Library 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.

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/MacOSX application binary interface (ABI) in our choice of callee- and caller-save registers.

Definition int_caller_save_regs :=
  R3 :: R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: nil.

Definition float_caller_save_regs :=
  F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: F8 :: F9 :: F10 :: nil.

Definition int_callee_save_regs :=
  R14 :: R15 :: R16 :: R17 :: R18 :: R19 :: R20 :: R21 :: R22 ::
  R23 :: R24 :: R25 :: R26 :: R27 :: R28 :: R29 :: R30 :: R31 :: nil.

Definition float_callee_save_regs :=
  F14 :: F15 :: F16 :: F17 :: F18 :: F19 :: F20 :: F21 :: F22 ::
  F23 :: F24 :: F25 :: F26 :: F27 :: F28 :: F29 :: F30 :: F31 :: nil.

Definition destroyed_at_call_regs :=
  int_caller_save_regs ++ float_caller_save_regs.

Definition destroyed_at_call :=
  List.map R destroyed_at_call_regs.

Definition int_temporaries := IT1 :: IT2 :: nil.

Definition float_temporaries := FT1 :: FT2 :: FT3 :: nil.

Definition temporaries :=
  R IT1 :: R IT2 :: R FT1 :: R FT2 :: R FT3 :: nil.

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
  | R14 => 0 | R15 => 1 | R16 => 2 | R17 => 3
  | R18 => 4 | R19 => 5 | R20 => 6 | R21 => 7
  | R22 => 8 | R23 => 9 | R24 => 10 | R25 => 11
  | R26 => 12 | R27 => 13 | R28 => 14 | R29 => 15
  | R30 => 16 | R31 => 17 | _ => -1
  end.

Definition index_float_callee_save (r: mreg) :=
  match r with
  | F14 => 0 | F15 => 1 | F16 => 2 | F17 => 3
  | F18 => 4 | F19 => 5 | F20 => 6 | F21 => 7
  | F22 => 8 | F23 => 9 | F24 => 10 | F25 => 11
  | F26 => 12 | F27 => 13 | F28 => 14 | F29 => 15
  | F30 => 16 | F31 => 17 | _ => -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.


Lemma index_float_callee_save_pos:
  forall r, In r float_callee_save_regs -> index_float_callee_save r >= 0.


Lemma index_int_callee_save_pos2:
  forall r, index_int_callee_save r >= 0 -> In r int_callee_save_regs.


Lemma index_float_callee_save_pos2:
  forall r, index_float_callee_save r >= 0 -> In r float_callee_save_regs.


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.


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.


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.


Lemma register_classification:
  forall r,
  (In (R r) temporaries \/ In (R r) destroyed_at_call) \/
  (In r int_callee_save_regs \/ In r float_callee_save_regs).


Lemma int_callee_save_not_destroyed:
  forall r,
    In (R r) temporaries \/ In (R r) destroyed_at_call ->
    ~(In r int_callee_save_regs).


Lemma float_callee_save_not_destroyed:
  forall r,
    In (R r) temporaries \/ In (R r) destroyed_at_call ->
    ~(In r float_callee_save_regs).


Lemma int_callee_save_type:
  forall r, In r int_callee_save_regs -> mreg_type r = Tint.


Lemma float_callee_save_type:
  forall r, In r float_callee_save_regs -> mreg_type r = Tfloat.


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.


Lemma float_callee_save_norepet:
  list_norepet float_callee_save_regs.


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
  end.

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.

Hint Resolve temporaries_not_acceptable: locs.

Lemma locs_acceptable_disj_temporaries:
  forall ll, locs_acceptable ll -> Loc.disjoint ll temporaries.


Lemma loc_acceptable_noteq_diff:
  forall l1 l2,
  loc_acceptable l1 -> l1 <> l2 -> Loc.diff l1 l2.


Lemma loc_acceptable_notin_notin:
  forall r ll,
  loc_acceptable r ->
  ~(In r ll) -> Loc.notin r ll.


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. To ensure binary interoperability of code generated by our compiler with libraries compiled by another PowerPC compiler, we implement the standard conventions defined in the PowerPC/MacOS X application binary interface.

Location of function result


The result value of a function is passed back to the caller in registers R3 or F1, 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) : mreg :=
  match s.(sig_res) with
  | None => R3
  | Some Tint => R3
  | Some Tfloat => F1
  end.

The result location has the type stated in the signature.

Lemma loc_result_type:
  forall sig,
  mreg_type (loc_result sig) =
  match sig.(sig_res) with None => Tint | Some ty => ty end.


The result location is acceptable.

Lemma loc_result_acceptable:
  forall sig, loc_acceptable (R (loc_result sig)).


The result location is a caller-save register.

Lemma loc_result_caller_save:
  forall (s: signature), In (R (loc_result s)) destroyed_at_call.


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).


Location of function arguments


The PowerPC ABI states the following convention for passing arguments to a function:
  • The first 8 integer arguments are passed in registers R3 to R10.
  • The first 10 float arguments are passed in registers F1 to F10.
  • Each float argument passed in a float register ``consumes'' two integer arguments.
  • Extra arguments are passed on the stack, in Outgoing slots, consecutively assigned (1 word for an integer argument, 2 words for a float), starting at word offset 0.
  • Stack space is reserved (as unused Outgoing slots) for the arguments that are passed in registers.


These conventions are somewhat baroque, but they are mandated by the ABI.

