gcc/dominance.c

   1 /* Calculate (post)dominators in slightly super-linear time.
   2    Copyright (C) 2000 Free Software Foundation, Inc.
   3    Contributed by Michael Matz (matz@ifh.de).
   4
   5    This file is part of GCC.
   6
   7    GCC is free software; you can redistribute it and/or modify it
   8    under the terms of the GNU General Public License as published by
   9    the Free Software Foundation; either version 2, or (at your option)
  10    any later version.
  11
  12    GCC is distributed in the hope that it will be useful, but WITHOUT
  13    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  14    or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
  15    License for more details.
  16
  17    You should have received a copy of the GNU General Public License
  18    along with GCC; see the file COPYING.  If not, write to the Free
  19    Software Foundation, 59 Temple Place - Suite 330, Boston, MA
  20    02111-1307, USA.  */
  21
  22 /* This file implements the well known algorithm from Lengauer and Tarjan
  23    to compute the dominators in a control flow graph.  A basic block D is said
  24    to dominate another block X, when all paths from the entry node of the CFG
  25    to X go also over D.  The dominance relation is a transitive reflexive
  26    relation and its minimal transitive reduction is a tree, called the
  27    dominator tree.  So for each block X besides the entry block exists a
  28    block I(X), called the immediate dominator of X, which is the parent of X
  29    in the dominator tree.
  30
  31    The algorithm computes this dominator tree implicitly by computing for
  32    each block its immediate dominator.  We use tree balancing and path
  33    compression, so its the O(e*a(e,v)) variant, where a(e,v) is the very
  34    slowly growing functional inverse of the Ackerman function.  */
  35
  36 #include "config.h"
  37 #include "system.h"
  38 #include "rtl.h"
  39 #include "hard-reg-set.h"
  40 #include "basic-block.h"
  41
  42
  43 /* We name our nodes with integers, beginning with 1.  Zero is reserved for
  44    'undefined' or 'end of list'.  The name of each node is given by the dfs
  45    number of the corresponding basic block.  Please note, that we include the
  46    artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to
  47    support multiple entry points.  As it has no real basic block index we use
  48    'last_basic_block' for that.  Its dfs number is of course 1.  */
  49
  50 /* Type of Basic Block aka. TBB */
  51 typedef unsigned int TBB;
  52
  53 /* We work in a poor-mans object oriented fashion, and carry an instance of
  54    this structure through all our 'methods'.  It holds various arrays
  55    reflecting the (sub)structure of the flowgraph.  Most of them are of type
  56    TBB and are also indexed by TBB.  */
  57
  58 struct dom_info
  59 {
  60   /* The parent of a node in the DFS tree.  */
  61   TBB *dfs_parent;
  62   /* For a node x key[x] is roughly the node nearest to the root from which
  63      exists a way to x only over nodes behind x.  Such a node is also called
  64      semidominator.  */
  65   TBB *key;
  66   /* The value in path_min[x] is the node y on the path from x to the root of
  67      the tree x is in with the smallest key[y].  */
  68   TBB *path_min;
  69   /* bucket[x] points to the first node of the set of nodes having x as key.  */
  70   TBB *bucket;
  71   /* And next_bucket[x] points to the next node.  */
  72   TBB *next_bucket;
  73   /* After the algorithm is done, dom[x] contains the immediate dominator
  74      of x.  */
  75   TBB *dom;
  76
  77   /* The following few fields implement the structures needed for disjoint
  78      sets.  */
  79   /* set_chain[x] is the next node on the path from x to the representant
  80      of the set containing x.  If set_chain[x]==0 then x is a root.  */
  81   TBB *set_chain;
  82   /* set_size[x] is the number of elements in the set named by x.  */
  83   unsigned int *set_size;
  84   /* set_child[x] is used for balancing the tree representing a set.  It can
  85      be understood as the next sibling of x.  */
