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. */
39 #include "hard-reg-set.h"
40 #include "basic-block.h"
42 #include "et-forest.h"
50 #define BB_NODE(info, bb) \
51 ((et_forest_node_t)VARRAY_GENERIC_PTR ((info)->varray, (bb)->index + 2))
52 #define SET_BB_NODE(info, bb, node) \
53 (VARRAY_GENERIC_PTR ((info)->varray, (bb)->index + 2) = (node))
55 /* We name our nodes with integers, beginning with 1. Zero is reserved for
56 'undefined' or 'end of list'. The name of each node is given by the dfs
57 number of the corresponding basic block. Please note, that we include the
58 artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to
59 support multiple entry points. As it has no real basic block index we use
60 'last_basic_block' for that. Its dfs number is of course 1. */
62 /* Type of Basic Block aka. TBB */
63 typedef unsigned int TBB
;
65 /* We work in a poor-mans object oriented fashion, and carry an instance of
66 this structure through all our 'methods'. It holds various arrays
67 reflecting the (sub)structure of the flowgraph. Most of them are of type
68 TBB and are also indexed by TBB. */
72 /* The parent of a node in the DFS tree. */
74 /* For a node x key[x] is roughly the node nearest to the root from which
75 exists a way to x only over nodes behind x. Such a node is also called
78 /* The value in path_min[x] is the node y on the path from x to the root of
79 the tree x is in with the smallest key[y]. */
81 /* bucket[x] points to the first node of the set of nodes having x as key. */
83 /* And next_bucket[x] points to the next node. */
85 /* After the algorithm is done, dom[x] contains the immediate dominator
89 /* The following few fields implement the structures needed for disjoint
91 /* set_chain[x] is the next node on the path from x to the representant
92 of the set containing x. If set_chain[x]==0 then x is a root. */
94 /* set_size[x] is the number of elements in the set named by x. */
95 unsigned int *set_size
;
96 /* set_child[x] is used for balancing the tree representing a set. It can
97 be understood as the next sibling of x. */
100 /* If b is the number of a basic block (BB->index), dfs_order[b] is the
101 number of that node in DFS order counted from 1. This is an index
102 into most of the other arrays in this structure. */
104 /* If x is the DFS-index of a node which corresponds with an basic block,
105 dfs_to_bb[x] is that basic block. Note, that in our structure there are
106 more nodes that basic blocks, so only dfs_to_bb[dfs_order[bb->index]]==bb
107 is true for every basic block bb, but not the opposite. */
108 basic_block
*dfs_to_bb
;
110 /* This is the next free DFS number when creating the DFS tree or forest. */
112 /* The number of nodes in the DFS tree (==dfsnum-1). */
116 static void init_dom_info
PARAMS ((struct dom_info
*));
117 static void free_dom_info
PARAMS ((struct dom_info
*));
118 static void calc_dfs_tree_nonrec
PARAMS ((struct dom_info
*,
120 enum cdi_direction
));
121 static void calc_dfs_tree
PARAMS ((struct dom_info
*,
122 enum cdi_direction
));
123 static void compress
PARAMS ((struct dom_info
*, TBB
));
124 static TBB eval
PARAMS ((struct dom_info
*, TBB
));
125 static void link_roots
PARAMS ((struct dom_info
*, TBB
, TBB
));
126 static void calc_idoms
PARAMS ((struct dom_info
*,
127 enum cdi_direction
));
128 void debug_dominance_info
PARAMS ((dominance_info
));
130 /* Helper macro for allocating and initializing an array,
131 for aesthetic reasons. */
132 #define init_ar(var, type, num, content) \
135 unsigned int i = 1; /* Catch content == i. */ \
137 (var) = (type *) xcalloc ((num), sizeof (type)); \
140 (var) = (type *) xmalloc ((num) * sizeof (type)); \
141 for (i = 0; i < num; i++) \
142 (var)[i] = (content); \
147 /* Allocate all needed memory in a pessimistic fashion (so we round up).
