diff options
Diffstat (limited to 'ia32/standard/Stacklayout.v')
| -rw-r--r-- | ia32/standard/Stacklayout.v | 102 |
1 files changed, 88 insertions, 14 deletions
diff --git a/ia32/standard/Stacklayout.v b/ia32/standard/Stacklayout.v index 135aba1e..1fa3fb3a 100644 --- a/ia32/standard/Stacklayout.v +++ b/ia32/standard/Stacklayout.v @@ -19,21 +19,15 @@ Require Import Bounds. from bottom (lowest offsets) to top: - Space for outgoing arguments to function calls. - Back link to parent frame -- Return address (formally; it's actually pushed elsewhere) - Local stack slots of integer type. - Saved values of integer callee-save registers used by the function. - Local stack slots of float type. - Saved values of float callee-save registers used by the function. -- Space for the stack-allocated data declared in Cminor. - -To facilitate some of the proofs, the Cminor stack-allocated data -starts at offset 0; the preceding areas in the activation record -therefore have negative offsets. This part (with negative offsets) -is called the ``frame'', by opposition with the ``Cminor stack data'' -which is the part with positive offsets. +- Space for the stack-allocated data declared in Cminor +- Return address. The [frame_env] compilation environment records the positions of -the boundaries between areas in the frame part. +the boundaries between these areas of the activation record. *) Definition fe_ofs_arg := 0. @@ -47,7 +41,8 @@ Record frame_env : Type := mk_frame_env { fe_num_int_callee_save: Z; fe_ofs_float_local: Z; fe_ofs_float_callee_save: Z; - fe_num_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 @@ -55,22 +50,101 @@ Record frame_env : Type := mk_frame_env { Definition make_env (b: bounds) := let olink := 4 * b.(bound_outgoing) in (* back link *) - let oretaddr := olink + 4 in (* return address *) - let oil := oretaddr + 4 in (* integer locals *) + let oil := olink + 4 in (* integer locals *) let oics := oil + 4 * b.(bound_int_local) in (* integer callee-saves *) let oendi := oics + 4 * b.(bound_int_callee_save) in let ofl := align oendi 8 in (* float locals *) let ofcs := ofl + 8 * b.(bound_float_local) in (* float callee-saves *) - let sz := ofcs + 8 * b.(bound_float_callee_save) in (* total frame size *) + let ostkdata := ofcs + 8 * b.(bound_float_callee_save) in (* stack data *) + let oretaddr := align (ostkdata + b.(bound_stack_data)) 4 in (* return address *) + let sz := oretaddr + 4 in (* total size *) mk_frame_env sz olink oretaddr oil oics b.(bound_int_callee_save) - ofl ofcs b.(bound_float_callee_save). + ofl ofcs b.(bound_float_callee_save) + ostkdata. + +(** Separation property *) + +Remark frame_env_separated: + forall b, + let fe := make_env b in + 0 <= fe_ofs_arg + /\ fe_ofs_arg + 4 * b.(bound_outgoing) <= fe.(fe_ofs_link) + /\ fe.(fe_ofs_link) + 4 <= fe.(fe_ofs_int_local) + /\ fe.(fe_ofs_int_local) + 4 * b.(bound_int_local) <= fe.(fe_ofs_int_callee_save) + /\ fe.(fe_ofs_int_callee_save) + 4 * b.(bound_int_callee_save) <= fe.(fe_ofs_float_local) + /\ fe.(fe_ofs_float_local) + 8 * b.(bound_float_local) <= 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_ofs_retaddr) + /\ fe.(fe_ofs_retaddr) + 4 <= fe.(fe_size). +Proof. + intros. + 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)) 4 (refl_equal _)). + unfold fe, make_env, fe_size, fe_ofs_link, fe_ofs_retaddr, + fe_ofs_int_local, fe_ofs_int_callee_save, + fe_num_int_callee_save, + fe_ofs_float_local, fe_ofs_float_callee_save, fe_num_float_callee_save, + fe_stack_data, fe_ofs_arg. + intros. + generalize (bound_int_local_pos b); intro; + generalize (bound_float_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. +Qed. +(** Alignment property *) +Remark frame_env_aligned: + forall b, + let fe := make_env b in + (4 | fe.(fe_ofs_link)) + /\ (4 | fe.(fe_ofs_int_local)) + /\ (4 | fe.(fe_ofs_int_callee_save)) + /\ (8 | fe.(fe_ofs_float_local)) + /\ (8 | fe.(fe_ofs_float_callee_save)) + /\ (4 | fe.(fe_ofs_retaddr)) + /\ (4 | fe.(fe_stack_data)) + /\ (4 | fe.(fe_size)). +Proof. + intros. + unfold fe, make_env, fe_size, fe_ofs_link, fe_ofs_retaddr, + fe_ofs_int_local, fe_ofs_int_callee_save, + fe_num_int_callee_save, + fe_ofs_float_local, fe_ofs_float_callee_save, fe_num_float_callee_save, + fe_stack_data. + set (x1 := 4 * bound_outgoing b). + assert (4 | x1). unfold x1; exists (bound_outgoing b); ring. + set (x2 := x1 + 4). + assert (4 | x2). unfold x2; apply Zdivide_plus_r; auto. exists 1; auto. + set (x3 := x2 + 4 * bound_int_local b). + assert (4 | x3). unfold x2; apply Zdivide_plus_r; auto. exists (bound_int_local b); ring. + set (x4 := x3 + 4 * bound_int_callee_save b). + set (x5 := align x4 8). + assert (8 | x5). unfold x5. apply align_divides. omega. + set (x6 := x5 + 8 * bound_float_local b). + assert (8 | x6). unfold x6. apply Zdivide_plus_r; auto. exists (bound_float_local b); ring. + set (x7 := x6 + 8 * bound_float_callee_save b). + assert (4 | x7). + apply Zdivides_trans with 8. exists 2; auto. + unfold x7. apply Zdivide_plus_r; auto. exists (bound_float_callee_save b); ring. + set (x8 := align (x7 + bound_stack_data b) 4). + assert (4 | x8). apply align_divides. omega. + set (x9 := x8 + 4). + assert (4 | x9). unfold x8; apply Zdivide_plus_r; auto. exists 1; auto. + tauto. +Qed. + +(* Remark align_float_part: forall b, 4 * bound_outgoing b + 4 + 4 + 4 * bound_int_local b + 4 * bound_int_callee_save b <= align (4 * bound_outgoing b + 4 + 4 + 4 * bound_int_local b + 4 * bound_int_callee_save b) 8. + Proof. intros. apply align_le. omega. Qed. +*)
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