser General Public License for more details.                   *)
(*                                                                        *)
(*  See the GNU Lesser General Public License version 2.1                 *)
(*  for more details (enclosed in the file LICENSE).                      *)
(*                                                                        *)
(**************************************************************************)

(* Note: this was not heavily tested or reviewed. *)

let _name = "Sentinel"

include Sva_quadrivalent

module Integer_Lattice = struct
  include Lattices.Unimplemented.Integer_Lattice(struct
      type t = unit
      let loc = __LOC__
    end)
end
type integer = Integer_Lattice.t
module Integer_Backward = Sva_Assert_False_Transfer_Functions.Integer_Backward
module Integer_Forward = Sva_Assert_False_Transfer_Functions.Integer_Forward

module Bitvector_Lattice = struct
  type t = Bot | Zero | NonZero | SentinelTop
  module L = Lattices.Unimplemented.Bitvector_Lattice(struct
      type nonrec t = t
      let loc = __LOC__
    end)
  include (L:module type of L with type t := t)

  let bottom ~size:_ = Bot
  let is_bottom ~size:_ = function Bot -> true | _ -> false

  let top ~size:_ = SentinelTop

  let pretty ~size:_ fmt =
    let open Format in function
    | Bot -> pp_print_string fmt "Bottom"
    | Zero -> pp_print_string fmt "Zero"
    | NonZero -> pp_print_string fmt "NonZero"
    | SentinelTop -> pp_print_string fmt "MbZero"

  let includes ~size:_ x y =
    match x,y with
    | _,Bot -> true
    | Zero,NonZero | NonZero,Zero -> false
    | Zero,Zero | NonZero,NonZero -> true
    | SentinelTop,_ -> true
    | _ -> false

  let join ~size:_ x y =
    match x,y with
    | Bot,a | a,Bot -> a
    | Zero,Zero -> Zero
    | NonZero,NonZero -> NonZero
    | _ -> SentinelTop

  let inter ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,NonZero | NonZero,Zero -> Bot
    | NonZero,_ | _,NonZero -> NonZero
    | Zero,_ | _,Zero -> Zero
    | SentinelTop,SentinelTop -> SentinelTop

  let hash = function
    | Bot -> Hashtbl.hash 0
    | Zero -> Hashtbl.hash 1
    | NonZero -> Hashtbl.hash 2
    | SentinelTop -> Hashtbl.hash 3

  let compare x y =
    match x,y with
    | Bot,Bot -> 0
    | Bot,_ -> -1
    | _,Bot -> 1
    | Zero,Zero -> 0
    | Zero,_ -> -1
    | _,Zero -> 1
    | NonZero,NonZero -> 0
    | NonZero, SentinelTop -> -1
    | SentinelTop, NonZero -> 1
    | SentinelTop, SentinelTop -> 0

  let equal x y = compare x y = 0

  let widen ~size ~previous x =
    join ~size previous x

  let includes_or_widen ~size ~previous x =
    if includes ~size previous x then (true, x) else (false, widen ~size ~previous x)

  let singleton ~size:_ i =
    if Z.equal i Z.zero then Zero
    else NonZero

  let is_singleton ~size _x = assert false
  let is_empty ~size _x = assert false
  let fold_crop_signed ~size _x ~inf ~sup _acc _f  = assert false
  let fold_crop_unsigned ~size _x ~inf ~sup _acc _f  = assert false


end

type bitvector = Bitvector_Lattice.t

module Bitvector_Forward = struct
  open Bitvector_Lattice

  let biconst ~size:_ const =
    if Z.equal const Z.zero then Zero
    else NonZero

  let biadd ~size:_ ~flags:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,Zero -> Zero
    | NonZero,Zero | Zero,NonZero -> NonZero
    | _ -> SentinelTop

  let bisub ~size:_ ~flags:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,Zero -> Zero
    | NonZero,Zero | Zero,NonZero -> NonZero
    | _ -> SentinelTop

  let bimul ~size:_ ~flags x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,_ | _,Zero -> Zero
    | NonZero,NonZero -> NonZero
    | _ -> SentinelTop

  let bimul_add ~size ~prod ~offset x =
    Integer_Forward.iadd 
      (Integer_Forward.imul (biconst ~size prod) x)
      (biconst ~size offset)

  let bisdiv ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot | _,Zero -> Bot
    | Zero,_ -> Zero
    | NonZero,_ -> SentinelTop
    | SentinelTop, (NonZero|SentinelTop) -> SentinelTop

  let bismod ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot | _,Zero -> Bot
    | Zero,_ -> Zero
    | _ -> SentinelTop

  let biudiv = bisdiv
  let biumod = bismod

  let band ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,_ | _,Zero -> Zero
    | _ -> SentinelTop

  let bor ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,Zero -> Zero
    | NonZero,_ | _,NonZero -> NonZero
    | _ -> SentinelTop

