Reviewed By: jberdine Differential Revision: D7783487 fbshipit-source-id: 15b4c84e1master
Mehdi Bouaziz
6 years ago
committed by
Facebook Github Bot
parent
c9b89b54dd
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(*
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* Copyright (c) 2018-present, Facebook, Inc.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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open! IStd
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module F = Format
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module Partition = struct
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type 'node t =
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| Empty
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| Node of {node: 'node; next: 'node t}
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| Component of {head: 'node; rest: 'node t; next: 'node t}
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let empty = Empty
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let add_node node next = Node {node; next}
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let add_component head rest next = Component {head; rest; next}
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let rec pp ~prefix ~pp_node fmt = function
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| Empty ->
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()
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| Node {node; next} ->
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F.fprintf fmt "%s%a" prefix pp_node node ;
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pp ~prefix:" " ~pp_node fmt next
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| Component {head; rest; next} ->
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F.fprintf fmt "%s(%a%a)" prefix pp_node head (pp ~prefix:" " ~pp_node) rest ;
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pp ~prefix:" " ~pp_node fmt next
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let pp ~pp_node = pp ~prefix:"" ~pp_node
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end
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module type S = sig
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module CFG : ProcCfg.S
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val make : CFG.t -> CFG.Node.t Partition.t
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end
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module type Make = functor (CFG : ProcCfg.S) -> S with module CFG = CFG
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module Bourdoncle_SCC (CFG : ProcCfg.S) = struct
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module CFG = CFG
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(**
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[dfn] contains a DFS pre-order indexing. A node is not in the map if it has never been visited.
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A node's dfn is +oo if it has been fully visited (head of cross-edges) or we want to hide it
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for building a subcomponent partition (head of highest back-edges).
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*)
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module Dfn = CFG.Node.IdMap
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(*
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Unlike Bourdoncle's paper version or OCamlGraph implementation, this implementation handles
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high DFS-depth graphs, which would stack-overflow otherwise.
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It still doesn't handle high component nesting, but it is pretty unlikely to happen in real
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code (means a lot of loop nesting).
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*)
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type stack =
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{ node: CFG.Node.t
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; node_id: CFG.Node.id
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; node_dfn: int
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; succs: CFG.Node.t list
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; mutable succs_to_visit: CFG.Node.t list
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; mutable head: int (** Minimum [dfn] of the nodes accessibles from [node]. *)
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; mutable component: CFG.Node.id ARList.t
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(** Nodes in the current strict-connected component. *)
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; mutable building_component: bool
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; next: stack option }
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let make cfg =
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let num = ref 0 in
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let dfn = ref Dfn.empty in
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let stack = ref None in
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let push_on_stack node =
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let node_id = CFG.Node.id node in
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incr num ;
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let node_dfn = !num in
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dfn := Dfn.add node_id node_dfn !dfn ;
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let succs = IContainer.to_rev_list ~fold:(CFG.fold_succs cfg) node in
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stack :=
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Some
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{ node
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; node_id
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; node_dfn
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; succs
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; succs_to_visit= succs
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; head= Int.max_value
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; component= ARList.empty
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; building_component= false
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; next= !stack }
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in
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let record_head ?add_to_component cur_head =
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let stack_top = Option.value_exn !stack in
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stack_top.head <- min stack_top.head cur_head ;
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Option.iter add_to_component ~f:(fun add ->
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stack_top.component <- ARList.append add stack_top.component )
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in
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let visit node =
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let node_id = CFG.Node.id node in
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match Dfn.find node_id !dfn with
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| node_dfn ->
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(*
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[node_dfn] is going to be either +oo (see [Dfn] for why), in which case [record_head]
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will have no effect; or be the [dfn] of the head of a back-edge or cross-edge in the
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current strictly connected component.
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*)
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record_head node_dfn
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| exception Caml.Not_found ->
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push_on_stack node
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| exception Not_found_s _ ->
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push_on_stack node
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in
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let rec process_stack partition =
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match !stack with
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| None ->
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()
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| Some ({succs_to_visit= succ :: succs_to_visit} as stack_top) ->
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stack_top.succs_to_visit <- succs_to_visit ;
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visit succ ;
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(process_stack [@tailcall]) partition
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| Some {succs_to_visit= []; building_component= true} ->
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()
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| Some
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{succs_to_visit= []; building_component= false; node_id; node_dfn; head; component; next}
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when head < node_dfn ->
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(* [node] is in a strictly connected component but is (locally) not its head. *)
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stack := next ;
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record_head head ~add_to_component:(ARList.cons node_id component) ;
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(process_stack [@tailcall]) partition
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| Some
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( { succs_to_visit= []
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; building_component= false
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; node
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; node_id
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; node_dfn
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; succs
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; head
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; component
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; next } as stack_top ) ->
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dfn := Dfn.add node_id Int.max_value !dfn ;
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if head > node_dfn then
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(* [node] is not (locally) in a strictly connected component *)
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partition := Partition.add_node node !partition
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else (
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(*
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head = node_dfn. [node] is (locally) the head of a strictly connected component.
