1 /* Calculate (post)dominators in slightly super-linear time.
2 Copyright (C) 2000-2024 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 3, 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 COPYING3. If not see
19 <http://www.gnu.org/licenses/>. */
21 /* This file implements the well known algorithm from Lengauer and Tarjan
22 to compute the dominators in a control flow graph. A basic block D is said
23 to dominate another block X, when all paths from the entry node of the CFG
24 to X go also over D. The dominance relation is a transitive reflexive
25 relation and its minimal transitive reduction is a tree, called the
26 dominator tree. So for each block X besides the entry block exists a
27 block I(X), called the immediate dominator of X, which is the parent of X
28 in the dominator tree.
30 The algorithm computes this dominator tree implicitly by computing for
31 each block its immediate dominator. We use tree balancing and path
32 compression, so it's the O(e*a(e,v)) variant, where a(e,v) is the very
33 slowly growing functional inverse of the Ackerman function. */
37 #include "coretypes.h"
40 #include "diagnostic-core.h"
42 #include "et-forest.h"
45 /* We name our nodes with integers, beginning with 1. Zero is reserved for
46 'undefined' or 'end of list'. The name of each node is given by the dfs
47 number of the corresponding basic block. Please note, that we include the
48 artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to
49 support multiple entry points. Its dfs number is of course 1. */
51 /* Type of Basic Block aka. TBB */
52 typedef unsigned int TBB
;
56 /* This class holds various arrays reflecting the (sub)structure of the
57 flowgraph. Most of them are of type TBB and are also indexed by TBB. */
62 dom_info (function
*, cdi_direction
);
63 dom_info (vec
<basic_block
>, cdi_direction
);
65 void calc_dfs_tree ();
68 inline basic_block
get_idom (basic_block
);
70 void calc_dfs_tree_nonrec (basic_block
);
74 void link_roots (TBB
, TBB
);
76 /* The parent of a node in the DFS tree. */
78 /* For a node x m_key[x] is roughly the node nearest to the root from which
79 exists a way to x only over nodes behind x. Such a node is also called
82 /* The value in m_path_min[x] is the node y on the path from x to the root of
83 the tree x is in with the smallest m_key[y]. */
85 /* m_bucket[x] points to the first node of the set of nodes having x as
88 /* And m_next_bucket[x] points to the next node. */
90 /* After the algorithm is done, m_dom[x] contains the immediate dominator
94 /* The following few fields implement the structures needed for disjoint
96 /* m_set_chain[x] is the next node on the path from x to the representative
97 of the set containing x. If m_set_chain[x]==0 then x is a root. */
99 /* m_set_size[x] is the number of elements in the set named by x. */
100 unsigned int *m_set_size
;
101 /* m_set_child[x] is used for balancing the tree representing a set. It can
102 be understood as the next sibling of x. */
105 /* If b is the number of a basic block (BB->index), m_dfs_order[b] is the
106 number of that node in DFS order counted from 1. This is an index
107 into most of the other arrays in this structure. */
109 /* Points to last element in m_dfs_order array. */
111 /* If x is the DFS-index of a node which corresponds with a basic block,
112 m_dfs_to_bb[x] is that basic block. Note, that in our structure there are
113 more nodes that basic blocks, so only
114 m_dfs_to_bb[m_dfs_order[bb->index]]==bb is true for every basic block bb,
115 but not the opposite. */
116 basic_block
*m_dfs_to_bb
;
118 /* This is the next free DFS number when creating the DFS tree. */
119 unsigned int m_dfsnum
;
120 /* The number of nodes in the DFS tree (==m_dfsnum-1). */
121 unsigned int m_nodes
;
123 /* Blocks with bits set here have a fake edge to EXIT. These are used
124 to turn a DFS forest into a proper tree. */
125 bitmap m_fake_exit_edge
;
127 /* Number of basic blocks in the function being compiled. */
128 unsigned m_n_basic_blocks
;
130 /* True, if we are computing postdominators (rather than dominators). */
133 /* Start block (the entry block for forward problem, exit block for backward
135 basic_block m_start_block
;
137 basic_block m_end_block
;
140 } // anonymous namespace
142 void debug_dominance_info (cdi_direction
);
143 void debug_dominance_tree (cdi_direction
, basic_block
);
145 /* Allocate and zero-initialize NUM elements of type T (T must be a
146 POD-type). Note: after transition to C++11 or later,
147 `x = new_zero_array <T> (num);' can be replaced with
148 `x = new T[num] {};'. */
151 inline T
*new_zero_array (unsigned num
)
153 T
*result
= new T
[num
];
154 memset (result
, 0, sizeof (T
) * num
);
158 /* Helper function for constructors to initialize a part of class members. */
161 dom_info::dom_init (void)
163 unsigned num
= m_n_basic_blocks
;
165 m_dfs_parent
= new_zero_array
<TBB
> (num
);
166 m_dom
= new_zero_array
<TBB
> (num
);
168 m_path_min
= new TBB
[num
];
169 m_key
= new TBB
[num
];
170 m_set_size
= new unsigned int[num
];
171 for (unsigned i
= 0; i
< num
; i
++)
173 m_path_min
[i
] = m_key
[i
] = i
;
177 m_bucket
= new_zero_array
<TBB
> (num
);
178 m_next_bucket
= new_zero_array
<TBB
> (num
);
180 m_set_chain
= new_zero_array
<TBB
> (num
