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).
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"
52 #define BB_NODE(info, bb) \
53 ((et_forest_node_t)VARRAY_GENERIC_PTR ((info)->varray, (bb)->index + 2))
54 #define SET_BB_NODE(info, bb, node) \
55 (VARRAY_GENERIC_PTR ((info)->varray, (bb)->index + 2) = (node))
57 /* We name our nodes with integers, beginning with 1. Zero is reserved for
58 'undefined' or 'end of list'. The name of each node is given by the dfs
59 number of the corresponding basic block. Please note, that we include the
60 artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to
61 support multiple entry points. As it has no real basic block index we use
62 'last_basic_block' for that. Its dfs number is of course 1. */
64 /* Type of Basic Block aka. TBB */
65 typedef unsigned int TBB
;
67 /* We work in a poor-mans object oriented fashion, and carry an instance of
68 this structure through all our 'methods'. It holds various arrays
69 reflecting the (sub)structure of the flowgraph. Most of them are of type
70 TBB and are also indexed by TBB. */
74 /* The parent of a node in the DFS tree. */
76 /* For a node x key[x] is roughly the node nearest to the root from which
77 exists a way to x only over nodes behind x. Such a node is also called
80 /* The value in path_min[x] is the node y on the path from x to the root of
81 the tree x is in with the smallest key[y]. */
83 /* bucket[x] points to the first node of the set of nodes having x as key. */
85 /* And next_bucket[x] points to the next node. */
87 /* After the algorithm is done, dom[x] contains the immediate dominator
91 /* The following few fields implement the structures needed for disjoint
93 /* set_chain[x] is the next node on the path from x to the representant
94 of the set containing x. If set_chain[x]==0 then x is a root. */
96 /* set_size[x] is the number of elements in the set named by x. */
97 unsigned int *set_size
;
98 /* set_child[x] is used for balancing the tree representing a set. It can
99 be understood as the next sibling of x. */
102 /* If b is the number of a basic block (BB->index), dfs_order[b] is the
103 number of that node in DFS order counted from 1. This is an index
104 into most of the other arrays in this structure. */
106 /* If x is the DFS-index of a node which corresponds with a basic block,
107 dfs_to_bb[x] is that basic block. Note, that in our structure there are
108 more nodes that basic blocks, so only dfs_to_bb[dfs_order[bb->index]]==bb
109 is true for every basic block bb, but not the opposite. */
110 basic_block
*dfs_to_bb
;
112 /* This is the next free DFS number when creating the DFS tree or forest. */
114 /* The number of nodes in the DFS tree (==dfsnum-1). */
118 static void init_dom_info
PARAMS ((struct dom_info
*));
119 static void free_dom_info
PARAMS ((struct dom_info
*));
120 static void calc_dfs_tree_nonrec
PARAMS ((struct dom_info
*,
122 enum cdi_direction
));
123 static void calc_dfs_tree
PARAMS ((struct dom_info
*,
124 enum cdi_direction
));
125 static void compress
PARAMS ((struct dom_info
*, TBB
));
126 static TBB eval
PARAMS ((struct dom_info
*, TBB
));
127 static void link_roots
PARAMS ((struct dom_info
*, TBB
, TBB
));
128 static void calc_idoms
PARAMS ((struct dom_info
*,
129 enum cdi_direction
));
130 void debug_dominance_info
PARAMS ((dominance_info
));
132 /* Helper macro for allocating and initializing an array,
133 for aesthetic reasons. */
134 #define init_ar(var, type, num, content) \
137 unsigned int i = 1; /* Catch content == i. */ \
139 (var) = (type *) xcalloc ((num), sizeof (type)); \
142 (var) = (type *) xmalloc ((num) * sizeof (type)); \
143 for (i = 0; i < num; i++) \
144 (var)[i] = (content); \
149 /* Allocate all needed memory in a pessimistic fashion (so we round up).
