Module Conventions

Function calling conventions and other conventions regarding the use of machine registers and stack slots.

Require Import Coqlib.
Require Import AST.
Require Import Locations.
Require Export Conventions1.

The processor-dependent and EABI-dependent definitions are in arch/abi/Conventions1.v. This file adds various processor-independent definitions and lemmas.

Acceptable locations for register allocation

The following predicate describes the locations that can be assigned to an RTL pseudo-register during register allocation: a non-temporary machine register or a Local stack slot are acceptable.

Definition loc_acceptable (l: loc) : Prop :=
  match l with
  | R r => ~(In l temporaries)
  | S (Local ofs ty) => ofs >= 0
  | S (Incoming _ _) => False
  | S (Outgoing _ _) => False

Definition locs_acceptable (ll: list loc) : Prop :=
  forall l, In l ll -> loc_acceptable l.

Lemma temporaries_not_acceptable:
  forall l, loc_acceptable l -> Loc.notin l temporaries.
  unfold loc_acceptable; destruct l.
  simpl. intuition congruence.
  destruct s; try contradiction.
  intro. simpl. tauto.
Hint Resolve temporaries_not_acceptable: locs.

Lemma locs_acceptable_disj_temporaries:
  forall ll, locs_acceptable ll -> Loc.disjoint ll temporaries.
  intros. apply Loc.notin_disjoint. intros.
  apply temporaries_not_acceptable. auto.

Lemma loc_acceptable_noteq_diff:
  forall l1 l2,
  loc_acceptable l1 -> l1 <> l2 -> Loc.diff l1 l2.
  unfold loc_acceptable, Loc.diff; destruct l1; destruct l2;
  try (destruct s); try (destruct s0); intros; auto; try congruence.
  case (zeq z z0); intro.
  compare t t0; intro.
  subst z0; subst t0; tauto.
  tauto. tauto.
  contradiction. contradiction.

Lemma loc_acceptable_notin_notin:
  forall r ll,
  loc_acceptable r ->
  ~(In r ll) -> Loc.notin r ll.
  induction ll; simpl; intros.
  split. apply loc_acceptable_noteq_diff. assumption.
  apply sym_not_equal. tauto.
  apply IHll. assumption. tauto.

Additional properties of result and argument locations

The result location is not a callee-save register.

Lemma loc_result_not_callee_save:
  forall (s: signature),
  ~(In (loc_result s) int_callee_save_regs \/ In (loc_result s) float_callee_save_regs).
  intros. generalize (loc_result_caller_save s).
  generalize (int_callee_save_not_destroyed (loc_result s)).
  generalize (float_callee_save_not_destroyed (loc_result s)).

Callee-save registers do not overlap with argument locations.

Lemma arguments_not_preserved:
  forall sig l,
  Loc.notin l destroyed_at_call -> loc_acceptable l ->
  Loc.notin l (loc_arguments sig).
  intros. destruct l; red in H0.
  apply Loc.reg_notin. red; intros.
  exploit Loc.notin_not_in; eauto. eapply arguments_caller_save; eauto.
  destruct s; try contradiction.
  unfold loc_arguments. apply loc_arguments_rec_notin_local.

There is no partial overlap between arguments and acceptable locations.

Lemma no_overlap_arguments:
  forall args sg,
  locs_acceptable args ->
  Loc.no_overlap args (loc_arguments sg).
  unfold Loc.no_overlap; intros.
  generalize (H r H0).
  generalize (loc_arguments_acceptable _ _ H1).
  destruct s; destruct r; simpl.
  intros. case (mreg_eq m0 m); intro. left; congruence. tauto.
  intros. right; destruct s; auto.
  intros. right. auto.
  destruct s; try tauto. destruct s0; tauto.

Location of function parameters

A function finds the values of its parameter in the same locations where its caller stored them, except that the stack-allocated arguments, viewed as Outgoing slots by the caller, are accessed via Incoming slots (at the same offsets and types) in the callee.

Definition parameter_of_argument (l: loc) : loc :=
  match l with
  | S (Outgoing n ty) => S (Incoming n ty)
  | _ => l

Definition loc_parameters (s: signature) := parameter_of_argument (loc_arguments s).

