summaryrefslogtreecommitdiff
path: root/gcc/dominance.c
blob: 5e69b077bf59c6108173dcfac0970c943b4fec83 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
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
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
/* Calculate (post)dominators in slightly super-linear time.
   Copyright (C) 2000 Free Software Foundation, Inc.
   Contributed by Michael Matz (matz@ifh.de).
  
   This file is part of GCC.
 
   GCC is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2, or (at your option)
   any later version.

   GCC is distributed in the hope that it will be useful, but WITHOUT
   ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
   or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
   License for more details.

   You should have received a copy of the GNU General Public License
   along with GCC; see the file COPYING.  If not, write to the Free
   Software Foundation, 59 Temple Place - Suite 330, Boston, MA
   02111-1307, USA.  */

/* This file implements the well known algorithm from Lengauer and Tarjan
   to compute the dominators in a control flow graph.  A basic block D is said
   to dominate another block X, when all paths from the entry node of the CFG
   to X go also over D.  The dominance relation is a transitive reflexive
   relation and its minimal transitive reduction is a tree, called the
   dominator tree.  So for each block X besides the entry block exists a
   block I(X), called the immediate dominator of X, which is the parent of X
   in the dominator tree.

   The algorithm computes this dominator tree implicitely by computing for
   each block its immediate dominator.  We use tree balancing and path
   compression, so its the O(e*a(e,v)) variant, where a(e,v) is the very
   slowly growing functional inverse of the Ackerman function.  */

#include "config.h"
#include "system.h"
#include "rtl.h"
#include "hard-reg-set.h"
#include "basic-block.h"


/* We name our nodes with integers, beginning with 1.  Zero is reserved for
   'undefined' or 'end of list'.  The name of each node is given by the dfs
   number of the corresponding basic block.  Please note, that we include the
   artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to
   support multiple entry points.  As it has no real basic block index we use
   'n_basic_blocks' for that.  Its dfs number is of course 1.  */

/* Type of Basic Block aka. TBB */
typedef unsigned int TBB;

/* We work in a poor-mans object oriented fashion, and carry an instance of
   this structure through all our 'methods'.  It holds various arrays
   reflecting the (sub)structure of the flowgraph.  Most of them are of type
   TBB and are also indexed by TBB.  */

struct dom_info
{
  /* The parent of a node in the DFS tree.  */
  TBB *dfs_parent;
  /* For a node x key[x] is roughly the node nearest to the root from which
     exists a way to x only over nodes behind x.  Such a node is also called
     semidominator.  */
  TBB *key;
  /* The value in path_min[x] is the node y on the path from x to the root of
     the tree x is in with the smallest key[y].  */
  TBB *path_min;
  /* bucket[x] points to the first node of the set of nodes having x as key.  */
  TBB *bucket;
  /* And next_bucket[x] points to the next node.  */
  TBB *next_bucket;
  /* After the algorithm is done, dom[x] contains the immediate dominator
     of x.  */
  TBB *dom;

  /* The following few fields implement the structures needed for disjoint
     sets.  */
  /* set_chain[x] is the next node on the path from x to the representant
     of the set containing x.  If set_chain[x]==0 then x is a root.  */
  TBB *set_chain;
  /* set_size[x] is the number of elements in the set named by x.  */
  unsigned int *set_size;
  /* set_child[x] is used for balancing the tree representing a set.  It can
     be understood as the next sibling of x.  */
  TBB *set_child;

  /* If b is the number of a basic block (BB->index), dfs_order[b] is the
     number of that node in DFS order counted from 1.  This is an index
     into most of the other arrays in this structure.  */
  TBB *dfs_order;
  /* If x is the DFS-index of a node which correspondends with an basic block,
     dfs_to_bb[x] is that basic block.  Note, that in our structure there are
     more nodes that basic blocks, so only dfs_to_bb[dfs_order[bb->index]]==bb
     is true for every basic block bb, but not the opposite.  */
  basic_block *dfs_to_bb;

