diff options
Diffstat (limited to 'powerpc/Stacklayout.v')
-rw-r--r-- | powerpc/Stacklayout.v | 171 |
1 files changed, 91 insertions, 80 deletions
diff --git a/powerpc/Stacklayout.v b/powerpc/Stacklayout.v index a751fd98..2b78fd11 100644 --- a/powerpc/Stacklayout.v +++ b/powerpc/Stacklayout.v @@ -13,6 +13,7 @@ (** Machine- and ABI-dependent layout information for activation records. *) Require Import Coqlib. +Require Import Memory Separation. Require Import Bounds. (** In the PowerPC/EABI application binary interface, @@ -25,8 +26,7 @@ Require Import Bounds. frame, we will not use these 4 bytes, and just reserve them. - Space for outgoing arguments to function calls. - Local stack slots. -- Saved values of integer callee-save registers used by the function. -- Saved values of float callee-save registers used by the function. +- 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 @@ -35,100 +35,111 @@ the boundaries between areas in the frame part. Definition fe_ofs_arg := 8. -Record frame_env : Type := mk_frame_env { - fe_size: Z; - fe_ofs_link: Z; - fe_ofs_retaddr: Z; - fe_ofs_local: Z; - fe_ofs_int_callee_save: Z; - fe_num_int_callee_save: Z; - fe_ofs_float_callee_save: Z; - fe_num_float_callee_save: Z; - fe_stack_data: Z -}. - (** Computation of the frame environment from the bounds of the current function. *) Definition make_env (b: bounds) := let ol := align (8 + 4 * b.(bound_outgoing)) 8 in (* locals *) let ora := ol + 4 * b.(bound_local) in (* saved return address *) - let oics := ora + 4 in (* integer callee-saves *) - let oendi := oics + 4 * b.(bound_int_callee_save) in - let ofcs := align oendi 8 in (* float callee-saves *) - let ostkdata := ofcs + 8 * b.(bound_float_callee_save) in (* stack data *) + let ocs := ora + 4 in (* callee-saves *) + let oendcs := size_callee_save_area b ocs in + let ostkdata := align oendcs 8 in (* stack data *) let sz := align (ostkdata + b.(bound_stack_data)) 16 in - mk_frame_env sz 0 ora - ol - oics b.(bound_int_callee_save) - ofcs b.(bound_float_callee_save) - ostkdata. + {| fe_size := sz; + fe_ofs_link := 0; + 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 *) -Remark frame_env_separated: - forall b, +Local Open Scope sep_scope. + +Lemma frame_env_separated: + forall b sp m P, let fe := make_env b in - 0 <= fe.(fe_ofs_link) - /\ fe.(fe_ofs_link) + 4 <= fe_ofs_arg - /\ fe_ofs_arg + 4 * b.(bound_outgoing) <= fe.(fe_ofs_local) - /\ fe.(fe_ofs_local) + 4 * b.(bound_local) <= fe.(fe_ofs_retaddr) - /\ fe.(fe_ofs_retaddr) + 4 <= fe.(fe_ofs_int_callee_save) - /\ fe.(fe_ofs_int_callee_save) + 4 * b.(bound_int_callee_save) <= fe.(fe_ofs_float_callee_save) - /\ fe.(fe_ofs_float_callee_save) + 8 * b.(bound_float_callee_save) <= fe.(fe_stack_data) - /\ fe.(fe_stack_data) + b.(bound_stack_data) <= fe.(fe_size) - /\ fe.(fe_ofs_retaddr) + 4 <= fe.(fe_size). + 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. - intros. - generalize (align_le (8 + 4 * b.(bound_outgoing)) 8 (refl_equal _)). - generalize (align_le (fe.(fe_ofs_int_callee_save) + 4 * b.(bound_int_callee_save)) 8 (refl_equal _)). - generalize (align_le (fe.(fe_stack_data) + b.(bound_stack_data)) 16 (refl_equal _)). - unfold fe, make_env, fe_size, fe_ofs_link, fe_ofs_retaddr, - fe_ofs_local, fe_ofs_int_callee_save, - fe_num_int_callee_save, - fe_ofs_float_callee_save, fe_num_float_callee_save, - fe_stack_data, fe_ofs_arg. - intros. - generalize (bound_local_pos b); intro; - generalize (bound_int_callee_save_pos b); intro; - generalize (bound_float_callee_save_pos b); intro; - generalize (bound_outgoing_pos b); intro; - generalize (bound_stack_data_pos b); intro. - omega. +Local Opaque Z.add Z.mul sepconj range. + intros; simpl. + set (ol := align (8 + 4 * b.