%% -*- erlang-indent-level: 2 -*-
%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2004-2013. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
%% compliance with the License. You should have received a copy of the
%% Erlang Public License along with this software. If not, it can be
%% retrieved online at http://www.erlang.org/.
%%
%% Software distributed under the License is distributed on an "AS IS"
%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
%% the License for the specific language governing rights and limitations
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%%
%%------------------------------------------------------------------------
%% File : hipe_dominators.erl
%% Author : Christoffer Vikström <[email protected]>
%% Daniel Deogun <[email protected]>
%% Jesper Bengtsson <[email protected]>
%% Created : 18 Mar 2002
%%
%% @doc
%% Contains utilities for creating and manipulating dominator trees
%% and dominance frontiers from a CFG.
%% @end
%%------------------------------------------------------------------------
-module(hipe_dominators).
-export([domTree_create/1,
domTree_getChildren/2,
domTree_dominates/3,
domFrontier_create/2,
domFrontier_get/2]).
-export_type([domTree/0]).
-include("cfg.hrl").
%%========================================================================
%%
%% CODE FOR CREATING AND MANIPULATING DOMINATOR TREES.
%%
%%========================================================================
-record(workDataCell, {dfnum = 0 :: non_neg_integer(),
dfparent = none :: 'none' | cfg_lbl(),
semi = none :: 'none' | cfg_lbl(),
ancestor = none :: 'none' | cfg_lbl(),
best = none :: 'none' | cfg_lbl(),
samedom = none :: 'none' | cfg_lbl(),
bucket = [] :: [cfg_lbl()]}).
-record(domTree, {root :: cfg_lbl(),
size = 0 :: non_neg_integer(),
nodes = gb_trees:empty() :: gb_tree()}).
-type domTree() :: #domTree{}.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_create/1
%% Purpose : Creates a complete dominator tree given a CFG.
%% Arguments : CFG - a Control Flow Graph representation
%% Returns : A dominator tree
%%>----------------------------------------------------------------------<
-spec domTree_create(cfg()) -> domTree().
domTree_create(CFG) ->
{WorkData, DFS, N} = dfs(CFG),
DomTree = domTree_empty(hipe_gen_cfg:start_label(CFG)),
{DomData, WorkData2} = getIdoms(CFG, DomTree, WorkData, N, DFS),
finalize(WorkData2, DomData, 1, N, DFS).
%%>----------------------------------------------------------------------<
%% Procedure : domTree_empty/0
%% Purpose : Creates an empty dominator tree.
%% Arguments : The root node
%% Returns : A dominator tree
%%>----------------------------------------------------------------------<
domTree_empty(Node) ->
#domTree{root = Node}.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_createNode/2
%% Purpose : Creates a new node and inserts it into the dominator tree.
%% Arguments : Node - The new node
%% DomTree - The target dominator tree
%% Returns : A dominator tree
%%>----------------------------------------------------------------------<
domTree_createNode(Node, DomTree) ->
DomTree2 = domTree_setNodes(DomTree,
gb_trees:enter(Node, {none,[]},
domTree_getNodes(DomTree))),
domTree_incSize(DomTree2).
%%>----------------------------------------------------------------------<
%% Procedure : domTree_getNode/2
%% Purpose : Returns a specific node in the dominator tree.
%% Arguments : Node - The new node
%% DomTree - The target dominator tree
%% Returns : Node
%%>----------------------------------------------------------------------<
domTree_getNode(Node, DomTree) ->
gb_trees:lookup(Node, domTree_getNodes(DomTree)).
%%>----------------------------------------------------------------------<
%% Procedure : domTree_getNodes/1
%% Purpose : Retrieves the nodes from a dominator tree.
%% Arguments : DomTree - The target dominator tree
%% Returns : A map containing the nodes of the dominator tree.
