1 /* Calculate (post)dominators in slightly super-linear time.
2 Copyright (C) 2000, 2003, 2004 Free Software Foundation, Inc.
3 Contributed by Michael Matz (matz@ifh.de).
5 This file is part of GCC.
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)
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.
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
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.
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. */
38 #include "coretypes.h"
41 #include "hard-reg-set.h"
42 #include "basic-block.h"
44 #include "et-forest.h"
46 /* Whether the dominators and the postdominators are available. */
47 enum dom_state dom_computed
[2];
49 /* We name our nodes with integers, beginning with 1. Zero is reserved for
50 'undefined' or 'end of list'. The name of each node is given by the dfs
51 number of the corresponding basic block. Please note, that we include the
52 artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to
53 support multiple entry points. As it has no real basic block index we use
54 'last_basic_block' for that. Its dfs number is of course 1. */
56 /* Type of Basic Block aka. TBB */
57 typedef unsigned int TBB
;
59 /* We work in a poor-mans object oriented fashion, and carry an instance of
60 this structure through all our 'methods'. It holds various arrays
61 reflecting the (sub)structure of the flowgraph. Most of them are of type
62 TBB and are also indexed by TBB. */
66 /* The parent of a node in the DFS tree. */
68 /* For a node x key[x] is roughly the node nearest to the root from which
69 exists a way to x only over nodes behind x. Such a node is also called
72 /* The value in path_min[x] is the node y on the path from x to the root of
73 the tree x is in with the smallest key[y]. */
75 /* bucket[x] points to the first node of the set of nodes having x as key. */
77 /* And next_bucket[x] points to the next node. */
79 /* After the algorithm is done, dom[x] contains the immediate dominator
83 /* The following few fields implement the structures needed for disjoint
85 /* set_chain[x] is the next node on the path from x to the representant
86 of the set containing x. If set_chain[x]==0 then x is a root. */
88 /* set_size[x] is the number of elements in the set named by x. */
89 unsigned int *set_size
;
90 /* set_child[x] is used for balancing the tree representing a set. It can
91 be understood as the next sibling of x. */
94 /* If b is the number of a basic block (BB->index), dfs_order[b] is the
95 number of that node in DFS order counted from 1. This is an index
96 into most of the other arrays in this structure. */
98 /* If x is the DFS-index of a node which corresponds with a basic block,
99 dfs_to_bb[x] is that basic block. Note, that in our structure there are
100 more nodes that basic blocks, so only dfs_to_bb[dfs_order[bb->index]]==bb
101 is true for every basic block bb, but not the opposite. */
102 basic_block
*dfs_to_bb
;
104 /* This is the next free DFS number when creating the DFS tree or forest. */
106 /* The number of nodes in the DFS tree (==dfsnum-1). */
110 static void init_dom_info (struct dom_info
*);
111 static void free_dom_info (struct dom_info
*);
112 static void calc_dfs_tree_nonrec (struct dom_info
*, basic_block
,
114 static void calc_dfs_tree (struct dom_info
*, enum cdi_direction
);
115 static void compress (struct dom_info
*, TBB
);
116 static TBB
eval (struct dom_info
*, TBB
);
117 static void link_roots (struct dom_info
*, TBB
, TBB
);
118 static void calc_idoms (struct dom_info
*, enum cdi_direction
);
119 void debug_dominance_info (enum cdi_direction
);
121 /* Keeps track of the*/
122 static unsigned n_bbs_in_dom_tree
[2];
124 /* Helper macro for allocating and initializing an array,
125 for aesthetic reasons. */
126 #define init_ar(var, type, num, content) \
129 unsigned int i = 1; /* Catch content == i. */ \
131 (var) = xcalloc ((num), sizeof (type)); \
134 (var) = xmalloc ((num) * sizeof (type)); \
135 for (i = 0; i < num; i++) \
136 (var)[i] = (content); \
141 /* Allocate all needed memory in a pessimistic fashion (so we round up).
