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diff --git a/arm/eabi/Conventions1.v b/arm/eabi/Conventions1.v new file mode 100644 index 0000000..1731eba --- /dev/null +++ b/arm/eabi/Conventions1.v @@ -0,0 +1,453 @@ +(* *********************************************************************) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Function calling conventions and other conventions regarding the use of + machine registers and stack slots. *) + +Require Import Coqlib. +Require Import AST. +Require Import Locations. + +(** * Classification of machine registers *) + +(** Machine registers (type [mreg] in module [Locations]) are divided in + the following groups: +- Temporaries used for spilling, reloading, and parallel move operations. +- Allocatable registers, that can be assigned to RTL pseudo-registers. + These are further divided into: +-- Callee-save registers, whose value is preserved across a function call. +-- Caller-save registers that can be modified during a function call. + + We follow the PowerPC application binary interface (ABI) in our choice + of callee- and caller-save registers. +*) + +Definition int_caller_save_regs := + R0 :: R1 :: R2 :: R3 :: R12 :: nil. + +Definition float_caller_save_regs := + F0 :: F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: nil. + +Definition int_callee_save_regs := + R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: R11 :: nil. + +Definition float_callee_save_regs := + F8 :: F9 :: F10 :: F11 :: F12 :: F13 :: F14 :: F15 :: nil. + +Definition destroyed_at_call := + int_caller_save_regs ++ float_caller_save_regs. + +Definition dummy_int_reg := R0. (**r Used in [Coloring]. *) +Definition dummy_float_reg := F0. (**r Used in [Coloring]. *) + +(** The [index_int_callee_save] and [index_float_callee_save] associate + a unique positive integer to callee-save registers. This integer is + used in [Stacking] to determine where to save these registers in + the activation record if they are used by the current function. *) + +Definition index_int_callee_save (r: mreg) := + match r with + | R4 => 0 | R5 => 1 | R6 => 2 | R7 => 3 + | R8 => 4 | R9 => 5 | R10 => 6 | R11 => 7 + | _ => -1 + end. + +Definition index_float_callee_save (r: mreg) := + match r with + | F8 => 0 | F9 => 1 | F10 => 2 | F11 => 3 + | F12 => 4 | F13 => 5 | F14 => 6 | F15 => 7 + | _ => -1 + end. + +Ltac ElimOrEq := + match goal with + | |- (?x = ?y) \/ _ -> _ => + let H := fresh in + (intro H; elim H; clear H; + [intro H; rewrite <- H; clear H | ElimOrEq]) + | |- False -> _ => + let H := fresh in (intro H; contradiction) + end. + +Ltac OrEq := + match goal with + | |- (?x = ?x) \/ _ => left; reflexivity + | |- (?x = ?y) \/ _ => right; OrEq + | |- False => fail + end. + +Ltac NotOrEq := + match goal with + | |- (?x = ?y) \/ _ -> False => + let H := fresh in ( + intro H; elim H; clear H; [intro; discriminate | NotOrEq]) + | |- False -> False => + contradiction + end. + +Lemma index_int_callee_save_pos: + forall r, In r int_callee_save_regs -> index_int_callee_save r >= 0. +Proof. + intro r. simpl; ElimOrEq; unfold index_int_callee_save; omega. +Qed. + +Lemma index_float_callee_save_pos: + forall r, In r float_callee_save_regs -> index_float_callee_save r >= 0. +Proof. + intro r. simpl; ElimOrEq; unfold index_float_callee_save; omega. +Qed. + +Lemma index_int_callee_save_pos2: + forall r, index_int_callee_save r >= 0 -> In r int_callee_save_regs. +Proof. + destruct r; simpl; intro; omegaContradiction || OrEq. +Qed. + +Lemma