package mopsa

  1. Overview
  2. Docs
package mopsa
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file quantified_offset.ml

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
(****************************************************************************)
(*                                                                          *)
(* This file is part of MOPSA, a Modular Open Platform for Static Analysis. *)
(*                                                                          *)
(* Copyright (C) 2017-2019 The MOPSA Project.                               *)
(*                                                                          *)
(* This program is free software: 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, either version 3 of the License, or     *)
(* (at your option) any later version.                                      *)
(*                                                                          *)
(* This program 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.                      *)
(*                                                                          *)
(* You should have received a copy of the GNU Lesser General Public License *)
(* along with this program.  If not, see <http://www.gnu.org/licenses/>.    *)
(*                                                                          *)
(****************************************************************************)

open Mopsa
open Universal.Ast
open Stubs.Ast
open Ast
open Top


(** Compute symbolic boundaries of a quantified offset. *)
(* FIXME: works only for linear expressions *)
let rec bound offset quants : expr * expr =
  match ekind @@ get_orig_expr offset with
  | E_constant _ -> offset, offset

  | E_var (v, _) when is_forall_quantified_var v quants ->
    find_quantified_var_interval v quants

  | E_var _ ->
    offset, offset

  | E_unop (O_minus, e) ->
    let l, u = bound e quants in
    { offset with ekind = E_unop (O_minus, u)},
    { offset with ekind = E_unop (O_minus, l)}

  | E_binop (O_plus, e1, e2) ->
    let l1, u1 = bound e1 quants in
    let l2, u2 = bound e2 quants in
    { offset with ekind = E_binop (O_plus, l1, l2)},
    { offset with ekind = E_binop (O_plus, u1, u2)}

  | E_binop (O_minus, e1, e2) ->
    let l1, u1 = bound e1 quants in
    let l2, u2 = bound e2 quants in
    { offset with ekind = E_binop (O_minus, l1, u2)},
    { offset with ekind = E_binop (O_minus, u1, l2)}

  | E_binop (O_mult, e, ({ ekind = E_constant (C_int c) } as const))
  | E_binop (O_mult, ({ ekind = E_constant (C_int c) } as const), e) ->
    let l, u = bound e quants in
    if Z.geq c Z.zero then
      { offset with ekind = E_binop (O_mult, l, { const with ekind = E_constant (C_int c) })},
      { offset with ekind = E_binop (O_mult, u, { const with ekind = E_constant (C_int c) })}
    else
      { offset with ekind = E_binop (O_mult, u, { const with ekind = E_constant (C_int c) })},
      { offset with ekind = E_binop (O_mult, l, { const with ekind = E_constant (C_int c) })}

  | E_c_cast(e, xplct) ->
    let l, u = bound e quants in
    { offset with ekind = E_c_cast (l, xplct)},
    { offset with ekind = E_c_cast (u, xplct)}

  | _ -> panic_at offset.erange
           "can not compute symbolic bounds of non-linear expression %a"
           pp_expr offset



(** [is_aligned o n man flow] checks whether the value of an
      expression [o] is aligned w.r.t. size sz *)
let is_aligned e sz man flow =
  (sz = Z.one) || (is_c_expr_equals_z e Z.zero flow) ||
  (man.eval e flow ~translate:"Universal" |>
   Cases.for_all_result (fun ee flow ->
       let open Universal.Numeric.Common in
       let i , c = ask_and_reduce man.ask (mk_int_congr_interval_query ee) flow in
       match i with
       | Bot.Nb(I.B.Finite a, I.B.Finite b) when  a = b && Z.rem a sz = Z.zero -> true
       | _ -> Universal.Numeric.Common.C.included_bot c (Bot.Nb (sz,Z.zero))
     )
  )


(** Compute symbolic boundaries of offset / den *)
let bound_div (offset:expr) (den:Z.t) quants man flow : (expr * expr) with_top =
  let rec doit offset den  =
    let range = erange offset in
    match ekind @@ get_orig_expr offset with
    | E_constant (C_int c) when Z.rem c den = Z.zero ->
      let r =
        if den = Z.one then offset
        else if c = Z.zero then offset
        else div offset (mk_z den range) range in
      r, r

    | E_var (v, _) when is_forall_quantified_var v quants ->
      if den = Z.one then
        find_quantified_var_interval v quants
      else
        raise Found_TOP

    | E_var (v,_) ->
      if not (is_aligned offset den man flow) then raise Found_TOP;
      let r = if den = Z.one then offset else div offset (mk_z den range) range in
      r, r

    | E_unop (O_minus, e) ->
      let l, u = doit e den in
      { offset with ekind = E_unop (O_minus, u)},
      { offset with ekind = E_unop (O_minus, l)}

    | E_binop (O_plus, e1, e2) ->
      let l1, u1 = doit e1 den in
      let l2, u2 = doit e2 den in
      { offset with ekind = E_binop (O_plus, l1, l2)},
      { offset with ekind = E_binop (O_plus, u1, u2)}

    | E_binop (O_minus, e1, e2) ->
      let l1, u1 = doit e1 den in
      let l2, u2 = doit e2 den in
      { offset with ekind = E_binop (O_minus, l1, u2)},
      { offset with ekind = E_binop (O_minus, u1, l2)}

    | E_binop (O_mult, e1, e2) ->
      let e1, c, e2 = match e1, e2 with
        | { ekind = E_constant (C_int c) }, _ -> e1, c, e2
        | _, { ekind = E_constant (C_int c) } -> e2, c, e1
        | _ -> raise Found_TOP
      in
      let gcd = Z.gcd c den in
      let c, den = Z.div c gcd, Z.div den gcd in
      let l, u = doit e2 den in
      if c = Z.one then l, u
      else if c >= Z.zero then
        { offset with ekind = E_binop (O_mult, l, { e1 with ekind = E_constant (C_int c) })},
        { offset with ekind = E_binop (O_mult, u, { e1 with ekind = E_constant (C_int c) })}
      else
        { offset with ekind = E_binop (O_mult, u, { e1 with ekind = E_constant (C_int c) })},
        { offset with ekind = E_binop (O_mult, l, { e1 with ekind = E_constant (C_int c) })}

    | E_binop (O_div, e, ({ ekind = E_constant (C_int c) })) ->
      doit e (Z.mul den c)

    | E_c_cast(e, xplct) ->
      let l, u = doit e den in
      { offset with ekind = E_c_cast (l, xplct)},
      { offset with ekind = E_c_cast (u, xplct)}

    | _ ->
      (*
      panic_at offset.erange
        "can not compute symbolic bounds of non-linear expression %a / %a"
        pp_expr offset Z.pp_print den
      *)
      raise Found_TOP
  in
  retop (doit offset) den

(*
let bound_div offset den man flow =
  Format.printf "bound_div %a / %a@." pp_expr offset Z.pp_print den;
  let l,u = bound_div offset den man flow in
  Format.printf "  [%a,@.   %a]@." pp_expr l pp_expr u;
  l, u
*)
OCaml

Innovation. Community. Security.

GitHub Discord Twitter Peertube RSS
About
Changelog Releases Industrial Users Academic Users Why OCaml
Ecosystem
Packages Community Events OCaml Planet Jobs
Resources
Install OCaml Get Started Platform Tools Language Manual Standard Library API Books Exercises Papers OCaml Playground Logo
Policies
Carbon Footprint Governance Privacy Code of Conduct