%%>----------------------------------------------------------------------<
domTree_getNodes(#domTree{nodes=Nodes}) -> Nodes.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_setNodes/2
%% Purpose : Replaces the set of nodes in a dominator tree with a
%% new set of nodes.
%% Arguments : Nodes - The new set of nodes
%% DomTree - The target dominator tree
%% Returns : DomTree
%%>----------------------------------------------------------------------<
domTree_setNodes(DomTree, Nodes) -> DomTree#domTree{nodes = Nodes}.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_setSize/2
%% Purpose : Sets the size of the dominator tree, i.e. the number of
%% nodes in it.
%% Arguments : Size - The new size of the target dominator tree
%% DomTree - The target dominator tree
%% Returns : A dominator tree
%%>----------------------------------------------------------------------<
domTree_setSize(DomTree, Size) -> DomTree#domTree{size = Size}.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_incSize/1
%% Purpose : Increases the size of the dominator tree with one.
%% Arguments : DomTree - The target dominator tree
%% Returns : DomTree
%%>----------------------------------------------------------------------<
domTree_incSize(DomTree) ->
Size = domTree_getSize(DomTree),
domTree_setSize(DomTree, Size + 1).
%%>----------------------------------------------------------------------<
%% Procedure : get IDom/2
%% Purpose : Retrieves the immediate dominators of a node in the
%% dominator tree.
%% Arguments : Node - The new node
%% DomTree - The target dominator tree
%% Returns : The immediate dominator
%%>----------------------------------------------------------------------<
domTree_getIDom(Node, DomTree) ->
case domTree_getNode(Node, DomTree) of
{value, {IDom, _}} ->
IDom;
none ->
[]
end.
%%>----------------------------------------------------------------------<
%% Procedure : getChildren/2
%% Purpose : Retrieves the children of a node in the dominator tree.
%% Arguments : Node - The new node
%% DomTree - The target dominator tree
%% Returns : [children]
%%>----------------------------------------------------------------------<
-spec domTree_getChildren(cfg_lbl(), domTree()) -> [cfg_lbl()].
domTree_getChildren(Node, DomTree) ->
case domTree_getNode(Node, DomTree) of
{value, {_, Children}} ->
Children;
none ->
[]
end.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_getSize/1
%% Purpose : Retrieves the size of a dominator tree.
%% Arguments : DomTree - The target dominator tree
%% Returns : A number denoting the size of the dominator tree
%%>----------------------------------------------------------------------<
domTree_getSize(#domTree{size=Size}) -> Size.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_getRoot/2
%% Purpose : Retrieves the number of the root node in the dominator tree.
%% Arguments : DomTree - The target dominator tree
%% Returns : Number
%%>----------------------------------------------------------------------<
domTree_getRoot(#domTree{root=Root}) -> Root.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_addChild/3
%% Purpose : Inserts a new node as a child to another node in the
%% dominator tree.
%% Arguments : Node - The old node that should get a new child
%% Child - The new child node
%% DomTree - The target dominator tree
%% Returns : DomTree
%%>----------------------------------------------------------------------<
domTree_addChild(Node, Child, DomTree) ->
{IDom, Children} = case domTree_getNode(Node, DomTree) of
{value, Tuple} ->
Tuple;
none ->
{none, []}
end,
Nodes = case lists:member(Child, Children) of
true ->
domTree_getNodes(DomTree);
false ->
gb_trees:enter(Node, {IDom, [Child|Children]},
domTree_getNodes(DomTree))
end,
domTree_setNodes(DomTree, Nodes).
%%>----------------------------------------------------------------------<
%% Procedure : setIDom/3
%% Purpose : Sets the immediate domminator of a node in the domminator tree.
%% Arguments : Node - The node whose immediate domminator we are seting
%% IDom - The immediate domminator
%% DomTree - The target dominator tree
%% Returns : DomTree
%% Notes : Is used to build the dominator tree.
