Source file global_deadcode.ml
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open Code
open Stdlib
let debug = Debug.find "globaldeadcode"
let times = Debug.find "times"
(** Definition of a variable [x]. *)
type def =
| Expr of expr (** [x] is defined by an expression. *)
| Param (** [x] is a block or closure parameter. *)
(** Liveness of a variable [x], forming a lattice structure. *)
type live =
| Top (** [x] is live and not a block. *)
| Live of IntSet.t (** [x] is a live block with a (non-empty) set of live fields. *)
| Dead (** [x] is dead. *)
module G = Dgraph.Make_Imperative (Var) (Var.ISet) (Var.Tbl)
module Domain = struct
type t = live
let equal l1 l2 =
match l1, l2 with
| Top, Top | Dead, Dead -> true
| Live f1, Live f2 -> IntSet.equal f1 f2
| Top, (Dead | Live _) | Live _, (Dead | Top) | Dead, (Live _ | Top) -> false
let bot = Dead
(** Join the liveness according to lattice structure. *)
let join l1 l2 =
match l1, l2 with
| _, Top | Top, _ -> Top
| Live f1, Live f2 -> Live (IntSet.union f1 f2)
| Dead, Live f | Live f, Dead -> Live f
| Dead, Dead -> Dead
end
module Solver = G.Solver (Domain)
let definitions prog =
let defs = Var.Tbl.make () Param in
let set_def x d = Var.Tbl.set defs x d in
Addr.Map.iter
(fun _ block ->
List.iter
~f:(fun (i, _) ->
match i with
| Let (x, e) -> set_def x (Expr e)
| Assign (x, _) -> set_def x Param
| Set_field (_, _, _) | Offset_ref (_, _) | Array_set (_, _, _) -> ())
block.body)
prog.blocks;
defs
let variable_may_escape x (global_info : Global_flow.info) =
match global_info.info_variable_may_escape.(Var.idx x) with
| Escape | Escape_constant -> true
| No -> false
(** Type of variable usage. *)
type usage_kind =
| Compute (** variable y is used to compute x *)
| Propagate (** values of y propagate to x *)
(** Compute the adjacency list for the dependency graph of given program. An edge between
variables [x] and [y] is marked [Compute] if [x] is used in the definition of [y]. It is marked
as [Propagate] if [x] is applied as a closure or block argument the parameter [y].
We use information from global flow to try to add edges between function calls and their return values
at known call sites. *)
let usages prog (global_info : Global_flow.info) : usage_kind Var.Map.t Var.Tbl.t =
let uses = Var.Tbl.make () Var.Map.empty in
let add_use kind x y = Var.Tbl.set uses y (Var.Map.add x kind (Var.Tbl.get uses y)) in
let add_arg_dep params args =
List.iter2 ~f:(fun x y -> add_use Propagate x y) params args
in
let add_cont_deps (pc, args) =
match try Some (Addr.Map.find pc prog.blocks) with Not_found -> None with
| Some block -> add_arg_dep block.params args
| None -> ()
in
let add_expr_uses x e : unit =
match e with
| Apply { f; args; _ } ->
(match Var.Tbl.get global_info.info_approximation f with
| Top -> ()
| Values { known; _ } ->
Var.Set.iter
(fun k ->
match global_info.info_defs.(Var.idx k) with
| Expr (Closure (params, _)) ->
if List.compare_lengths params args = 0
then (
let return_values = Var.Map.find k global_info.info_return_vals in
Var.Set.iter (add_use Propagate x) return_values;
List.iter2 ~f:(add_use Propagate) params args)
| _ -> ())
known);
add_use Compute x f;
List.iter
~f:(fun a -> if variable_may_escape a global_info then add_use Compute x a)
args
| Block (_, vars, _) -> Array.iter ~f:(add_use Compute x) vars
| Field (z, _) -> add_use Compute x z
| Constant _ -> ()
| Special _ -> ()
| Closure (_, cont) -> add_cont_deps cont
| Prim (_, args) ->
List.iter
~f:(fun arg ->
match arg with
| Pv v -> add_use Compute x v
| Pc _ -> ())
args
in
Addr.Map.iter
(fun _ block ->
List.iter
~f:(fun (i, _) ->
match i with
| Let (x, e) -> add_expr_uses x e
| Assign (x, y) -> add_use Propagate x y
| Set_field (_, _, _) | Offset_ref (_, _) | Array_set (_, _, _) -> ())
block.body;
match fst block.branch with
| Return _ | Raise _ | Stop -> ()
| Branch cont -> add_cont_deps cont
| Cond (_, cont1, cont2) ->
add_cont_deps cont1;
add_cont_deps cont2
| Switch (_, a) -> Array.iter ~f:add_cont_deps a
| Pushtrap (cont, _, cont_h) ->
add_cont_deps cont;
add_cont_deps cont_h
| Poptrap cont -> add_cont_deps cont)
prog.blocks;
uses
(** Return the set of variables used in a given expression *)
let expr_vars e =
let vars = Var.Set.empty in
match e with
| Apply { f; args; _ } ->
let vars = Var.Set.add f vars in
List.fold_left ~f:(fun acc x -> Var.Set.add x acc) ~init:vars args
| Block (_, params, _) ->
Array.fold_left ~f:(fun acc x -> Var.Set.add x acc) ~init:vars params
| Field (z, _) -> Var.Set.add z vars
| Prim (_, args) ->
List.fold_left
~f:(fun acc v ->
match v with
| Pv v -> Var.Set.add v acc
| Pc _ -> acc)
~init:vars
args
| Constant _ | Closure (_, _) | Special _ -> vars
(** Compute the initial liveness of each variable in the program.