Lemma loc_parameters_type:
  forall sig, Loc.type (loc_parameters sig) = sig.(sig_args).
  intros. unfold loc_parameters.
  rewrite list_map_compose.
  rewrite <- loc_arguments_type.
  apply list_map_exten.
  intros. destruct x; simpl. auto.
  destruct s; reflexivity.

Lemma loc_parameters_length:
  forall sg, List.length (loc_parameters sg) = List.length sg.(sig_args).
  intros. unfold loc_parameters. rewrite list_length_map.
  apply loc_arguments_length.

Lemma loc_parameters_not_temporaries:
  forall sig, Loc.disjoint (loc_parameters sig) temporaries.
  intro; red; intros.
  unfold loc_parameters in H.
  elim (list_in_map_inv _ _ _ H). intros y [EQ IN].
  generalize (loc_arguments_not_temporaries sig y x2 IN H0).
  subst x1. destruct x2.
  destruct y; simpl. auto. destruct s; auto.
  byContradiction. generalize H0. simpl. NotOrEq.

Lemma no_overlap_parameters:
  forall params sg,
  locs_acceptable params ->
  Loc.no_overlap (loc_parameters sg) params.
  unfold Loc.no_overlap; intros.
  unfold loc_parameters in H0.
  elim (list_in_map_inv _ _ _ H0). intros t [EQ IN].
  rewrite EQ.
  generalize (loc_arguments_acceptable _ _ IN).
  generalize (H s H1).
  destruct s; destruct t; simpl.
  intros. case (mreg_eq m0 m); intro. left; congruence. tauto.
  intros. right; destruct s; simpl; auto.
  intros; right; auto.
  destruct s; try tauto. destruct s0; try tauto.
  intros; simpl. tauto.

Lemma incoming_slot_in_parameters:
  forall ofs ty sg,
  In (S (Incoming ofs ty)) (loc_parameters sg) ->
  In (S (Outgoing ofs ty)) (loc_arguments sg).
  unfold loc_parameters in H.
  change (S (Incoming ofs ty)) with (parameter_of_argument (S (Outgoing ofs ty))) in H.
  exploit list_in_map_inv. eexact H. intros [x [A B]]. simpl in A.
  exploit loc_arguments_acceptable; eauto. unfold loc_argument_acceptable; intros.
  destruct x; simpl in A; try discriminate.
  destruct s; try contradiction.
  inv A. auto.

Tail calls

A tail-call is possible for a signature if the corresponding arguments are all passed in registers.

Definition tailcall_possible (s: signature) : Prop :=
  forall l, In l (loc_arguments s) ->
  match l with R _ => True | S _ => False end.

Decide whether a tailcall is possible.

Definition tailcall_is_possible (sg: signature) : bool :=
  let fix tcisp (l: list loc) :=
    match l with
    | nil => true
    | R _ :: l' => tcisp l'
    | S _ :: l' => false
  in tcisp (loc_arguments sg).

Lemma tailcall_is_possible_correct:
  forall s, tailcall_is_possible s = true -> tailcall_possible s.
  intro s. unfold tailcall_is_possible, tailcall_possible.
  generalize (loc_arguments s). induction l; simpl; intros.
  elim H0.
  destruct a.
  destruct H0. subst l0. auto. apply IHl. auto. auto. discriminate.

Counting temporaries

Given a list tys of types representing arguments to an operator, arity_ok tys returns true if there are enough temporaries to reload all arguments into temporaries.

Fixpoint arity_ok_rec (tys: list typ) (itmps ftmps: list mreg)
                      {struct tys} : bool :=
  match tys with
  | nil => true
  | Tint :: ts =>
      match itmps with
      | nil => false
      | it1 :: its => arity_ok_rec ts its ftmps
  | Tfloat :: ts =>
      match ftmps with
      | nil => false
      | ft1 :: fts => arity_ok_rec ts itmps fts

Definition arity_ok (tys: list typ) :=
  arity_ok_rec tys int_temporaries float_temporaries.