%%>----------------------------------------------------------------------<
setIDom(Node, IDom, DomTree) ->
DomTree1 = case domTree_getNode(Node, DomTree) of
none ->
domTree_createNode(Node, DomTree);
_ ->
DomTree
end,
DomTree2 = domTree_addChild(IDom, Node, DomTree1),
{value, {_, Children}} = domTree_getNode(Node, DomTree2),
domTree_setNodes(DomTree2,
gb_trees:enter(Node, {IDom, Children},
domTree_getNodes(DomTree2))).
%%>----------------------------------------------------------------------<
%% Procedure : lookup
%% Purpose : This function is used as a wrapper for the lookup function.
%% The function retrieves a particular element (defined by
%% Field) stored in a workDataCell in the table (defined by
%% Table).
%% Arguments : Field - Value defined in the workDataCell record
%% Key - Value used as a key in the table
%% Table - Table storing workDataCells
%% Returns : A value defined in the workDataCell record
%%>----------------------------------------------------------------------<
lookup({Field, Key}, Table) when is_integer(Key) ->
WD = lookup_table(Key, Table),
case Field of
ancestor -> WD#workDataCell.ancestor;
best -> WD#workDataCell.best;
bucket -> WD#workDataCell.bucket;
dfnum -> WD#workDataCell.dfnum;
dfparent -> WD#workDataCell.dfparent;
samedom -> WD#workDataCell.samedom;
semi -> WD#workDataCell.semi
end.
lookup_table(Key, Table) when is_integer(Key) ->
case gb_trees:lookup(Key, Table) of
{value, Data} ->
Data;
none ->
#workDataCell{}
end.
%%>----------------------------------------------------------------------<
%% Procedure : update
%% Purpose : This function is used as a wrapper for the update function
%% The main purpose of the update function is therefore
%% change a particular cell in the table (Table) to the
%% value given as an argument (Value).
%% Arguments : Key - Value used as a key in the table
%% Field - Value defined in the workDataCell record.
%% Value - The new value that should replace the old in the table
%% Table - Table storing workDataCells
%% Returns : NewTable
%%>----------------------------------------------------------------------<
update(Key, {Field, Value}, Table) ->
gb_trees:enter(Key, updateCell(Value, Field, lookup_table(Key, Table)), Table);
update(Key, List, Table) ->
gb_trees:enter(Key, update(List, lookup_table(Key, Table)), Table).
update([{Field, Value} | T], WD) ->
update(T, updateCell(Value, Field, WD));
update([], WD) -> WD.
updateCell(Value, Field, WD) ->
case Field of
dfnum -> WD#workDataCell{dfnum = Value};
dfparent -> WD#workDataCell{dfparent= Value};
semi -> WD#workDataCell{semi = Value};
ancestor -> WD#workDataCell{ancestor= Value};
best -> WD#workDataCell{best = Value};
samedom -> WD#workDataCell{samedom = Value};
bucket -> WD#workDataCell{bucket = Value}
end.
%%>----------------------------------------------------------------------<
%% Procedure : dfs/1
%% Purpose : The main purpose of this function is to traverse the CFG in
%% a depth first order. It is aslo used to initialize certain
%% elements defined in a workDataCell.
%% Arguments : CFG - a Control Flow Graph representation
%% Returns : A table (WorkData) and the total number of elements in
%% the CFG.
%%>----------------------------------------------------------------------<
dfs(CFG) ->
{WorkData, DFS, N} = dfs(CFG, hipe_gen_cfg:start_label(CFG),
none, 1, gb_trees:empty(), gb_trees:empty()),
{WorkData, DFS, N-1}.
dfs(CFG, Node, Parent, N, WorkData, DFS) ->
case lookup({dfnum, Node}, WorkData) of
0 ->
WorkData2 = update(Node, [{dfnum, N}, {dfparent, Parent},
{semi, Node}, {best, Node}], WorkData),
DFS2 = gb_trees:enter(N, Node, DFS),
dfsTraverse(hipe_gen_cfg:succ(CFG, Node), CFG, Node,
N + 1, WorkData2, DFS2);
_ -> {WorkData, DFS, N}
end.