index_float_callee_save_pos2: + forall r, index_float_callee_save r >= 0 -> In r float_callee_save_regs. +Proof. + destruct r; simpl; intro; omegaContradiction || OrEq. +Qed. + +Lemma index_int_callee_save_inj: + forall r1 r2, + In r1 int_callee_save_regs -> + In r2 int_callee_save_regs -> + r1 <> r2 -> + index_int_callee_save r1 <> index_int_callee_save r2. +Proof. + intros r1 r2. + simpl; ElimOrEq; ElimOrEq; unfold index_int_callee_save; + intros; congruence. +Qed. + +Lemma index_float_callee_save_inj: + forall r1 r2, + In r1 float_callee_save_regs -> + In r2 float_callee_save_regs -> + r1 <> r2 -> + index_float_callee_save r1 <> index_float_callee_save r2. +Proof. + intros r1 r2. + simpl; ElimOrEq; ElimOrEq; unfold index_float_callee_save; + intros; congruence. +Qed. + +(** The following lemmas show that + (temporaries, destroyed at call, integer callee-save, float callee-save) + is a partition of the set of machine registers. *) + +Lemma int_float_callee_save_disjoint: + list_disjoint int_callee_save_regs float_callee_save_regs. +Proof. + red; intros r1 r2. simpl; ElimOrEq; ElimOrEq; discriminate. +Qed. + +Lemma register_classification: + forall r, + In r destroyed_at_call \/ In r int_callee_save_regs \/ In r float_callee_save_regs. +Proof. + destruct r; + try (left; simpl; OrEq); + try (right; left; simpl; OrEq); + try (right; right; simpl; OrEq). +Qed. + + +Lemma int_callee_save_not_destroyed: + forall r, + In r destroyed_at_call -> In r int_callee_save_regs -> False. +Proof. + intros. revert H0 H. simpl. ElimOrEq; NotOrEq. +Qed. + +Lemma float_callee_save_not_destroyed: + forall r, + In r destroyed_at_call -> In r float_callee_save_regs -> False. +Proof. + intros. revert H0 H. simpl. ElimOrEq; NotOrEq. +Qed. + +Lemma int_callee_save_type: + forall r, In r int_callee_save_regs -> mreg_type r = Tint. +Proof. + intro. simpl; ElimOrEq; reflexivity. +Qed. + +Lemma float_callee_save_type: + forall r, In r float_callee_save_regs -> mreg_type r = Tfloat. +Proof. + intro. simpl; ElimOrEq; reflexivity. +Qed. + +Ltac NoRepet := + match goal with + | |- list_norepet nil => + apply list_norepet_nil + | |- list_norepet (?a :: ?b) => + apply list_norepet_cons; [simpl; intuition discriminate | NoRepet] + end. + +Lemma int_callee_save_norepet: + list_norepet int_callee_save_regs. +Proof. + unfold int_callee_save_regs; NoRepet. +Qed. + +Lemma float_callee_save_norepet: + list_norepet float_callee_save_regs. +Proof. + unfold float_callee_save_regs; NoRepet. +Qed. + +(** * Function calling conventions *) + +(** The functions in this section determine the locations (machine registers + and stack slots) used to communicate arguments and results between the + caller and the callee during function calls. These locations are functions + of the signature of the function and of the call instruction. + Agreement between the caller and the callee on the locations to use + is guaranteed by our dynamic semantics for Cminor and RTL, which demand + that the signature of the call instruction is identical to that of the + called function. + + Calling conventions are largely arbitrary: they must respect the properties + proved in this section (such as no overlapping between the locations + of function arguments), but this leaves much liberty in choosing actual + locations. *) + +(** ** Location of function result *) + +(** The result value of a function is passed back to the caller in + registers [R0] or [F0] or [R0,R1], depending on the type of the + returned value. We treat a function without result as a function + with one integer result. *) + +Definition loc_result (s: signature) : list mreg := + match s.