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[node] is marked as already visited (line dfn := ... above).
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All nodes in the current [component] are marked as not visited.
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And we recursively construct a WTO for the component.
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*)
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Container.iter component ~fold:ARList.fold_unordered ~f:(fun nid ->
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dfn := Dfn.remove nid !dfn ) ;
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let component_partition =
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let partition = ref Partition.empty in
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stack_top.building_component <- true ;
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stack_top.succs_to_visit <- succs ;
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process_stack partition ;
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!partition
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in
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partition := Partition.add_component node component_partition !partition ) ;
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stack := next ;
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(process_stack [@tailcall]) partition
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in
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let partition = ref Partition.empty in
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push_on_stack (CFG.start_node cfg) ;
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process_stack partition ;
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!partition
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end
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@ -0,0 +1,55 @@
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(*
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* Copyright (c) 2018-present, Facebook, Inc.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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open! IStd
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module F = Format
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(* The definitions below taken from [Bou] "Efficient chaotic iteration strategies with widenings"
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by François Bourdoncle.
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*)
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(**
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A hierarchical ordering of a set is a well-parenthesized permutation of its elements without two
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consecutive "(". I defines a total order <= over its elements.
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The elements between two matching parentheses are called a Component.
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The first element of a Component is called the head.
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Let denote by H(v) the set of head of the nested components containing v.
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*)
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module Partition : sig
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type 'node t = private
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| Empty
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| Node of {node: 'node; next: 'node t}
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| Component of {head: 'node; rest: 'node t; next: 'node t}
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val pp : pp_node:(F.formatter -> 'node -> unit) -> F.formatter -> 'node t -> unit
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end
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(**
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A weak topological ordering (WTO) of a directed graph is a hierarchical ordering of its vertices
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such that for every edge u -> v,
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u < v and v is not in H(u) (forward edge)
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or
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v <= u and v is in H(u) (feedback edge)
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A WTO of a directed graph is such that the head u of every feedback edge u -> v is the head of a
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component containing its tail v.
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*)
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module type S = sig
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module CFG : ProcCfg.S
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val make : CFG.t -> CFG.Node.t Partition.t
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end
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module type Make = functor (CFG : ProcCfg.S) -> S with module CFG = CFG
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(**
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Implementation of Bourdoncle's "Hierarchical decomposition of a directed graph into strongly
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connected components and subcomponents". See [Bou] Figure 4, page 10.
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*)
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module Bourdoncle_SCC : Make
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@ -0,0 +1,94 @@
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(*
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* Copyright (c) 2018-present, Facebook, Inc.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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open! IStd
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module MockProcCfg = SchedulerTests.MockProcCfg
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module WTO = WeakTopologicalOrder.Bourdoncle_SCC (MockProcCfg)
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let inputs_from_scheduler_tests =
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SchedulerTests.inputs |> List.map ~f:(fun (name, cfg, _, wto) -> (name, cfg, wto))
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let inputs =
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inputs_from_scheduler_tests
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@ [ ( "bourdoncle_fig1"
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, [(1, [2]); (2, [3; 8]); (3, [4]); (4, [5; 7]); (5, [6]); (6, [5; 7]); (7, [3; 8])]
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, "1 2 (3 4 (5 6) 7) 8" )
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; ( "bourdoncle_fig2left"
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, [(1, [2; 4]); (2, [3]); (3, []); (4, [5; 3]); (5, [4])]
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, "1 2 (4 5) 3" )
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; ("bourdoncle_fig2right", [(1, [2; 4]); (2, [3]); (3, [1]); (4, [3])], "(1 2 4 3)")
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; ( "bourdoncle_fig5"
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, [ (1, [4; 2])
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; (2, [3])
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; (3, [6])
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; (4, [10])
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; (10, [20; 40])
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; (40, [1])
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; (20, [30])
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; (30, [60])
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; (60, [5])
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; (50, [60])
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; (6, [50])
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; (5, [6]) ]
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, "(1 4 10 40) 20 30 2 3 (6 50 60 5)" )
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; ( "elder_fig1"
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, [(1, [2]); (2, [3]); (7, [2; 8]); (3, [4]); (6, [7; 3]); (4, [5]); (5, [6; 2])]
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, "1 (2 (3 4 5 6) 7) 8" )
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; ( "jjb1" (* corresponds to tests/codetoanalyze/c/frontend/gotostmt/jjb1.c *)
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, [ (1, [19])
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; (19, [6])
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; (6, [7; 8])
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; (7, [16])
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; (8, [9])
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; (16, [13])
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; (13, [14; 15])
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; (5 (* no preds, dead node *), [4])
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; (14, [4])
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; (15, [12])
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; (4, [3])
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; (12, [11])
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; (3, [2])
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; (11, [10])
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; (10, [9])
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; (9, [18])
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; (18, [17])
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; (17, [16]) ]
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, "1 19 6 7 8 (9 18 17 16 13 15 12 11 10) 14 4 3 2" )
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; ("self_loop", [(1, [1])], "(1)")
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; ( "nested_loops_two_entries"
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, [(1, [60; 6]); (60, [5; 50]); (5, [6]); (6, [50]); (50, [60])]
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, "1 (6 (50 60) 5)" )
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; ( "nested_loops2"
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, [ (1, [2])
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; (2, [9])
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; (6, [2; 7])
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; (7, [8; 5])
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; (5, [7; 6])
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; (9, [3; 10])
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; (3, [4])
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; (4, [5])
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; (8, [4; 3]) ]
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, "1 (2 9 (3 (4 (5 6 7) 8))) 10" ) ]
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let create_test cfg expected_result _ =
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let result =
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let partition = WTO.make cfg in
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Format.asprintf "%a"
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(WeakTopologicalOrder.Partition.pp ~pp_node:MockProcCfg.Node.pp_id)
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partition
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in
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OUnit2.assert_equal ~printer:Fn.id expected_result result
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let tests =
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let open OUnit2 in
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let test_list =
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inputs |> List.map ~f:(fun (name, test, expected) -> name >:: create_test test expected)
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in
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"wto_suite" >::: test_list
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@ -0,0 +1,30 @@
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/*
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* Copyright (c) 2018-present, Facebook, Inc.