150 This initializes the contents of DI, which already must be allocated. */
156 /* We need memory for n_basic_blocks nodes and the ENTRY_BLOCK or
158 unsigned int num
= n_basic_blocks
+ 1 + 1;
159 init_ar (di
->dfs_parent
, TBB
, num
, 0);
160 init_ar (di
->path_min
, TBB
, num
, i
);
161 init_ar (di
->key
, TBB
, num
, i
);
162 init_ar (di
->dom
, TBB
, num
, 0);
164 init_ar (di
->bucket
, TBB
, num
, 0);
165 init_ar (di
->next_bucket
, TBB
, num
, 0);
167 init_ar (di
->set_chain
, TBB
, num
, 0);
168 init_ar (di
->set_size
, unsigned int, num
, 1);
169 init_ar (di
->set_child
, TBB
, num
, 0);
171 init_ar (di
->dfs_order
, TBB
, (unsigned int) last_basic_block
+ 1, 0);
172 init_ar (di
->dfs_to_bb
, basic_block
, num
, 0);
180 /* Free all allocated memory in DI, but not DI itself. */
186 free (di
->dfs_parent
);
191 free (di
->next_bucket
);
192 free (di
->set_chain
);
194 free (di
->set_child
);
195 free (di
->dfs_order
);
196 free (di
->dfs_to_bb
);
199 /* The nonrecursive variant of creating a DFS tree. DI is our working
200 structure, BB the starting basic block for this tree and REVERSE
201 is true, if predecessors should be visited instead of successors of a
202 node. After this is done all nodes reachable from BB were visited, have
203 assigned their dfs number and are linked together to form a tree. */
206 calc_dfs_tree_nonrec (di
, bb
, reverse
)
209 enum cdi_direction reverse
;
211 /* We never call this with bb==EXIT_BLOCK_PTR (ENTRY_BLOCK_PTR if REVERSE). */
212 /* We call this _only_ if bb is not already visited. */
214 TBB child_i
, my_i
= 0;
217 /* Start block (ENTRY_BLOCK_PTR for forward problem, EXIT_BLOCK for backward
219 basic_block en_block
;
221 basic_block ex_block
;
223 stack
= (edge
*) xmalloc ((n_basic_blocks
+ 3) * sizeof (edge
));
226 /* Initialize our border blocks, and the first edge. */
230 en_block
= EXIT_BLOCK_PTR
;
231 ex_block
= ENTRY_BLOCK_PTR
;
236 en_block
= ENTRY_BLOCK_PTR
;
237 ex_block
= EXIT_BLOCK_PTR
;
240 /* When the stack is empty we break out of this loop. */
245 /* This loop traverses edges e in depth first manner, and fills the
251 /* Deduce from E the current and the next block (BB and BN), and the
257 /* If the next node BN is either already visited or a border
258 block the current edge is useless, and simply overwritten
259 with the next edge out of the current node. */
260 if (bn
== ex_block
|| di
->dfs_order
[bn
->index
])
271 if (bn
== ex_block
|| di
->dfs_order
[bn
->index
])
283 /* Fill the DFS tree info calculatable _before_ recursing. */
285 my_i
= di
->dfs_order
[bb
->index
];
287 my_i
= di
->dfs_order
[last_basic_block
];
288 child_i
= di
->dfs_order
[bn
->index
] = di
->dfsnum
++;
289 di
->dfs_to_bb
[child_i
] = bn
;
290 di
->dfs_parent
[child_i
] = my_i
;
292 /* Save the current point in the CFG on the stack, and recurse. */
301 /* OK. The edge-list was exhausted, meaning normally we would
302 end the recursion. After returning from the recursive call,
303 there were (may be) other statements which were run after a
304 child node was completely considered by DFS. Here is the
305 point to do it in the non-recursive variant.
306 E.g. The block just completed is in e->dest for forward DFS,
307 the block not yet completed (the parent of the one above)
308 in e->src. This could be used e.g. for computing the number of
309 descendants or the tree depth. */
318 /* The main entry for calculating the DFS tree or forest. DI is our working
319 structure and REVERSE is true, if we are interested in the reverse flow
320 graph. In that case the result is not necessarily a tree but a forest,
321 because there may be nodes from which the EXIT_BLOCK is unreachable. */
324 calc_dfs_tree (di
, reverse
)
326 enum cdi_direction reverse
;
328 /* The first block is the ENTRY_BLOCK (or EXIT_BLOCK if REVERSE). */
329 basic_block begin
= reverse
? EXIT_BLOCK_PTR
: ENTRY_BLOCK_PTR
;
330 di
->dfs_order
[last_basic_block
] = di
->dfsnum
;
331 di
->dfs_to_bb
[di
->dfsnum
] = begin
;
334 calc_dfs_tree_nonrec (di
, begin
, reverse
);
338 /* In the post-dom case we may have nodes without a path to EXIT_BLOCK.
