(* *********************************************************************) (* *) (* The Compcert verified compiler *) (* *) (* Xavier Leroy, INRIA Paris *) (* *) (* 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 AST Memory Separation. Require Import Bounds. Local Open Scope sep_scope. (** The general shape of activation records is as follows, from bottom (lowest offsets) to top: - Space for outgoing arguments to function calls. - Back link to parent frame - Saved values of integer callee-save registers used by the function. - Saved values of float callee-save registers used by the function. - Local stack slots. - Space for the stack-allocated data declared in Cminor - Return address. *) Definition fe_ofs_arg := 0. Definition make_env (b: bounds) : frame_env := let w := if Archi.ptr64 then 8 else 4 in let olink := align (4 * b.(bound_outgoing)) w in (* back link *) let ocs := olink + w in (* callee-saves *) let ol := align (size_callee_save_area b ocs) 8 in (* locals *) let ostkdata := align (ol + 4 * b.(bound_local)) 8 in (* stack data *) let oretaddr := align (ostkdata + b.(bound_stack_data)) w in (* return address *) let sz := oretaddr + w in (* total size *) {| fe_size := sz; fe_ofs_link := olink; fe_ofs_retaddr := oretaddr; fe_ofs_local := ol; fe_ofs_callee_save := ocs; fe_stack_data := ostkdata; fe_used_callee_save := b.(used_callee_save) |}. 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 + size_chunk Mptr) ** range sp (fe_ofs_retaddr fe) (fe_ofs_retaddr fe + size_chunk Mptr) ** 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 (w := if Archi.ptr64 then 8 else 4). set (olink := align (4 * b.(bound_outgoing)) w). set (ocs := olink + w). set (ol := align (size_callee_save_area b ocs) 8). set (ostkdata := align (ol + 4 * b.(bound_local)) 8). set (oretaddr := align (ostkdata + b.(bound_stack_data)) w). replace (size_chunk Mptr) with w by (rewrite size_chunk_Mptr; auto). assert (0 < w) by (unfold w; destruct Archi.ptr64; omega). generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros. assert (0 <= 4 * b.(bound_outgoing)) by omega. assert (4 * b.(bound_outgoing) <= olink) by (apply align_le; omega). assert (olink + w <= ocs) by (unfold ocs; omega). assert (ocs <= size_callee_save_area b ocs) by (apply size_callee_save_area_incr). assert (size_callee_save_area b ocs <= ol) by (apply align_le; omega). assert (ol + 4 * b.(bound_local) <= ostkdata) by (apply align_le; omega). assert (ostkdata + bound_stack_data b <= oretaddr) by (apply align_le; omega). (* Reorder as: outgoing back link callee-save local retaddr *) rewrite sep_swap12. rewrite sep_swap23. rewrite sep_swap45. rewrite sep_swap34. (* Apply range_split and range_split2 repeatedly *) unfold fe_ofs_arg. apply range_split_2. fold olink. omega. omega. apply range_split. omega. apply range_split_2. fold ol. omega. omega. apply range_drop_right with ostkdata. omega. rewrite sep_swap. apply range_drop_left with (ostkdata + bound_stack_data b). omega. rewrite sep_swap. exact 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 (w := if Archi.ptr64 then 8 else 4). set (olink := align (4 * b.(bound_outgoing)) w). set (ocs := olink + w). set (ol := align (size_callee_save_area b ocs) 8). set (ostkdata := align (ol + 4 * b.(bound_local)) 8). set (oretaddr := align (ostkdata + b.(bound_stack_data)) w). assert (0 < w) by (unfold w; destruct Archi.ptr64; omega). generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros. assert (0 <= 4 * b.(bound_outgoing)) by omega. assert (4 * b.(bound_outgoing) <= olink) by (apply align_le; omega). assert (olink + w <= ocs) by (unfold ocs; omega). assert (ocs <= size_callee_save_area b ocs) by (apply size_callee_save_area_incr). assert (size_callee_save_area b ocs <= ol) by (apply align_le; omega). assert (ol + 4 * b.(bound_local) <= ostkdata) by (apply align_le; omega). assert (ostkdata + bound_stack_data b <= oretaddr) by (apply align_le; omega). split. omega. omega. 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) /\ (align_chunk Mptr | fe_ofs_link fe) /\ (align_chunk Mptr | fe_ofs_retaddr fe). Proof. intros; simpl. set (w := if Archi.ptr64 then 8 else 4). set (olink := align (4 * b.(bound_outgoing)) w). set (ocs := olink + w). set (ol := align (size_callee_save_area b ocs) 8). set (ostkdata := align (ol + 4 * b.(bound_local)) 8). set (oretaddr := align (ostkdata + b.(bound_stack_data)) w). assert (0 < w) by (unfold w; destruct Archi.ptr64; omega). replace (align_chunk Mptr) with w by (rewrite align_chunk_Mptr; auto). split. apply Z.divide_0_r. split. apply align_divides; omega. split. apply align_divides; omega. split. apply align_divides; omega. apply align_divides; omega. Qed.