  86   TBB *set_child;
  87
  88   /* If b is the number of a basic block (BB->index), dfs_order[b] is the
  89      number of that node in DFS order counted from 1.  This is an index
  90      into most of the other arrays in this structure.  */
  91   TBB *dfs_order;
  92   /* If x is the DFS-index of a node which corresponds with an basic block,
  93      dfs_to_bb[x] is that basic block.  Note, that in our structure there are
  94      more nodes that basic blocks, so only dfs_to_bb[dfs_order[bb->index]]==bb
  95      is true for every basic block bb, but not the opposite.  */
  96   basic_block *dfs_to_bb;
  97
  98   /* This is the next free DFS number when creating the DFS tree or forest.  */
  99   unsigned int dfsnum;
 100   /* The number of nodes in the DFS tree (==dfsnum-1).  */
 101   unsigned int nodes;
 102 };
 103
 104 static void init_dom_info               PARAMS ((struct dom_info *));
 105 static void free_dom_info               PARAMS ((struct dom_info *));
 106 static void calc_dfs_tree_nonrec        PARAMS ((struct dom_info *,
 107                                                  basic_block,
 108                                                  enum cdi_direction));
 109 static void calc_dfs_tree               PARAMS ((struct dom_info *,
 110                                                  enum cdi_direction));
 111 static void compress                    PARAMS ((struct dom_info *, TBB));
 112 static TBB eval                         PARAMS ((struct dom_info *, TBB));
 113 static void link_roots                  PARAMS ((struct dom_info *, TBB, TBB));
 114 static void calc_idoms                  PARAMS ((struct dom_info *,
 115                                                  enum cdi_direction));
 116 static void idoms_to_doms               PARAMS ((struct dom_info *,
 117                                                  sbitmap *));
 118
 119 /* Helper macro for allocating and initializing an array,
 120    for aesthetic reasons.  */
 121 #define init_ar(var, type, num, content)                        \
 122   do                                                            \
 123     {                                                           \
 124       unsigned int i = 1;    /* Catch content == i.  */         \
 125       if (! (content))                                          \
 126         (var) = (type *) xcalloc ((num), sizeof (type));        \
 127       else                                                      \
 128         {                                                       \
 129           (var) = (type *) xmalloc ((num) * sizeof (type));     \
 130           for (i = 0; i < num; i++)                             \
 131             (var)[i] = (content);                               \
 132         }                                                       \
 133     }                                                           \
 134   while (0)
 135
 136 /* Allocate all needed memory in a pessimistic fashion (so we round up).
 137    This initialises the contents of DI, which already must be allocated.  */
 138
 139 static void
 140 init_dom_info (di)
 141      struct dom_info *di;
 142 {
 143   /* We need memory for n_basic_blocks nodes and the ENTRY_BLOCK or
 144      EXIT_BLOCK.  */
 145   unsigned int num = n_basic_blocks + 1 + 1;
 146   init_ar (di->dfs_parent, TBB, num, 0);
 147   init_ar (di->path_min, TBB, num, i);
 148   init_ar (di->key, TBB, num, i);
 149   init_ar (di->dom, TBB, num, 0);
 150
 151   init_ar (di->bucket, TBB, num, 0);
 152   init_ar (di->next_bucket, TBB, num, 0);
 153
 154   init_ar (di->set_chain, TBB, num, 0);
 155   init_ar (di->set_size, unsigned int, num, 1);
 156   init_ar (di->set_child, TBB, num, 0);
 157
 158   init_ar (di->dfs_order, TBB, (unsigned int) last_basic_block + 1, 0);
 159   init_ar (di->dfs_to_bb, basic_block, num, 0);
 160
 161   di->dfsnum = 1;
 162   di->nodes = 0;
 163 }
 164
 165 #undef init_ar
 166
 167 /* Free all allocated memory in DI, but not DI itself.  */
 168
 169 static void
 170 free_dom_info (di)
 171      struct dom_info *di;
 172 {
