blob: f6e01e0c2eda58b8641ce6f41cb8bf37e1093215 (
plain)
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
|
(* *********************************************************************)
(* *)
(* The Compcert verified compiler *)
(* *)
(* Xavier Leroy, INRIA Paris-Rocquencourt *)
(* *)
(* Copyright Institut National de Recherche en Informatique et en *)
(* Automatique. All rights reserved. This file is distributed *)
(* under the terms of the INRIA Non-Commercial License Agreement. *)
(* *)
(* *********************************************************************)
(** Machine- and ABI-dependent layout information for activation records. *)
Require Import Coqlib.
Require Import Memory Separation.
Require Import Bounds.
(** The general shape of activation records is as follows,
from bottom (lowest offsets) to top:
- Space for outgoing arguments to function calls.
- Pointer to activation record of the caller.
- Saved return address into caller.
- Local stack slots.
- Saved values of callee-save registers used by the function.
- Space for the stack-allocated data declared in Cminor.
The [frame_env] compilation environment records the positions of
the boundaries between areas in the frame part.
*)
Definition fe_ofs_arg := 0.
(** Computation of the frame environment from the bounds of the current
function. *)
Definition make_env (b: bounds) :=
let olink := 4 * b.(bound_outgoing) in (* back link*)
let ora := olink + 4 in (* return address *)
let ol := align (ora + 4) 8 in (* locals *)
let ocs := ol + 4 * b.(bound_local) in (* callee-saves *)
let ostkdata := align (size_callee_save_area b ocs) 8 in (* retaddr *)
let sz := align (ostkdata + b.(bound_stack_data)) 8 in
{| fe_size := sz;
fe_ofs_link := olink;
fe_ofs_retaddr := ora;
fe_ofs_local := ol;
fe_ofs_callee_save := ocs;
fe_stack_data := ostkdata;
fe_used_callee_save := b.(used_callee_save) |}.
(** Separation property *)
Local Open Scope sep_scope.
Lemma frame_env_separated:
forall b sp m P,
let fe := make_env b in
m |= range sp 0 (fe_stack_data fe) ** range sp (fe_stack_data fe + bound_stack_data b) (fe_size fe) ** P ->
m |= range sp (fe_ofs_local fe) (fe_ofs_local fe + 4 * bound_local b)
** range sp fe_ofs_arg (fe_ofs_arg + 4 * bound_outgoing b)
** range sp (fe_ofs_link fe) (fe_ofs_link fe + 4)
** range sp (fe_ofs_retaddr fe) (fe_ofs_retaddr fe + 4)
** range sp (fe_ofs_callee_save fe) (size_callee_save_area b (fe_ofs_callee_save fe))
** P.
Proof.
Local Opaque Z.add Z.mul sepconj range.
intros; simpl.
set (olink := 4 * b.(bound_outgoing));
set (ora := olink + 4);
set (ol := align (ora + 4) 8);
set (ocs := ol + 4 * b.(bound_local));
set (ostkdata := align (size_callee_save_area b ocs) 8).
generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros.
assert (0 <= olink) by (unfold olink; lia).
assert (olink <= ora) by (unfold ora; lia).
assert (ora + 4 <= ol) by (apply align_le; lia).
assert (ol + 4 * b.(bound_local) <= ocs) by (unfold ocs; lia).
assert (ocs <= size_callee_save_area b ocs) by apply size_callee_save_area_incr.
assert (size_callee_save_area b ocs <= ostkdata) by (apply align_le; lia).
(* Reorder as:
outgoing
back link
retaddr
local
callee-save *)
rewrite sep_swap12.
rewrite sep_swap23.
rewrite sep_swap34.
(* Apply range_split and range_split2 repeatedly *)
unfold fe_ofs_arg.
apply range_split. lia.
apply range_split. lia.
apply range_split_2. fold ol; lia. lia.
apply range_split. lia.
apply range_drop_right with ostkdata. lia.
eapply sep_drop2. eexact H.
Qed.
Lemma frame_env_range:
forall b,
let fe := make_env b in
0 <= fe_stack_data fe /\ fe_stack_data fe + bound_stack_data b <= fe_size fe.
Proof.
intros; simpl.
set (olink := 4 * b.(bound_outgoing));
set (ora := olink + 4);
set (ol := align (ora + 4) 8);
set (ocs := ol + 4 * b.(bound_local));
set (ostkdata := align (size_callee_save_area b ocs) 8).
generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros.
assert (0 <= olink) by (unfold olink; lia).
assert (olink <= ora) by (unfold ora; lia).
assert (ora + 4 <= ol) by (apply align_le; lia).
assert (ol + 4 * b.(bound_local) <= ocs) by (unfold ocs; lia).
assert (ocs <= size_callee_save_area b ocs) by apply size_callee_save_area_incr.
assert (size_callee_save_area b ocs <= ostkdata) by (apply align_le; lia).
split. lia. apply align_le; lia.
Qed.
Lemma frame_env_aligned:
forall b,
let fe := make_env b in
(8 | fe_ofs_arg)
/\ (8 | fe_ofs_local fe)
/\ (8 | fe_stack_data fe)
/\ (4 | fe_ofs_link fe)
/\ (4 | fe_ofs_retaddr fe).
Proof.
intros; simpl.
set (olink := 4 * b.(bound_outgoing));
set (ora := olink + 4);
set (ol := align (ora + 4) 8);
set (ocs := ol + 4 * b.(bound_local));
set (ostkdata := align (size_callee_save_area b ocs) 8).
split. apply Z.divide_0_r.
split. apply align_divides; lia.
split. apply align_divides; lia.
unfold ora, olink; auto using Z.divide_mul_l, Z.divide_add_r, Z.divide_refl.
Qed.
|