  /* This is the next free DFS number when creating the DFS tree or forest.  */
  unsigned int dfsnum;
  /* The number of nodes in the DFS tree (==dfsnum-1).  */
  unsigned int nodes;
};

static void init_dom_info		PARAMS ((struct dom_info *));
static void free_dom_info		PARAMS ((struct dom_info *));
static void calc_dfs_tree_nonrec	PARAMS ((struct dom_info *,
						 basic_block,
						 enum cdi_direction));
static void calc_dfs_tree		PARAMS ((struct dom_info *,
						 enum cdi_direction));
static void compress			PARAMS ((struct dom_info *, TBB));
static TBB eval				PARAMS ((struct dom_info *, TBB));
static void link_roots			PARAMS ((struct dom_info *, TBB, TBB));
static void calc_idoms			PARAMS ((struct dom_info *,
						 enum cdi_direction));
static void idoms_to_doms		PARAMS ((struct dom_info *,
						 sbitmap *));

/* Helper macro for allocating and initializing an array,
   for aesthetic reasons.  */
#define init_ar(var, type, num, content)			\
  do {								\
    unsigned int i = 1;    /* Catch content == i.  */		\
    if (! (content))						\
      (var) = (type *) xcalloc ((num), sizeof (type));		\
    else							\
      {								\
        (var) = (type *) xmalloc ((num) * sizeof (type));	\
	for (i = 0; i < num; i++)				\
	  (var)[i] = (content);					\
      }								\
  } while (0)

/* Allocate all needed memory in a pessimistic fashion (so we round up).
   This initialises the contents of DI, which already must be allocated.  */

static void
init_dom_info (di)
     struct dom_info *di;
{
  /* We need memory for n_basic_blocks nodes and the ENTRY_BLOCK or
     EXIT_BLOCK.  */
  unsigned int num = n_basic_blocks + 1 + 1;
  init_ar (di->dfs_parent, TBB, num, 0);
  init_ar (di->path_min, TBB, num, i);
  init_ar (di->key, TBB, num, i);
  init_ar (di->dom, TBB, num, 0);

  init_ar (di->bucket, TBB, num, 0);
  init_ar (di->next_bucket, TBB, num, 0);

  init_ar (di->set_chain, TBB, num, 0);
  init_ar (di->set_size, unsigned int, num, 1);
  init_ar (di->set_child, TBB, num, 0);

  init_ar (di->dfs_order, TBB, (unsigned int) n_basic_blocks + 1, 0);
  init_ar (di->dfs_to_bb, basic_block, num, 0);

  di->dfsnum = 1;
  di->nodes = 0;
}

#undef init_ar

/* Free all allocated memory in DI, but not DI itself.  */

static void
free_dom_info (di)
     struct dom_info *di;
{
  free (di->dfs_parent);
  free (di->path_min);
  free (di->key);
  free (di->dom);
  free (di->bucket);
  free (di->next_bucket);
  free (di->set_chain);
  free (di->set_size);
  free (di->set_child);
  free (di->dfs_order);
  free (di->dfs_to_bb);
}

/* The nonrecursive variant of creating a DFS tree.  DI is our working
   structure, BB the starting basic block for this tree and REVERSE
   is true, if predecessors should be visited instead of successors of a
   node.  After this is done all nodes reachable from BB were visited, have
   assigned their dfs number and are linked together to form a tree.  */

static void
calc_dfs_tree_nonrec (di, bb, reverse)
     struct dom_info *di;
     basic_block bb;
     enum cdi_direction reverse;
{
  /* We never call this with bb==EXIT_BLOCK_PTR (ENTRY_BLOCK_PTR if REVERSE).  */
  /* We call this _only_ if bb is not already visited.  */
  edge e;
  TBB child_i, my_i = 0;
  edge *stack;
  int sp;
  /* Start block (ENTRY_BLOCK_PTR for forward problem, EXIT_BLOCK for backward
     problem).  */
  basic_block en_block;
  /* Ending block.  */
  basic_block ex_block;

  stack = (edge *) xmalloc ((n_basic_blocks + 3) * sizeof (edge));
  sp = 0;

  /* Initialize our border blocks, and the first edge.  */
  if (reverse)
    {
      e = bb->pred;
      en_block = EXIT_BLOCK_PTR;
      ex_block = ENTRY_BLOCK_PTR;
    }
  else
    {
      e = bb->succ;
      en_block = ENTRY_BLOCK_PTR;
      ex_block = EXIT_BLOCK_PTR;
    }