142 This initializes the contents of DI, which already must be allocated. */
145 init_dom_info (struct dom_info
*di
)
147 /* We need memory for n_basic_blocks nodes and the ENTRY_BLOCK or
149 unsigned int num
= n_basic_blocks
+ 1 + 1;
150 init_ar (di
->dfs_parent
, TBB
, num
, 0);
151 init_ar (di
->path_min
, TBB
, num
, i
);
152 init_ar (di
->key
, TBB
, num
, i
);
153 init_ar (di
->dom
, TBB
, num
, 0);
155 init_ar (di
->bucket
, TBB
, num
, 0);
156 init_ar (di
->next_bucket
, TBB
, num
, 0);
158 init_ar (di
->set_chain
, TBB
, num
, 0);
159 init_ar (di
->set_size
, unsigned int, num
, 1);
160 init_ar (di
->set_child
, TBB
, num
, 0);
162 init_ar (di
->dfs_order
, TBB
, (unsigned int) last_basic_block
+ 1, 0);
163 init_ar (di
->dfs_to_bb
, basic_block
, num
, 0);
171 /* Free all allocated memory in DI, but not DI itself. */
174 free_dom_info (struct dom_info
*di
)
176 free (di
->dfs_parent
);
181 free (di
->next_bucket
);
182 free (di
->set_chain
);
184 free (di
->set_child
);
185 free (di
->dfs_order
);
186 free (di
->dfs_to_bb
);
189 /* The nonrecursive variant of creating a DFS tree. DI is our working
190 structure, BB the starting basic block for this tree and REVERSE
191 is true, if predecessors should be visited instead of successors of a
192 node. After this is done all nodes reachable from BB were visited, have
193 assigned their dfs number and are linked together to form a tree. */
196 calc_dfs_tree_nonrec (struct dom_info
*di
, basic_block bb
, enum cdi_direction reverse
)
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. */
201 TBB child_i
, my_i
= 0;
204 /* Start block (ENTRY_BLOCK_PTR for forward problem, EXIT_BLOCK for backward
206 basic_block en_block
;
208 basic_block ex_block
;
210 stack
= xmalloc ((n_basic_blocks
+ 3) * sizeof (edge
));
213 /* Initialize our border blocks, and the first edge. */
217 en_block
= EXIT_BLOCK_PTR
;
218 ex_block
= ENTRY_BLOCK_PTR
;
223 en_block
= ENTRY_BLOCK_PTR
;
224 ex_block
= EXIT_BLOCK_PTR
;
227 /* When the stack is empty we break out of this loop. */
232 /* This loop traverses edges e in depth first manner, and fills the
238 /* Deduce from E the current and the next block (BB and BN), and the
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
])
258 if (bn
== ex_block
|| di
->dfs_order
[bn
->index
])
270 /* Fill the DFS tree info calculatable _before_ recursing. */
272 my_i
= di
->dfs_order
[bb
->index
];
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
;
279 /* Save the current point in the CFG on the stack, and recurse. */
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. */
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. */
311 calc_dfs_tree (struct dom_info
*di
, enum cdi_direction reverse
)
313 /* The first block is the ENTRY_BLOCK (or EXIT_BLOCK if REVERSE). */
314 basic_block begin
= reverse
? EXIT_BLOCK_PTR
: ENTRY_BLOCK_PTR
;
315 di
->dfs_order
[last_basic_block
] = di
->dfsnum
;
316 di
->dfs_to_bb
[di
->dfsnum
] = begin
;
319 calc_dfs_tree_nonrec (di
, begin
, reverse
);
323 /* In the post-dom case we may have nodes without a path to EXIT_BLOCK.
324 They are reverse-unreachable. In the dom-case we disallow such
325 nodes, but in post-dom we have to deal with them, so we simply
326 include them in the DFS tree which actually becomes a forest. */
328 FOR_EACH_BB_REVERSE (b
)
330 if (di
->dfs_order
[b
->index
])
332 di
->dfs_order
[b
->index
] = di
->dfsnum
;
333 di
->dfs_to_bb
[di
->dfsnum
] = b
;
335 calc_dfs_tree_nonrec (di
, b
, reverse
);
339 di
->nodes
= di
->dfsnum
- 1;
341 /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all. */
342 if (di
->nodes
!= (unsigned int) n_basic_blocks
+ 1)
346 /* Compress the path from V to the root of its set and update path_min at the
347 same time. After compress(di, V) set_chain[V] is the root of the set V is
348 in and path_min[V] is the node with the smallest key[] value on the path
349 from V to that root. */
352 compress (struct dom_info
*di
, TBB v
)
354 /* Btw. It's not worth to unrecurse compress() as the depth is usually not
355 greater than 5 even for huge graphs (I've not seen call depth > 4).