A variable [x] is marked as [Top] if
+ It is used in an impure expression (as defined by [Pure_fun.pure_expr]);
+ It is used in a conditonal/switch;
+ It is raised by an exception;
+ It is used in another stateful instruction (like setting a block or array field);
+ Or, it is returned or applied to a function and the global flow analysis marked it as escaping.
A variable [x[i]] is marked as [Live {i}] if it is used in an instruction where field [i] is referenced or set. *)
let liveness prog pure_funs (global_info : Global_flow.info) =
let live_vars = Var.Tbl.make () Dead in
let add_top v = Var.Tbl.set live_vars v Top in
let add_live_field v i =
let live_fields =
match Var.Tbl.get live_vars v with
| Live fields -> Live (IntSet.add i fields)
| Top | Dead -> Live (IntSet.singleton i)
in
Var.Tbl.set live_vars v live_fields
in
let live_instruction i =
match i with
| Let (_, e) -> (
if not (Pure_fun.pure_expr pure_funs e)
then
match e with
| Apply { f; args; _ } ->
add_top f;
List.iter
~f:(fun x -> if variable_may_escape x global_info then add_top x)
args
| Block (_, _, _)
| Field (_, _)
| Closure (_, _)
| Constant _
| Prim (_, _)
| Special _ ->
let vars = expr_vars e in
Var.Set.iter add_top vars)
| Set_field (x, i, y) ->
add_live_field x i;
add_top y
| Array_set (x, y, z) ->
add_top x;
add_top y;
add_top z
| Offset_ref (x, _) -> add_live_field x 0
| Assign (_, _) -> ()
in
let live_block block =
List.iter ~f:(fun (i, _) -> live_instruction i) block.body;
match fst block.branch with
| Return x -> if variable_may_escape x global_info then add_top x
| Raise (x, _) -> add_top x
| Cond (x, _, _) -> add_top x
| Switch (x, _) -> add_top x
| Stop | Branch _ | Poptrap _ | Pushtrap _ -> ()
in
Addr.Map.iter (fun _ block -> live_block block) prog.blocks;
Code.traverse
{ Code.fold = Code.fold_children }
(fun pc () ->
match Addr.Map.find pc prog.blocks with
| { branch = Return x, _; _ } -> add_top x
| _ -> ())
prog.start
prog.blocks
();
live_vars
let variables deps =
let vars = Var.ISet.empty () in
Var.Tbl.iter (fun v _ -> Var.ISet.add vars v) deps;
vars
(** Propagate liveness of the usages of a variable [x] to [x]. The liveness of [x] is
defined by joining its current liveness and the contribution of each vairable [y]
that uses [x]. *)
let propagate uses defs live_vars live_table x =
let contribution y usage_kind =
match usage_kind with
| Compute -> (
match Var.Tbl.get live_table y with
| Dead -> Dead
| Live fields -> (
match Var.Tbl.get defs y with
| Expr (Block (_, vars, _)) ->
let found = ref false in
Array.iteri
~f:(fun i v ->
if Var.equal v x && IntSet.mem i fields then found := true)
vars;
if !found then Top else Dead
| Expr (Field (_, i)) -> Live (IntSet.singleton i)
| _ -> Top)
| Top -> (
match Var.Tbl.get defs y with
| Expr (Field (_, i)) -> Live (IntSet.singleton i)
| _ -> Top))
| Propagate -> Var.Tbl.get live_table y
in
Var.Map.fold
(fun y usage_kind live -> Domain.join (contribution y usage_kind) live)
(Var.Tbl.get uses x)
(Domain.join (Var.Tbl.get live_vars x) (Var.Tbl.get live_table x))
let solver vars uses defs live_vars =
let g =
{ G.domain = vars
; G.iter_children = (fun f x -> Var.Map.iter (fun y _ -> f y) (Var.Tbl.get uses x))
}
in
Solver.f () (G.invert () g) (propagate uses defs live_vars)
(** Replace each instance of a dead variable with a sentinal value.