339 They are reverse-unreachable. In the dom-case we disallow such
340 nodes, but in post-dom we have to deal with them, so we simply
341 include them in the DFS tree which actually becomes a forest. */
343 FOR_EACH_BB_REVERSE (b
)
345 if (di
->dfs_order
[b
->index
])
347 di
->dfs_order
[b
->index
] = di
->dfsnum
;
348 di
->dfs_to_bb
[di
->dfsnum
] = b
;
350 calc_dfs_tree_nonrec (di
, b
, reverse
);
354 di
->nodes
= di
->dfsnum
- 1;
356 /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all. */
357 if (di
->nodes
!= (unsigned int) n_basic_blocks
+ 1)
361 /* Compress the path from V to the root of its set and update path_min at the
362 same time. After compress(di, V) set_chain[V] is the root of the set V is
363 in and path_min[V] is the node with the smallest key[] value on the path
364 from V to that root. */
371 /* Btw. It's not worth to unrecurse compress() as the depth is usually not
372 greater than 5 even for huge graphs (I've not seen call depth > 4).
373 Also performance wise compress() ranges _far_ behind eval(). */
374 TBB parent
= di
->set_chain
[v
];
375 if (di
->set_chain
[parent
])
377 compress (di
, parent
);
378 if (di
->key
[di
->path_min
[parent
]] < di
->key
[di
->path_min
[v
]])
379 di
->path_min
[v
] = di
->path_min
[parent
];
380 di
->set_chain
[v
] = di
->set_chain
[parent
];
384 /* Compress the path from V to the set root of V if needed (when the root has
385 changed since the last call). Returns the node with the smallest key[]
386 value on the path from V to the root. */
393 /* The representant of the set V is in, also called root (as the set
394 representation is a tree). */
395 TBB rep
= di
->set_chain
[v
];
397 /* V itself is the root. */
399 return di
->path_min
[v
];
401 /* Compress only if necessary. */
402 if (di
->set_chain
[rep
])
405 rep
= di
->set_chain
[v
];
408 if (di
->key
[di
->path_min
[rep
]] >= di
->key
[di
->path_min
[v
]])
409 return di
->path_min
[v
];
411 return di
->path_min
[rep
];
414 /* This essentially merges the two sets of V and W, giving a single set with
415 the new root V. The internal representation of these disjoint sets is a
416 balanced tree. Currently link(V,W) is only used with V being the parent
420 link_roots (di
, v
, w
)
426 /* Rebalance the tree. */
427 while (di
->key
[di
->path_min
[w
]] < di
->key
[di
->path_min
[di
->set_child
[s
]]])
429 if (di
->set_size
[s
] + di
->set_size
[di
->set_child
[di
->set_child
[s
]]]
430 >= 2 * di
->set_size
[di
->set_child
[s
]])
432 di
->set_chain
[di
->set_child
[s
]] = s
;
433 di
->set_child
[s
] = di
->set_child
[di
->set_child
[s
]];
437 di
->set_size
[di
->set_child
[s
]] = di
->set_size
[s
];
438 s
= di
->set_chain
[s
] = di
->set_child
[s
];
442 di
->path_min
[s
] = di
->path_min
[w
];
443 di
->set_size
[v
] += di
->set_size
[w
];
444 if (di
->set_size
[v
] < 2 * di
->set_size
[w
])
447 s
= di
->set_child
[v
];
448 di
->set_child
[v
] = tmp
;
451 /* Merge all subtrees. */
454 di
->set_chain
[s
] = v
;
455 s
= di
->set_child
[s
];
459 /* This calculates the immediate dominators (or post-dominators if REVERSE is
460 true). DI is our working structure and should hold the DFS forest.