);
181 m_set_child
= new_zero_array
<TBB
> (num
);
183 m_dfs_to_bb
= new_zero_array
<basic_block
> (num
);
189 /* Allocate all needed memory in a pessimistic fashion (so we round up). */
191 dom_info::dom_info (function
*fn
, cdi_direction dir
)
193 m_n_basic_blocks
= n_basic_blocks_for_fn (fn
);
197 unsigned last_bb_index
= last_basic_block_for_fn (fn
);
198 m_dfs_order
= new_zero_array
<TBB
> (last_bb_index
+ 1);
199 m_dfs_last
= &m_dfs_order
[last_bb_index
];
205 m_fake_exit_edge
= NULL
;
206 m_start_block
= ENTRY_BLOCK_PTR_FOR_FN (fn
);
207 m_end_block
= EXIT_BLOCK_PTR_FOR_FN (fn
);
209 case CDI_POST_DOMINATORS
:
211 m_fake_exit_edge
= BITMAP_ALLOC (NULL
);
212 m_start_block
= EXIT_BLOCK_PTR_FOR_FN (fn
);
213 m_end_block
= ENTRY_BLOCK_PTR_FOR_FN (fn
);
220 /* Constructor for reducible region REGION. */
222 dom_info::dom_info (vec
<basic_block
> region
, cdi_direction dir
)
224 m_n_basic_blocks
= region
.length ();
225 unsigned nm1
= m_n_basic_blocks
- 1;
229 /* Determine max basic block index in region. */
230 int max_index
= region
[0]->index
;
231 for (unsigned i
= 1; i
<= nm1
; i
++)
232 if (region
[i
]->index
> max_index
)
233 max_index
= region
[i
]->index
;
234 max_index
+= 1; /* set index on the first bb out of region. */
236 m_dfs_order
= new_zero_array
<TBB
> (max_index
+ 1);
237 m_dfs_last
= &m_dfs_order
[max_index
];
239 m_fake_exit_edge
= NULL
; /* Assume that region is reducible. */
245 m_start_block
= region
[0];
246 m_end_block
= region
[nm1
];
248 case CDI_POST_DOMINATORS
:
250 m_start_block
= region
[nm1
];
251 m_end_block
= region
[0];
259 dom_info::get_idom (basic_block bb
)
261 TBB d
= m_dom
[m_dfs_order
[bb
->index
]];
262 return m_dfs_to_bb
[d
];
265 /* Map dominance calculation type to array index used for various
266 dominance information arrays. This version is simple -- it will need
267 to be modified, obviously, if additional values are added to
270 static inline unsigned int
271 dom_convert_dir_to_idx (cdi_direction dir
)
273 gcc_checking_assert (dir
== CDI_DOMINATORS
|| dir
== CDI_POST_DOMINATORS
);
277 /* Free all allocated memory in dom_info. */
279 dom_info::~dom_info ()
281 delete[] m_dfs_parent
;
286 delete[] m_next_bucket
;
287 delete[] m_set_chain
;
289 delete[] m_set_child
;
290 delete[] m_dfs_order
;
291 delete[] m_dfs_to_bb
;
292 BITMAP_FREE (m_fake_exit_edge
);
295 /* The nonrecursive variant of creating a DFS tree. BB is the starting basic
296 block for this tree and m_reverse is true, if predecessors should be visited
297 instead of successors of a node. After this is done all nodes reachable
298 from BB were visited, have assigned their dfs number and are linked together
302 dom_info::calc_dfs_tree_nonrec (basic_block bb
)
304 edge_iterator
*stack
= new edge_iterator
[m_n_basic_blocks
+ 1];
306 unsigned d_i
= dom_convert_dir_to_idx (m_reverse
? CDI_POST_DOMINATORS
309 /* Initialize the first edge. */
310 edge_iterator ei
= m_reverse
? ei_start (bb
->preds
)
311 : ei_start (bb
->succs
);
313 /* When the stack is empty we break out of this loop. */
317 edge_iterator einext
;
319 /* This loop traverses edges e in depth first manner, and fills the
321 while (!ei_end_p (ei
))
323 edge e
= ei_edge (ei
);
325 /* Deduce from E the current and the next block (BB and BN), and the
331 /* If the next node BN is either already visited or a border
332 block or out of region the current edge is useless, and simply
333 overwritten with the next edge out of the current node. */
334 if (bn
== m_end_block
|| bn
->dom
[d_i
] == NULL
335 || m_dfs_order
[bn
->index
])
341 einext
= ei_start (bn
->preds
);
346 if (bn
== m_end_block
|| bn
->dom
[d_i
] == NULL
347 || m_dfs_order
[bn
->index
])
353 einext
= ei_start (bn
->succs
);
356 gcc_assert (bn
!= m_start_block
);
358 /* Fill the DFS tree info calculatable _before_ recursing. */
360 if (bb
!= m_start_block
)
361 my_i
= m_dfs_order
[bb
->index
];
364 TBB child_i
= m_dfs_order
[bn
->index
] = m_dfsnum
++;
365 m_dfs_to_bb
[child_i
] = bn
;
366 m_dfs_parent
[child_i
] = my_i
;
368 /* Save the current point in the CFG on the stack, and recurse. */
377 /* OK. The edge-list was exhausted, meaning normally we would
378 end the recursion. After returning from the recursive call,
379 there were (may be) other statements which were run after a
380 child node was completely considered by DFS. Here is the
381 point to do it in the non-recursive variant.
382 E.g. The block just completed is in e->dest for forward DFS,
383 the block not yet completed (the parent of the one above)
384 in e->src. This could be used e.g. for computing the number of
385 descendants or the tree depth. */
391 /* The main entry for calculating the DFS tree or forest. m_reverse is true,
392 if we are interested in the reverse flow graph. In that case the result is
393 not necessarily a tree but a forest, because there may be nodes from which
394 the EXIT_BLOCK is unreachable. */
397 dom_info::calc_dfs_tree ()
399 *m_dfs_last
= m_dfsnum
;
400 m_dfs_to_bb
[m_dfsnum
] = m_start_block
;
403 calc_dfs_tree_nonrec (m_start_block
);
405 if (m_fake_exit_edge
)
407 /* In the post-dom case we may have nodes without a path to EXIT_BLOCK.
408 They are reverse-unreachable. In the dom-case we disallow such
409 nodes, but in post-dom we have to deal with them.