148 This initializes the contents of DI, which already must be allocated. */
154 /* We need memory for n_basic_blocks nodes and the ENTRY_BLOCK or
156 unsigned int num
= n_basic_blocks
+ 1 + 1;
157 init_ar (di
->dfs_parent
, TBB
, num
, 0);
158 init_ar (di
->path_min
, TBB
, num
, i
);
159 init_ar (di
->key
, TBB
, num
, i
);
160 init_ar (di
->dom
, TBB
, num
, 0);
162 init_ar (di
->bucket
, TBB
, num
, 0);
163 init_ar (di
->next_bucket
, TBB
, num
, 0);
165 init_ar (di
->set_chain
, TBB
, num
, 0);
166 init_ar (di
->set_size
, unsigned int, num
, 1);
167 init_ar (di
->set_child
, TBB
, num
, 0);
169 init_ar (di
->dfs_order
, TBB
, (unsigned int) last_basic_block
+ 1, 0);
170 init_ar (di
->dfs_to_bb
, basic_block
, num
, 0);
178 /* Free all allocated memory in DI, but not DI itself. */
184 free (di
->dfs_parent
);
189 free (di
->next_bucket
);
190 free (di
->set_chain
);
192 free (di
->set_child
);
193 free (di
->dfs_order
);
194 free (di
->dfs_to_bb
);
197 /* The nonrecursive variant of creating a DFS tree. DI is our working
198 structure, BB the starting basic block for this tree and REVERSE
199 is true, if predecessors should be visited instead of successors of a
200 node. After this is done all nodes reachable from BB were visited, have
201 assigned their dfs number and are linked together to form a tree. */
204 calc_dfs_tree_nonrec (di
, bb
, reverse
)
207 enum cdi_direction reverse
;
209 /* We never call this with bb==EXIT_BLOCK_PTR (ENTRY_BLOCK_PTR if REVERSE). */
210 /* We call this _only_ if bb is not already visited. */
212 TBB child_i
, my_i
= 0;
215 /* Start block (ENTRY_BLOCK_PTR for forward problem, EXIT_BLOCK for backward
217 basic_block en_block
;
219 basic_block ex_block
;
221 stack
= (edge
*) xmalloc ((n_basic_blocks
+ 3) * sizeof (edge
));
224 /* Initialize our border blocks, and the first edge. */
228 en_block
= EXIT_BLOCK_PTR
;
229 ex_block
= ENTRY_BLOCK_PTR
;
234 en_block
= ENTRY_BLOCK_PTR
;
235 ex_block
= EXIT_BLOCK_PTR
;
238 /* When the stack is empty we break out of this loop. */
243 /* This loop traverses edges e in depth first manner, and fills the
249 /* Deduce from E the current and the next block (BB and BN), and the
255 /* If the next node BN is either already visited or a border
256 block the current edge is useless, and simply overwritten
257 with the next edge out of the current node. */
258 if (bn
== ex_block
|| di
->dfs_order
[bn
->index
])
269 if (bn
== ex_block
|| di
->dfs_order
[bn
->index
])
281 /* Fill the DFS tree info calculatable _before_ recursing. */
283 my_i
= di
->dfs_order
[bb
->index
];
285 my_i
= di
->dfs_order
[last_basic_block
];
286 child_i
= di
->dfs_order
[bn
->index
] = di
->dfsnum
++;
287 di
->dfs_to_bb
[child_i
] = bn
;
288 di
->dfs_parent
[child_i
] = my_i
;
290 /* Save the current point in the CFG on the stack, and recurse. */
299 /* OK. The edge-list was exhausted, meaning normally we would
300 end the recursion. After returning from the recursive call,
301 there were (may be) other statements which were run after a
302 child node was completely considered by DFS. Here is the
303 point to do it in the non-recursive variant.
304 E.g. The block just completed is in e->dest for forward DFS,
305 the block not yet completed (the parent of the one above)
306 in e->src. This could be used e.g. for computing the number of
307 descendants or the tree depth. */
316 /* The main entry for calculating the DFS tree or forest. DI is our working
317 structure and REVERSE is true, if we are interested in the reverse flow
318 graph. In that case the result is not necessarily a tree but a forest,
319 because there may be nodes from which the EXIT_BLOCK is unreachable. */
322 calc_dfs_tree (di
, reverse
)
324 enum cdi_direction reverse
;
326 /* The first block is the ENTRY_BLOCK (or EXIT_BLOCK if REVERSE). */
327 basic_block begin
= reverse
? EXIT_BLOCK_PTR
: ENTRY_BLOCK_PTR
;
328 di
->dfs_order
[last_basic_block
] = di
->dfsnum
;
329 di
->dfs_to_bb
[di
->dfsnum
] = begin
;
332 calc_dfs_tree_nonrec (di
, begin
, reverse
);
336 /* In the post-dom case we may have nodes without a path to EXIT_BLOCK.