  let bxor ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,Zero -> Zero
    | Zero,NonZero | NonZero,Zero -> NonZero
    | _ -> SentinelTop

  let bshl ~size:_ ~flags:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,_ -> Zero
    | NonZero,Zero -> NonZero
    | _ -> SentinelTop

  let bashr ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,_ -> Zero
    | NonZero,Zero -> NonZero
    | _ -> SentinelTop

  let blshr ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,_ -> Zero
    | NonZero,Zero -> NonZero
    | _ -> SentinelTop

  let bconcat ~size1:_ ~size2:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Bot
    | Zero,Zero -> Zero
    | NonZero,_ | _,NonZero -> NonZero
    | _ -> SentinelTop

  let beq ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Lattices.Quadrivalent.Bottom
    | Zero,Zero -> Lattices.Quadrivalent.True
    | Zero,NonZero | NonZero,Zero -> Lattices.Quadrivalent.False
    | _ -> Lattices.Quadrivalent.Top

  let bisle ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Lattices.Quadrivalent.Bottom
    | _ -> Lattices.Quadrivalent.Top

  let biule ~size:_ x y =
    match x,y with
    | Bot,_ | _,Bot -> Lattices.Quadrivalent.Bottom
    | Zero,_ -> Lattices.Quadrivalent.True
    | NonZero,Zero -> Lattices.Quadrivalent.False
    | _ -> Lattices.Quadrivalent.Top

  let buext ~size:_ ~oldsize:_ x =
    x
  let bsext ~size:_ ~oldsize:_ x =
    x
  let bextract ~size:_ ~index:_ ~oldsize:_ = function
    | Bot -> Bot
    | Zero -> Zero
    | _ -> SentinelTop

  let bofbool ~size:_ =
    let open Lattices.Quadrivalent in function
    | Bottom -> Bot
    | False -> Zero
    | True -> NonZero
    | Top -> SentinelTop
end

module Bitvector_Backward = struct
  open Bitvector_Lattice

  let beq ~size:_ x y res =
    match res with
    | Lattices.Quadrivalent.True ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some Zero
      | SentinelTop,Zero -> Some Zero, None
      | NonZero,SentinelTop -> None, Some NonZero
      | SentinelTop,NonZero -> Some NonZero, None
      | Zero,Zero | NonZero,NonZero -> None,None
      | SentinelTop,SentinelTop -> None,None
      | Bot,_ | _,Bot -> None,None
      | NonZero,Zero | Zero,NonZero -> assert false
      end
    | Lattices.Quadrivalent.False ->
      begin match x,y with
      | SentinelTop,Zero -> Some NonZero, None
      | Zero,SentinelTop -> None, Some NonZero
      | Zero,Zero -> Some Bot, Some Bot
      | _ -> None,None
      end
     | _ -> None,None

  let biule ~size:_ x y res =
    match res with
    | Lattices.Quadrivalent.True ->
      begin match x,y with
      | SentinelTop,Zero -> Some Zero, None
      | NonZero,SentinelTop -> None, Some NonZero
      | _ -> None,None
      end
    | Lattices.Quadrivalent.False ->
      begin match x,y with
      | SentinelTop,Zero | SentinelTop,NonZero -> Some NonZero, None
      | _ -> None,None
      end
    | _ -> None,None

  let bisle ~size:_ x y res =
    match res with
    | Lattices.Quadrivalent.True -> None,None
    | Lattices.Quadrivalent.False ->
      begin match x,y with
      | SentinelTop,Zero -> Some NonZero, None
      | Zero,SentinelTop -> None, Some NonZero
      | _ -> None,None
      end
    | _ -> None,None

  let biadd ~size:_ ~flags:_ x y = function
    | Zero ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some Zero
      | SentinelTop,Zero -> Some Zero, None
      | NonZero,SentinelTop -> None, Some NonZero
      | SentinelTop,NonZero -> Some NonZero, None
      | _ -> None,None
      end
    | NonZero ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some NonZero
      | SentinelTop,Zero -> Some NonZero, None
      | _ -> None,None
      end
    | _ -> None,None

  let bisub ~size:_ ~flags:_ x y = function
    | Zero ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some Zero
      | SentinelTop,Zero -> Some Zero, None
      | NonZero,SentinelTop -> None, Some NonZero
      | SentinelTop,NonZero -> Some NonZero, None
      | _ -> None,None
      end
    | NonZero ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some NonZero
      | SentinelTop,Zero -> Some NonZero, None
      | _ -> None,None
      end
    | _ -> None,None

  let bimul ~size:_ ~flags:_ x y = function
    | Zero ->
      begin match x,y with
      | NonZero,SentinelTop -> None, Some Zero
      | SentinelTop,NonZero -> Some Zero, None
      | _ -> None,None
      end
    | NonZero ->
      begin match x,y with
      | SentinelTop,SentinelTop -> Some NonZero, Some NonZero
      | NonZero,SentinelTop -> None, Some NonZero
      | SentinelTop,NonZero -> Some NonZero, None
      | _ -> None,None
      end
    | _ -> None,None