411 There are two situations in which this occurs. First, noreturn
412 functions. Second, infinite loops. In the first case we need to
413 pretend that there is an edge to the exit block. In the second
414 case, we wind up with a forest. We need to process all noreturn
415 blocks before we know if we've got any infinite loops. */
418 bool saw_unconnected
= false;
420 FOR_BB_BETWEEN (b
, m_start_block
->prev_bb
, m_end_block
, prev_bb
)
422 if (EDGE_COUNT (b
->succs
) > 0)
424 if (m_dfs_order
[b
->index
] == 0)
425 saw_unconnected
= true;
428 bitmap_set_bit (m_fake_exit_edge
, b
->index
);
429 m_dfs_order
[b
->index
] = m_dfsnum
;
430 m_dfs_to_bb
[m_dfsnum
] = b
;
431 m_dfs_parent
[m_dfsnum
] = *m_dfs_last
;
433 calc_dfs_tree_nonrec (b
);
438 FOR_BB_BETWEEN (b
, m_start_block
->prev_bb
, m_end_block
, prev_bb
)
440 if (m_dfs_order
[b
->index
])
442 basic_block b2
= dfs_find_deadend (b
);
443 gcc_checking_assert (m_dfs_order
[b2
->index
] == 0);
444 bitmap_set_bit (m_fake_exit_edge
, b2
->index
);
445 m_dfs_order
[b2
->index
] = m_dfsnum
;
446 m_dfs_to_bb
[m_dfsnum
] = b2
;
447 m_dfs_parent
[m_dfsnum
] = *m_dfs_last
;
449 calc_dfs_tree_nonrec (b2
);
450 gcc_checking_assert (m_dfs_order
[b
->index
]);
455 m_nodes
= m_dfsnum
- 1;
457 /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all. */
458 gcc_assert (m_nodes
== (unsigned int) m_n_basic_blocks
- 1);
461 /* Compress the path from V to the root of its set and update path_min at the
462 same time. After compress(di, V) set_chain[V] is the root of the set V is
463 in and path_min[V] is the node with the smallest key[] value on the path
464 from V to that root. */
467 dom_info::compress (TBB v
)
469 /* Btw. It's not worth to unrecurse compress() as the depth is usually not
470 greater than 5 even for huge graphs (I've not seen call depth > 4).
471 Also performance wise compress() ranges _far_ behind eval(). */
472 TBB parent
= m_set_chain
[v
];
473 if (m_set_chain
[parent
])
476 if (m_key
[m_path_min
[parent
]] < m_key
[m_path_min
[v
]])
477 m_path_min
[v
] = m_path_min
[parent
];
478 m_set_chain
[v
] = m_set_chain
[parent
];
482 /* Compress the path from V to the set root of V if needed (when the root has
483 changed since the last call). Returns the node with the smallest key[]
484 value on the path from V to the root. */
487 dom_info::eval (TBB v
)
489 /* The representative of the set V is in, also called root (as the set
490 representation is a tree). */
491 TBB rep
= m_set_chain
[v
];
493 /* V itself is the root. */
495 return m_path_min
[v
];
497 /* Compress only if necessary. */
498 if (m_set_chain
[rep
])
501 rep
= m_set_chain
[v
];
504 if (m_key
[m_path_min
[rep
]] >= m_key
[m_path_min
[v
]])
505 return m_path_min
[v
];
507 return m_path_min
[rep
];
510 /* This essentially merges the two sets of V and W, giving a single set with
511 the new root V. The internal representation of these disjoint sets is a
512 balanced tree. Currently link(V,W) is only used with V being the parent
516 dom_info::link_roots (TBB v
, TBB w
)
520 /* Rebalance the tree. */
521 while (m_key
[m_path_min
[w
]] < m_key
[m_path_min
[m_set_child
[s
]]])
523 if (m_set_size
[s
] + m_set_size
[m_set_child
[m_set_child
[s
]]]
524 >= 2 * m_set_size
[m_set_child
[s
]])
526 m_set_chain
[m_set_child
[s
]] = s
;
527 m_set_child
[s
] = m_set_child
[m_set_child
[s
]];
531 m_set_size
[m_set_child
[s
]] = m_set_size
[s
];
532 s
= m_set_chain
[s
] = m_set_child
[s
];
536 m_path_min
[s
] = m_path_min
[w
];
537 m_set_size
[v
] += m_set_size
[w
];
538 if (m_set_size
[v
] < 2 * m_set_size
[w
])
539 std::swap (m_set_child
[v
], s
);
541 /* Merge all subtrees. */
549 /* This calculates the immediate dominators (or post-dominators). THIS is our
550 working structure and should hold the DFS forest.
551 On return the immediate dominator to node V is in m_dom[V]. */
554 dom_info::calc_idoms ()
556 /* Go backwards in DFS order, to first look at the leafs. */
557 for (TBB v
= m_nodes
; v
> 1; v
--)
559 basic_block bb
= m_dfs_to_bb
[v
];
562 TBB par
= m_dfs_parent
[v
];
565 edge_iterator ei
= m_reverse
? ei_start (bb
->succs
)
566 : ei_start (bb
->preds
);
567 edge_iterator einext
;
569 if (m_fake_exit_edge
)
571 /* If this block has a fake edge to exit, process that first. */
572 if (bitmap_bit_p (m_fake_exit_edge
, bb
->index
))
576 goto do_fake_exit_edge
;
580 /* Search all direct predecessors for the smallest node with a path
581 to them. That way we have the smallest node with also a path to
582 us only over nodes behind us. In effect we search for our
584 while (!ei_end_p (ei
))
590 b
= m_reverse
? e
->dest
: e
->src
;
594 if (b
== m_start_block
)
600 k1
= m_dfs_order
[b
->index
];
602 /* Call eval() only if really needed. If k1 is above V in DFS tree,
603 then we know, that eval(k1) == k1 and key[k1] == k1. */
605 k1
= m_key
[eval (k1
)];
614 m_next_bucket
[v
] = m_bucket
[k
];
617 /* Transform semidominators into dominators. */
618 for (TBB w
= m_bucket
[par
]; w
; w
= m_next_bucket
[w
])
621 if (m_key
[k
] < m_key
[w
])
626 /* We don't need to cleanup next_bucket[]. */
630 /* Explicitly define the dominators. */
632 for (TBB v
= 2; v
<= m_nodes
; v
++)
633 if (m_dom
[v
] != m_key
[v
])
634 m_dom
[v
] = m_dom
[m_dom
[v
]];
637 /* Assign dfs numbers starting from NUM to NODE and its sons. */
640 assign_dfs_numbers (struct et_node
*node
, int *num