 173   free (di->dfs_parent);
 174   free (di->path_min);
 175   free (di->key);
 176   free (di->dom);
 177   free (di->bucket);
 178   free (di->next_bucket);
 179   free (di->set_chain);
 180   free (di->set_size);
 181   free (di->set_child);
 182   free (di->dfs_order);
 183   free (di->dfs_to_bb);
 184 }
 185
 186 /* The nonrecursive variant of creating a DFS tree.  DI is our working
 187    structure, BB the starting basic block for this tree and REVERSE
 188    is true, if predecessors should be visited instead of successors of a
 189    node.  After this is done all nodes reachable from BB were visited, have
 190    assigned their dfs number and are linked together to form a tree.  */
 191
 192 static void
 193 calc_dfs_tree_nonrec (di, bb, reverse)
 194      struct dom_info *di;
 195      basic_block bb;
 196      enum cdi_direction reverse;
 197 {
 198   /* We never call this with bb==EXIT_BLOCK_PTR (ENTRY_BLOCK_PTR if REVERSE).  */
 199   /* We call this _only_ if bb is not already visited.  */
 200   edge e;
 201   TBB child_i, my_i = 0;
 202   edge *stack;
 203   int sp;
 204   /* Start block (ENTRY_BLOCK_PTR for forward problem, EXIT_BLOCK for backward
 205      problem).  */
 206   basic_block en_block;
 207   /* Ending block.  */
 208   basic_block ex_block;
 209
 210   stack = (edge *) xmalloc ((n_basic_blocks + 3) * sizeof (edge));
 211   sp = 0;
 212
 213   /* Initialize our border blocks, and the first edge.  */
 214   if (reverse)
 215     {
 216       e = bb->pred;
 217       en_block = EXIT_BLOCK_PTR;
 218       ex_block = ENTRY_BLOCK_PTR;
 219     }
 220   else
 221     {
 222       e = bb->succ;
 223       en_block = ENTRY_BLOCK_PTR;
 224       ex_block = EXIT_BLOCK_PTR;
 225     }
 226
 227   /* When the stack is empty we break out of this loop.  */
 228   while (1)
 229     {
 230       basic_block bn;
 231
 232       /* This loop traverses edges e in depth first manner, and fills the
 233          stack.  */
 234       while (e)
 235         {
 236           edge e_next;
 237
 238           /* Deduce from E the current and the next block (BB and BN), and the
 239              next edge.  */
 240           if (reverse)
 241             {
 242               bn = e->src;
 243
 244               /* If the next node BN is either already visited or a border
 245                  block the current edge is useless, and simply overwritten
 246                  with the next edge out of the current node.  */
 247               if (bn == ex_block || di->dfs_order[bn->index])
 248                 {
 249                   e = e->pred_next;
 250                   continue;
 251                 }
 252               bb = e->dest;
 253               e_next = bn->pred;
 254             }
 255           else
 256             {
 257               bn = e->dest;
 258               if (bn == ex_block || di->dfs_order[bn->index])
 259                 {
 260                   e = e->succ_next;
 261                   continue;
 262                 }
 263               bb = e->src;
 264               e_next = bn->succ;
 265             }
 266
 267           if (bn == en_block)
 268             abort ();
 269
 270           /* Fill the DFS tree info calculatable _before_ recursing.  */
 271           if (bb != en_block)
 272             my_i = di->dfs_order[bb->index];
 273           else
 274             my_i = di->dfs_order[last_basic_block];
 275           child_i = di->dfs_order[bn->index] = di->dfsnum++;
 276           di->dfs_to_bb[child_i] = bn;
 277           di->dfs_parent[child_i] = my_i;
 278
 279           /* Save the current point in the CFG on the stack, and recurse.  */
 280           stack[sp++] = e;
 281           e = e_next;
 282         }
 283
 284       if (!sp)
 285         break;
 286       e = stack[--sp];
 287
 288       /* OK.  The edge-list was exhausted, meaning normally we would
 289          end the recursion.  After returning from the recursive call,
 290          there were (may be) other statements which were run after a
 291          child node was completely considered by DFS.  Here is the
 292          point to do it in the non-recursive variant.