%%>----------------------------------------------------------------------<
%% Procedure : dfsTraverse/6
%% Purpose : This function acts as a help function for the dfs algorithm
%% in the sence that it traverses a list of nodes given by the
%% CFG.
%% Arguments : Node - The first element in the node list
%% SuccLst - The remainder of the node list
%% CFG - Control Flow Graph representation
%% Parent - Node representing the parent of the Node defined
%% above.
%% N - The total number of processed nodes.
%% WorkData - Table consisting of workDataCells
%% Returns : An updated version of the table (WorkData) and the
%% total number of nodes processed.
%%>----------------------------------------------------------------------<
dfsTraverse([Node|T], CFG, Parent, N, WorkData, DFS) ->
{WorkData2, DFS2, N2} = dfs(CFG, Node, Parent, N, WorkData, DFS),
dfsTraverse(T, CFG, Parent, N2, WorkData2, DFS2);
dfsTraverse([], _, _, N, WorkData, DFS) -> {WorkData, DFS, N}.
%%>----------------------------------------------------------------------<
%% Procedure : getIdoms/6
%% Purpose : The purpose of this function is to compute the immediate
%% dominators. This is accomplished by traversing the CFG nodes
%% by their depth first number in a bottom up manner. That is,
%% the nodes are processed in a backward order (highest to
%% lowest number).
%% Arguments : CFG - Control Flow Graph representation
%% DomData - Table consisting of domTree cells
%% WorkData - Table consisting of workDataCells
%% Index - The index used for retrieving the node to be
%% processed
%% Returns : An updated version of the tables DomData and WorkData
%%>----------------------------------------------------------------------<
getIdoms(CFG, DomData, WorkData, Index, DFS)
when is_integer(Index), Index > 1 ->
Node = lookup_table(Index, DFS),
PredLst = hipe_gen_cfg:pred(CFG, Node),
Par = lookup({dfparent, Node}, WorkData),
DfNumN = lookup({dfnum, Node}, WorkData),
{S, WorkData2} = getSemiDominator(PredLst, DfNumN, Par, WorkData),
WorkData3 = update(Node, {semi, S}, WorkData2),
OldBucket = lookup({bucket, S}, WorkData3),
WorkData4 = update(S, {bucket, [Node | OldBucket]}, WorkData3),
WorkData5 = linkTrees(Par, Node, WorkData4),
{WorkData6, DomData2} = filterBucket(lookup({bucket, Par}, WorkData5),
Par, WorkData5, DomData),
WorkData7 = update(Par, {bucket, []}, WorkData6),
getIdoms(CFG, DomData2, WorkData7, Index - 1, DFS);
getIdoms(_, DomData, WorkData, 1, _) ->
{DomData, WorkData}.
%%>----------------------------------------------------------------------<
%% Procedure : getSemiDominator/4
%% Purpose : The main purpose of this algorithm is to compute the semi
%% dominator of the node Node based on the Semidominator Theorem
%% Arguments : Preds - The list of predecessors of the node Node
%% Node - Node in the CFG
%% S - Parent of node Node (depth first parent)
%% WorkData - Table consisting of workDataCells
%% Returns : A tuple containing the semidominator and an updated version
%% of the table WorkData.
%%>----------------------------------------------------------------------<
getSemiDominator([Pred|Preds], DfNumChild, S, WorkData) ->
{Sp, WorkData3} =
case lookup({dfnum, Pred}, WorkData) =< DfNumChild of
true ->
{Pred, WorkData};
false ->
{AncLowSemi, WorkData2} = getAncestorWithLowestSemi(Pred, WorkData),
{lookup({semi, AncLowSemi}, WorkData2), WorkData2}
end,
S2 = case lookup({dfnum, Sp}, WorkData3) < lookup({dfnum, S}, WorkData3) of
true -> Sp;
false -> S
end,
getSemiDominator(Preds, DfNumChild, S2, WorkData3);
getSemiDominator([], _, S, WorkData) ->
{S, WorkData}.
