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/* Calculate (post)dominators in slightly super-linear time. Copyright (C) 2000, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. Contributed by Michael Matz (matz@ifh.de). This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GCC; see the file COPYING3. If not see <http://www.gnu.org/licenses/>. */ /* This file implements the well known algorithm from Lengauer and Tarjan to compute the dominators in a control flow graph. A basic block D is said to dominate another block X, when all paths from the entry node of the CFG to X go also over D. The dominance relation is a transitive reflexive relation and its minimal transitive reduction is a tree, called the dominator tree. So for each block X besides the entry block exists a block I(X), called the immediate dominator of X, which is the parent of X in the dominator tree. The algorithm computes this dominator tree implicitly by computing for each block its immediate dominator. We use tree balancing and path compression, so it's the O(e*a(e,v)) variant, where a(e,v) is the very slowly growing functional inverse of the Ackerman function. */ #include "config.h" #include "system.h" #include "coretypes.h" #include "tm.h" #include "rtl.h" #include "hard-reg-set.h" #include "obstack.h" #include "basic-block.h" #include "toplev.h" #include "et-forest.h" #include "timevar.h" #include "vecprim.h" #include "pointer-set.h" #include "graphds.h" /* We name our nodes with integers, beginning with 1. Zero is reserved for 'undefined' or 'end of list'. The name of each node is given by the dfs number of the corresponding basic block. Please note, that we include the artificial ENTRY_BLOCK (or EXIT_BLOCK in the post-dom case) in our lists to support multiple entry points. Its dfs number is of course 1. */ /* Type of Basic Block aka. TBB */ typedef unsigned int TBB; /* We work in a poor-mans object oriented fashion, and carry an instance of this structure through all our 'methods'. It holds various arrays reflecting the (sub)structure of the flowgraph. Most of them are of type TBB and are also indexed by TBB. */ struct dom_info { /* The parent of a node in the DFS tree. */ TBB *dfs_parent; /* For a node x key[x] is roughly the node nearest to the root from which exists a way to x only over nodes behind x. Such a node is also called semidominator. */ TBB *key; /* The value in path_min[x] is the node y on the path from x to the root of the tree x is in with the smallest key[y]. */ TBB *path_min; /* bucket[x] points to the first node of the set of nodes having x as key. */ TBB *bucket; /* And next_bucket[x] points to the next node. */ TBB *next_bucket; /* After the algorithm is done, dom[x] contains the immediate dominator of x. */ TBB *dom; /* The following few fields implement the structures needed for disjoint sets. */ /* set_chain[x] is the next node on the path from x to the representative of the set containing x. If set_chain[x]==0 then x is a root. */ TBB *set_chain; /* set_size[x] is the number of elements in the set named by x. */ unsigned int *set_size; /* set_child[x] is used for balancing the tree representing a set. It can be understood as the next sibling of x. */ TBB *set_child; /* If b is the number of a basic block (BB->index), dfs_order[b] is the number of that node in DFS order counted from 1. This is an index into most of the other arrays in this structure. */ TBB *dfs_order; /* If x is the DFS-index of a node which corresponds with a basic block, dfs_to_bb[x] is that basic block. Note, that in our structure there are more nodes that basic blocks, so only dfs_to_bb[dfs_order[bb->index]]==bb is true for every basic block bb, but not the opposite. */ basic_block *dfs_to_bb; /* This is the next free DFS number when creating the DFS tree. */ unsigned int dfsnum; /* The number of nodes in the DFS tree (==dfsnum-1). */ unsigned int nodes; /* Blocks with bits set here have a fake edge to EXIT. These are used to turn a DFS forest into a proper tree. */ bitmap fake_exit_edge; }; static void init_dom_info (struct dom_info *, enum cdi_direction); static void free_dom_info (struct dom_info *); static void calc_dfs_tree_nonrec (struct dom_info *, basic_block, bool); static void calc_dfs_tree (struct dom_info *, bool); static void compress (struct dom_info *, TBB); static TBB eval (struct dom_info *, TBB); static void link_roots (struct dom_info *, TBB, TBB); static void calc_idoms (struct dom_info *, bool); void debug_dominance_info (enum cdi_direction); void debug_dominance_tree (enum cdi_direction, basic_block); /* Helper macro for allocating and initializing an array, for aesthetic reasons. */ #define init_ar(var, type, num, content) \ do \ { \ unsigned int i = 1; /* Catch content == i. */ \ if (! (content)) \ (var) = XCNEWVEC (type, num); \ else \ { \ (var) = XNEWVEC (type, (num)); \ for (i = 0; i < num; i++) \ (var)[i] = (content); \ } \ } \ while (0) /* Allocate all needed memory in a pessimistic fashion (so we round up). This initializes the contents of DI, which already must be allocated. */ static void init_dom_info (struct dom_info *di, enum cdi_direction dir) { /* We need memory for n_basic_blocks nodes. */ unsigned int num = n_basic_blocks; init_ar (di->dfs_parent, TBB, num, 0); init_ar (di->path_min, TBB, num, i); init_ar (di->key, TBB, num, i); init_ar (di->dom, TBB, num, 0); init_ar (di->bucket, TBB, num, 0); init_ar (di->next_bucket, TBB, num, 0); init_ar (di->set_chain, TBB, num, 0); init_ar (di->set_size, unsigned int, num, 1); init_ar (di->set_child, TBB, num, 0); init_ar (di->dfs_order, TBB, (unsigned int) last_basic_block + 1, 0); init_ar (di->dfs_to_bb, basic_block, num, 0); di->dfsnum = 1; di->nodes = 0; switch (dir) { case CDI_DOMINATORS: di->fake_exit_edge = NULL; break; case CDI_POST_DOMINATORS: di->fake_exit_edge = BITMAP_ALLOC (NULL); break; default: gcc_unreachable (); break; } } #undef init_ar /* Map dominance calculation type to array index used for various dominance information arrays. This version is simple -- it will need to be modified, obviously, if additional values are added to cdi_direction. */ static unsigned int dom_convert_dir_to_idx (enum cdi_direction dir) { gcc_assert (dir == CDI_DOMINATORS || dir == CDI_POST_DOMINATORS); return dir - 1; } /* Free all allocated memory in DI, but not DI itself. */ static void free_dom_info (struct dom_info *di) { free (di->dfs_parent); free (di->path_min); free (di->key); free (di->dom); free (di->bucket); free (di->next_bucket); free (di->set_chain); free (di->set_size); free (di->set_child); free (di->dfs_order); free (di->dfs_to_bb); BITMAP_FREE (di->fake_exit_edge); } /* The nonrecursive variant of creating a DFS tree. DI is our working structure, BB the starting basic block for this tree and REVERSE is true, if predecessors should be visited instead of successors of a node. After this is done all nodes reachable from BB were visited, have assigned their dfs number and are linked together to form a tree. */ static void calc_dfs_tree_nonrec (struct dom_info *di, basic_block bb, bool reverse) { /* We call this _only_ if bb is not already visited. */ edge e; TBB child_i, my_i = 0; edge_iterator *stack; edge_iterator ei, einext; int sp; /* Start block (ENTRY_BLOCK_PTR for forward problem, EXIT_BLOCK for backward problem). */ basic_block en_block; /* Ending block. */ basic_block ex_block; stack = XNEWVEC (edge_iterator, n_basic_blocks + 1); sp = 0; /* Initialize our border blocks, and the first edge. */ if (reverse) { ei = ei_start (bb->preds); en_block = EXIT_BLOCK_PTR; ex_block = ENTRY_BLOCK_PTR; } else { ei = ei_start (bb->succs); en_block = ENTRY_BLOCK_PTR; ex_block = EXIT_BLOCK_PTR; } /* When the stack is empty we break out of this loop. */ while (1) { basic_block bn; /* This loop traverses edges e in depth first manner, and fills the stack. */ while (!ei_end_p (ei)) { e = ei_edge (ei); /* Deduce from E the current and the next block (BB and BN), and the next edge. */ if (reverse) { bn = e->src; /* If the next node BN is either already visited or a border block the current edge is useless, and simply overwritten with the next edge out of the current node. */ if (bn == ex_block || di->dfs_order[bn->index]) { ei_next (&ei); continue; } bb = e->dest; einext = ei_start (bn->preds); } else { bn = e->dest; if (bn == ex_block || di->dfs_order[bn->index]) { ei_next (&ei); continue; } bb = e->src; einext = ei_start (bn->succs); } gcc_assert (bn != en_block); /* Fill the DFS tree info calculatable _before_ recursing. */ if (bb != en_block) my_i = di->dfs_order[bb->index]; else my_i = di->dfs_order[last_basic_block]; child_i = di->dfs_order[bn->index] = di->dfsnum++; di->dfs_to_bb[child_i] = bn; di->dfs_parent[child_i] = my_i; /* Save the current point in the CFG on the stack, and recurse. */ stack[sp++] = ei; ei = einext; } if (!sp) break; ei = stack[--sp]; /* OK. The edge-list was exhausted, meaning normally we would end the recursion. After returning from the recursive call, there were (may be) other statements which were run after a child node was completely considered by DFS. Here is the point to do it in the non-recursive variant. E.g. The block just completed is in e->dest for forward DFS, the block not yet completed (the parent of the one above) in e->src. This could be used e.g. for computing the number of descendants or the tree depth. */ ei_next (&ei); } free (stack); } /* The main entry for calculating the DFS tree or forest. DI is our working structure and REVERSE is true, if we are interested in the reverse flow graph. In that case the result is not necessarily a tree but a forest, because there may be nodes from which the EXIT_BLOCK is