461 On return the immediate dominator to node V is in di->dom[V]. */
464 calc_idoms (di
, reverse
)
466 enum cdi_direction reverse
;
469 basic_block en_block
;
471 en_block
= EXIT_BLOCK_PTR
;
473 en_block
= ENTRY_BLOCK_PTR
;
475 /* Go backwards in DFS order, to first look at the leafs. */
479 basic_block bb
= di
->dfs_to_bb
[v
];
482 par
= di
->dfs_parent
[v
];
489 /* Search all direct predecessors for the smallest node with a path
490 to them. That way we have the smallest node with also a path to
491 us only over nodes behind us. In effect we search for our
493 for (; e
; e
= e_next
)
501 e_next
= e
->succ_next
;
506 e_next
= e
->pred_next
;
509 k1
= di
->dfs_order
[last_basic_block
];
511 k1
= di
->dfs_order
[b
->index
];
513 /* Call eval() only if really needed. If k1 is above V in DFS tree,
514 then we know, that eval(k1) == k1 and key[k1] == k1. */
516 k1
= di
->key
[eval (di
, k1
)];
522 link_roots (di
, par
, v
);
523 di
->next_bucket
[v
] = di
->bucket
[k
];
526 /* Transform semidominators into dominators. */
527 for (w
= di
->bucket
[par
]; w
; w
= di
->next_bucket
[w
])
530 if (di
->key
[k
] < di
->key
[w
])
535 /* We don't need to cleanup next_bucket[]. */
540 /* Explicitly define the dominators. */
542 for (v
= 2; v
<= di
->nodes
; v
++)
543 if (di
->dom
[v
] != di
->key
[v
])
544 di
->dom
[v
] = di
->dom
[di
->dom
[v
]];
547 /* The main entry point into this module. IDOM is an integer array with room
548 for last_basic_block integers, DOMS is a preallocated sbitmap array having
549 room for last_basic_block^2 bits, and POST is true if the caller wants to
550 know post-dominators.
552 On return IDOM[i] will be the BB->index of the immediate (post) dominator
553 of basic block i, and DOMS[i] will have set bit j if basic block j is a
554 (post)dominator for block i.
556 Either IDOM or DOMS may be NULL (meaning the caller is not interested in
557 immediate resp. all dominators). */
560 calculate_dominance_info (reverse
)
561 enum cdi_direction reverse
;
567 /* allocate structure for dominance information. */
568 info
= xmalloc (sizeof (struct dominance_info
));
569 info
->forest
= et_forest_create ();
570 VARRAY_GENERIC_PTR_INIT (info
->varray
, last_basic_block
+ 3, "dominance info");
572 /* Add the two well-known basic blocks. */
573 SET_BB_NODE (info
, ENTRY_BLOCK_PTR
, et_forest_add_node (info
->forest
,
575 SET_BB_NODE (info
, EXIT_BLOCK_PTR
, et_forest_add_node (info
->forest
,
578 SET_BB_NODE (info
, b
, et_forest_add_node (info
->forest
, b
));
581 calc_dfs_tree (&di
, reverse
);
582 calc_idoms (&di
, reverse
);
587 TBB d
= di
.dom
[di
.dfs_order
[b
->index
]];
590 et_forest_add_edge (info
->forest
, BB_NODE (info
, di
.dfs_to_bb
[d
]), BB_NODE (info
, b
));
597 /* Free dominance information. */
599 free_dominance_info (info
)
604 /* Allow users to create new basic block without setting up the dominance
605 information for them. */
607 if (bb
->index
< (int)(info
->varray
->num_elements
- 2)
608 && BB_NODE (info
, bb
))
609 delete_from_dominance_info (info
, bb
);
610 delete_from_dominance_info (info
, ENTRY_BLOCK_PTR
);
611 delete_from_dominance_info (info
, EXIT_BLOCK_PTR
);
612 et_forest_delete (info
->forest
);
613 VARRAY_GROW (info
->varray
, 0);
617 /* Return the immediate dominator of basic block BB. */
619 get_immediate_dominator (dom
, bb
)
623 return et_forest_node_value (dom