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|
*
|
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|
* This source code is licensed under the MIT license found in the
|
||||||
|
* LICENSE file in the root directory of this source tree.
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*/
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extern void print_int(int);
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int jjb1() {
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int x, y;
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x++;
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if (x / 2) {
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L0:
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if (x <= 0)
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goto L3;
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x--;
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print_int(x);
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goto L1;
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} else {
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L1:
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y++;
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print_int(y);
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goto L0;
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}
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L3:
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return 0;
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}
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@ -0,0 +1,80 @@
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/* @generated */
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digraph cfg {
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"jjb1.9d6085e324f8fe61c38e804980fa5cf1_1" [label="1: Start jjb1\nFormals: \nLocals: y:int x:int \n " color=yellow style=filled]
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"jjb1.9d6085e324f8fe61c38e804980fa5cf1_1" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_19" ;
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"jjb1.9d6085e324f8fe61c38e804980fa5cf1_2" [label="2: Exit jjb1 \n " color=yellow style=filled]
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|
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|
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"jjb1.9d6085e324f8fe61c38e804980fa5cf1_3" [label="3: Return Stmt \n *&return:int=0 [line 29, column 3]\n " shape="box"]
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|
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"jjb1.9d6085e324f8fe61c38e804980fa5cf1_3" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_2" ;
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"jjb1.9d6085e324f8fe61c38e804980fa5cf1_4" [label="4: Skip GotoLabel_L3 \n " color="gray"]
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|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_4" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_3" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_5" [label="5: + \n " ]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_5" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_4" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_6" [label="6: BinaryOperatorStmt: Div \n n$1=*&x:int [line 14, column 7]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_6" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_7" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_6" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_8" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_7" [label="7: Prune (true branch, if) \n PRUNE((n$1 / 2), true); [line 14, column 7]\n " shape="invhouse"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_7" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_16" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_8" [label="8: Prune (false branch, if) \n PRUNE(!(n$1 / 2), false); [line 14, column 7]\n " shape="invhouse"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_8" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_9" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_9" [label="9: Skip GotoLabel_L1 \n " color="gray"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_9" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_18" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_10" [label="10: Call _fun_print_int \n n$3=*&x:int [line 19, column 15]\n n$4=_fun_print_int(n$3:int) [line 19, column 5]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_10" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_9" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_11" [label="11: UnaryOperator \n n$5=*&x:int [line 18, column 5]\n *&x:int=(n$5 - 1) [line 18, column 5]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_11" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_10" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_12" [label="12: + \n " ]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_12" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_11" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_13" [label="13: BinaryOperatorStmt: LE \n n$6=*&x:int [line 16, column 9]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_13" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_14" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_13" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_15" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_14" [label="14: Prune (true branch, if) \n PRUNE((n$6 <= 0), true); [line 16, column 9]\n " shape="invhouse"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_14" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_4" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_15" [label="15: Prune (false branch, if) \n PRUNE(!(n$6 <= 0), false); [line 16, column 9]\n " shape="invhouse"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_15" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_12" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_16" [label="16: Skip GotoLabel_L0 \n " color="gray"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_16" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_13" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_17" [label="17: Call _fun_print_int \n n$12=*&y:int [line 24, column 15]\n n$13=_fun_print_int(n$12:int) [line 24, column 5]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_17" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_16" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_18" [label="18: UnaryOperator \n n$14=*&y:int [line 23, column 5]\n *&y:int=(n$14 + 1) [line 23, column 5]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_18" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_17" ;
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_19" [label="19: UnaryOperator \n n$17=*&x:int [line 13, column 3]\n *&x:int=(n$17 + 1) [line 13, column 3]\n " shape="box"]
|
||||||
|
|
||||||
|
|
||||||
|
"jjb1.9d6085e324f8fe61c38e804980fa5cf1_19" -> "jjb1.9d6085e324f8fe61c38e804980fa5cf1_6" ;
|
||||||
|
}
|
||||||
Loading…
Reference in new issue