Fixpoint loc_arguments_rec
    (tyl: list typ) (iregl: list mreg) (fregl: list mreg)
    (ofs: Z) {struct tyl} : list loc :=
  match tyl with
  | nil => nil
  | Tint :: tys =>
      match iregl with
      | nil =>
          S (Outgoing ofs Tint) :: loc_arguments_rec tys nil fregl (ofs + 1)
      | ireg :: iregs =>
          R ireg :: loc_arguments_rec tys iregs fregl ofs
      end
  | Tfloat :: tys =>
      match fregl with
      | nil =>
          S (Outgoing ofs Tfloat) :: loc_arguments_rec tys iregl nil (ofs + 2)
      | freg :: fregs =>
          R freg :: loc_arguments_rec tys (list_drop 2%nat iregl) fregs ofs
      end
  end.

Definition int_param_regs :=
  R3 :: R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: nil.
Definition float_param_regs :=
  F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: F8 :: F9 :: F10 :: nil.

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) int_param_regs float_param_regs 8.

size_arguments s returns the number of Outgoing slots used to call a function with signature s.

Fixpoint size_arguments_rec
    (tyl: list typ) (iregl: list mreg) (fregl: list mreg)
    (ofs: Z) {struct tyl} : Z :=
  match tyl with
  | nil => ofs
  | Tint :: tys =>
      match iregl with
      | nil => size_arguments_rec tys nil fregl (ofs + 1)
      | ireg :: iregs => size_arguments_rec tys iregs fregl ofs
      end
  | Tfloat :: tys =>
      match fregl with
      | nil => size_arguments_rec tys iregl nil (ofs + 2)
      | freg :: fregs => size_arguments_rec tys (list_drop 2%nat iregl) fregs ofs
      end
  end.

Definition size_arguments (s: signature) : Z :=
  size_arguments_rec s.(sig_args) int_param_regs float_param_regs 8.

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.

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 l temporaries)
  | S (Outgoing ofs ty) => ofs >= 0
  | _ => False
  end.

Remark loc_arguments_rec_charact:
  forall tyl iregl fregl ofs l,
  In l (loc_arguments_rec tyl iregl fregl ofs) ->
  match l with
  | R r => In r iregl \/ In r fregl
  | S (Outgoing ofs' ty) => ofs' >= ofs
  | S _ => False
  end.


Lemma loc_arguments_acceptable:
  forall (s: signature) (r: loc),
  In r (loc_arguments s) -> loc_argument_acceptable r.

Hint Resolve loc_arguments_acceptable: locs.

Arguments are parwise disjoint (in the sense of Loc.norepet).

Remark loc_arguments_rec_notin_reg:
  forall tyl iregl fregl ofs r,
  ~(In r iregl) -> ~(In r fregl) ->
  Loc.notin (R r) (loc_arguments_rec tyl iregl fregl ofs).


Remark loc_arguments_rec_notin_local:
  forall tyl iregl fregl ofs ofs0 ty0,
  Loc.notin (S (Local ofs0 ty0)) (loc_arguments_rec tyl iregl fregl ofs).


Remark loc_arguments_rec_notin_outgoing:
  forall tyl iregl fregl ofs ofs0 ty0,
  ofs0 + typesize ty0 <= ofs ->
  Loc.notin (S (Outgoing ofs0 ty0)) (loc_arguments_rec tyl iregl fregl ofs).


Lemma loc_arguments_norepet:
  forall (s: signature), Loc.norepet (loc_arguments s).


The offsets of Outgoing arguments are below size_arguments s.

Remark size_arguments_rec_above:
  forall tyl iregl fregl ofs0,
  ofs0 <= size_arguments_rec tyl iregl fregl ofs0.


Lemma size_arguments_above:
  forall s, size_arguments s >= 0.


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.


Temporary registers do not overlap with argument locations.

Lemma loc_arguments_not_temporaries:
  forall sig, Loc.disjoint (loc_arguments sig) temporaries.

Hint Resolve loc_arguments_not_temporaries: locs.

Argument registers are caller-save.

Lemma arguments_caller_save:
  forall sig r,
  In (R r) (loc_arguments sig) -> In (R r) destroyed_at_call.


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).

Hint Resolve arguments_not_preserved: locs.

Argument locations agree in number with the function signature.

Lemma loc_arguments_length:
  forall sig,
  List.length (loc_arguments sig) = List.length sig.(sig_args).


Argument locations agree in types with the function signature.

Lemma loc_arguments_type:
  forall sig, List.map Loc.type (loc_arguments sig) = sig.(sig_args).


There is no partial overlap between an argument location and an acceptable location: they are either identical or disjoint.

Lemma no_overlap_arguments:
  forall args sg,
  locs_acceptable args ->
  Loc.no_overlap args (loc_arguments sg).


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
    end
  in tcisp (loc_arguments sg).

Lemma tailcall_is_possible_correct:
  forall s, tailcall_is_possible s = true -> tailcall_possible s.


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
  end.

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

Lemma loc_parameters_type:
  forall sig, List.map Loc.type (loc_parameters sig) = sig.(sig_args).


Lemma loc_parameters_length:
  forall sg, List.length (loc_parameters sg) = List.length sg.(sig_args).


Lemma loc_parameters_not_temporaries:
  forall sig, Loc.disjoint (loc_parameters sig) temporaries.


Lemma no_overlap_parameters:
  forall params sg,
  locs_acceptable params ->
  Loc.no_overlap (loc_parameters sg) params.