337 They are reverse-unreachable. In the dom-case we disallow such
338 nodes, but in post-dom we have to deal with them, so we simply
339 include them in the DFS tree which actually becomes a forest. */
341 FOR_EACH_BB_REVERSE (b
)
343 if (di
->dfs_order
[b
->index
])
345 di
->dfs_order
[b
->index
] = di
->dfsnum
;
346 di
->dfs_to_bb
[di
->dfsnum
] = b
;
348 calc_dfs_tree_nonrec (di
, b
, reverse
);
352 di
->nodes
= di
->dfsnum
- 1;
354 /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all. */
355 if (di
->nodes
!= (unsigned int) n_basic_blocks
+ 1)
359 /* Compress the path from V to the root of its set and update path_min at the
360 same time. After compress(di, V) set_chain[V] is the root of the set V is
361 in and path_min[V] is the node with the smallest key[] value on the path
362 from V to that root. */
369 /* Btw. It's not worth to unrecurse compress() as the depth is usually not
370 greater than 5 even for huge graphs (I've not seen call depth > 4).
371 Also performance wise compress() ranges _far_ behind eval(). */
372 TBB parent
= di
->set_chain
[v
];
373 if (di
->set_chain
[parent
])
375 compress (di
, parent
);
376 if (di
->key
[di
->path_min
[parent
]] < di
->key
[di
->path_min
[v
]])
377 di
->path_min
[v
] = di
->path_min
[parent
];
378 di
->set_chain
[v
] = di
->set_chain
[parent
];
382 /* Compress the path from V to the set root of V if needed (when the root has
383 changed since the last call). Returns the node with the smallest key[]
384 value on the path from V to the root. */
391 /* The representant of the set V is in, also called root (as the set
392 representation is a tree). */
393 TBB rep
= di
->set_chain
[v
];
395 /* V itself is the root. */
397 return di
->path_min
[v
];
399 /* Compress only if necessary. */
400 if (di
->set_chain
[rep
])
403 rep
= di
->set_chain
[v
];
406 if (di
->key
[di
->path_min
[rep
]] >= di
->key
[di
->path_min
[v
]])
407 return di
->path_min
[v
];
409 return di
->path_min
[rep
];
412 /* This essentially merges the two sets of V and W, giving a single set with
413 the new root V. The internal representation of these disjoint sets is a
414 balanced tree. Currently link(V,W) is only used with V being the parent
418 link_roots (di
, v
, w
)
424 /* Rebalance the tree. */
425 while (di
->key
[di
->path_min
[w
]] < di
->key
[di
->path_min
[di
->set_child
[s
]]])
427 if (di
->set_size
[s
] + di
->set_size
[di
->set_child
[di
->set_child
[s
]]]
428 >= 2 * di
->set_size
[di
->set_child
[s
]])
430 di
->set_chain
[di
->set_child
[s
]] = s
;
431 di
->set_child
[s
] = di
->set_child
[di
->set_child
[s
]];
435 di
->set_size
[di
->set_child
[s
]] = di
->set_size
[s
];
436 s
= di
->set_chain
[s
] = di
->set_child
[s
];
440 di
->path_min
[s
] = di
->path_min
[w
];
441 di
->set_size
[v
] += di
->set_size
[w
];
442 if (di
->set_size
[v
] < 2 * di
->set_size
[w
])
445 s
= di
->set_child
[v
];
446 di
->set_child
[v
] = tmp
;
449 /* Merge all subtrees. */
452 di
->set_chain
[s
] = v
;
453 s
= di
->set_child
[s
];
457 /* This calculates the immediate dominators (or post-dominators if REVERSE is
458 true). DI is our working structure and should hold the DFS forest.