unreachable. */ static void calc_dfs_tree (struct dom_info *di, bool reverse) { /* The first block is the ENTRY_BLOCK (or EXIT_BLOCK if REVERSE). */ basic_block begin = reverse ? EXIT_BLOCK_PTR : ENTRY_BLOCK_PTR; di->dfs_order[last_basic_block] = di->dfsnum; di->dfs_to_bb[di->dfsnum] = begin; di->dfsnum++; calc_dfs_tree_nonrec (di, begin, reverse); if (reverse) { /* In the post-dom case we may have nodes without a path to EXIT_BLOCK. They are reverse-unreachable. In the dom-case we disallow such nodes, but in post-dom we have to deal with them. There are two situations in which this occurs. First, noreturn functions. Second, infinite loops. In the first case we need to pretend that there is an edge to the exit block. In the second case, we wind up with a forest. We need to process all noreturn blocks before we know if we've got any infinite loops. */ basic_block b; bool saw_unconnected = false; FOR_EACH_BB_REVERSE (b) { if (EDGE_COUNT (b->succs) > 0) { if (di->dfs_order[b->index] == 0) saw_unconnected = true; continue; } bitmap_set_bit (di->fake_exit_edge, b->index); di->dfs_order[b->index] = di->dfsnum; di->dfs_to_bb[di->dfsnum] = b; di->dfs_parent[di->dfsnum] = di->dfs_order[last_basic_block]; di->dfsnum++; calc_dfs_tree_nonrec (di, b, reverse); } if (saw_unconnected) { FOR_EACH_BB_REVERSE (b) { if (di->dfs_order[b->index]) continue; bitmap_set_bit (di->fake_exit_edge, b->index); di->dfs_order[b->index] = di->dfsnum; di->dfs_to_bb[di->dfsnum] = b; di->dfs_parent[di->dfsnum] = di->dfs_order[last_basic_block]; di->dfsnum++; calc_dfs_tree_nonrec (di, b, reverse); } } } di->nodes = di->dfsnum - 1; /* This aborts e.g. when there is _no_ path from ENTRY to EXIT at all. */ gcc_assert (di->nodes == (unsigned int) n_basic_blocks - 1); } /* Compress the path from V to the root of its set and update path_min at the same time. After compress(di, V) set_chain[V] is the root of the set V is in and path_min[V] is the node with the smallest key[] value on the path from V to that root. */ static void compress (struct dom_info *di, TBB v) { /* Btw. It's not worth to unrecurse compress() as the depth is usually not greater than 5 even for huge graphs (I've not seen call depth > 4). Also performance wise compress() ranges _far_ behind eval(). */ TBB parent = di->set_chain[v]; if (di->set_chain[parent]) { compress (di, parent); if (di->key[di->path_min[parent]] < di->key[di->path_min[v]]) di->path_min[v] = di->path_min[parent]; di->set_chain[v] = di->set_chain[parent]; } } /* Compress the path from V to the set root of V if needed (when the root has changed since the last call). Returns the node with the smallest key[] value on the path from V to the root. */ static inline TBB eval (struct dom_info *di, TBB v) { /* The representative of the set V is in, also called root (as the set representation is a tree). */ TBB rep = di->set_chain[v]; /* V itself is the root. */ if (!rep) return di->path_min[v]; /* Compress only if necessary. */ if (di->set_chain[rep]) { compress (di, v); rep = di->set_chain[v]; } if (di->key[di->path_min[rep]] >= di->key[di->path_min[v]]) return di->path_min[v]; else return di->path_min[rep]; } /* This essentially merges the two sets of V and W, giving a single set with the new root V. The internal representation of these disjoint sets is a balanced tree. Currently link(V,W) is only used with V being the parent of W. */ static void link_roots (struct dom_info *di, TBB v, TBB w) { TBB s = w; /* Rebalance the tree. */ while (di->key[di->path_min[w]] < di->key[di->path_min[di->set_child[s]]]) { if (di->set_size[s] + di->set_size[di->set_child[di->set_child[s]]] >= 2 * di->set_size[di->set_child[s]]) { di->set_chain[di->set_child[s]] = s; di->set_child[s] = di->set_child[di->set_child[s]]; } else { di->set_size[di->set_child[s]] = di->set_size[s]; s = di->set_chain[s] = di->set_child[s]; } } di->path_min[s] = di->path_min[w]; di->set_size[v] += di->set_size[w]; if (di->set_size[v] < 2 * di->set_size[w]) { TBB tmp = s; s = di->set_child[v]; di->set_child[v] = tmp; } /* Merge all subtrees. */ while (s) { di->set_chain[s] = v; s = di->set_child[s]; } } /* This calculates the immediate dominators (or post-dominators if REVERSE is true). DI is our working structure and should hold the DFS forest. On return the immediate dominator to node V is in di->dom[V]. */ static void calc_idoms (struct dom_info *di, bool reverse) { TBB v, w, k, par; basic_block en_block; edge_iterator ei, einext; if (reverse) en_block = EXIT_BLOCK_PTR; else en_block = ENTRY_BLOCK_PTR; /* Go backwards in DFS order, to first look at the leafs. */ v = di->nodes; while (v > 1) { basic_block bb = di->dfs_to_bb[v]; edge e; par = di->dfs_parent[v]; k = v; ei = (reverse) ? ei_start (bb->succs) : ei_start (bb->preds); if (reverse) { /* If this block has a fake edge to exit, process that first. */ if (bitmap_bit_p (di->fake_exit_edge, bb->index)) { einext = ei; einext.index = 0; goto do_fake_exit_edge; } } /* Search all direct predecessors for the smallest node with a path to them. That way we have the smallest node with also a path to us only over nodes behind us. In effect we search for our semidominator. */ while (!ei_end_p (ei)) { TBB k1; basic_block b; e = ei_edge (ei); b = (reverse) ? e->dest : e->src; einext = ei; ei_next (&einext); if (b == en_block) { do_fake_exit_edge: k1 = di->dfs_order[last_basic_block]; } else k1 = di->dfs_order[b->index]; /* Call eval() only if really needed. If k1 is above V in DFS tree, then we know, that eval(k1) == k1 and key[k1] == k1. */ if (k1 > v) k1 = di->key[eval (di, k1)]; if (k1 < k) k = k1; ei = einext; } di->key[v] = k; link_roots (di, par, v); di->next_bucket[v] = di->bucket[k]; di->bucket[k] = v; /* Transform semidominators into dominators. */ for (w = di->bucket[par]; w; w = di->next_bucket[w]) { k = eval (di, w); if (di->key[k] < di->key[w]) di->dom[w] = k; else di->dom[w] = par; } /* We don't need to cleanup next_bucket[]. */ di->bucket[par] = 0; v--; } /* Explicitly define the dominators. */ di->dom[1] = 0; for (v = 2; v <= di->nodes; v++) if (di->dom[v] != di->key[v]) di->dom[v] = di->dom[di->dom[v]]; } /* Assign dfs numbers starting from NUM to NODE and its sons. */ static void assign_dfs_numbers (struct et_node *node, int *num) { struct et_node *son; node->dfs_num_in = (*num)++; if (node->son) { assign_dfs_numbers (node->son, num); for (son = node->son->right; son != node->son; son = son->right) assign_dfs_numbers (son, num); } node->dfs_num_out = (*num)++; } /* Compute the data necessary for fast resolving of dominator queries in a static dominator tree. */ static void compute_dom_fast_query (enum cdi_direction dir) { int num = 0; basic_block bb; unsigned int dir_index = dom_convert_dir_to_idx (dir); gcc_assert (dom_info_available_p (dir)); if (dom_computed[dir_index] == DOM_OK) return; FOR_ALL_BB (bb) { if (!bb->dom[dir_index]->father) assign_dfs_numbers (bb->dom[dir_index], &num); } dom_computed[dir_index] = DOM_OK; } /* The main entry point into this module. DIR is set depending on whether we want to compute dominators or postdominators. */ void calculate_dominance_info (enum cdi_direction dir) { struct dom_info di; basic_block b; unsigned int dir_index = dom_convert_dir_to_idx (dir); bool reverse = (dir == CDI_POST_DOMINATORS) ? true : false; if (dom_computed[dir_index] == DOM_OK) return; timevar_push (TV_DOMINANCE); if (!dom_info_available_p (dir)) { gcc_assert (!n_bbs_in_dom_tree[dir_index]); FOR_ALL_BB (b) { b->dom[dir_index] = et_new_tree (b); } n_bbs_in_dom_tree[dir_index] = n_basic_blocks; init_dom_info (&di, dir); calc_dfs_tree (&di, reverse); calc_idoms (&di, reverse); FOR_EACH_BB (b) { TBB d = di.dom[di.dfs_order[b->index]]; if (di.dfs_to_bb[d]) et_set_father (b->dom[dir_index], di.dfs_to_bb[d]->dom[dir_index]); } free_dom_info (&di); dom_computed[dir_index] = DOM_NO_FAST_QUERY; } compute_dom_fast_query (dir); timevar_pop (TV_DOMINANCE); } /* Free dominance information for direction DIR. */ void free_dominance_info (enum cdi_direction dir) { basic_block bb; unsigned int dir_index = dom_convert_dir_to_idx (dir); if (!dom_info_available_p (dir)) return; FOR_ALL_BB (bb) { et_free_tree_force (bb->dom[dir_index]); bb->dom[dir_index] = NULL; } et_free_pools (); n_bbs_in_dom_tree[dir_index] = 0; dom_computed[dir_index] = DOM_NONE; } /* Return the immediate dominator of basic block BB. */ basic_block get_immediate_dominator (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *node = bb->dom[dir_index]; gcc_assert (dom_computed[dir_index]); if (!node->father) return NULL; return (basic_block) node->father->data; } /* Set the immediate dominator of the block possibly removing existing edge. NULL can be used to remove any edge. */ void set_immediate_dominator (enum cdi_direction dir, basic_block bb, basic_block dominated_by) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *node = bb->dom[dir_index]; gcc_assert (dom_computed[dir_index]); if (node->father) { if (node->father->data == dominated_by) return; et_split (node); } if (dominated_by) et_set_father (node, dominated_by->dom[dir_index]); if (dom_computed[dir_index] == DOM_OK) dom_computed[dir_index] = DOM_NO_FAST_QUERY; } /* Returns the list of basic blocks immediately dominated by BB, in the direction DIR. */ VEC (basic_block, heap) * get_dominated_by (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *node = bb->dom[dir_index], *son = node->son, *ason; VEC (basic_block, heap) *bbs = NULL; gcc_assert (dom_computed[dir_index]); if (!son) return NULL; VEC_safe_push (basic_block, heap, bbs, (basic_block) son->data); for (ason = son->right; ason != son; ason = ason->right) VEC_safe_push (basic_block, heap, bbs, (basic_block) ason->data); return bbs; } /* Returns the list of basic blocks that are immediately dominated (in direction DIR) by some block between N_REGION ones stored in REGION, except for blocks in the REGION itself. */ VEC (basic_block, heap) * get_dominated_by_region (enum cdi_direction dir, basic_block *region, unsigned n_region) { unsigned i; basic_block dom; VEC (basic_block, heap) *doms = NULL; for (i = 0; i < n_region; i++) region[i]->flags |= BB_DUPLICATED; for (i = 0; i < n_region; i++) for (dom = first_dom_son (dir, region[i]); dom; dom = next_dom_son (dir, dom)) if (!