 293          E.g. The block just completed is in e->dest for forward DFS,
 294          the block not yet completed (the parent of the one above)
 295          in e->src.  This could be used e.g. for computing the number of
 296          descendants or the tree depth.  */
 297       if (reverse)
 298         e = e->pred_next;
 299       else
 300         e = e->succ_next;
 301     }
 302   free (stack);
 303 }
 304
 305 /* The main entry for calculating the DFS tree or forest.  DI is our working
 306    structure and REVERSE is true, if we are interested in the reverse flow
 307    graph.  In that case the result is not necessarily a tree but a forest,
 308    because there may be nodes from which the EXIT_BLOCK is unreachable.  */
 309
 310 static void
 311 calc_dfs_tree (di, reverse)
 312      struct dom_info *di;
 313      enum cdi_direction reverse;
 314 {
 315   /* The first block is the ENTRY_BLOCK (or EXIT_BLOCK if REVERSE).  */
 316   basic_block begin = reverse ? EXIT_BLOCK_PTR : ENTRY_BLOCK_PTR;
 317   di->dfs_order[last_basic_block] = di->dfsnum;
 318   di->dfs_to_bb[di->dfsnum] = begin;
 319   di->dfsnum++;
 320
 321   calc_dfs_tree_nonrec (di, begin, reverse);
 322
 323   if (reverse)
 324     {
 325       /* In the post-dom case we may have nodes without a path to EXIT_BLOCK.
 326          They are reverse-unreachable.  In the dom-case we disallow such
 327          nodes, but in post-dom we have to deal with them, so we simply
 328          include them in the DFS tree which actually becomes a forest.  */
 329       basic_block b;
 330       FOR_EACH_BB_REVERSE (b)
 331         {
 332           if (di->dfs_order[b->index])
 333             continue;
 334           di->dfs_order[b->index] = di->dfsnum;
 335           di->dfs_to_bb[di->dfsnum] = b;
 336           di->dfsnum++;
 337           calc_dfs_tree_nonrec (di, b, reverse);
 338         }
 339     }
 340
 341   di->nodes = di->dfsnum - 1;
 342
 343   /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all.  */
 344   if (di->nodes != (unsigned int) n_basic_blocks + 1)
 345     abort ();
 346 }
 347
 348 /* Compress the path from V to the root of its set and update path_min at the
 349    same time.  After compress(di, V) set_chain[V] is the root of the set V is
 350    in and path_min[V] is the node with the smallest key[] value on the path
 351    from V to that root.  */
 352
 353 static void
 354 compress (di, v)
 355      struct dom_info *di;
 356      TBB v;
 357 {
 358   /* Btw. It's not worth to unrecurse compress() as the depth is usually not
 359      greater than 5 even for huge graphs (I've not seen call depth > 4).
 360      Also performance wise compress() ranges _far_ behind eval().  */
 361   TBB parent = di->set_chain[v];
 362   if (di->set_chain[parent])
 363     {
 364       compress (di, parent);
 365       if (di->key[di->path_min[parent]] < di->key[di->path_min[v]])
 366         di->path_min[v] = di->path_min[parent];
 367       di->set_chain[v] = di->set_chain[parent];
 368     }
 369 }
 370
 371 /* Compress the path from V to the set root of V if needed (when the root has
 372    changed since the last call).  Returns the node with the smallest key[]
 373    value on the path from V to the root.  */
 374
 375 static inline TBB
 376 eval (di, v)
 377      struct dom_info *di;
 378      TBB v;
 379 {
 380   /* The representant of the set V is in, also called root (as the set
 381      representation is a tree).  */
 382   TBB rep = di->set_chain[v];
 383
 384   /* V itself is the root.  */
 385   if (!rep)
 386     return di->path_min[v];
 387
 388   /* Compress only if necessary.  */
 389   if (di->set_chain[rep])
 390     {
 391       compress (di, v);
 392       rep = di->set_chain[v];
 393     }
 394