)
645 n
->dfs_num_in
= (*num
)++;
650 while (!n
->right
|| n
->right
== n
->father
->son
)
652 n
->dfs_num_out
= (*num
)++;
657 n
->dfs_num_out
= (*num
)++;
663 /* Compute the data necessary for fast resolving of dominator queries in a
664 static dominator tree. */
667 compute_dom_fast_query (enum cdi_direction dir
)
671 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
673 gcc_checking_assert (dom_info_available_p (dir
));
675 if (dom_computed
[dir_index
] == DOM_OK
)
678 FOR_ALL_BB_FN (bb
, cfun
)
680 if (!bb
->dom
[dir_index
]->father
)
681 assign_dfs_numbers (bb
->dom
[dir_index
], &num
);
684 dom_computed
[dir_index
] = DOM_OK
;
687 /* Analogous to the previous function but compute the data for reducible
691 compute_dom_fast_query_in_region (enum cdi_direction dir
,
692 vec
<basic_block
> region
)
696 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
698 gcc_checking_assert (dom_info_available_p (dir
));
700 if (dom_computed
[dir_index
] == DOM_OK
)
703 /* Assign dfs numbers for region nodes except for entry and exit nodes. */
704 for (unsigned int i
= 1; i
< region
.length () - 1; i
++)
707 if (!bb
->dom
[dir_index
]->father
)
708 assign_dfs_numbers (bb
->dom
[dir_index
], &num
);
711 dom_computed
[dir_index
] = DOM_OK
;
714 /* The main entry point into this module. DIR is set depending on whether
715 we want to compute dominators or postdominators. If COMPUTE_FAST_QUERY
716 is false then the DFS numbers allowing for a O(1) dominance query
720 calculate_dominance_info (cdi_direction dir
, bool compute_fast_query
)
722 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
724 if (dom_computed
[dir_index
] == DOM_OK
)
726 checking_verify_dominators (dir
);
730 timevar_push (TV_DOMINANCE
);
731 if (!dom_info_available_p (dir
))
733 gcc_assert (!n_bbs_in_dom_tree
[dir_index
]);
736 FOR_ALL_BB_FN (b
, cfun
)
738 b
->dom
[dir_index
] = et_new_tree (b
);
740 n_bbs_in_dom_tree
[dir_index
] = n_basic_blocks_for_fn (cfun
);
742 dom_info
di (cfun
, dir
);
746 FOR_EACH_BB_FN (b
, cfun
)
748 if (basic_block d
= di
.get_idom (b
))
749 et_set_father (b
->dom
[dir_index
], d
->dom
[dir_index
]);
752 dom_computed
[dir_index
] = DOM_NO_FAST_QUERY
;
755 checking_verify_dominators (dir
);
757 if (compute_fast_query
)
758 compute_dom_fast_query (dir
);
760 timevar_pop (TV_DOMINANCE
);
763 /* Analogous to the previous function but compute dominance info for regions
764 which are single entry, multiple exit regions for CDI_DOMINATORs and
765 multiple entry, single exit regions for CDI_POST_DOMINATORs. */
768 calculate_dominance_info_for_region (cdi_direction dir
,
769 vec
<basic_block
> region
)
771 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
775 if (dom_computed
[dir_index
] == DOM_OK
)
778 timevar_push (TV_DOMINANCE
);
779 /* Assume that dom info is not partially computed. */
780 gcc_assert (!dom_info_available_p (dir
));
782 FOR_EACH_VEC_ELT (region
, i
, bb
)
784 bb
->dom
[dir_index
] = et_new_tree (bb
);
786 dom_info
di (region
, dir
);
790 FOR_EACH_VEC_ELT (region
, i
, bb
)
791 if (basic_block d
= di
.get_idom (bb
))
792 et_set_father (bb
->dom
[dir_index
], d
->dom
[dir_index
]);
794 dom_computed
[dir_index
] = DOM_NO_FAST_QUERY
;
795 compute_dom_fast_query_in_region (dir
, region
);
797 timevar_pop (TV_DOMINANCE
);
800 /* Free dominance information for direction DIR. */
802 free_dominance_info (function
*fn
, enum cdi_direction dir
)
805 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
807 if (!dom_info_available_p (fn
, dir
))
810 FOR_ALL_BB_FN (bb
, fn
)
812 et_free_tree_force (bb
->dom
[dir_index
]);
813 bb
->dom
[dir_index
] = NULL
;
817 fn
->cfg
->x_n_bbs_in_dom_tree
[dir_index
] = 0;
819 fn
->cfg
->x_dom_computed
[dir_index
] = DOM_NONE
;
823 free_dominance_info (enum cdi_direction dir
)
825 free_dominance_info (cfun
, dir
);
828 /* Free dominance information for direction DIR in region REGION. */
831 free_dominance_info_for_region (function
*fn
,
832 enum cdi_direction dir
,
833 vec
<basic_block
> region
)
837 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
839 if (!dom_info_available_p (dir
))
842 FOR_EACH_VEC_ELT (region
, i
, bb
)
844 et_free_tree_force (bb
->dom
[dir_index
]);
845 bb
->dom
[dir_index
] = NULL
;
849 fn
->cfg
->x_dom_computed
[dir_index
] = DOM_NONE
;
851 fn
->cfg
->x_n_bbs_in_dom_tree
[dir_index
] = 0;
854 /* Return the immediate dominator of basic block BB. */
856 get_immediate_dominator (enum cdi_direction dir
, basic_block bb
)
858 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
859 struct et_node
*node
= bb
->dom
[dir_index
];
861 gcc_checking_assert (dom_computed
[dir_index
]);
866 return (basic_block
) node
->father
->data
;
869 /* Set the immediate dominator of the block possibly removing
870 existing edge. NULL can be used to remove any edge. */
872 set_immediate_dominator (enum cdi_direction dir
, basic_block bb
,
873 basic_block dominated_by
)
875 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
876 struct et_node
*node
= bb
->dom
[dir_index
];
878 gcc_checking_assert (dom_computed
[dir_index
]);
882 if (node
->father
->data
== dominated_by
)
888 et_set_father (node
, dominated_by
->dom
[dir_index
]);
890 if (dom_computed
[dir_index
] == DOM_OK
)
891 dom_computed
[dir_index
] = DOM_NO_FAST_QUERY
;
894 /* Returns the list of basic blocks immediately dominated by BB, in the
896 auto_vec
