Module Deadcode

Elimination of unneeded computations over RTL.

Require Import Coqlib Maps Errors Integers Floats Lattice Kildall.
Require Import AST Linking.
Require Import Memory Registers Op RTL.
Require Import ValueDomain ValueAnalysis NeedDomain NeedOp.

Part 1: the static analysis

Definition add_need_all (r: reg) (ne: nenv) : nenv :=
  NE.set r All ne.

Definition add_need (r: reg) (nv: nval) (ne: nenv) : nenv :=
  NE.set r (nlub nv (NE.get r ne)) ne.

Fixpoint add_needs_all (rl: list reg) (ne: nenv) : nenv :=
  match rl with
  | nil => ne
  | r1 :: rs => add_need_all r1 (add_needs_all rs ne)

Fixpoint add_needs (rl: list reg) (nvl: list nval) (ne: nenv) : nenv :=
  match rl, nvl with
  | nil, _ => ne
  | r1 :: rs, nil => add_needs_all rl ne
  | r1 :: rs, nv1 :: nvs => add_need r1 nv1 (add_needs rs nvs ne)

Definition add_ros_need_all (ros: reg + ident) (ne: nenv) : nenv :=
  match ros with
  | inl r => add_need_all r ne
  | inr s => ne

Definition add_opt_need_all (or: option reg) (ne: nenv) : nenv :=
  match or with
  | Some r => add_need_all r ne
  | None => ne

Definition kill (r: reg) (ne: nenv) : nenv := NE.set r Nothing ne.

Definition is_dead (v: nval) :=
  match v with Nothing => true | _ => false end.

Definition is_int_zero (v: nval) :=
  match v with I n => Int.eq n | _ => false end.

Fixpoint transfer_builtin_arg (nv: nval) (na: NA.t) (a: builtin_arg reg) : NA.t :=
  let (ne, nm) := na in
  match a with
  | BA r => (add_need r nv ne, nm)
  | BA_int _ | BA_long _ | BA_float _ | BA_single _
  | BA_addrstack _ | BA_addrglobal _ _ => (ne, nm)
  | BA_loadstack chunk ofs => (ne, nmem_add nm (Stk ofs) (size_chunk chunk))
  | BA_loadglobal chunk id ofs => (ne, nmem_add nm (Gl id ofs) (size_chunk chunk))
  | BA_splitlong hi lo =>
      transfer_builtin_arg All (transfer_builtin_arg All na hi) lo

Definition transfer_builtin_args (na: NA.t) (al: list (builtin_arg reg)) : NA.t :=
  List.fold_left (transfer_builtin_arg All) al na.

Definition kill_builtin_res (res: builtin_res reg) (ne: NE.t) : NE.t :=
  match res with
  | BR r => kill r ne
  | _ => ne

Function transfer_builtin (app: VA.t) (ef: external_function)
                          (args: list (builtin_arg reg)) (res: builtin_res reg)
                          (ne: NE.t) (nm: nmem) : NA.t :=
  match ef, args with
  | EF_vload chunk, a1::nil =>
      transfer_builtin_arg All
        (kill_builtin_res res ne,
         nmem_add nm (aaddr_arg app a1) (size_chunk chunk))
  | EF_vstore chunk, a1::a2::nil =>
      transfer_builtin_arg All
          (transfer_builtin_arg (store_argument chunk)
                                (kill_builtin_res res ne, nm) a2)
  | EF_memcpy sz al, dst::src::nil =>
      if nmem_contains nm (aaddr_arg app dst) sz then
           (kill_builtin_res res ne,
            nmem_add (nmem_remove nm (aaddr_arg app dst) sz) (aaddr_arg app src) sz)
      else (ne, nm)
  | (EF_annot _ _ | EF_annot_val _ _), _ =>
      transfer_builtin_args (kill_builtin_res res ne, nm) args
  | EF_debug _ _ _, _ =>
      (kill_builtin_res res ne, nm)
  | _, _ =>
      transfer_builtin_args (kill_builtin_res res ne, nmem_all) args