(dom->flags & BB_DUPLICATED)) VEC_safe_push (basic_block, heap, doms, dom); for (i = 0; i < n_region; i++) region[i]->flags &= ~BB_DUPLICATED; return doms; } /* Returns the list of basic blocks including BB dominated by BB, in the direction DIR. The vector will be sorted in preorder. */ VEC (basic_block, heap) * get_all_dominated_blocks (enum cdi_direction dir, basic_block bb) { VEC(basic_block, heap) *bbs = NULL; unsigned i; i = 0; VEC_safe_push (basic_block, heap, bbs, bb); do { basic_block son; bb = VEC_index (basic_block, bbs, i++); for (son = first_dom_son (dir, bb); son; son = next_dom_son (dir, son)) VEC_safe_push (basic_block, heap, bbs, son); } while (i < VEC_length (basic_block, bbs)); return bbs; } /* Redirect all edges pointing to BB to TO. */ void redirect_immediate_dominators (enum cdi_direction dir, basic_block bb, basic_block to) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *bb_node, *to_node, *son; bb_node = bb->dom[dir_index]; to_node = to->dom[dir_index]; gcc_assert (dom_computed[dir_index]); if (!bb_node->son) return; while (bb_node->son) { son = bb_node->son; et_split (son); et_set_father (son, to_node); } if (dom_computed[dir_index] == DOM_OK) dom_computed[dir_index] = DOM_NO_FAST_QUERY; } /* Find first basic block in the tree dominating both BB1 and BB2. */ basic_block nearest_common_dominator (enum cdi_direction dir, basic_block bb1, basic_block bb2) { unsigned int dir_index = dom_convert_dir_to_idx (dir); gcc_assert (dom_computed[dir_index]); if (!bb1) return bb2; if (!bb2) return bb1; return (basic_block) et_nca (bb1->dom[dir_index], bb2->dom[dir_index])->data; } /* Find the nearest common dominator for the basic blocks in BLOCKS, using dominance direction DIR. */ basic_block nearest_common_dominator_for_set (enum cdi_direction dir, bitmap blocks) { unsigned i, first; bitmap_iterator bi; basic_block dom; first = bitmap_first_set_bit (blocks); dom = BASIC_BLOCK (first); EXECUTE_IF_SET_IN_BITMAP (blocks, 0, i, bi) if (dom != BASIC_BLOCK (i)) dom = nearest_common_dominator (dir, dom, BASIC_BLOCK (i)); return dom; } /* Given a dominator tree, we can determine whether one thing dominates another in constant time by using two DFS numbers: 1. The number for when we visit a node on the way down the tree 2. The number for when we visit a node on the way back up the tree You can view these as bounds for the range of dfs numbers the nodes in the subtree of the dominator tree rooted at that node will contain. The dominator tree is always a simple acyclic tree, so there are only three possible relations two nodes in the dominator tree have to each other: 1. Node A is above Node B (and thus, Node A dominates node B) A | C / \ B D In the above case, DFS_Number_In of A will be <= DFS_Number_In of B, and DFS_Number_Out of A will be >= DFS_Number_Out of B. This is because we must hit A in the dominator tree *before* B on the walk down, and we will hit A *after* B on the walk back up 2. Node A is below node B (and thus, node B dominates node A) B | A / \ C D In the above case, DFS_Number_In of A will be >= DFS_Number_In of B, and DFS_Number_Out of A will be <= DFS_Number_Out of B. This is because we must hit A in the dominator tree *after* B on the walk down, and we will hit A *before* B on the walk back up 3. Node A and B are siblings (and thus, neither dominates the other) C | D / \ A B In the above case, DFS_Number_In of A will *always* be <= DFS_Number_In of B, and DFS_Number_Out of A will *always* be <= DFS_Number_Out of B. This is because we will always finish the dfs walk of one of the subtrees before the other, and thus, the dfs numbers for one subtree can't intersect with the range of dfs numbers for the other subtree. If you swap A and B's position in the dominator tree, the comparison changes direction, but the point is that both comparisons will always go the same way if there is no dominance relationship. Thus, it is sufficient to write A_Dominates_B (node A, node B) { return DFS_Number_In(A) <= DFS_Number_In(B) && DFS_Number_Out (A) >= DFS_Number_Out(B); } A_Dominated_by_B (node A, node B) { return DFS_Number_In(A) >= DFS_Number_In(A) && DFS_Number_Out (A) <= DFS_Number_Out(B); } */ /* Return TRUE in case BB1 is dominated by BB2. */ bool dominated_by_p (enum cdi_direction dir, const_basic_block