<basic_block
>
897 get_dominated_by (enum cdi_direction dir
, basic_block bb
)
899 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
900 struct et_node
*node
= bb
->dom
[dir_index
], *son
= node
->son
, *ason
;
901 auto_vec
<basic_block
> bbs
;
903 gcc_checking_assert (dom_computed
[dir_index
]);
908 bbs
.safe_push ((basic_block
) son
->data
);
909 for (ason
= son
->right
; ason
!= son
; ason
= ason
->right
)
910 bbs
.safe_push ((basic_block
) ason
->data
);
915 /* Returns the list of basic blocks that are immediately dominated (in
916 direction DIR) by some block between N_REGION ones stored in REGION,
917 except for blocks in the REGION itself. */
919 auto_vec
<basic_block
>
920 get_dominated_by_region (enum cdi_direction dir
, basic_block
*region
,
925 auto_vec
<basic_block
> doms
;
927 for (i
= 0; i
< n_region
; i
++)
928 region
[i
]->flags
|= BB_DUPLICATED
;
929 for (i
= 0; i
< n_region
; i
++)
930 for (dom
= first_dom_son (dir
, region
[i
]);
932 dom
= next_dom_son (dir
, dom
))
933 if (!(dom
->flags
& BB_DUPLICATED
))
934 doms
.safe_push (dom
);
935 for (i
= 0; i
< n_region
; i
++)
936 region
[i
]->flags
&= ~BB_DUPLICATED
;
941 /* Returns the list of basic blocks including BB dominated by BB, in the
942 direction DIR up to DEPTH in the dominator tree. The DEPTH of zero will
943 produce a vector containing all dominated blocks. The vector will be sorted
946 auto_vec
<basic_block
>
947 get_dominated_to_depth (enum cdi_direction dir
, basic_block bb
, int depth
)
949 auto_vec
<basic_block
> bbs
;
951 unsigned next_level_start
;
955 next_level_start
= 1; /* = bbs.length (); */
962 for (son
= first_dom_son (dir
, bb
);
964 son
= next_dom_son (dir
, son
))
967 if (i
== next_level_start
&& --depth
)
968 next_level_start
= bbs
.length ();
970 while (i
< next_level_start
);
975 /* Returns the list of basic blocks including BB dominated by BB, in the
976 direction DIR. The vector will be sorted in preorder. */
978 auto_vec
<basic_block
>
979 get_all_dominated_blocks (enum cdi_direction dir
, basic_block bb
)
981 return get_dominated_to_depth (dir
, bb
, 0);
984 /* Redirect all edges pointing to BB to TO. */
986 redirect_immediate_dominators (enum cdi_direction dir
, basic_block bb
,
989 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
990 struct et_node
*bb_node
, *to_node
, *son
;
992 bb_node
= bb
->dom
[dir_index
];
993 to_node
= to
->dom
[dir_index
];
995 gcc_checking_assert (dom_computed
[dir_index
]);
1000 while (bb_node
->son
)
1005 et_set_father (son
, to_node
);
1008 if (dom_computed
[dir_index
] == DOM_OK
)
1009 dom_computed
[dir_index
] = DOM_NO_FAST_QUERY
;
1012 /* Find first basic block in the tree dominating both BB1 and BB2. */
1014 nearest_common_dominator (enum cdi_direction dir
, basic_block bb1
, basic_block bb2
)
1016 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1018 gcc_checking_assert (dom_computed
[dir_index
]);
1025 return (basic_block
) et_nca (bb1
->dom
[dir_index
], bb2
->dom
[dir_index
])->data
;
1029 /* Find the nearest common dominator for the basic blocks in BLOCKS,
1030 using dominance direction DIR. */
1033 nearest_common_dominator_for_set (enum cdi_direction dir
, bitmap blocks
)
1039 first
= bitmap_first_set_bit (blocks
);
1040 dom
= BASIC_BLOCK_FOR_FN (cfun
, first
);
1041 EXECUTE_IF_SET_IN_BITMAP (blocks
, 0, i
, bi
)
1042 if (dom
!= BASIC_BLOCK_FOR_FN (cfun
, i
))
1043 dom
= nearest_common_dominator (dir
, dom
, BASIC_BLOCK_FOR_FN (cfun
, i
));
1048 /* Given a dominator tree, we can determine whether one thing
1049 dominates another in constant time by using two DFS numbers:
1051 1. The number for when we visit a node on the way down the tree
1052 2. The number for when we visit a node on the way back up the tree
1054 You can view these as bounds for the range of dfs numbers the
1055 nodes in the subtree of the dominator tree rooted at that node
1058 The dominator tree is always a simple acyclic tree, so there are
1059 only three possible relations two nodes in the dominator tree have
1062 1. Node A is above Node B (and thus, Node A dominates node B)
1071 In the above case, DFS_Number_In of A will be <= DFS_Number_In of
1072 B, and DFS_Number_Out of A will be >= DFS_Number_Out of B. This is
1073 because we must hit A in the dominator tree *before* B on the walk
1074 down, and we will hit A *after* B on the walk back up
1076 2. Node A is below node B (and thus, node B dominates node A)
1085 In the above case, DFS_Number_In of A will be >= DFS_Number_In of
1086 B, and DFS_Number_Out of A will be <= DFS_Number_Out of B.
1088 This is because we must hit A in the dominator tree *after* B on
1089 the walk down, and we will hit A *before* B on the walk back up
1091 3. Node A and B are siblings (and thus, neither dominates the other)
1099 In the above case, DFS_Number_In of A will *always* be <=
1100 DFS_Number_In of B, and DFS_Number_Out of A will *always* be <=
1101 DFS_Number_Out of B. This is because we will always finish the dfs
1102 walk of one of the subtrees before the other, and thus, the dfs
1103 numbers for one subtree can't intersect with the range of dfs
1104 numbers for the other subtree. If you swap A and B's position in
1105 the dominator tree, the comparison changes direction, but the point
1106 is that both comparisons will always go the same way if there is no
1107 dominance relationship.