356 Also performance wise compress() ranges _far_ behind eval(). */
357 TBB parent
= di
->set_chain
[v
];
358 if (di
->set_chain
[parent
])
360 compress (di
, parent
);
361 if (di
->key
[di
->path_min
[parent
]] < di
->key
[di
->path_min
[v
]])
362 di
->path_min
[v
] = di
->path_min
[parent
];
363 di
->set_chain
[v
] = di
->set_chain
[parent
];
367 /* Compress the path from V to the set root of V if needed (when the root has
368 changed since the last call). Returns the node with the smallest key[]
369 value on the path from V to the root. */
372 eval (struct dom_info
*di
, TBB v
)
374 /* The representant of the set V is in, also called root (as the set
375 representation is a tree). */
376 TBB rep
= di
->set_chain
[v
];
378 /* V itself is the root. */
380 return di
->path_min
[v
];
382 /* Compress only if necessary. */
383 if (di
->set_chain
[rep
])
386 rep
= di
->set_chain
[v
];
389 if (di
->key
[di
->path_min
[rep
]] >= di
->key
[di
->path_min
[v
]])
390 return di
->path_min
[v
];
392 return di
->path_min
[rep
];
395 /* This essentially merges the two sets of V and W, giving a single set with
396 the new root V. The internal representation of these disjoint sets is a
397 balanced tree. Currently link(V,W) is only used with V being the parent
401 link_roots (struct dom_info
*di
, TBB v
, TBB w
)
405 /* Rebalance the tree. */
406 while (di
->key
[di
->path_min
[w
]] < di
->key
[di
->path_min
[di
->set_child
[s
]]])
408 if (di
->set_size
[s
] + di
->set_size
[di
->set_child
[di
->set_child
[s
]]]
409 >= 2 * di
->set_size
[di
->set_child
[s
]])
411 di
->set_chain
[di
->set_child
[s
]] = s
;
412 di
->set_child
[s
] = di
->set_child
[di
->set_child
[s
]];
416 di
->set_size
[di
->set_child
[s
]] = di
->set_size
[s
];
417 s
= di
->set_chain
[s
] = di
->set_child
[s
];
421 di
->path_min
[s
] = di
->path_min
[w
];
422 di
->set_size
[v
] += di
->set_size
[w
];
423 if (di
->set_size
[v
] < 2 * di
->set_size
[w
])
426 s
= di
->set_child
[v
];
427 di
->set_child
[v
] = tmp
;
430 /* Merge all subtrees. */
433 di
->set_chain
[s
] = v
;
434 s
= di
->set_child
[s
];
438 /* This calculates the immediate dominators (or post-dominators if REVERSE is
439 true). DI is our working structure and should hold the DFS forest.
440 On return the immediate dominator to node V is in di->dom[V]. */
443 calc_idoms (struct dom_info
*di
, enum cdi_direction reverse
)
446 basic_block en_block
;
448 en_block
= EXIT_BLOCK_PTR
;
450 en_block
= ENTRY_BLOCK_PTR
;
452 /* Go backwards in DFS order, to first look at the leafs. */
456 basic_block bb
= di
->dfs_to_bb
[v
];
459 par
= di
->dfs_parent
[v
];
466 /* Search all direct predecessors for the smallest node with a path
467 to them. That way we have the smallest node with also a path to
468 us only over nodes behind us. In effect we search for our
470 for (; e
; e
= e_next
)
478 e_next
= e
->succ_next
;
483 e_next
= e
->pred_next
;
486 k1
= di
->dfs_order
[last_basic_block
];
488 k1
= di
->dfs_order
[b
->index
];
490 /* Call eval() only if really needed. If k1 is above V in DFS tree,
491 then we know, that eval(k1) == k1 and key[k1] == k1. */
493 k1
= di
->key
[eval (di
, k1
)];
499 link_roots (di
, par
, v
);
500 di
->next_bucket
[v
] = di
->bucket
[k
];
503 /* Transform semidominators into dominators. */
504 for (w
= di
->bucket
[par
]; w
; w
= di
->next_bucket
[w
])
507 if (di
->key
[k
] < di
->key
[w
])
512 /* We don't need to cleanup next_bucket[]. */
517 /* Explicitly define the dominators. */
519 for (v
= 2; v