Blocks that end in dead variables are compacted to the first live entry.
Dead variables are replaced when
+ They appear in a dead field of a block; or
+ They are returned; or
+ They are applied to a function.
*)
let zero prog sentinal live_table =
let compact_vars vars =
let i = ref (Array.length vars - 1) in
while !i >= 0 && Var.equal vars.(!i) sentinal do
i := !i - 1
done;
if !i + 1 < Array.length vars then Array.sub vars ~pos:0 ~len:(!i + 1) else vars
in
let is_live v =
match Var.Tbl.get live_table v with
| Dead -> false
| Top | Live _ -> true
in
let zero_var x = if is_live x then x else sentinal in
let zero_instr instr =
match instr with
| Let (x, e) -> (
match e with
| Block (start, vars, is_array) -> (
match Var.Tbl.get live_table x with
| Live fields ->
let vars =
Array.mapi
~f:(fun i v -> if IntSet.mem i fields then v else sentinal)
vars
|> compact_vars
in
let e = Block (start, vars, is_array) in
Let (x, e)
| _ -> instr)
| Apply ap ->
let args = List.map ~f:zero_var ap.args in
Let (x, Apply { ap with args })
| Field (_, _) | Closure (_, _) | Constant _ | Prim (_, _) | Special _ -> instr)
| Assign (_, _) | Set_field (_, _, _) | Offset_ref (_, _) | Array_set (_, _, _) ->
instr
in
let zero_block block =
let body = List.map ~f:(fun (instr, loc) -> zero_instr instr, loc) block.body in
let branch =
match block.branch with
| Return x, loc ->
let tc =
match List.last body with
| Some (Let (x', Apply _), _) when Code.Var.equal x' x -> true
| Some _ | None -> false
in
if tc then Return x, loc else Return (zero_var x), loc
| Raise (_, _), _
| Stop, _
| Branch _, _
| Cond (_, _, _), _
| Switch (_, _), _
| Pushtrap (_, _, _), _
| Poptrap _, _ -> block.branch
in
{ block with body; branch }
in
let blocks = prog.blocks |> Addr.Map.map zero_block in
{ prog with blocks }
module Print = struct
let live_to_string = function
| Live fields ->
"live { " ^ IntSet.fold (fun i s -> s ^ Format.sprintf "%d " i) fields "" ^ "}"
| Top -> "top"
| Dead -> "dead"
let print_uses uses =
Format.eprintf "Usages:\n";
Var.Tbl.iter
(fun v ds ->
Format.eprintf "%a: { " Var.print v;
Var.Map.iter
(fun d k ->
Format.eprintf
"(%a, %s) "
Var.print
d
(match k with
| Compute -> "C"
| Propagate -> "P"))
ds;
Format.eprintf "}\n")
uses
let print_liveness live_vars =
Format.eprintf "Liveness:\n";
Var.Tbl.iter
(fun v l -> Format.eprintf "%a: %s\n" Var.print v (live_to_string l))
live_vars
let print_live_tbl live_table =
Format.eprintf "Liveness with dependencies:\n";
Var.Tbl.iter
(fun v l -> Format.eprintf "%a: %s\n" Var.print v (live_to_string l))
live_table
end
(** Add a sentinal variable declaration to the IR. The fresh variable is assigned to `undefined`. *)
let add_sentinal p sentinal =
let instr, loc = Let (sentinal, Special Undefined), noloc in
Code.prepend p [ instr, loc ]
(** Run the liveness analysis and replace dead variables with the given sentinal. *)
let f p ~deadcode_sentinal global_info =
Code.invariant p;
let t = Timer.make () in
let p = add_sentinal p deadcode_sentinal in
let defs = definitions p in
let uses = usages p global_info in
let pure_funs = Pure_fun.f p in
let live_vars = liveness p pure_funs global_info in
let vars = variables uses in
let live_table = solver vars uses defs live_vars in
if debug ()
then (
Format.eprintf "Before Zeroing:\n";
Code.Print.program (fun _ _ -> "") p;
Print.print_liveness live_vars;
Print.print_uses uses;
Print.print_live_tbl live_table);
let p = zero p deadcode_sentinal live_table in
if debug ()
then (
Format.printf "After Zeroing:\n";
Code.Print.program (fun _ _ -> "") p);
if times () then Format.eprintf " deadcode dgraph.: %a@." Timer.print t;
p