  /* When the stack is empty we break out of this loop.  */
  while (1)
    {
      basic_block bn;

      /* This loop traverses edges e in depth first manner, and fills the
         stack.  */
      while (e)
	{
	  edge e_next;

	  /* Deduce from E the current and the next block (BB and BN), and the
	     next edge.  */
	  if (reverse)
	    {
	      bn = e->src;

	      /* If the next node BN is either already visited or a border
	         block the current edge is useless, and simply overwritten
	         with the next edge out of the current node.  */
	      if (bn == ex_block || di->dfs_order[bn->index])
		{
		  e = e->pred_next;
		  continue;
		}
	      bb = e->dest;
	      e_next = bn->pred;
	    }
	  else
	    {
	      bn = e->dest;
	      if (bn == ex_block || di->dfs_order[bn->index])
		{
		  e = e->succ_next;
		  continue;
		}
	      bb = e->src;
	      e_next = bn->succ;
	    }

	  if (bn == en_block)
	    abort ();

	  /* Fill the DFS tree info calculatable _before_ recursing.  */
	  if (bb != en_block)
	    my_i = di->dfs_order[bb->index];
	  else
	    my_i = di->dfs_order[n_basic_blocks];
	  child_i = di->dfs_order[bn->index] = di->dfsnum++;
	  di->dfs_to_bb[child_i] = bn;
	  di->dfs_parent[child_i] = my_i;

	  /* Save the current point in the CFG on the stack, and recurse.  */
	  stack[sp++] = e;
	  e = e_next;
	}

      if (!sp)
	break;
      e = stack[--sp];

      /* OK.  The edge-list was exhausted, meaning normally we would
         end the recursion.  After returning from the recursive call,
         there were (may be) other statements which were run after a
         child node was completely considered by DFS.  Here is the
         point to do it in the non-recursive variant.
         E.g. The block just completed is in e->dest for forward DFS,
         the block not yet completed (the parent of the one above)
         in e->src.  This could be used e.g. for computing the number of
         descendants or the tree depth.  */
      if (reverse)
	e = e->pred_next;
      else
	e = e->succ_next;
    }
  free (stack);
}

/* The main entry for calculating the DFS tree or forest.  DI is our working
   structure and REVERSE is true, if we are interested in the reverse flow
   graph.  In that case the result is not necessarily a tree but a forest,
   because there may be nodes from which the EXIT_BLOCK is unreachable.  */

static void
calc_dfs_tree (di, reverse)
     struct dom_info *di;
     enum cdi_direction reverse;
{
  /* The first block is the ENTRY_BLOCK (or EXIT_BLOCK if REVERSE).  */
  basic_block begin = reverse ? EXIT_BLOCK_PTR : ENTRY_BLOCK_PTR;
  di->dfs_order[n_basic_blocks] = di->dfsnum;
  di->dfs_to_bb[di->dfsnum] = begin;
  di->dfsnum++;

  calc_dfs_tree_nonrec (di, begin, reverse);

  if (reverse)
    {
      /* In the post-dom case we may have nodes without a path to EXIT_BLOCK.
         They are reverse-unreachable.  In the dom-case we disallow such
         nodes, but in post-dom we have to deal with them, so we simply
         include them in the DFS tree which actually becomes a forest.  */
      int i;
      for (i = n_basic_blocks - 1; i >= 0; i--)
	{
	  basic_block b = BASIC_BLOCK (i);
	  if (di->dfs_order[b->index])
	    continue;
	  di->dfs_order[b->index] = di->dfsnum;
	  di->dfs_to_bb[di->dfsnum] = b;
	  di->dfsnum++;
	  calc_dfs_tree_nonrec (di, b, reverse);
	}
    }

  di->nodes = di->dfsnum - 1;

  /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all.  */
  if (di->nodes != (unsigned int) n_basic_blocks + 1)
    abort ();
}