(sig_res) with + | None => R0 :: nil + | Some Tint => R0 :: nil + | Some Tfloat => F0 :: nil + | Some Tlong => R1 :: R0 :: nil + end. + +(** The result location is a caller-save register or a temporary *) + +Lemma loc_result_caller_save: + forall (s: signature) (r: mreg), + In r (loc_result s) -> In r destroyed_at_call. +Proof. + intros. + assert (r = R0 \/ r = R1 \/ r = F0). + unfold loc_result in H. destruct (sig_res s); [destruct t|idtac]; simpl in H; intuition. + destruct H0 as [A | [A | A]]; subst r; simpl; OrEq. +Qed. + +(** ** Location of function arguments *) + +(** We use the following calling conventions, adapted from the ARM EABI: +- The first 4 integer arguments are passed in registers [R0] to [R3]. +- The first 2 float arguments are passed in registers [F0] and [F1]. +- Each float argument passed in a float register ``consumes'' an aligned pair + of two integer registers. +- Each long integer argument is passed in an aligned pair of two integer + registers. +- Extra arguments are passed on the stack, in [Outgoing] slots, consecutively + assigned (1 word for an integer argument, 2 words for a float or a long), + starting at word offset 0. +*) + +Definition ireg_param (n: Z) : mreg := + if zeq n (-4) then R0 + else if zeq n (-3) then R1 + else if zeq n (-2) then R2 + else R3. + +Definition freg_param (n: Z) : mreg := + if zeq n (-4) then F0 else F1. + +Fixpoint loc_arguments_rec (tyl: list typ) (ofs: Z) {struct tyl} : list loc := + match tyl with + | nil => nil + | Tint :: tys => + (if zle 0 ofs then S Outgoing ofs Tint else R (ireg_param ofs)) + :: loc_arguments_rec tys (ofs + 1) + | Tfloat :: tys => + let ofs := align ofs 2 in + (if zle 0 ofs then S Outgoing ofs Tfloat else R (freg_param ofs)) + :: loc_arguments_rec tys (ofs + 2) + | Tlong :: tys => + let ofs := align ofs 2 in + (if zle 0 ofs then S Outgoing (ofs + 1) Tint else R (ireg_param (ofs + 1))) + :: (if zle 0 ofs then S Outgoing ofs Tint else R (ireg_param ofs)) + :: loc_arguments_rec tys (ofs + 2) + end. + +(** [loc_arguments s] returns the list of locations where to store arguments + when calling a function with signature [s]. *) + +Definition loc_arguments (s: signature) : list loc := + loc_arguments_rec s.(sig_args) (-4). + +(** [size_arguments s] returns the number of [Outgoing] slots used + to call a function with signature [s]. *) + +Fixpoint size_arguments_rec (tyl: list typ) (ofs: Z) {struct tyl} : Z := + match tyl with + | nil => ofs + | Tint :: tys => size_arguments_rec tys (ofs + 1) + | (Tfloat | Tlong) :: tys => size_arguments_rec tys (align ofs 2 + 2) + end. + +Definition size_arguments (s: signature) : Z := + Zmax 0 (size_arguments_rec s.(sig_args) (-4)). + +(** Argument locations are either non-temporary registers or [Outgoing] + stack slots at nonnegative offsets. *) + +Definition loc_argument_acceptable (l: loc) : Prop := + match l with + | R r => In r destroyed_at_call + | S Outgoing ofs ty => ofs >= 0 /\ ty <> Tlong + | _ => False + end. + +(* +Lemma align_monotone: + forall x1 x2 y, y > 0 -> x1 <= x2 -> align x1 y <= align x2 y. +Proof. + intros. unfold align. apply Zmult_le_compat_r. apply Z_div_le. + omega. omega. omega. +Qed. +*) + +Remark ireg_param_caller_save: + forall n, In (ireg_param n) destroyed_at_call. +Proof. + unfold ireg_param; intros. + destruct (zeq n (-4)). simpl; auto. + destruct (zeq n (-3)). simpl; auto. + destruct (zeq