 395   if (di->key[di->path_min[rep]] >= di->key[di->path_min[v]])
 396     return di->path_min[v];
 397   else
 398     return di->path_min[rep];
 399 }
 400
 401 /* This essentially merges the two sets of V and W, giving a single set with
 402    the new root V.  The internal representation of these disjoint sets is a
 403    balanced tree.  Currently link(V,W) is only used with V being the parent
 404    of W.  */
 405
 406 static void
 407 link_roots (di, v, w)
 408      struct dom_info *di;
 409      TBB v, w;
 410 {
 411   TBB s = w;
 412
 413   /* Rebalance the tree.  */
 414   while (di->key[di->path_min[w]] < di->key[di->path_min[di->set_child[s]]])
 415     {
 416       if (di->set_size[s] + di->set_size[di->set_child[di->set_child[s]]]
 417           >= 2 * di->set_size[di->set_child[s]])
 418         {
 419           di->set_chain[di->set_child[s]] = s;
 420           di->set_child[s] = di->set_child[di->set_child[s]];
 421         }
 422       else
 423         {
 424           di->set_size[di->set_child[s]] = di->set_size[s];
 425           s = di->set_chain[s] = di->set_child[s];
 426         }
 427     }
 428
 429   di->path_min[s] = di->path_min[w];
 430   di->set_size[v] += di->set_size[w];
 431   if (di->set_size[v] < 2 * di->set_size[w])
 432     {
 433       TBB tmp = s;
 434       s = di->set_child[v];
 435       di->set_child[v] = tmp;
 436     }
 437
 438   /* Merge all subtrees.  */
 439   while (s)
 440     {
 441       di->set_chain[s] = v;
 442       s = di->set_child[s];
 443     }
 444 }
 445
 446 /* This calculates the immediate dominators (or post-dominators if REVERSE is
 447    true).  DI is our working structure and should hold the DFS forest.
 448    On return the immediate dominator to node V is in di->dom[V].  */
 449
 450 static void
 451 calc_idoms (di, reverse)
 452      struct dom_info *di;
 453      enum cdi_direction reverse;
 454 {
 455   TBB v, w, k, par;
 456   basic_block en_block;
 457   if (reverse)
 458     en_block = EXIT_BLOCK_PTR;
 459   else
 460     en_block = ENTRY_BLOCK_PTR;
 461
 462   /* Go backwards in DFS order, to first look at the leafs.  */
 463   v = di->nodes;
 464   while (v > 1)
 465     {
 466       basic_block bb = di->dfs_to_bb[v];
 467       edge e, e_next;
 468
 469       par = di->dfs_parent[v];
 470       k = v;
 471       if (reverse)
 472         e = bb->succ;
 473       else
 474         e = bb->pred;
 475
 476       /* Search all direct predecessors for the smallest node with a path
 477          to them.  That way we have the smallest node with also a path to
 478          us only over nodes behind us.  In effect we search for our
 479          semidominator.  */
 480       for (; e; e = e_next)
 481         {
 482           TBB k1;
 483           basic_block b;
 484
 485           if (reverse)
 486             {
 487               b = e->dest;
 488               e_next = e->succ_next;
 489             }
 490           else
 491             {
 492               b = e->src;
 493               e_next = e->pred_next;
 494             }
 495           if (b == en_block)
 496             k1 = di->dfs_order[last_basic_block];
 497           else
 498             k1 = di->dfs_order[b->index];
 499
 500           /* Call eval() only if really needed.  If k1 is above V in DFS tree,
 501              then we know, that eval(k1) == k1 and key[k1] == k1.  */
 502           if (k1 > v)
 503             k1 = di->key[eval (di, k1)];
 504           if (k1 < k)
 505             k = k1;
 506         }
 507
 508       di->key[v] = k;
 509       link_roots (di, par, v);
 510       di->next_bucket[v] = di->bucket[k];
 511       di->bucket[k] = v;
 512
 513       /* Transform semidominators into dominators.  */
 514       for (w = di->bucket[par]; w; w = di->next_bucket[w])