%%>----------------------------------------------------------------------<
%% Procedure : getAncestorWithLowestSemi/2
%% Purpose : The main purpose of this function is to retrieve the ancestor
%% of a node with the lowest depth first number (semi). The
%% function is also using path compression, i.e. it remembers the
%% best node (the one with the lowest semi number) and hence the
%% algorithm is only processing the minimal number of nodes.
%% Arguments : Node - Node in the tree
%% WorkData - Table consisting of workDataCells
%% Returns : A node (the one with the lowest semi) and an updated version
%% of the table WorkData.
%%>----------------------------------------------------------------------<
getAncestorWithLowestSemi(Node, WorkData) ->
Best = lookup({best, Node}, WorkData),
case lookup({ancestor, Node}, WorkData) of
none -> {Best, WorkData};
A ->
case lookup({ancestor, A}, WorkData) of
none ->
{Best, WorkData};
_ ->
{B, WorkData2} = getAncestorWithLowestSemi(A, WorkData),
AncA = lookup({ancestor, A}, WorkData2),
WorkData3 = update(Node, {ancestor, AncA}, WorkData2),
DfSemiB = lookup({dfnum, lookup({semi, B}, WorkData3)}, WorkData3),
BestN = lookup({best, Node}, WorkData3),
SemiB = lookup({semi, BestN}, WorkData3),
DfSemiBestN = lookup({dfnum, SemiB}, WorkData3),
case DfSemiB < DfSemiBestN of
true ->
{B, update(Node, {best, B}, WorkData3)};
false ->
{BestN, WorkData3}
end
end
end.
%%>----------------------------------------------------------------------<
%% Procedure : linkTrees/3
%% Purpose : The main purpose of this function is to combine two trees
%% into one (accomplished by setting the ancestor for node
%% Node to Parent). The algorithm is also updating the best field
%% in the workDataCell for node Node to the value of itself.
%% Arguments : Parent - The parent of the node Node.
%% Node - The node to process
%% WorkData - Table consisting of workDataCells
%% Returns : An updated version of table WorkData
%%>----------------------------------------------------------------------<
linkTrees(Parent, Node, WorkData) ->
update(Node, [{ancestor, Parent}, {best, Node}], WorkData).
%%>----------------------------------------------------------------------<
%% Procedure : filterBucket/4
%% Purpose : The purpose of this algorith is to compute the dominator of
%% the node Node by utilizing the first clause of the Dominator
%% Theorem. If the first clause of the theorem doesn't apply
%% then the computation of that particular node is deferred to
%% a later stage (see finalize).
%% Arguments : Nodes - The list of CFG nodes that need to be computed.
%% Parent - The parent of the nodes in the list Nodes
%% WorkData - Table consisting of workDataCells
%% DomData - Table consisting of domTree cells.
%% Returns : An updated version of the tables WorkData and DomData
%%>----------------------------------------------------------------------<
filterBucket([Node|Nodes], Parent, WorkData, DomData) ->
{Y, WorkData2} = getAncestorWithLowestSemi(Node, WorkData),
{WorkData3, DomData2} =
case lookup({semi, Y}, WorkData2) =:= lookup({semi, Node}, WorkData2) of
true -> {WorkData2, setIDom(Node, Parent, DomData)};
false -> {update(Node, {samedom, Y}, WorkData2), DomData}
end,
filterBucket(Nodes, Parent, WorkData3, DomData2);
filterBucket([], _, WorkData, DomData) ->
{WorkData, DomData}.
%%>----------------------------------------------------------------------<
%% Procedure : finalize/5
%% Purpose : This algorithm finishes up the second clause of the Dominator
%% Theorem. Hence, the main purpose of this function is therefore
%% to update the dominator tree with the nodes that were deferred
%% in the filterBucket algorithm.
