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-(* *********************************************************************)
-(* *)
-(* 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 Bounds.
-
-(** The general shape of activation records is as follows,
- from bottom (lowest offsets) to top:
-- 24 reserved bytes. The first 4 bytes hold the back pointer to the
- activation record of the caller. We use the 4 bytes at offset 12
- to store the return address. (These are reserved by the PowerPC
- application binary interface.) The remaining bytes are unused.
-- Space for outgoing arguments to function calls.
-- Local stack slots of integer type.
-- Saved values of integer callee-save registers used by the function.
-- One word of padding, if necessary to align the following data
- on a 8-byte boundary.
-- 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.
-
-The [frame_env] compilation environment records the positions of
-the boundaries between areas in the frame part.
-*)
-
-Definition fe_ofs_arg := 24.
-
-Record frame_env : Type := mk_frame_env {
- fe_size: Z;
- fe_ofs_link: Z;
- fe_ofs_retaddr: Z;
- fe_ofs_int_local: Z;
- fe_ofs_int_callee_save: Z;
- fe_num_int_callee_save: Z;
- fe_ofs_float_local: 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 oil := 24 + 4 * b.(bound_outgoing) 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 ostkdata := ofcs + 8 * b.(bound_float_callee_save) in (* stack data *)
- let sz := align (ostkdata + b.(bound_stack_data)) 16 in
- mk_frame_env sz 0 12
- oil oics b.(bound_int_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.(fe_ofs_link)
- /\ fe.(fe_ofs_link) + 4 <= fe.(fe_ofs_retaddr)
- /\ fe.(fe_ofs_retaddr) + 4 <= fe_ofs_arg
- /\ fe_ofs_arg + 4 * b.(bound_outgoing) <= 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_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)) 16 (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))
- /\ (16 | 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 := 24 + 4 * bound_outgoing b).
- assert (4 | x1). unfold x1; apply Zdivide_plus_r. exists 6; auto. exists (bound_outgoing b); ring.
- set (x2 := x1 + 4 * bound_int_local b).
- assert (4 | x2). unfold x2; apply Zdivide_plus_r; auto. exists (bound_int_local b); ring.
- set (x3 := x2 + 4 * bound_int_callee_save b).
- set (x4 := align x3 8).
- assert (8 | x4). unfold x4. apply align_divides. omega.
- set (x5 := x4 + 8 * bound_float_local b).
- assert (8 | x5). unfold x5. apply Zdivide_plus_r; auto. exists (bound_float_local b); ring.
- set (x6 := x5 + 8 * bound_float_callee_save b).
- assert (4 | x6).
- apply Zdivides_trans with 8. exists 2; auto.
- unfold x6. apply Zdivide_plus_r; auto. exists (bound_float_callee_save b); ring.
- set (x7 := align (x6 + bound_stack_data b) 16).
- assert (16 | x7). unfold x7; apply align_divides. omega.
- intuition.
- exists 3; auto.
-Qed.
generated by cgit (git 2.34.1) at 2024-06-30 11:29:35 +0000