 515         {
 516           k = eval (di, w);
 517           if (di->key[k] < di->key[w])
 518             di->dom[w] = k;
 519           else
 520             di->dom[w] = par;
 521         }
 522       /* We don't need to cleanup next_bucket[].  */
 523       di->bucket[par] = 0;
 524       v--;
 525     }
 526
 527   /* Explicitly define the dominators.  */
 528   di->dom[1] = 0;
 529   for (v = 2; v <= di->nodes; v++)
 530     if (di->dom[v] != di->key[v])
 531       di->dom[v] = di->dom[di->dom[v]];
 532 }
 533
 534 /* Convert the information about immediate dominators (in DI) to sets of all
 535    dominators (in DOMINATORS).  */
 536
 537 static void
 538 idoms_to_doms (di, dominators)
 539      struct dom_info *di;
 540      sbitmap *dominators;
 541 {
 542   TBB i, e_index;
 543   int bb, bb_idom;
 544   sbitmap_vector_zero (dominators, last_basic_block);
 545   /* We have to be careful, to not include the ENTRY_BLOCK or EXIT_BLOCK
 546      in the list of (post)-doms, so remember that in e_index.  */
 547   e_index = di->dfs_order[last_basic_block];
 548
 549   for (i = 1; i <= di->nodes; i++)
 550     {
 551       if (i == e_index)
 552         continue;
 553       bb = di->dfs_to_bb[i]->index;
 554
 555       if (di->dom[i] && (di->dom[i] != e_index))
 556         {
 557           bb_idom = di->dfs_to_bb[di->dom[i]]->index;
 558           sbitmap_copy (dominators[bb], dominators[bb_idom]);
 559         }
 560       else
 561         {
 562           /* It has no immediate dom or only ENTRY_BLOCK or EXIT_BLOCK.
 563              If it is a child of ENTRY_BLOCK that's OK, and it's only
 564              dominated by itself; if it's _not_ a child of ENTRY_BLOCK, it
 565              means, it is unreachable.  That case has been disallowed in the
 566              building of the DFS tree, so we are save here.  For the reverse
 567              flow graph it means, it has no children, so, to be compatible
 568              with the old code, we set the post_dominators to all one.  */
 569           if (!di->dom[i])
 570             {
 571               sbitmap_ones (dominators[bb]);
 572             }
 573         }
 574       SET_BIT (dominators[bb], bb);
 575     }
 576 }
 577
 578 /* The main entry point into this module.  IDOM is an integer array with room
 579    for last_basic_block integers, DOMS is a preallocated sbitmap array having
 580    room for last_basic_block^2 bits, and POST is true if the caller wants to
 581    know post-dominators.
 582
 583    On return IDOM[i] will be the BB->index of the immediate (post) dominator
 584    of basic block i, and DOMS[i] will have set bit j if basic block j is a
 585    (post)dominator for block i.
 586
 587    Either IDOM or DOMS may be NULL (meaning the caller is not interested in
 588    immediate resp. all dominators).  */
 589
 590 void
 591 calculate_dominance_info (idom, doms, reverse)
 592      int *idom;
 593      sbitmap *doms;
 594      enum cdi_direction reverse;
 595 {
 596   struct dom_info di;
 597
 598   if (!doms && !idom)
 599     return;
 600   init_dom_info (&di);
 601   calc_dfs_tree (&di, reverse);
 602   calc_idoms (&di, reverse);
 603
 604   if (idom)
 605     {
 606       basic_block b;
 607
 608       FOR_EACH_BB (b)
 609         {
 610           TBB d = di.dom[di.dfs_order[b->index]];
 611
 612           /* The old code didn't modify array elements of nodes having only
 613              itself as dominator (d==0) or only ENTRY_BLOCK (resp. EXIT_BLOCK)
 614              (d==1).  */
 615           if (d > 1)
 616             idom[b->index] = di.dfs_to_bb[d]->index;
 617         }
 618     }
 619   if (doms)
 620     idoms_to_doms (&di, doms);
 621
 622   free_dom_info (&di);
 623 }