bb1, const_basic_block bb2) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *n1 = bb1->dom[dir_index], *n2 = bb2->dom[dir_index]; gcc_assert (dom_computed[dir_index]); if (dom_computed[dir_index] == DOM_OK) return (n1->dfs_num_in >= n2->dfs_num_in && n1->dfs_num_out <= n2->dfs_num_out); return et_below (n1, n2); } /* Returns the entry dfs number for basic block BB, in the direction DIR. */ unsigned bb_dom_dfs_in (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *n = bb->dom[dir_index]; gcc_assert (dom_computed[dir_index] == DOM_OK); return n->dfs_num_in; } /* Returns the exit dfs number for basic block BB, in the direction DIR. */ unsigned bb_dom_dfs_out (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *n = bb->dom[dir_index]; gcc_assert (dom_computed[dir_index] == DOM_OK); return n->dfs_num_out; } /* Verify invariants of dominator structure. */ void verify_dominators (enum cdi_direction dir) { int err = 0; basic_block bb, imm_bb, imm_bb_correct; struct dom_info di; bool reverse = (dir == CDI_POST_DOMINATORS) ? true : false; gcc_assert (dom_info_available_p (dir)); init_dom_info (&di, dir); calc_dfs_tree (&di, reverse); calc_idoms (&di, reverse); FOR_EACH_BB (bb) { imm_bb = get_immediate_dominator (dir, bb); if (!imm_bb) { error ("dominator of %d status unknown", bb->index); err = 1; } imm_bb_correct = di.dfs_to_bb[di.dom[di.dfs_order[bb->index]]]; if (imm_bb != imm_bb_correct) { error ("dominator of %d should be %d, not %d", bb->index, imm_bb_correct->index, imm_bb->index); err = 1; } } free_dom_info (&di); gcc_assert (!err); } /* Determine immediate dominator (or postdominator, according to DIR) of BB, assuming that dominators of other blocks are correct. We also use it to recompute the dominators in a restricted area, by iterating it until it reaches a fixed point. */ basic_block recompute_dominator (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); basic_block dom_bb = NULL; edge e; edge_iterator ei; gcc_assert (dom_computed[dir_index]); if (dir == CDI_DOMINATORS) { FOR_EACH_EDGE (e, ei, bb->preds) { if (!dominated_by_p (dir, e->src, bb)) dom_bb = nearest_common_dominator (dir, dom_bb, e->src); } } else { FOR_EACH_EDGE (e, ei, bb->succs) { if (!dominated_by_p (dir, e->dest, bb)) dom_bb = nearest_common_dominator (dir, dom_bb, e->dest); } } return dom_bb; } /* Use simple heuristics (see iterate_fix_dominators) to determine dominators of BBS. We assume that all the immediate dominators except for those of the blocks in BBS are correct. If CONSERVATIVE is true, we also assume that the currently recorded immediate dominators of blocks in BBS really dominate the blocks. The basic blocks for that we determine the dominator are removed from BBS. */ static void prune_bbs_to_update_dominators (VEC (basic_block, heap) *bbs, bool conservative) { unsigned i; bool single; basic_block bb, dom = NULL; edge_iterator ei; edge e; for (i = 0; VEC_iterate (basic_block, bbs, i, bb);) { if (bb == ENTRY_BLOCK_PTR) goto succeed; if (single_pred_p (bb)) { set_immediate_dominator (CDI_DOMINATORS, bb, single_pred (bb)); goto succeed; } if (!conservative) goto fail; single = true; dom = NULL; FOR_EACH_EDGE (e, ei, bb->preds) { if (dominated_by_p (CDI_DOMINATORS, e->src, bb)) continue; if (!dom) dom = e->src; else { single = false; dom = nearest_common_dominator (CDI_DOMINATORS, dom, e->src); } } gcc_assert (dom != NULL); if (single || find_edge (dom, bb)) { set_immediate_dominator (CDI_DOMINATORS, bb, dom); goto succeed; } fail: i++; continue; succeed: VEC_unordered_remove (basic_block, bbs, i); } } /* Returns root of the dominance tree in the direction DIR that contains BB. */ static basic_block root_of_dom_tree (enum cdi_direction dir, basic_block bb) { return (basic_block) et_root (bb->dom[dom_convert_dir_to_idx (dir)])->data; } /* See the comment in iterate_fix_dominators. Finds the immediate dominators for the sons of Y, found using the SON and BROTHER arrays representing the dominance tree of graph G. BBS maps the vertices of G to the basic blocks. */ static void determine_dominators_for_sons (struct graph *g, VEC (basic_block, heap) *bbs, int y, int *son, int *brother) { bitmap gprime; int i, a, nc; VEC (int, heap) **sccs; basic_block bb, dom, ybb; unsigned si; edge e; edge_iterator ei; if (son[y] == -1) return; if (y == (int) VEC_length (basic_block, bbs)) ybb = ENTRY_BLOCK_PTR; else ybb = VEC_index (basic_block, bbs, y); if (brother[son[y]] == -1) { /* Handle the common case Y has just one son specially. */ bb = VEC_index (basic_block, bbs, son[y]); set_immediate_dominator (CDI_DOMINATORS, bb, recompute_dominator (CDI_DOMINATORS, bb)); identify_vertices (g, y, son[y]); return; } gprime = BITMAP_ALLOC (NULL); for (a = son[y]; a != -1; a = brother[a]) bitmap_set_bit (gprime, a); nc = graphds_scc (g, gprime); BITMAP_FREE (gprime); sccs = XCNEWVEC (VEC (int, heap) *, nc); for (a = son[y]; a != -1; a = brother[a]) VEC_safe_push (int, heap, sccs[g->vertices[a].component], a); for (i = nc - 1; i >= 0; i--) { dom = NULL; for (si = 0; VEC_iterate (int, sccs[i], si, a); si++) { bb = VEC_index (basic_block, bbs, a); FOR_EACH_EDGE (e, ei, bb->preds) { if (root_of_dom_tree (CDI_DOMINATORS, e->src) != ybb) continue; dom = nearest_common_dominator (CDI_DOMINATORS, dom, e->src); } } gcc_assert (dom != NULL); for (si = 0; VEC_iterate (int, sccs[i], si, a); si++) { bb = VEC_index (basic_block, bbs, a); set_immediate_dominator (CDI_DOMINATORS, bb, dom); } } for (i = 0; i < nc; i++) VEC_free (int, heap, sccs[i]); free (sccs); for (a = son[y]; a != -1; a = brother[a]) identify_vertices (g, y, a); } /* Recompute dominance information for basic blocks in the set BBS. The function assumes that the immediate dominators of all the other blocks in CFG are correct, and that there are no unreachable blocks. If CONSERVATIVE is true, we additionally assume that all the ancestors of a block of BBS in the current dominance tree dominate it. */ void iterate_fix_dominators (enum cdi_direction dir, VEC (basic_block, heap) *bbs, bool conservative) { unsigned i; basic_block bb, dom; struct graph *g; int n, y; size_t dom_i; edge e; edge_iterator ei; struct pointer_map_t *map; int *parent, *son, *brother; unsigned int dir_index = dom_convert_dir_to_idx (dir); /* We only support updating dominators. There are some problems with updating postdominators (need to add fake edges from infinite loops and noreturn functions), and since we do not currently use iterate_fix_dominators for postdominators, any attempt to handle these problems would be unused, untested, and almost surely buggy. We keep the DIR argument for consistency with the rest of the dominator analysis interface. */ gcc_assert (dir == CDI_DOMINATORS); gcc_assert (dom_computed[dir_index]); /* The algorithm we use takes inspiration from the following papers, although the details are quite different from any of them: [1] G. Ramalingam, T. Reps, An Incremental Algorithm for Maintaining the Dominator Tree of a Reducible Flowgraph [2] V. C. Sreedhar, G. R. Gao, Y.-F. Lee: Incremental computation of dominator trees [3] K. D. Cooper, T. J. Harvey and K. Kennedy: A Simple, Fast Dominance Algorithm First, we use the following heuristics to decrease the size of the BBS set: a) if BB has a single predecessor, then its immediate dominator is this predecessor additionally, if CONSERVATIVE is true: b) if all the predecessors of BB except for one (X) are dominated by BB, then X is the immediate dominator of BB c) if the nearest common ancestor of the predecessors of BB is X and X -> BB is an edge in CFG, then X is the immediate dominator of BB Then, we need to establish the dominance relation among the basic blocks in BBS. We split the dominance tree by removing the immediate dominator edges from BBS, creating a forest F. We form a graph G whose vertices are BBS and ENTRY and X -> Y is an edge of G if there exists an edge X' -> Y in CFG such that X' belongs to the tree of the dominance forest whose root is X. We then determine dominance tree of G. Note that for X, Y in BBS, X dominates Y in CFG if and only if X dominates Y in G. In this step, we can use arbitrary algorithm to determine dominators. We decided to prefer the algorithm [3] to the algorithm of Lengauer and Tarjan, since the set BBS is usually small (rarely exceeding 10 during gcc bootstrap), and [3] should perform better in this case. Finally, we need to determine the immediate dominators for the basic blocks of BBS. If the immediate dominator of X in G is Y, then the immediate dominator of X in CFG belongs to the tree of F rooted in Y. We process the dominator tree T of G recursively, starting from leaves. Suppose that X_1, X_2, ..., X_k are the sons of Y in T, and that the subtrees of the dominance tree of CFG rooted in X_i are already correct. Let G' be the subgraph of G induced by {X_1, X_2, ..., X_k}. We make the following observations: (i) the immediate dominator of all blocks in a strongly connected component of G' is the same (ii) if X has no predecessors in G', then the immediate dominator of X is the nearest common ancestor of the predecessors of X in the subtree of F rooted in Y Therefore, it suffices to find the topological ordering of G', and process the nodes X_i in this order using the rules (i) and (ii). Then, we contract all the nodes X_i with Y in G, so that the further steps work correctly. */ if (!conservative) { /* Split the tree now. If the idoms of blocks in BBS are not conservatively correct, setting the dominators using the heuristics in prune_bbs_to_update_dominators could create cycles in the dominance "tree", and cause ICE. */ for (i = 0; VEC_iterate (basic_block, bbs, i, bb); i++) set_immediate_dominator (CDI_DOMINATORS, bb, NULL); } prune_bbs_to_update_dominators (bbs, conservative); n = VEC_length (basic_block, bbs); if (n == 0) return; if (n == 1) { bb = VEC_index (basic_block, bbs, 0); set_immediate_dominator (CDI_DOMINATORS, bb, recompute_dominator (CDI_DOMINATORS, bb)); return; } /* Construct the graph G. */ map = pointer_map_create (); for (i = 0; VEC_iterate (basic_block, bbs, i, bb); i++) { /* If the dominance tree is conservatively correct, split it now. */ if (conservative) set_immediate_dominator (CDI_DOMINATORS, bb, NULL); *pointer_map_insert (map, bb) = (void *) (size_t) i; } *pointer_map_insert (map, ENTRY_BLOCK_PTR) = (void *) (size_t) n; g = new_graph (n + 1); for (y = 0; y < g->n_vertices; y++) g->vertices[y].data = BITMAP_ALLOC (NULL); for (i = 0; VEC_iterate (basic_block, bbs, i, bb); i++) { FOR_EACH_EDGE (e, ei, bb->preds) { dom = root_of_dom_tree (CDI_DOMINATORS, e->src); if (dom == bb) continue; dom_i = (size_t) *pointer_map_contains (map, dom); /* Do not include parallel edges to G. */ if (bitmap_bit_p ((bitmap) g->vertices[dom_i].data, i)) continue; bitmap_set_bit ((bitmap) g->vertices[dom_i].data, i); add_edge (g, dom_i, i); } } for (y = 0; y < g->n_vertices; y++) BITMAP_FREE (g->vertices[y].data); pointer_map_destroy (map); /* Find the dominator tree of G. */ son = XNEWVEC (int, n + 1); brother = XNEWVEC (int, n + 1); parent = XNEWVEC (int, n + 1); graphds_domtree (g, n, parent, son, brother); /* Finally, traverse the tree and find the immediate dominators. */ for (y = n; son[y] != -1; y = son[y]) continue; while (y != -1) { determine_dominators_for_sons (g, bbs, y, son, brother); if (brother[y] != -1) { y = brother[y]; while (son[y] != -1) y = son[y]; } else y = parent[y]; } free (son); free (brother); free (parent); free_graph (g); } void add_to_dominance_info (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); gcc_assert (dom_computed[dir_index]); gcc_assert (!bb->dom[dir_index]); n_bbs_in_dom_tree[dir_index]++; bb->dom[dir_index] = et_new_tree (bb); if (dom_computed[dir_index] == DOM_OK) dom_computed[dir_index] = DOM_NO_FAST_QUERY; } void delete_from_dominance_info (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); gcc_assert (dom_computed[dir_index]); et_free_tree (bb->dom[dir_index]); bb->dom[dir_index] = NULL; n_bbs_in_dom_tree[dir_index]--; if (dom_computed[dir_index] == DOM_OK) dom_computed[dir_index] = DOM_NO_FAST_QUERY; } /* Returns the first son of BB in the dominator or postdominator tree as determined by DIR. */ basic_block first_dom_son (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *son = bb->dom[dir_index]->son; return (basic_block) (son ? son->data : NULL); } /* Returns the next dominance son after BB in the dominator or postdominator tree as determined by DIR, or NULL if it was the last one. */ basic_block next_dom_son (enum cdi_direction dir, basic_block bb) { unsigned int dir_index = dom_convert_dir_to_idx (dir); struct et_node *next = bb->dom[dir_index]->right; return (basic_block) (next->father->son == next ? NULL : next->data); } /* Return dominance availability for dominance info DIR. */ enum dom_state dom_info_state (enum cdi_direction dir) { unsigned int dir_index = dom_convert_dir_to_idx (dir); return dom_computed[dir_index]; } /* Set the dominance availability for dominance info DIR to NEW_STATE. */ void set_dom_info_availability (enum cdi_direction dir, enum dom_state new_state) { unsigned int dir_index = dom_convert_dir_to_idx (dir); dom_computed[dir_index] = new_state; } /* Returns true if dominance information for direction DIR is available. */ bool dom_info_available_p (enum cdi_direction dir) { unsigned int dir_index = dom_convert_dir_to_idx (dir); return dom_computed[dir_index] != DOM_NONE; } void debug_dominance_info (enum cdi_direction dir) { basic_block bb, bb2; FOR_EACH_BB (bb) if ((bb2 = get_immediate_dominator (dir, bb))) fprintf (stderr, "%i %i\n", bb->index, bb2->index); } /* Prints to stderr representation of the dominance tree (for direction DIR) rooted in ROOT, indented by INDENT tabulators. If INDENT_FIRST is false, the first line of the output is not indented. */ static void debug_dominance_tree_1 (enum cdi_direction dir, basic_block root, unsigned indent, bool indent_first) { basic_block son; unsigned i; bool first = true; if (indent_first) for (i = 0; i < indent; i++) fprintf (stderr, "\t"); fprintf (stderr, "%d\t", root->index); for (son = first_dom_son (dir, root); son; son = next_dom_son (dir, son)) { debug_dominance_tree_1 (dir, son, indent + 1, !first); first = false; } if (first) fprintf (stderr, "\n"); } /* Prints to stderr representation of the dominance tree (for direction DIR) rooted in ROOT. */ void debug_dominance_tree (enum cdi_direction dir, basic_block root) { debug_dominance_tree_1 (dir, root, 0, false); }
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