<= di
->nodes
; v
++)
520 if (di
->dom
[v
] != di
->key
[v
])
521 di
->dom
[v
] = di
->dom
[di
->dom
[v
]];
524 /* Assign dfs numbers starting from NUM to NODE and its sons. */
527 assign_dfs_numbers (struct et_node
*node
, int *num
)
531 node
->dfs_num_in
= (*num
)++;
535 assign_dfs_numbers (node
->son
, num
);
536 for (son
= node
->son
->right
; son
!= node
->son
; son
= son
->right
)
537 assign_dfs_numbers (son
, num
);
540 node
->dfs_num_out
= (*num
)++;
543 /* Compute the data necessary for fast resolving of dominator queries in a
544 static dominator tree. */
547 compute_dom_fast_query (enum cdi_direction dir
)
552 if (dom_computed
[dir
] < DOM_NO_FAST_QUERY
)
555 if (dom_computed
[dir
] == DOM_OK
)
560 if (!bb
->dom
[dir
]->father
)
561 assign_dfs_numbers (bb
->dom
[dir
], &num
);
564 dom_computed
[dir
] = DOM_OK
;
567 /* The main entry point into this module. DIR is set depending on whether
568 we want to compute dominators or postdominators. */
571 calculate_dominance_info (enum cdi_direction dir
)
576 if (dom_computed
[dir
] == DOM_OK
)
579 if (dom_computed
[dir
] != DOM_NO_FAST_QUERY
)
581 if (dom_computed
[dir
] != DOM_NONE
)
582 free_dominance_info (dir
);
584 if (n_bbs_in_dom_tree
[dir
])
589 b
->dom
[dir
] = et_new_tree (b
);
591 n_bbs_in_dom_tree
[dir
] = n_basic_blocks
+ 2;
594 calc_dfs_tree (&di
, dir
);
595 calc_idoms (&di
, dir
);
599 TBB d
= di
.dom
[di
.dfs_order
[b
->index
]];
602 et_set_father (b
->dom
[dir
], di
.dfs_to_bb
[d
]->dom
[dir
]);
606 dom_computed
[dir
] = DOM_NO_FAST_QUERY
;
609 compute_dom_fast_query (dir
);
612 /* Free dominance information for direction DIR. */
614 free_dominance_info (enum cdi_direction dir
)
618 if (!dom_computed
[dir
])
623 delete_from_dominance_info (dir
, bb
);
626 /* If there are any nodes left, something is wrong. */
627 if (n_bbs_in_dom_tree
[dir
])
630 dom_computed
[dir
] = DOM_NONE
;
633 /* Return the immediate dominator of basic block BB. */
635 get_immediate_dominator (enum cdi_direction dir
, basic_block bb
)
637 struct et_node
*node
= bb
->dom
[dir
];
639 if (!dom_computed
[dir
])
645 return node
->father
->data
;
648 /* Set the immediate dominator of the block possibly removing
649 existing edge. NULL can be used to remove any edge. */
651 set_immediate_dominator (enum cdi_direction dir
, basic_block bb
,
652 basic_block dominated_by
)
654 struct et_node
*node
= bb
->dom
[dir
];
656 if (!dom_computed
[dir
])
661 if (node
->father
->data
== dominated_by
)
667 et_set_father (node
, dominated_by
->dom
[dir
]);
669 if (dom_computed
[dir
] == DOM_OK
)
670 dom_computed
[dir
] = DOM_NO_FAST_QUERY
;
673 /* Store all basic blocks immediately dominated by BB into BBS and return
676 get_dominated_by (enum cdi_direction dir
, basic_block bb
, basic_block
**bbs
)
679 struct et_node
*node
= bb
->dom
[dir
], *son
= node
->son
, *ason
;
681 if (!dom_computed
[dir
])
690 for (ason
= son
->right
, n
= 1; ason
!= son
; ason
= ason
->right
)
693 *bbs
= xmalloc (n
* sizeof (basic_block
));
694 (*bbs
)[0] = son
->data
;
695 for (ason
= son
->right
, n
= 1; ason
!= son
; ason
= ason
->right
)
696 (*bbs
)[n
++] = ason
->data
;
701 /* Redirect all edges pointing to BB to TO. */
703 redirect_immediate_dominators (enum cdi_direction dir
, basic_block bb
,
706 struct et_node
*bb_node
= bb
->dom
[dir
], *to_node
= to
->dom
[dir
], *son
;
708 if (!dom_computed
[dir
])
719 et_set_father (son
, to_node
);
722 if (dom_computed
[dir
] == DOM_OK
)
723 dom_computed
[dir
] = DOM_NO_FAST_QUERY
;