  let bimul_add ~size ~prod ~offset x res =
    let prod = Bitvector_Forward.biconst ~size prod in
    let mul = Integer_Forward.imul prod x in
    (* We could check that the second arguments match the constants here, and
      raise bottom if that is not the case... *)
    match Integer_Backward.iadd mul (Bitvector_Forward.biconst ~size offset) |> fst with
    | None -> None
    | Some mul -> Integer_Backward.imul prod x |> snd

  let band ~size:_ _ _ = function
    | NonZero -> Some NonZero, Some NonZero
    | _ -> None,None

  let bor ~size:_ x y = function
    | Zero -> Some Zero, Some Zero
    | NonZero ->
      begin match x,y with
      | SentinelTop,Zero -> Some NonZero, None
      | Zero,SentinelTop -> None, Some NonZero
      | _ -> None,None
      end
    | _ -> None,None

  let bxor ~size:_ x y = function
    | Zero ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some Zero
      | SentinelTop,Zero -> Some Zero, None
      | NonZero,SentinelTop -> None, Some NonZero
      | SentinelTop,NonZero -> Some NonZero, None
      | _ -> None,None
      end
    | NonZero ->
      begin match x,y with
      | Zero,SentinelTop -> None, Some NonZero
      | SentinelTop,Zero -> Some NonZero, None
      | _ -> None,None
      end
    | _ -> None,None

  let bisdiv ~size:_ x y = function
    | Zero -> Some Zero, None
    | NonZero -> Some NonZero, Some NonZero
    | Bot ->
      begin match x,y with
      | Bot,_ | _,Bot -> None,None
      | _ -> None, Some Zero
      end
    | _ -> None,None

  let biudiv ~size:_ x y = function
    | Zero -> Some Zero, None
    | NonZero -> Some NonZero, Some NonZero
    | Bot ->
      begin match x,y with
      | Bot,_ | _,Bot -> None,None
      | _ -> None, Some Zero
      end
    | _ -> None,None

  let bismod ~size:_ x y = function
    | NonZero -> Some NonZero, Some NonZero
    | Bot ->
      begin match x,y with
      | Bot,_ | _,Bot -> None,None
      | _ -> None, Some Zero
      end
    | _ -> None,None

  let biumod ~size:_ x y = function
    | NonZero -> Some NonZero, Some NonZero
    | Bot ->
      begin match x,y with
      | Bot,_ | _,Bot -> None,None
      | _ -> None, Some Zero
      end
    | _ -> None,None

  let bashr ~size:_ x y = function
    | Zero ->
      begin match x,y with
      | SentinelTop,Zero -> Some Zero, None
      | NonZero,SentinelTop -> None, Some NonZero
      | _ -> None,None
      end
    | NonZero -> Some NonZero, None
    | _ -> None,None

  let blshr ~size x y = bashr ~size x y

  let bshl ~size ~flags x y = bashr ~size x y

  let bsext ~size:_ ~oldsize:_ _ _ = (None)
  let buext ~size:_ ~oldsize:_ _ _ = (None)
  let bconcat ~size1:_ ~size2:_ _ _ _ = (None,None)
  let bextract ~size:_ ~index:_ ~oldsize:_ _ _ = (None)

  let bofbool ~size:_ _bool =
    let open Lattices.Quadrivalent in function
    | Bot -> Some Bottom
    | Zero -> Some False
    | NonZero -> Some True
    | SentinelTop -> Some Top
end

let _binary_to_ival ~signed ~size =
  let open Bitvector_Lattice in function
  | Zero -> Framac_ival.Ival.of_int 0
  | NonZero ->
      if signed then Framac_ival.Ival.top
      else
        (* Range is [1,2^size-1]. *)
        Framac_ival.Ival.inject_range (Some Z.one)
          (Some (Z.sub (Z.shift_left Z.one size) Z.one))
  | SentinelTop -> Framac_ival.Ival.top
  | Bot -> Framac_ival.Ival.bottom

let _binary_is_singleton ~size:_ =
  let open Bitvector_Lattice in function
  | Zero -> Some Z.zero
  | _ -> None

let _binary_is_empty ~size:_ =
  let open Bitvector_Lattice in function
  | Bot -> true
  | _ -> false

let is_zero = function
| Bitvector_Lattice.(Bot | Zero) -> true
| Bitvector_Lattice.(NonZero | SentinelTop) -> false

let zero = Bitvector_Lattice.Zero
let nonzero = Bitvector_Lattice.NonZero

let _binary_to_known_bits ~size =
  let open Bitvector_Lattice in
  function
  | Bot -> Lattices.Known_Bits.bottom ~size
  | Zero -> (Z.zero, Z.zero)
  | NonZero | SentinelTop -> Lattices.Known_Bits.top ~size