/* Compress the path from V to the root of its set and update path_min at the
   same time.  After compress(di, V) set_chain[V] is the root of the set V is
   in and path_min[V] is the node with the smallest key[] value on the path
   from V to that root.  */

static void
compress (di, v)
     struct dom_info *di;
     TBB v;
{
  /* Btw. It's not worth to unrecurse compress() as the depth is usually not
     greater than 5 even for huge graphs (I've not seen call depth > 4).
     Also performance wise compress() ranges _far_ behind eval().  */
  TBB parent = di->set_chain[v];
  if (di->set_chain[parent])
    {
      compress (di, parent);
      if (di->key[di->path_min[parent]] < di->key[di->path_min[v]])
	di->path_min[v] = di->path_min[parent];
      di->set_chain[v] = di->set_chain[parent];
    }
}

/* Compress the path from V to the set root of V if needed (when the root has
   changed since the last call).  Returns the node with the smallest key[]
   value on the path from V to the root.  */

static inline TBB
eval (di, v)
     struct dom_info *di;
     TBB v;
{
  /* The representant of the set V is in, also called root (as the set
     representation is a tree).  */
  TBB rep = di->set_chain[v];

  /* V itself is the root.  */
  if (!rep)
    return di->path_min[v];

  /* Compress only if necessary.  */
  if (di->set_chain[rep])
    {
      compress (di, v);
      rep = di->set_chain[v];
    }

  if (di->key[di->path_min[rep]] >= di->key[di->path_min[v]])
    return di->path_min[v];
  else
    return di->path_min[rep];
}

/* This essentially merges the two sets of V and W, giving a single set with
   the new root V.  The internal representation of these disjoint sets is a
   balanced tree.  Currently link(V,W) is only used with V being the parent
   of W.  */

static void
link_roots (di, v, w)
     struct dom_info *di;
     TBB v, w;
{
  TBB s = w;

  /* Rebalance the tree.  */
  while (di->key[di->path_min[w]] < di->key[di->path_min[di->set_child[s]]])
    {
      if (di->set_size[s] + di->set_size[di->set_child[di->set_child[s]]]
	  >= 2 * di->set_size[di->set_child[s]])
	{
	  di->set_chain[di->set_child[s]] = s;
	  di->set_child[s] = di->set_child[di->set_child[s]];
	}
      else
	{
	  di->set_size[di->set_child[s]] = di->set_size[s];
	  s = di->set_chain[s] = di->set_child[s];
	}
    }

  di->path_min[s] = di->path_min[w];
  di->set_size[v] += di->set_size[w];
  if (di->set_size[v] < 2 * di->set_size[w])
    {
      TBB tmp = s;
      s = di->set_child[v];
      di->set_child[v] = tmp;
    }

  /* Merge all subtrees.  */
  while (s)
    {
      di->set_chain[s] = v;
      s = di->set_child[s];
    }
}

/* This calculates the immediate dominators (or post-dominators if REVERSE is
   true).  DI is our working structure and should hold the DFS forest.
   On return the immediate dominator to node V is in di->dom[V].  */

static void
calc_idoms (di, reverse)
     struct dom_info *di;
     enum cdi_direction reverse;
{
  TBB v, w, k, par;
  basic_block en_block;
  if (reverse)
    en_block = EXIT_BLOCK_PTR;
  else
    en_block = ENTRY_BLOCK_PTR;

  /* Go backwards in DFS order, to first look at the leafs.  */
  v = di->nodes;
  while (v > 1)
    {
      basic_block bb = di->dfs_to_bb[v];
      edge e, e_next;

      par = di->dfs_parent[v];
      k = v;
      if (reverse)
	e = bb->succ;
      else
	e = bb->pred;

      /* Search all direct predecessors for the smallest node with a path
         to them.  That way we have the smallest node with also a path to
         us only over nodes behind us.  In effect we search for our
         semidominator.  */
      for (; e; e = e_next)
	{
	  TBB k1;
	  basic_block b;

	  if (reverse)
	    {
	      b = e->dest;
	      e_next = e->succ_next;
	    }
	  else
	    {
	      b = e->src;
	      e_next = e->pred_next;
	    }
	  if (b == en_block)
	    k1 = di->dfs_order[n_basic_blocks];
	  else
	    k1 = di->dfs_order[b->index];