459 On return the immediate dominator to node V is in di->dom[V]. */
462 calc_idoms (di
, reverse
)
464 enum cdi_direction reverse
;
467 basic_block en_block
;
469 en_block
= EXIT_BLOCK_PTR
;
471 en_block
= ENTRY_BLOCK_PTR
;
473 /* Go backwards in DFS order, to first look at the leafs. */
477 basic_block bb
= di
->dfs_to_bb
[v
];
480 par
= di
->dfs_parent
[v
];
487 /* Search all direct predecessors for the smallest node with a path
488 to them. That way we have the smallest node with also a path to
489 us only over nodes behind us. In effect we search for our
491 for (; e
; e
= e_next
)
499 e_next
= e
->succ_next
;
504 e_next
= e
->pred_next
;
507 k1
= di
->dfs_order
[last_basic_block
];
509 k1
= di
->dfs_order
[b
->index
];
511 /* Call eval() only if really needed. If k1 is above V in DFS tree,
512 then we know, that eval(k1) == k1 and key[k1] == k1. */
514 k1
= di
->key
[eval (di
, k1
)];
520 link_roots (di
, par
, v
);
521 di
->next_bucket
[v
] = di
->bucket
[k
];
524 /* Transform semidominators into dominators. */
525 for (w
= di
->bucket
[par
]; w
; w
= di
->next_bucket
[w
])
528 if (di
->key
[k
] < di
->key
[w
])
533 /* We don't need to cleanup next_bucket[]. */
538 /* Explicitly define the dominators. */
540 for (v
= 2; v
<= di
->nodes
; v
++)
541 if (di
->dom
[v
] != di
->key
[v
])
542 di
->dom
[v
] = di
->dom
[di
->dom
[v
]];
545 /* The main entry point into this module. IDOM is an integer array with room
546 for last_basic_block integers, DOMS is a preallocated sbitmap array having
547 room for last_basic_block^2 bits, and POST is true if the caller wants to
548 know post-dominators.
550 On return IDOM[i] will be the BB->index of the immediate (post) dominator
551 of basic block i, and DOMS[i] will have set bit j if basic block j is a
552 (post)dominator for block i.
554 Either IDOM or DOMS may be NULL (meaning the caller is not interested in
555 immediate resp. all dominators). */
558 calculate_dominance_info (reverse
)
559 enum cdi_direction reverse
;
565 /* allocate structure for dominance information. */
566 info
= xmalloc (sizeof (struct dominance_info
));
567 info
->forest
= et_forest_create ();
568 VARRAY_GENERIC_PTR_INIT (info
->varray
, last_basic_block
+ 3, "dominance info");
570 /* Add the two well-known basic blocks. */
571 SET_BB_NODE (info
, ENTRY_BLOCK_PTR
, et_forest_add_node (info
->forest
,
573 SET_BB_NODE (info
, EXIT_BLOCK_PTR
, et_forest_add_node (info
->forest
,
576 SET_BB_NODE (info
, b
, et_forest_add_node (info
->forest
, b
));
579 calc_dfs_tree (&di
, reverse
);
580 calc_idoms (&di
, reverse
);
585 TBB d
= di
.dom
[di
.dfs_order
[b
->index
]];
588 et_forest_add_edge (info
->forest
, BB_NODE (info
, di
.dfs_to_bb
[d
]), BB_NODE (info
, b
));
595 /* Free dominance information. */
597 free_dominance_info (info
)
602 /* Allow users to create new basic block without setting up the dominance
603 information for them. */
605 if (bb
->index
< (int)(info
->varray
->num_elements
- 2)
606 && BB_NODE (info
, bb
))
607 delete_from_dominance_info (info
, bb
);
608 delete_from_dominance_info (info
, ENTRY_BLOCK_PTR
);
609 delete_from_dominance_info (info
, EXIT_BLOCK_PTR
);
610 et_forest_delete (info
->forest
);
611 VARRAY_GROW (info
->varray
, 0);
615 /* Return the immediate dominator of basic block BB. */
617 get_immediate_dominator (dom
, bb
)
621 return et_forest_node_value (dom