%% Arguments : WorkData - Table consisting of workDataCells
%% DomData - Table consisting of domTree cells
%% N - The index used for retrieving the node to be
%% processed
%% Max - Maximum node index
%% Returns : An updated version of the table DomData
%%>----------------------------------------------------------------------<
finalize(WorkData, DomData, N, Max, DFS) when N =< Max ->
Node = lookup_table(N, DFS),
case lookup({samedom, Node}, WorkData) of
none ->
finalize(WorkData, DomData, N + 1, Max, DFS);
SameDomN ->
case domTree_getIDom(SameDomN, DomData) of
IdomSameDomN when is_integer(IdomSameDomN) ->
DomData2 = setIDom(Node, IdomSameDomN, DomData),
finalize(WorkData, DomData2, N + 1, Max, DFS)
end
end;
finalize(_, DomData, _, _, _) ->
DomData.
%%>----------------------------------------------------------------------<
%% Procedure : domTree_dominates/3
%% Purpose : checks wheter Node1 dominates Node2 with respect to the
%% dominator tree DomTree
%% Arguments : Node1 the possible dominator, Node2 which might be dominated
%% and DomTree - the target dominator tree.
%% Notes : Relies on lists:any to return false when the a list is empty
%%>----------------------------------------------------------------------<
-spec domTree_dominates(cfg_lbl(), cfg_lbl(), domTree()) -> boolean().
domTree_dominates(Node1, Node1, _DomTree) ->
true;
domTree_dominates(Node1, Node2, DomTree) ->
Children = domTree_getChildren(Node1, DomTree),
lists:any(fun(X) -> domTree_dominates(X, Node2, DomTree) end, Children).
%%>----------------------------------------------------------------------<
%% Procedure : pp/1
%% Purpose : Pretty Printing a dominator tree.
%% Arguments : DomTree - the target dominator tree.
%% Notes : Uses pp/2 and pp_children to perform its task.
%%>----------------------------------------------------------------------<
-ifdef(DEBUG).
domTree_pp(DomTree) ->
io:format("Domtree:\nRoot: ~w\nSize: ~w\n", [domTree_getRoot(DomTree),
domTree_getSize(DomTree)]),
domTree_pp(domTree_getRoot(DomTree), DomTree).
domTree_pp(N, DomTree) ->
case domTree_getNode(N, DomTree) of
{value, {IDom, Children}} ->
io:format("Node: ~w\n\tIDom: ~w\n\tChildren: ~w\n\n",
[N, IDom, Children]),
domTree_pp_children(Children, DomTree);
none ->
failed
end.
domTree_pp_children([Child|T], DomTree) ->
domTree_pp(Child, DomTree),
domTree_pp_children(T, DomTree);
domTree_pp_children([], _) ->
ok.
-endif. %% DEBUG
%%========================================================================
%%
%% CODE FOR CREATING AND MANIPULATING DOMINANCE FRONTIERS.
%%
%%========================================================================
-type domFrontier() :: gb_tree().
%%>----------------------------------------------------------------------<
%% Procedure : domFrontier_create
%% Purpose : This function calculates the Dominance Frontiers given
%% a CFG and a Dominator Tree.
%% Arguments : SuccMap - The successor map of the CFG we are working with.
%% DomTree - The dominance tree of the CFG.
%% Notes : DomTree must actually be the dominance tree of the CFG.
%%>----------------------------------------------------------------------<
-spec domFrontier_create(cfg(), domTree()) -> domFrontier().
domFrontier_create(SuccMap, DomTree) ->
df_create(domTree_getRoot(DomTree), SuccMap, DomTree, df__empty()).
df_create(Node, SuccMap, DomTree, DF) ->
Children = domTree_getChildren(Node, DomTree),
Succ = hipe_gen_cfg:succ(SuccMap, Node),
DF1 = checkIDomList(Succ, Node, DomTree, DF),
makeDFChildren(Children, Node, SuccMap, DomTree, DF1).