	  /* Call eval() only if really needed.  If k1 is above V in DFS tree,
	     then we know, that eval(k1) == k1 and key[k1] == k1.  */
	  if (k1 > v)
	    k1 = di->key[eval (di, k1)];
	  if (k1 < k)
	    k = k1;
	}

      di->key[v] = k;
      link_roots (di, par, v);
      di->next_bucket[v] = di->bucket[k];
      di->bucket[k] = v;

      /* Transform semidominators into dominators.  */
      for (w = di->bucket[par]; w; w = di->next_bucket[w])
	{
	  k = eval (di, w);
	  if (di->key[k] < di->key[w])
	    di->dom[w] = k;
	  else
	    di->dom[w] = par;
	}
      /* We don't need to cleanup next_bucket[].  */
      di->bucket[par] = 0;
      v--;
    }

  /* Explicitely define the dominators.  */
  di->dom[1] = 0;
  for (v = 2; v <= di->nodes; v++)
    if (di->dom[v] != di->key[v])
      di->dom[v] = di->dom[di->dom[v]];
}

/* Convert the information about immediate dominators (in DI) to sets of all
   dominators (in DOMINATORS).  */

static void
idoms_to_doms (di, dominators)
     struct dom_info *di;
     sbitmap *dominators;
{
  TBB i, e_index;
  int bb, bb_idom;
  sbitmap_vector_zero (dominators, n_basic_blocks);
  /* We have to be careful, to not include the ENTRY_BLOCK or EXIT_BLOCK
     in the list of (post)-doms, so remember that in e_index.  */
  e_index = di->dfs_order[n_basic_blocks];

  for (i = 1; i <= di->nodes; i++)
    {
      if (i == e_index)
	continue;
      bb = di->dfs_to_bb[i]->index;

      if (di->dom[i] && (di->dom[i] != e_index))
	{
	  bb_idom = di->dfs_to_bb[di->dom[i]]->index;
	  sbitmap_copy (dominators[bb], dominators[bb_idom]);
	}
      else
	{
	  /* It has no immediate dom or only ENTRY_BLOCK or EXIT_BLOCK.
	     If it is a child of ENTRY_BLOCK that's OK, and it's only
	     dominated by itself; if it's _not_ a child of ENTRY_BLOCK, it
	     means, it is unreachable.  That case has been disallowed in the
	     building of the DFS tree, so we are save here.  For the reverse
	     flow graph it means, it has no children, so, to be compatible
	     with the old code, we set the post_dominators to all one.  */
	  if (!di->dom[i])
	    {
	      sbitmap_ones (dominators[bb]);
	    }
	}
      SET_BIT (dominators[bb], bb);
    }
}

/* The main entry point into this module.  IDOM is an integer array with room
   for n_basic_blocks integers, DOMS is a preallocated sbitmap array having
   room for n_basic_blocks^2 bits, and POST is true if the caller wants to
   know post-dominators.

   On return IDOM[i] will be the BB->index of the immediate (post) dominator
   of basic block i, and DOMS[i] will have set bit j if basic block j is a
   (post)dominator for block i.

   Either IDOM or DOMS may be NULL (meaning the caller is not interested in
   immediate resp. all dominators).  */

void
calculate_dominance_info (idom, doms, reverse)
     int *idom;
     sbitmap *doms;
     enum cdi_direction reverse;
{
  struct dom_info di;

  if (!doms && !idom)
    return;
  init_dom_info (&di);
  calc_dfs_tree (&di, reverse);
  calc_idoms (&di, reverse);

  if (idom)
    {
      int i;
      for (i = 0; i < n_basic_blocks; i++)
	{
	  basic_block b = BASIC_BLOCK (i);
	  TBB d = di.dom[di.dfs_order[b->index]];

	  /* The old code didn't modify array elements of nodes having only
	     itself as dominator (d==0) or only ENTRY_BLOCK (resp. EXIT_BLOCK)
	     (d==1).  */
	  if (d > 1)
	    idom[i] = di.dfs_to_bb[d]->index;
	}
    }
  if (doms)
    idoms_to_doms (&di, doms);

  free_dom_info (&di);
}