->forest
,
622 et_forest_parent (dom
->forest
,
626 /* Set the immediate dominator of the block possibly removing
627 existing edge. NULL can be used to remove any edge. */
629 set_immediate_dominator (dom
, bb
, dominated_by
)
631 basic_block bb
, dominated_by
;
634 et_forest_node_t bb_node
= BB_NODE (dom
, bb
);
636 aux_bb_node
= et_forest_parent (dom
->forest
, bb_node
);
638 et_forest_remove_edge (dom
->forest
, aux_bb_node
, bb_node
);
639 if (dominated_by
!= NULL
)
641 if (bb
== dominated_by
)
643 if (!et_forest_add_edge (dom
->forest
, BB_NODE (dom
, dominated_by
), bb_node
))
648 /* Store all basic blocks dominated by BB into BBS and return their number. */
650 get_dominated_by (dom
, bb
, bbs
)
657 *bbs
= xmalloc (n_basic_blocks
* sizeof (basic_block
));
658 n
= et_forest_enumerate_sons (dom
->forest
, BB_NODE (dom
, bb
), (et_forest_node_t
*)*bbs
);
659 for (i
= 0; i
< n
; i
++)
660 (*bbs
)[i
] = et_forest_node_value (dom
->forest
, (et_forest_node_t
)(*bbs
)[i
]);
664 /* Redirect all edges pointing to BB to TO. */
666 redirect_immediate_dominators (dom
, bb
, to
)
671 et_forest_node_t
*bbs
= xmalloc (n_basic_blocks
* sizeof (basic_block
));
672 et_forest_node_t node
= BB_NODE (dom
, bb
);
673 et_forest_node_t node2
= BB_NODE (dom
, to
);
674 int n
= et_forest_enumerate_sons (dom
->forest
, node
, bbs
);
677 for (i
= 0; i
< n
; i
++)
679 et_forest_remove_edge (dom
->forest
, node
, bbs
[i
]);
680 et_forest_add_edge (dom
->forest
, node2
, bbs
[i
]);
685 /* Find first basic block in the tree dominating both BB1 and BB2. */
687 nearest_common_dominator (dom
, bb1
, bb2
)
696 return et_forest_node_value (dom
->forest
,
697 et_forest_common_ancestor (dom
->forest
,
703 /* Return TRUE in case BB1 is dominated by BB2. */
705 dominated_by_p (dom
, bb1
, bb2
)
710 return nearest_common_dominator (dom
, bb1
, bb2
) == bb2
;
713 /* Verify invariants of dominator structure. */
715 verify_dominators (dom
)
725 dom_bb
= recount_dominator (dom
, bb
);
726 if (dom_bb
!= get_immediate_dominator (dom
, bb
))
728 error ("dominator of %d should be %d, not %d",
729 bb
->index
, dom_bb
->index
, get_immediate_dominator(dom
, bb
)->index
);
737 /* Recount dominator of BB. */
739 recount_dominator (dom
, bb
)
743 basic_block dom_bb
= NULL
;
746 for (e
= bb
->pred
; e
; e
= e
->pred_next
)
748 if (!dominated_by_p (dom
, e
->src
, bb
))
749 dom_bb
= nearest_common_dominator (dom
, dom_bb
, e
->src
);
755 /* Iteratively recount dominators of BBS. The change is supposed to be local
756 and not to grow further. */
758 iterate_fix_dominators (dom
, bbs
, n
)
764 basic_block old_dom
, new_dom
;
769 for (i
= 0; i
< n
; i
++)
771 old_dom
= get_immediate_dominator (dom
, bbs
[i
]);
772 new_dom
= recount_dominator (dom
, bbs
[i
]);
773 if (old_dom
!= new_dom
)
776 set_immediate_dominator (dom
, bbs
[i
], new_dom
);
783 add_to_dominance_info (dom
, bb
)
787 VARRAY_GROW (dom
->varray
, last_basic_block
+ 3);
788 #ifdef ENABLE_CHECKING
789 if (BB_NODE (dom
, bb
))
792 SET_BB_NODE (dom
, bb
, et_forest_add_node (dom
->forest
, bb
));
796 delete_from_dominance_info (dom
, bb
)
800 et_forest_remove_node (dom
->forest
, BB_NODE (dom
, bb
));
801 SET_BB_NODE (dom
, bb
, NULL
);
805 debug_dominance_info (dom
)
810 if ((bb2
= get_immediate_dominator (dom
, bb
)))
811 fprintf (stderr
, "%i %i\n", bb
->index
, bb2
->index
);