1109 Thus, it is sufficient to write
1111 A_Dominates_B (node A, node B)
1113 return DFS_Number_In(A) <= DFS_Number_In(B)
1114 && DFS_Number_Out (A) >= DFS_Number_Out(B);
1117 A_Dominated_by_B (node A, node B)
1119 return DFS_Number_In(A) >= DFS_Number_In(B)
1120 && DFS_Number_Out (A) <= DFS_Number_Out(B);
1123 /* Return TRUE in case BB1 is dominated by BB2. */
1125 dominated_by_p (enum cdi_direction dir
, const_basic_block bb1
, const_basic_block bb2
)
1127 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1128 struct et_node
*n1
= bb1
->dom
[dir_index
], *n2
= bb2
->dom
[dir_index
];
1130 gcc_checking_assert (dom_computed
[dir_index
]);
1132 if (dom_computed
[dir_index
] == DOM_OK
)
1133 return (n1
->dfs_num_in
>= n2
->dfs_num_in
1134 && n1
->dfs_num_out
<= n2
->dfs_num_out
);
1136 return et_below (n1
, n2
);
1139 /* Returns the entry dfs number for basic block BB, in the direction DIR. */
1142 bb_dom_dfs_in (enum cdi_direction dir
, basic_block bb
)
1144 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1145 struct et_node
*n
= bb
->dom
[dir_index
];
1147 gcc_checking_assert (dom_computed
[dir_index
] == DOM_OK
);
1148 return n
->dfs_num_in
;
1151 /* Returns the exit dfs number for basic block BB, in the direction DIR. */
1154 bb_dom_dfs_out (enum cdi_direction dir
, basic_block bb
)
1156 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1157 struct et_node
*n
= bb
->dom
[dir_index
];
1159 gcc_checking_assert (dom_computed
[dir_index
] == DOM_OK
);
1160 return n
->dfs_num_out
;
1163 /* Verify invariants of dominator structure. */
1165 verify_dominators (cdi_direction dir
)
1167 gcc_assert (dom_info_available_p (dir
));
1169 dom_info
di (cfun
, dir
);
1170 di
.calc_dfs_tree ();
1175 FOR_EACH_BB_FN (bb
, cfun
)
1177 basic_block imm_bb
= get_immediate_dominator (dir
, bb
);
1180 error ("dominator of %d status unknown", bb
->index
);
1185 basic_block imm_bb_correct
= di
.get_idom (bb
);
1186 if (imm_bb
!= imm_bb_correct
)
1188 error ("dominator of %d should be %d, not %d",
1189 bb
->index
, imm_bb_correct
->index
, imm_bb
->index
);
1197 /* Determine immediate dominator (or postdominator, according to DIR) of BB,
1198 assuming that dominators of other blocks are correct. We also use it to
1199 recompute the dominators in a restricted area, by iterating it until it
1200 reaches a fixed point. */
1203 recompute_dominator (enum cdi_direction dir
, basic_block bb
)
1205 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1206 basic_block dom_bb
= NULL
;
1210 gcc_checking_assert (dom_computed
[dir_index
]);
1212 if (dir
== CDI_DOMINATORS
)
1214 FOR_EACH_EDGE (e
, ei
, bb
->preds
)
1216 if (!dominated_by_p (dir
, e
->src
, bb
))
1217 dom_bb
= nearest_common_dominator (dir
, dom_bb
, e
->src
);
1222 FOR_EACH_EDGE (e
, ei
, bb
->succs
)
1224 if (!dominated_by_p (dir
, e
->dest
, bb
))
1225 dom_bb
= nearest_common_dominator (dir
, dom_bb
, e
->dest
);
1232 /* Use simple heuristics (see iterate_fix_dominators) to determine dominators
1233 of BBS. We assume that all the immediate dominators except for those of the
1234 blocks in BBS are correct. If CONSERVATIVE is true, we also assume that the
1235 currently recorded immediate dominators of blocks in BBS really dominate the
1236 blocks. The basic blocks for that we determine the dominator are removed
1240 prune_bbs_to_update_dominators (vec
<basic_block
> &bbs
,
1245 basic_block bb
, dom
= NULL
;
1249 for (i
= 0; bbs
.iterate (i
, &bb
);)
1251 if (bb
== ENTRY_BLOCK_PTR_FOR_FN (cfun
))
1254 if (single_pred_p (bb
))
1256 set_immediate_dominator (CDI_DOMINATORS
, bb
, single_pred (bb
));
1265 FOR_EACH_EDGE (e
, ei
, bb
->preds
)
1267 if (dominated_by_p (CDI_DOMINATORS
, e
->src
, bb
))
1275 dom
= nearest_common_dominator (CDI_DOMINATORS
, dom
, e
->src
);
1279 gcc_assert (dom
!= NULL
);
1281 || find_edge (dom
, bb
))
1283 set_immediate_dominator (CDI_DOMINATORS
, bb
, dom
);
1292 bbs
.unordered_remove (i
);
1296 /* Returns root of the dominance tree in the direction DIR that contains
1300 root_of_dom_tree (enum cdi_direction dir
, basic_block bb
)
1302 return (basic_block
) et_root (bb
->dom
[dom_convert_dir_to_idx (dir
)])->data
;
1305 /* See the comment in iterate_fix_dominators. Finds the immediate dominators
1306 for the sons of Y, found using the SON and BROTHER arrays representing
1307 the dominance tree of graph G. BBS maps the vertices of G to the basic
1311 determine_dominators_for_sons (struct graph
*g
, vec
<basic_block
> bbs
,
1312 int y
, int *son
, int *brother
)
1317 basic_block bb
, dom
, ybb
;
1324 if (y
== (int) bbs
.length ())
1325 ybb
= ENTRY_BLOCK_PTR_FOR_FN (cfun
);
1329 if (brother
[son
[y
]] == -1)
1331 /* Handle the common case Y has just one son specially. */
1333 set_immediate_dominator (CDI_DOMINATORS
, bb
,
1334 recompute_dominator (CDI_DOMINATORS
, bb
));