n (-2)); simpl; auto. +Qed. + +Remark freg_param_caller_save: + forall n, In (freg_param n) destroyed_at_call. +Proof. + unfold freg_param; intros. destruct (zeq n (-4)); simpl; OrEq. +Qed. + +Remark loc_arguments_rec_charact: + forall tyl ofs l, + In l (loc_arguments_rec tyl ofs) -> + match l with + | R r => In r destroyed_at_call + | S Outgoing ofs' ty => ofs' >= 0 /\ ofs <= ofs' /\ ty <> Tlong + | S _ _ _ => False + end. +Proof. + induction tyl; simpl loc_arguments_rec; intros. + elim H. + destruct a. +- (* Tint *) + destruct H. + subst l. destruct (zle 0 ofs). + split. omega. split. omega. congruence. + apply ireg_param_caller_save. + exploit IHtyl; eauto. destruct l; auto. destruct sl; auto. intuition omega. +- (* Tfloat *) + assert (ofs <= align ofs 2) by (apply align_le; omega). + destruct H. + subst l. destruct (zle 0 (align ofs 2)). + split. omega. split. auto. congruence. + apply freg_param_caller_save. + exploit IHtyl; eauto. destruct l; auto. destruct sl; auto. intuition omega. +- (* Tlong *) + assert (ofs <= align ofs 2) by (apply align_le; omega). + destruct H. + subst l. destruct (zle 0 (align ofs 2)). + split. omega. split. omega. congruence. + apply ireg_param_caller_save. + destruct H. + subst l. destruct (zle 0 (align ofs 2)). + split. omega. split. omega. congruence. + apply ireg_param_caller_save. + exploit IHtyl; eauto. destruct l; auto. destruct sl; auto. intuition omega. +Qed. + +Lemma loc_arguments_acceptable: + forall (s: signature) (r: loc), + In r (loc_arguments s) -> loc_argument_acceptable r. +Proof. + unfold loc_arguments, loc_argument_acceptable; intros. + generalize (loc_arguments_rec_charact _ _ _ H). + destruct r; auto. + destruct sl; auto. + tauto. +Qed. +Hint Resolve loc_arguments_acceptable: locs. + +(** The offsets of [Outgoing] arguments are below [size_arguments s]. *) + +Remark size_arguments_rec_above: + forall tyl ofs, + ofs <= size_arguments_rec tyl ofs. +Proof. + induction tyl; simpl; intros. + omega. + destruct a. + apply Zle_trans with (ofs + 1); auto; omega. + assert (ofs <= align ofs 2) by (apply align_le; omega). + apply Zle_trans with (align ofs 2 + 2); auto; omega. + assert (ofs <= align ofs 2) by (apply align_le; omega). + apply Zle_trans with (align ofs 2 + 2); auto; omega. +Qed. + +Lemma size_arguments_above: + forall s, size_arguments s >= 0. +Proof. + intros; unfold size_arguments. apply Zle_ge. apply Zmax1. +Qed. + +Lemma loc_arguments_bounded: + forall (s: signature) (ofs: Z) (ty: typ), + In (S Outgoing ofs ty) (loc_arguments s) -> + ofs + typesize ty <= size_arguments s. +Proof. + intros. + assert (forall tyl ofs0, + 0 <= ofs0 -> + ofs0 <= Zmax 0 (size_arguments_rec tyl ofs0)). + { + intros. generalize (size_arguments_rec_above tyl ofs0). intros. + rewrite Zmax_spec. rewrite zlt_false. auto. omega. + } + assert (forall tyl ofs0, + In (S Outgoing ofs ty) (loc_arguments_rec tyl ofs0) -> + ofs + typesize ty <= Zmax 0 (size_arguments_rec tyl ofs0)). + { + induction tyl; simpl; intros. + elim H1. + destruct a. + - (* Tint *) + destruct H1; auto. destruct (zle 0 ofs0); inv H1. apply H0. omega. + - (* Tfloat *) + destruct H1; auto. destruct (zle 0 (align ofs0 2)); inv H1. apply H0. omega. + - (* Tlong *) + destruct H1. + destruct (zle 0 (align ofs0 2)); inv H1. + eapply Zle_trans. 2: apply H0. simpl typesize; omega. omega. + destruct H1; auto. + destruct (zle 0 (align ofs0 2)); inv H1. + eapply Zle_trans. 2: apply H0. simpl typesize; omega. omega. + } + unfold size_arguments. apply H1. auto. +Qed. |