(bound_outgoing)) 8). + set (ora := ol + 4 * b.(bound_local)). + set (ocs := ora + 4). + set (oendcs := size_callee_save_area b ocs). + set (ostkdata := align oendcs 8). + generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros. + unfold fe_ofs_arg. + assert (8 + 4 * b.(bound_outgoing) <= ol) by (apply align_le; omega). + assert (ol <= ora) by (unfold ora; omega). + assert (ora <= ocs) by (unfold ocs; omega). + assert (ocs <= oendcs) by (apply size_callee_save_area_incr). + assert (oendcs <= ostkdata) by (apply align_le; omega). +(* Reorder as: + back link + outgoing + locals + retaddr + callee-save *) + rewrite sep_swap3. +(* Apply range_split and range_split2 repeatedly *) + apply range_drop_right with 8. omega. + apply range_split. omega. + apply range_split_2. fold ol; omega. omega. + apply range_split. omega. + apply range_split. omega. + apply range_drop_right with ostkdata. omega. + eapply sep_drop2. eexact H. Qed. -(** Alignment property *) +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 (ol := align (8 + 4 * b.(bound_outgoing)) 8). + set (ora := ol + 4 * b.(bound_local)). + set (ocs := ora + 4). + set (oendcs := size_callee_save_area b ocs). + set (ostkdata := align oendcs 8). + generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros. + unfold fe_ofs_arg. + assert (8 + 4 * b.(bound_outgoing) <= ol) by (apply align_le; omega). + assert (ol <= ora) by (unfold ora; omega). + assert (ora <= ocs) by (unfold ocs; omega). + assert (ocs <= oendcs) by (apply size_callee_save_area_incr). + assert (oendcs <= ostkdata) by (apply align_le; omega). + split. omega. apply align_le. omega. +Qed. -Remark frame_env_aligned: +Lemma frame_env_aligned: forall b, let fe := make_env b in - (4 | fe.(fe_ofs_link)) - /\ (8 | fe.(fe_ofs_local)) - /\ (4 | fe.(fe_ofs_int_callee_save)) - /\ (8 | fe.(fe_ofs_float_callee_save)) - /\ (4 | fe.(fe_ofs_retaddr)) - /\ (8 | fe.(fe_stack_data)) - /\ (16 | fe.(fe_size)). + (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. - unfold fe, make_env, fe_size, fe_ofs_link, fe_ofs_retaddr, - fe_ofs_local, fe_ofs_int_callee_save, - fe_num_int_callee_save, - fe_ofs_float_callee_save, fe_num_float_callee_save, - fe_stack_data. - set (x1 := align (8 + 4 * bound_outgoing b) 8). - assert (8 | x1). unfold x1; apply align_divides. omega. - set (x2 := x1 + 4 * bound_local b). - assert (4 | x2). unfold x2; apply Zdivide_plus_r; auto. - apply Zdivides_trans with 8. exists 2; auto. auto. - exists (bound_local b); ring. - set (x3 := x2 + 4). - assert (4 | x3). unfold x3; apply Zdivide_plus_r; auto. exists 1; auto. - set (x4 := align (x3 + 4 * bound_int_callee_save b) 8). - assert (8 | x4). unfold x4. apply align_divides. omega. - set (x5 := x4 + 8 * bound_float_callee_save b). - assert (8 | x5). unfold x5. apply Zdivide_plus_r; auto. exists (bound_float_callee_save b); ring. - set (x6 := align (x5 + bound_stack_data b) 16). - assert (16 | x6). unfold x6; apply align_divides. omega. - intuition. + intros; simpl. + set (ol := align (8 + 4 * b.(bound_outgoing)) 8). + set (ora := ol + 4 * b.(bound_local)). + set (ocs := ora + 4). + set (oendcs := size_callee_save_area b ocs). + set (ostkdata := align oendcs 8). + split. exists (fe_ofs_arg / 8); reflexivity. + split. apply align_divides; omega. + split. apply align_divides; omega. + split. apply Zdivide_0. + apply Z.divide_add_r. + apply Zdivide_trans with 8. exists 2; auto. apply align_divides; omega. + apply Z.divide_factor_l. Qed. |