1335 identify_vertices (g
, y
, son
[y
]);
1339 gprime
= BITMAP_ALLOC (NULL
);
1340 for (a
= son
[y
]; a
!= -1; a
= brother
[a
])
1341 bitmap_set_bit (gprime
, a
);
1343 nc
= graphds_scc (g
, gprime
);
1344 BITMAP_FREE (gprime
);
1346 /* ??? Needed to work around the pre-processor confusion with
1347 using a multi-argument template type as macro argument. */
1348 typedef vec
<int> vec_int_heap
;
1349 sccs
= XCNEWVEC (vec_int_heap
, nc
);
1350 for (a
= son
[y
]; a
!= -1; a
= brother
[a
])
1351 sccs
[g
->vertices
[a
].component
].safe_push (a
);
1353 for (i
= nc
- 1; i
>= 0; i
--)
1356 FOR_EACH_VEC_ELT (sccs
[i
], si
, a
)
1359 FOR_EACH_EDGE (e
, ei
, bb
->preds
)
1361 if (root_of_dom_tree (CDI_DOMINATORS
, e
->src
) != ybb
)
1364 dom
= nearest_common_dominator (CDI_DOMINATORS
, dom
, e
->src
);
1368 gcc_assert (dom
!= NULL
);
1369 FOR_EACH_VEC_ELT (sccs
[i
], si
, a
)
1372 set_immediate_dominator (CDI_DOMINATORS
, bb
, dom
);
1376 for (i
= 0; i
< nc
; i
++)
1380 for (a
= son
[y
]; a
!= -1; a
= brother
[a
])
1381 identify_vertices (g
, y
, a
);
1384 /* Recompute dominance information for basic blocks in the set BBS. The
1385 function assumes that the immediate dominators of all the other blocks
1386 in CFG are correct, and that there are no unreachable blocks.
1388 If CONSERVATIVE is true, we additionally assume that all the ancestors of
1389 a block of BBS in the current dominance tree dominate it. */
1392 iterate_fix_dominators (enum cdi_direction dir
, vec
<basic_block
> &bbs
,
1396 basic_block bb
, dom
;
1402 int *parent
, *son
, *brother
;
1403 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1405 /* We only support updating dominators. There are some problems with
1406 updating postdominators (need to add fake edges from infinite loops
1407 and noreturn functions), and since we do not currently use
1408 iterate_fix_dominators for postdominators, any attempt to handle these
1409 problems would be unused, untested, and almost surely buggy. We keep
1410 the DIR argument for consistency with the rest of the dominator analysis
1412 gcc_checking_assert (dir
== CDI_DOMINATORS
&& dom_computed
[dir_index
]);
1414 /* The algorithm we use takes inspiration from the following papers, although
1415 the details are quite different from any of them:
1417 [1] G. Ramalingam, T. Reps, An Incremental Algorithm for Maintaining the
1418 Dominator Tree of a Reducible Flowgraph
1419 [2] V. C. Sreedhar, G. R. Gao, Y.-F. Lee: Incremental computation of
1421 [3] K. D. Cooper, T. J. Harvey and K. Kennedy: A Simple, Fast Dominance
1424 First, we use the following heuristics to decrease the size of the BBS
1426 a) if BB has a single predecessor, then its immediate dominator is this
1428 additionally, if CONSERVATIVE is true:
1429 b) if all the predecessors of BB except for one (X) are dominated by BB,
1430 then X is the immediate dominator of BB
1431 c) if the nearest common ancestor of the predecessors of BB is X and
1432 X -> BB is an edge in CFG, then X is the immediate dominator of BB
1434 Then, we need to establish the dominance relation among the basic blocks
1435 in BBS. We split the dominance tree by removing the immediate dominator
1436 edges from BBS, creating a forest F. We form a graph G whose vertices
1437 are BBS and ENTRY and X -> Y is an edge of G if there exists an edge
1438 X' -> Y in CFG such that X' belongs to the tree of the dominance forest
1439 whose root is X. We then determine dominance tree of G. Note that
1440 for X, Y in BBS, X dominates Y in CFG if and only if X dominates Y in G.
1441 In this step, we can use arbitrary algorithm to determine dominators.
1442 We decided to prefer the algorithm [3] to the algorithm of
1443 Lengauer and Tarjan, since the set BBS is usually small (rarely exceeding
1444 10 during gcc bootstrap), and [3] should perform better in this case.
1446 Finally, we need to determine the immediate dominators for the basic
1447 blocks of BBS. If the immediate dominator of X in G is Y, then
1448 the immediate dominator of X in CFG belongs to the tree of F rooted in
1449 Y. We process the dominator tree T of G recursively, starting from leaves.
1450 Suppose that X_1, X_2, ..., X_k are the sons of Y in T, and that the
1451 subtrees of the dominance tree of CFG rooted in X_i are already correct.
1452 Let G' be the subgraph of G induced by {X_1, X_2, ..., X_k}. We make
1453 the following observations:
1454 (i) the immediate dominator of all blocks in a strongly connected
1455 component of G' is the same
1456 (ii) if X has no predecessors in G', then the immediate dominator of X
1457 is the nearest common ancestor of the predecessors of X in the
1458 subtree of F rooted in Y
1459 Therefore, it suffices to find the topological ordering of G', and
1460 process the nodes X_i in this order using the rules (i) and (ii).