Definition transfer (f: function) (approx: PMap.t VA.t)
                    (pc: node) (after: NA.t) : NA.t :=
  let (ne, nm) := after in
  match f.(fn_code)!pc with
  | None =>
  | Some (Inop s) =>
  | Some (Iop op args res s) =>
      let nres := nreg ne res in
      if is_dead nres then after
      else if is_int_zero nres then (kill res ne, nm)
      else (add_needs args (needs_of_operation op nres) (kill res ne), nm)
  | Some (Iload chunk addr args dst s) =>
      let ndst := nreg ne dst in
      if is_dead ndst then after
      else if is_int_zero ndst then (kill dst ne, nm)
      else (add_needs_all args (kill dst ne),
            nmem_add nm (aaddressing approx!!pc addr args) (size_chunk chunk))
  | Some (Istore chunk addr args src s) =>
      let p := aaddressing approx!!pc addr args in
      if nmem_contains nm p (size_chunk chunk)
      then (add_needs_all args (add_need src (store_argument chunk) ne),
            nmem_remove nm p (size_chunk chunk))
      else after
  | Some(Icall sig ros args res s) =>
      (add_needs_all args (add_ros_need_all ros (kill res ne)), nmem_all)
  | Some(Itailcall sig ros args) =>
      (add_needs_all args (add_ros_need_all ros,
       nmem_dead_stack f.(fn_stacksize))
  | Some(Ibuiltin ef args res s) =>
      transfer_builtin approx!!pc ef args res ne nm
  | Some(Icond cond args s1 s2) =>
      (add_needs args (needs_of_condition cond) ne, nm)
  | Some(Ijumptable arg tbl) =>
      (add_need_all arg ne, nm)
  | Some(Ireturn optarg) =>
      (add_opt_need_all optarg ne, nmem_dead_stack f.(fn_stacksize))

Module DS := Backward_Dataflow_Solver(NA)(NodeSetBackward).

Definition analyze (approx: PMap.t VA.t) (f: function): option (PMap.t NA.t) :=
  DS.fixpoint f.(fn_code) successors_instr
              (transfer f approx).

Part 2: the code transformation

Definition transf_instr (approx: PMap.t VA.t) (an: PMap.t NA.t)
                        (pc: node) (instr: instruction) :=
  match instr with
  | Iop op args res s =>
      let nres := nreg (fst an!!pc) res in
      if is_dead nres then
        Inop s
      else if is_int_zero nres then
        Iop (Ointconst nil res s
      else if operation_is_redundant op nres then
        match args with
        | arg :: _ => Iop Omove (arg :: nil) res s
        | nil => instr
  | Iload chunk addr args dst s =>
      let ndst := nreg (fst an!!pc) dst in
      if is_dead ndst then
        Inop s
      else if is_int_zero ndst then
        Iop (Ointconst nil dst s
  | Istore chunk addr args src s =>
      let p := aaddressing approx!!pc addr args in
      if nmem_contains (snd an!!pc) p (size_chunk chunk)
      then instr
      else Inop s
  | Ibuiltin (EF_memcpy sz al) (dst :: src :: nil) res s =>
      if nmem_contains (snd an!!pc) (aaddr_arg approx!!pc dst) sz
      then instr
      else Inop s
  | _ =>

Definition transf_function (rm: romem) (f: function) : res function :=
  let approx := ValueAnalysis.analyze rm f in
  match analyze approx f with
  | Some an =>
      OK {| fn_sig := f.(fn_sig);
            fn_params := f.(fn_params);
            fn_stacksize := f.(fn_stacksize);
            fn_code := (transf_instr approx an) f.(fn_code);
            fn_entrypoint := f.(fn_entrypoint) |}
  | None =>
      Error (msg "Neededness analysis failed")

Definition transf_fundef (rm: romem) (fd: fundef) : res fundef :=
  AST.transf_partial_fundef (transf_function rm) fd.

Definition transf_program (p: program) : res program :=
  transform_partial_program (transf_fundef (romem_for p)) p.