%%>----------------------------------------------------------------------<
%% Procedure : domFrontier_get
%% Purpose : This function returns the Dominance Frontier for Node.
%% Arguments : Node - The node whose Dominance Frontier we request
%% DF - The Dominance Frontier structure
%% Returns :
%%>----------------------------------------------------------------------<
-spec domFrontier_get(cfg_lbl(), domFrontier()) -> [cfg_lbl()].
domFrontier_get(Node, DF) ->
case gb_trees:lookup(Node, DF) of
{value, List} -> List;
none -> []
end.
%%>----------------------------------------------------------------------<
%% Procedure : df__empty
%% Purpose : This function creates an empty instance of the Dominance
%% Frontiers (DF) structure.
%%>----------------------------------------------------------------------<
df__empty() ->
gb_trees:empty().
%%>----------------------------------------------------------------------<
%% Procedure : df__add
%% Purpose : This function adds Node to N in DF.
%% Arguments : N - The value being inserted
%% Node - The node getting the value
%% DF - The Dominance Frontiers
%% Returns : DF
%% Notes : If Node already exists at position N, it is not added again.
%%>----------------------------------------------------------------------<
df__add_to_node(N, Node, DF) ->
case gb_trees:lookup(N, DF) of
{value, DFList} ->
case lists:member(Node, DFList) of
true ->
DF;
false ->
gb_trees:update(N, [Node|DFList], DF)
end;
none ->
gb_trees:insert(N, [Node], DF)
end.
%%>----------------------------------------------------------------------<
%% Procedure : makeDFChildren
%% Purpose : This function calculates the dominance frontiers of the
%% children of the parent and adds the nodes in these
%% dominance frontiers who are not immediate dominantors of
%% the parent to parents dominance frontier.
%% Arguments : ChildList - The list of children that the function traverses
%% Parent - The parent of the children
%% SuccMap - The successor map of the CFG
%% DomTree - The dominantor tree of the CFG
%% DF - The dominance frontiers so far
%%>----------------------------------------------------------------------<
makeDFChildren([Child|T], Parent, SuccMap, DomTree, DF) ->
DF1 = df_create(Child, SuccMap, DomTree, DF),
DF2 = checkIDomList(domFrontier_get(Child, DF1), Parent, DomTree, DF1),
makeDFChildren(T, Parent, SuccMap, DomTree, DF2);
makeDFChildren([], _, _, _, DF) ->
DF.
%%>----------------------------------------------------------------------<
%% Procedure : checIDomList
%% Purpose : Adds all the nodes in the list to the parents dominance
%% frontier who do not have parent as immediate dominator.
%% Arguments : NodeList - The list of nodes that the function traverses
%% Parent - The parent of the nodes
%% DomTree - Our dominator tree
%% DF - The dominance frontiers so far
%%>----------------------------------------------------------------------<
checkIDomList([Node|T], Parent, DomTree, DF) ->
DF1 = checkIDom(Node, Parent, DomTree, DF),
checkIDomList(T, Parent, DomTree, DF1);
checkIDomList([], _, _, DF) ->
DF.
%%>----------------------------------------------------------------------<
%% Procedure : checkIdom
%% Purpose : Adds Node1 to Node2's dominance frontier if Node2 is not
%% Node1's immediate dominator.
%% Arguments : Node1 - a node
%% Node2 - another node
%% DomTree - the dominator tree
%% DF - the dominance frontier so far
%%>----------------------------------------------------------------------<
checkIDom(Node1, Node2, DomTree, DF) ->
case domTree_getIDom(Node1, DomTree) of
Node2 ->
DF;
none ->
DF;
_ ->
df__add_to_node(Node2, Node1, DF)
end.