1461 Then, we contract all the nodes X_i with Y in G, so that the further
1462 steps work correctly. */
1466 /* Split the tree now. If the idoms of blocks in BBS are not
1467 conservatively correct, setting the dominators using the
1468 heuristics in prune_bbs_to_update_dominators could
1469 create cycles in the dominance "tree", and cause ICE. */
1470 FOR_EACH_VEC_ELT (bbs
, i
, bb
)
1471 set_immediate_dominator (CDI_DOMINATORS
, bb
, NULL
);
1474 prune_bbs_to_update_dominators (bbs
, conservative
);
1483 set_immediate_dominator (CDI_DOMINATORS
, bb
,
1484 recompute_dominator (CDI_DOMINATORS
, bb
));
1488 timevar_push (TV_DOMINANCE
);
1490 /* Construct the graph G. */
1491 hash_map
<basic_block
, int> map (251);
1492 FOR_EACH_VEC_ELT (bbs
, i
, bb
)
1494 /* If the dominance tree is conservatively correct, split it now. */
1496 set_immediate_dominator (CDI_DOMINATORS
, bb
, NULL
);
1499 map
.put (ENTRY_BLOCK_PTR_FOR_FN (cfun
), n
);
1501 g
= new_graph (n
+ 1);
1502 for (y
= 0; y
< g
->n_vertices
; y
++)
1503 g
->vertices
[y
].data
= BITMAP_ALLOC (NULL
);
1504 FOR_EACH_VEC_ELT (bbs
, i
, bb
)
1506 FOR_EACH_EDGE (e
, ei
, bb
->preds
)
1508 dom
= root_of_dom_tree (CDI_DOMINATORS
, e
->src
);
1512 dom_i
= *map
.get (dom
);
1514 /* Do not include parallel edges to G. */
1515 if (!bitmap_set_bit ((bitmap
) g
->vertices
[dom_i
].data
, i
))
1518 add_edge (g
, dom_i
, i
);
1521 for (y
= 0; y
< g
->n_vertices
; y
++)
1522 BITMAP_FREE (g
->vertices
[y
].data
);
1524 /* Find the dominator tree of G. */
1525 son
= XNEWVEC (int, n
+ 1);
1526 brother
= XNEWVEC (int, n
+ 1);
1527 parent
= XNEWVEC (int, n
+ 1);
1528 graphds_domtree (g
, n
, parent
, son
, brother
);
1530 /* Finally, traverse the tree and find the immediate dominators. */
1531 for (y
= n
; son
[y
] != -1; y
= son
[y
])
1535 determine_dominators_for_sons (g
, bbs
, y
, son
, brother
);
1537 if (brother
[y
] != -1)
1540 while (son
[y
] != -1)
1553 timevar_pop (TV_DOMINANCE
);
1557 add_to_dominance_info (enum cdi_direction dir
, basic_block bb
)
1559 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1561 gcc_checking_assert (dom_computed
[dir_index
] && !bb
->dom
[dir_index
]);
1563 n_bbs_in_dom_tree
[dir_index
]++;
1565 bb
->dom
[dir_index
] = et_new_tree (bb
);
1567 if (dom_computed
[dir_index
] == DOM_OK
)
1568 dom_computed
[dir_index
] = DOM_NO_FAST_QUERY
;
1572 delete_from_dominance_info (enum cdi_direction dir
, basic_block bb
)
1574 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1576 gcc_checking_assert (dom_computed
[dir_index
]);
1578 et_free_tree (bb
->dom
[dir_index
]);
1579 bb
->dom
[dir_index
] = NULL
;
1580 n_bbs_in_dom_tree
[dir_index
]--;
1582 if (dom_computed
[dir_index
] == DOM_OK
)
1583 dom_computed
[dir_index
] = DOM_NO_FAST_QUERY
;
1586 /* Returns the first son of BB in the dominator or postdominator tree
1587 as determined by DIR. */
1590 first_dom_son (enum cdi_direction dir
, basic_block bb
)
1592 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1593 struct et_node
*son
= bb
->dom
[dir_index
]->son
;
1595 return (basic_block
) (son
? son
->data
: NULL
);
1598 /* Returns the next dominance son after BB in the dominator or postdominator
1599 tree as determined by DIR, or NULL if it was the last one. */
1602 next_dom_son (enum cdi_direction dir
, basic_block bb
)
1604 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1605 struct et_node
*next
= bb
->dom
[dir_index
]->right
;
1607 return (basic_block
) (next
->father
->son
== next
? NULL
: next
->data
);
1610 /* Return dominance availability for dominance info DIR. */
1613 dom_info_state (function
*fn
, enum cdi_direction dir
)
1618 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1619 return fn
->cfg
->x_dom_computed
[dir_index
];
1623 dom_info_state (enum cdi_direction dir
)
1625 return dom_info_state (cfun
, dir
);
1628 /* Set the dominance availability for dominance info DIR to NEW_STATE. */
1631 set_dom_info_availability (enum cdi_direction dir
, enum dom_state new_state
)
1633 unsigned int dir_index
= dom_convert_dir_to_idx (dir
);
1635 dom_computed
[dir_index
] = new_state
;
1638 /* Returns true if dominance information for direction DIR is available. */
1641 dom_info_available_p (function
*fn
, enum cdi_direction dir
)
1643 return dom_info_state (fn
, dir
) != DOM_NONE
;
1647 dom_info_available_p (enum cdi_direction dir
)
1649 return dom_info_available_p (cfun
, dir
);
1653 debug_dominance_info (enum cdi_direction dir
)
1655 basic_block bb
, bb2
;
1656 FOR_EACH_BB_FN (bb
, cfun
)
1657 if ((bb2
= get_immediate_dominator (dir
, bb
)))
1658 fprintf (stderr
, "%i %i\n", bb
->index
, bb2
->index
);
1661 /* Prints to stderr representation of the dominance tree (for direction DIR)
1662 rooted in ROOT, indented by INDENT tabulators. If INDENT_FIRST is false,
1663 the first line of the output is not indented. */
1666 debug_dominance_tree_1 (enum cdi_direction dir
, basic_block root
,
1667 unsigned indent
, bool indent_first
)
1674 for (i
= 0; i
< indent
; i
++)
1675 fprintf (stderr
, "\t");
1676 fprintf (stderr
, "%d\t", root
->index
);
1678 for (son
= first_dom_son (dir
, root
);
1680 son
= next_dom_son (dir
, son
))
1682 debug_dominance_tree_1 (dir
, son
, indent
+ 1, !first
);
1687 fprintf (stderr
, "\n");
1690 /* Prints to stderr representation of the dominance tree (for direction DIR)
1694 debug_dominance_tree (enum cdi_direction dir
, basic_block root
)
1696 debug_dominance_tree_1 (dir
, root
, 0, false);