diff options
Diffstat (limited to 'backend/CSE2.v')
| -rw-r--r-- | backend/CSE2.v | 140 |
1 files changed, 104 insertions, 36 deletions
diff --git a/backend/CSE2.v b/backend/CSE2.v index 38a46c1b..41adba7b 100644 --- a/backend/CSE2.v +++ b/backend/CSE2.v @@ -29,13 +29,30 @@ Proof. decide equality. Defined. +Definition pset := PTree.t unit. + +Definition pset_inter : pset -> pset -> pset := + PTree.combine_null + (fun ov1 ov2 => Some tt). + +Definition pset_empty : pset := PTree.empty unit. +Definition pset_add (i : positive) (s : pset) := PTree.set i tt s. +Definition pset_remove (i : positive) (s : pset) := PTree.remove i s. + +Record relmap := mkrel { + var_to_sym : PTree.t sym_val ; + mem_used : pset ; + reg_used : PTree.t pset + }. + Module RELATION. - -Definition t := (PTree.t sym_val). + +Definition t := relmap. + Definition eq (r1 r2 : t) := - forall x, (PTree.get x r1) = (PTree.get x r2). + forall x, (PTree.get x (var_to_sym r1)) = (PTree.get x (var_to_sym r2)). -Definition top : t := PTree.empty sym_val. +Definition top : t := mkrel (PTree.empty sym_val) pset_empty (PTree.empty pset). Lemma eq_refl: forall x, eq x x. Proof. @@ -58,27 +75,27 @@ Qed. Definition sym_val_beq (x y : sym_val) := if eq_sym_val x y then true else false. -Definition beq (r1 r2 : t) := PTree.beq sym_val_beq r1 r2. +Definition beq (r1 r2 : t) := PTree.beq sym_val_beq (var_to_sym r1) (var_to_sym r2). Lemma beq_correct: forall r1 r2, beq r1 r2 = true -> eq r1 r2. Proof. unfold beq, eq. intros r1 r2 EQ x. - pose proof (PTree.beq_correct sym_val_beq r1 r2) as CORRECT. + pose proof (PTree.beq_correct sym_val_beq (var_to_sym r1) (var_to_sym r2)) as CORRECT. destruct CORRECT as [CORRECTF CORRECTB]. pose proof (CORRECTF EQ x) as EQx. clear CORRECTF CORRECTB EQ. unfold sym_val_beq in *. - destruct (r1 ! x) as [R1x | ] in *; - destruct (r2 ! x) as [R2x | ] in *; + destruct ((var_to_sym r1) ! x) as [R1x | ] in *; + destruct ((var_to_sym r2) ! x) as [R2x | ] in *; trivial; try contradiction. destruct (eq_sym_val R1x R2x) in *; congruence. Qed. Definition ge (r1 r2 : t) := forall x, - match PTree.get x r1 with + match PTree.get x (var_to_sym r1) with | None => True - | Some v => (PTree.get x r2) = Some v + | Some v => (PTree.get x (var_to_sym r2)) = Some v end. Lemma ge_refl: forall r1 r2, eq r1 r2 -> ge r1 r2. @@ -87,7 +104,7 @@ Proof. intros r1 r2 EQ x. pose proof (EQ x) as EQx. clear EQ. - destruct (r1 ! x). + destruct ((var_to_sym r1) ! x). - congruence. - trivial. Qed. @@ -98,12 +115,13 @@ Proof. intros r1 r2 r3 GE12 GE23 x. pose proof (GE12 x) as GE12x; clear GE12. pose proof (GE23 x) as GE23x; clear GE23. - destruct (r1 ! x); trivial. - destruct (r2 ! x); congruence. + destruct ((var_to_sym r1) ! x); trivial. + destruct ((var_to_sym r2) ! x); congruence. Qed. Definition lub (r1 r2 : t) := - PTree.combine + mkrel + (PTree.combine (fun ov1 ov2 => match ov1, ov2 with | (Some v1), (Some v2) => @@ -113,12 +131,19 @@ Definition lub (r1 r2 : t) := | None, _ | _, None => None end) - r1 r2. + (var_to_sym r1) (var_to_sym r2)) + (pset_inter (mem_used