726 /* Find first basic block in the tree dominating both BB1 and BB2. */
728 nearest_common_dominator (enum cdi_direction dir
, basic_block bb1
, basic_block bb2
)
730 if (!dom_computed
[dir
])
738 return et_nca (bb1
->dom
[dir
], bb2
->dom
[dir
])->data
;
741 /* Return TRUE in case BB1 is dominated by BB2. */
743 dominated_by_p (enum cdi_direction dir
, basic_block bb1
, basic_block bb2
)
745 struct et_node
*n1
= bb1
->dom
[dir
], *n2
= bb2
->dom
[dir
];
747 if (!dom_computed
[dir
])
750 if (dom_computed
[dir
] == DOM_OK
)
751 return (n1
->dfs_num_in
>= n2
->dfs_num_in
752 && n1
->dfs_num_out
<= n2
->dfs_num_out
);
754 return et_below (n1
, n2
);
757 /* Verify invariants of dominator structure. */
759 verify_dominators (enum cdi_direction dir
)
764 if (!dom_computed
[dir
])
771 dom_bb
= recount_dominator (dir
, bb
);
772 if (dom_bb
!= get_immediate_dominator (dir
, bb
))
774 error ("dominator of %d should be %d, not %d",
775 bb
->index
, dom_bb
->index
, get_immediate_dominator(dir
, bb
)->index
);
783 /* Determine immediate dominator (or postdominator, according to DIR) of BB,
784 assuming that dominators of other blocks are correct. We also use it to
785 recompute the dominators in a restricted area, by iterating it until it
786 reaches a fixed point. */
789 recount_dominator (enum cdi_direction dir
, basic_block bb
)
791 basic_block dom_bb
= NULL
;
794 if (!dom_computed
[dir
])
797 if (dir
== CDI_DOMINATORS
)
799 for (e
= bb
->pred
; e
; e
= e
->pred_next
)
801 if (!dominated_by_p (dir
, e
->src
, bb
))
802 dom_bb
= nearest_common_dominator (dir
, dom_bb
, e
->src
);
807 for (e
= bb
->succ
; e
; e
= e
->succ_next
)
809 if (!dominated_by_p (dir
, e
->dest
, bb
))
810 dom_bb
= nearest_common_dominator (dir
, dom_bb
, e
->dest
);
817 /* Iteratively recount dominators of BBS. The change is supposed to be local
818 and not to grow further. */
820 iterate_fix_dominators (enum cdi_direction dir
, basic_block
*bbs
, int n
)
823 basic_block old_dom
, new_dom
;
825 if (!dom_computed
[dir
])
831 for (i
= 0; i
< n
; i
++)
833 old_dom
= get_immediate_dominator (dir
, bbs
[i
]);
834 new_dom
= recount_dominator (dir
, bbs
[i
]);
835 if (old_dom
!= new_dom
)
838 set_immediate_dominator (dir
, bbs
[i
], new_dom
);
845 add_to_dominance_info (enum cdi_direction dir
, basic_block bb
)
847 if (!dom_computed
[dir
])
853 n_bbs_in_dom_tree
[dir
]++;
855 bb
->dom
[dir
] = et_new_tree (bb
);
857 if (dom_computed
[dir
] == DOM_OK
)
858 dom_computed
[dir
] = DOM_NO_FAST_QUERY
;
862 delete_from_dominance_info (enum cdi_direction dir
, basic_block bb
)
864 if (!dom_computed
[dir
])
867 et_free_tree (bb
->dom
[dir
]);
869 n_bbs_in_dom_tree
[dir
]--;
871 if (dom_computed
[dir
] == DOM_OK
)
872 dom_computed
[dir
] = DOM_NO_FAST_QUERY
;
875 /* Returns the first son of BB in the dominator or postdominator tree
876 as determined by DIR. */
879 first_dom_son (enum cdi_direction dir
, basic_block bb
)
881 struct et_node
*son
= bb
->dom
[dir
]->son
;
883 return son
? son
->data
: NULL
;
886 /* Returns the next dominance son after BB in the dominator or postdominator
887 tree as determined by DIR, or NULL if it was the last one. */
890 next_dom_son (enum cdi_direction dir
, basic_block bb
)
892 struct et_node
*next
= bb
->dom
[dir
]->right
;
894 return next
->father
->son
== next
? NULL
: next
->data
;
898 debug_dominance_info (enum cdi_direction dir
)
902 if ((bb2
= get_immediate_dominator (dir
, bb
)))
903 fprintf (stderr
, "%i %i\n", bb
->index
, bb2
->index
);