aboutsummaryrefslogblamecommitdiffstats
path: root/lib/hipe/flow/hipe_dominators.erl
blob: 50d45c7c723c6250becd0bac7c298a715fccca08 (plain) (tree)
1
2
3
4
5
6
7
8
9
10
11
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
                                 
                   
  
                                                        
  



                                                                      
  


                                                                         
  


                                                                          
                                                           















                                                                           
                          
















                                                                          
                                                                


















































































































































































































































































































































































































































































































































                                                                                 
                                       


























































































































                                                                           
%% -*- erlang-indent-level: 2 -*-
%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2004-2014. 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
%% under the License.
%%
%% %CopyrightEnd%
%%
%%------------------------------------------------------------------------
%% File    : hipe_dominators.erl
%% Author  : Christoffer Vikström <chvi3471@student.uu.se>
%%           Daniel Deogun        <dade4543@student.uu.se>
%%           Jesper Bengtsson     <jebe8371@student.uu.se>
%% 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_trees: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_trees: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.