r1) (mem_used r2)) + (PTree.combine_null + (fun x y => let r := pset_inter x y in + if PTree.bempty_canon r + then None + else Some r) + (reg_used r1) (reg_used r2)). Lemma ge_lub_left: forall x y, ge (lub x y) x. Proof. unfold ge, lub. - intros r1 r2 x. + intros r1 r2 x. simpl. rewrite PTree.gcombine by reflexivity. destruct (_ ! _); trivial. destruct (_ ! _); trivial. @@ -128,7 +153,7 @@ Qed. Lemma ge_lub_right: forall x y, ge (lub x y) y. Proof. unfold ge, lub. - intros r1 r2 x. + intros r1 r2 x. simpl. rewrite PTree.gcombine by reflexivity. destruct (_ ! _); trivial. destruct (_ ! _); trivial. @@ -250,21 +275,53 @@ Module ADD_BOTTOM(L : SEMILATTICE_WITHOUT_BOTTOM). - apply L.ge_refl. apply L.eq_refl. Qed. + + Definition top := Some RELATION.top. End ADD_BOTTOM. Module RB := ADD_BOTTOM(RELATION). Module DS := Dataflow_Solver(RB)(NodeSetForward). -Definition kill_sym_val (dst : reg) (sv : sym_val) := +Definition kill_sym_val (dst : reg) (sv : sym_val) : bool := match sv with | SMove src => if peq dst src then true else false | SOp op args => List.existsb (peq dst) args | SLoad chunk addr args => List.existsb (peq dst) args end. - -Definition kill_reg (dst : reg) (rel : RELATION.t) := - PTree.filter1 (fun x => negb (kill_sym_val dst x)) - (PTree.remove dst rel). + +Definition referenced_by sv := + match sv with + | SMove src => src :: nil + | SOp op args => args + | SLoad chunk addr args => args + end. + +Definition referenced_by' osv := + match osv with + | None => nil + | Some sv => referenced_by sv + end. + +Definition remove_from_sets + (to_remove : reg) : + list reg -> PTree.t pset -> PTree.t pset := + List.fold_left + (fun sets reg => + match PTree.get reg sets with + | None => sets + | Some xset => + let xset' := PTree.remove to_remove xset in + if PTree.bempty_canon xset' + then PTree.remove reg sets + else PTree.set reg xset' sets + end). + +Definition kill_reg (dst : reg) (rel : RELATION.t) : RELATION.t := + let rel' := PTree.remove dst (var_to_sym rel) in + mkrel (PTree.filter1 (fun x => negb (kill_sym_val dst x)) rel') + (pset_remove dst (mem_used rel)) + (remove_from_sets dst (referenced_by' (PTree.get dst (var_to_sym rel))) + (PTree.remove dst (reg_used rel))). Definition kill_sym_val_mem (sv: sym_val) := match sv with @@ -274,17 +331,23 @@ Definition kill_sym_val_mem (sv: sym_val) := end. Definition kill_mem (rel : RELATION.t) := - PTree.filter1 (fun x => negb (kill_sym_val_mem x)) rel. + mkrel + (PTree.remove_t (var_to_sym rel) (mem_used rel)) + pset_empty + (reg_used rel). (* FIXME *) Definition forward_move (rel : RELATION.t) (x : reg) : reg := - match rel ! x with + match (var_to_sym rel) ! x with | Some (SMove org) => org | _ => x end. Definition move (src dst : reg) (rel : RELATION.t) := - PTree.set dst (SMove (forward_move rel src)) (kill_reg dst rel). + let rel0 := kill_reg dst rel in + mkrel (PTree.set dst (SMove (forward_move rel src)) (var_to_sym rel0)) + (mem_used rel0) + (reg_used rel0). (* FIXME *) Definition find_op_fold op args (already : option reg) x sv := match already with @@ -300,7 +363,7 @@ Definition find_op_fold op args (already : option reg) x sv := end. Definition find_op (rel : RELATION.t) (op : operation) (args : list reg) := - PTree.fold (find_op_fold op args) rel None. + PTree.fold (find_op_fold op args) (var_to_sym rel) None. Definition find_load_fold chunk addr args (already : option reg) x sv := match already with @@ -318,37 +381,42 @@ Definition find_load_fold chunk addr args (already : option reg) x sv := end. Definition find_load (rel : RELATION.t) (chunk : memory_chunk) (addr : addressing) (args : list reg) := - PTree.fold (find_load_fold chunk addr args) rel None. + PTree.fold (find_load_fold chunk addr args) (var_to_sym rel) None. Definition oper2 (op: operation) (dst : reg) (args : list reg) - (rel : RELATION.t) := + (rel : RELATION.t) : RELATION.t := let rel' := kill_reg dst rel in - PTree.set dst (SOp op (List.map (forward_move rel') args)) rel'. + mkrel (PTree.set dst (SOp op (List.map (forward_move rel') args)) (var_to_sym rel')) + (if op_depends_on_memory op then (pset_add dst (mem_used rel')) + else mem_used rel') + (reg_used rel'). (* FIXME *) Definition oper1 (op: operation) (dst : reg) (args : list reg) - (rel : RELATION.t) := + (rel : RELATION.t) : RELATION.t := if List.in_dec peq dst args then kill_reg dst rel else oper2 op dst args rel. Definition oper (op: operation) (dst : reg) (args : list reg) - (rel : RELATION.t) := + (rel : RELATION.t) : RELATION.t := match find_op rel op (List.map (forward_move rel) args) with | Some r => move r dst rel | None => oper1 op dst args rel end. Definition gen_oper (op: operation) (dst : reg) (args : list reg) - (rel : RELATION.t) := + (rel : RELATION.t) : RELATION.t := match op, args with | Omove, src::nil => move src dst rel | _, _ => oper op dst args rel end. Definition load2 (chunk: memory_chunk) (addr : addressing) - (dst : reg) (args : list reg) (rel : RELATION.t) := + (dst : reg) (args : list reg) (rel : RELATION.t) : RELATION.t := let rel' := kill_reg dst rel in - PTree.set dst (SLoad chunk addr (List.map (forward_move rel') args)) rel'. + mkrel (PTree.set dst (SLoad chunk addr (List.map (forward_move rel') args)) (var_to_sym rel')) + (pset_add dst (mem_used rel')) + (reg_used rel'). (* FIXME *) Definition load1 (chunk: memory_chunk) (addr : addressing) (dst : reg) (args : list reg) (rel : RELATION.t) := @@ -415,7 +483,7 @@ Definition apply_instr' code (pc : node) (ro : RB.t) : RB.t := Definition forward_map (f : RTL.function) := DS.fixpoint (RTL.fn_code f) RTL.successors_instr - (apply_instr' (RTL.fn_code f)) (RTL.fn_entrypoint f) (Some RELATION.top). + (apply_instr' (RTL.fn_code f)) (RTL.fn_entrypoint f) RB.top. Definition forward_move_b (rb : RB.t) (x : reg) := match rb with @@ -457,7 +525,7 @@ Definition transf_instr (fmap : option (PMap.t RB.t)) match instr with | Iop op args dst s => let args' := subst_args fmap pc args in - match find_op_in_fmap fmap pc op args' with + match (if is_trivial_op op then None else find_op_in_fmap fmap pc op args') with | None => Iop op args' dst s | Some src => Iop Omove (src::nil) dst s end |