->forest
,
624 et_forest_parent (dom
->forest
,
628 /* Set the immediate dominator of the block possibly removing
629 existing edge. NULL can be used to remove any edge. */
631 set_immediate_dominator (dom
, bb
, dominated_by
)
633 basic_block bb
, dominated_by
;
636 et_forest_node_t bb_node
= BB_NODE (dom
, bb
);
638 aux_bb_node
= et_forest_parent (dom
->forest
, bb_node
);
640 et_forest_remove_edge (dom
->forest
, aux_bb_node
, bb_node
);
641 if (dominated_by
!= NULL
)
643 if (bb
== dominated_by
)
645 if (!et_forest_add_edge (dom
->forest
, BB_NODE (dom
, dominated_by
), bb_node
))
650 /* Store all basic blocks dominated by BB into BBS and return their number. */
652 get_dominated_by (dom
, bb
, bbs
)
659 *bbs
= xmalloc (n_basic_blocks
* sizeof (basic_block
));
660 n
= et_forest_enumerate_sons (dom
->forest
, BB_NODE (dom
, bb
), (et_forest_node_t
*)*bbs
);
661 for (i
= 0; i
< n
; i
++)
662 (*bbs
)[i
] = et_forest_node_value (dom
->forest
, (et_forest_node_t
)(*bbs
)[i
]);
666 /* Redirect all edges pointing to BB to TO. */
668 redirect_immediate_dominators (dom
, bb
, to
)
673 et_forest_node_t
*bbs
= xmalloc (n_basic_blocks
* sizeof (basic_block
));
674 et_forest_node_t node
= BB_NODE (dom
, bb
);
675 et_forest_node_t node2
= BB_NODE (dom
, to
);
676 int n
= et_forest_enumerate_sons (dom
->forest
, node
, bbs
);
679 for (i
= 0; i
< n
; i
++)
681 et_forest_remove_edge (dom
->forest
, node
, bbs
[i
]);
682 et_forest_add_edge (dom
->forest
, node2
, bbs
[i
]);
687 /* Find first basic block in the tree dominating both BB1 and BB2. */
689 nearest_common_dominator (dom
, bb1
, bb2
)
698 return et_forest_node_value (dom
->forest
,
699 et_forest_common_ancestor (dom
->forest
,
705 /* Return TRUE in case BB1 is dominated by BB2. */
707 dominated_by_p (dom
, bb1
, bb2
)
712 return nearest_common_dominator (dom
, bb1
, bb2
) == bb2
;
715 /* Verify invariants of dominator structure. */
717 verify_dominators (dom
)
727 dom_bb
= recount_dominator (dom
, bb
);
728 if (dom_bb
!= get_immediate_dominator (dom
, bb
))
730 error ("dominator of %d should be %d, not %d",
731 bb
->index
, dom_bb
->index
, get_immediate_dominator(dom
, bb
)->index
);
739 /* Recount dominator of BB. */
741 recount_dominator (dom
, bb
)
745 basic_block dom_bb
= NULL
;
748 for (e
= bb
->pred
; e
; e
= e
->pred_next
)
750 if (!dominated_by_p (dom
, e
->src
, bb
))
751 dom_bb
= nearest_common_dominator (dom
, dom_bb
, e
->src
);
757 /* Iteratively recount dominators of BBS. The change is supposed to be local
758 and not to grow further. */
760 iterate_fix_dominators (dom
, bbs
, n
)
766 basic_block old_dom
, new_dom
;
771 for (i
= 0; i
< n
; i
++)
773 old_dom
= get_immediate_dominator (dom
, bbs
[i
]);
774 new_dom
= recount_dominator (dom
, bbs
[i
]);
775 if (old_dom
!= new_dom
)
778 set_immediate_dominator (dom
, bbs
[i
], new_dom
);
785 add_to_dominance_info (dom
, bb
)
789 VARRAY_GROW (dom
->varray
, last_basic_block
+ 3);
790 #ifdef ENABLE_CHECKING
791 if (BB_NODE (dom
, bb
))
794 SET_BB_NODE (dom
, bb
, et_forest_add_node (dom
->forest
, bb
));
798 delete_from_dominance_info (dom
, bb
)
802 et_forest_remove_node (dom
->forest
, BB_NODE (dom
, bb
));
803 SET_BB_NODE (dom
, bb
, NULL
);
807 debug_dominance_info (dom
)
812 if ((bb2
= get_immediate_dominator (dom
, bb
)))
813 fprintf (stderr
, "%i %i\n", bb
->index
, bb2
->index
);