/* Calculate (post)dominators in slightly super-linear time.
Copyright (C) 2000 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 2, 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 COPYING. If not, write to the Free
Software Foundation, 59 Temple Place - Suite 330, Boston, MA
02111-1307, USA. */
/* 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 its 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 "rtl.h"
#include "hard-reg-set.h"
#include "basic-block.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. As it has no real basic block index we use
'n_basic_blocks' for that. 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 representant
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 an 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 or forest. */
unsigned int dfsnum;
/* The number of nodes in the DFS tree (==dfsnum-1). */
unsigned int nodes;
};
static void init_dom_info PARAMS ((struct dom_info *));
static void free_dom_info PARAMS ((struct dom_info *));
static void calc_dfs_tree_nonrec PARAMS ((struct dom_info *,
basic_block,
enum cdi_direction));
static void calc_dfs_tree PARAMS ((struct dom_info *,
enum cdi_direction));
static void compress PARAMS ((struct dom_info *, TBB));
static TBB eval PARAMS ((struct dom_info *, TBB));
static void link_roots PARAMS ((struct dom_info *, TBB, TBB));
static void calc_idoms PARAMS ((struct dom_info *,
enum cdi_direction));
static void idoms_to_doms PARAMS ((struct dom_info *,
sbitmap *));
/* 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) = (type *) xcalloc ((num), sizeof (type)); \
else \
{ \
(var) = (type *) xmalloc ((num) * sizeof (type)); \
for (i = 0; i < num; i++) \
(var)[i] = (content); \
} \
} while (0)
/* Allocate all needed memory in a pessimistic fashion (so we round up).
This initialises the contents of DI, which already must be allocated. */
static void
init_dom_info (di)
struct dom_info *di;
{
/* We need memory for n_basic_blocks nodes and the ENTRY_BLOCK or
EXIT_BLOCK. */
unsigned int num = n_basic_blocks + 1 + 1;
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) n_basic_blocks + 1, 0);
init_ar (di->dfs_to_bb, basic_block, num, 0);
di->dfsnum = 1;
di->nodes = 0;
}
#undef init_ar
/* Free all allocated memory in DI, but not DI itself. */
static void
free_dom_info (di)
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);
}
/* 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 (di, bb, reverse)
struct dom_info *di;
basic_block bb;
enum cdi_direction reverse;
{
/* We never call this with bb==EXIT_BLOCK_PTR (ENTRY_BLOCK_PTR if REVERSE). */
/* We call this _only_ if bb is not already visited. */
edge e;
TBB child_i, my_i = 0;
edge *stack;
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 = (edge *) xmalloc ((n_basic_blocks + 3) * sizeof (edge));
sp = 0;
/* Initialize our border blocks, and the first edge. */
if (reverse)
{
e = bb->pred;
en_block = EXIT_BLOCK_PTR;
ex_block = ENTRY_BLOCK_PTR;
}
else
{
e = bb->succ;
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 (e)
{
edge e_next;
/* 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])
{
e = e->pred_next;
continue;
}
bb = e->dest;
e_next = bn->pred;
}
else
{
bn = e->dest;
if (bn == ex_block || di->dfs_order[bn->index])
{
e = e->succ_next;
continue;
}
bb = e->src;
e_next = bn->succ;
}
if (bn == en_block)
abort ();
/* 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[n_basic_blocks];
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++] = e;
e = e_next;
}
if (!sp)
break;
e = 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. */
if (reverse)
e = e->pred_next;
else
e = e->succ_next;
}
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 (di, reverse)
struct dom_info *di;
enum cdi_direction 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[n_basic_blocks] = 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, so we simply
include them in the DFS tree which actually becomes a forest. */
int i;
for (i = n_basic_blocks - 1; i >= 0; i--)
{
basic_block b = BASIC_BLOCK (i);
if (di->dfs_order[b->index])
continue;
di->dfs_order[b->index] = di->dfsnum;
di->dfs_to_bb[di->dfsnum] = b;
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. */
if (di->nodes != (unsigned int) n_basic_blocks + 1)
abort ();
}
/* 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 (di, v)
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 (di, v)
struct dom_info *di;
TBB v;
{
/* The representant 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 (di, v, w)
struct dom_info *di;
TBB v, 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 (di, reverse)
struct dom_info *di;
enum cdi_direction reverse;
{
TBB v, w, k, par;
basic_block en_block;
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, e_next;
par = di->dfs_parent[v];
k = v;
if (reverse)
e = bb->succ;
else
e = bb->pred;
/* 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. */
for (; e; e = e_next)
{
TBB k1;
basic_block b;
if (reverse)
{
b = e->dest;
e_next = e->succ_next;
}
else
{
b = e->src;
e_next = e->pred_next;
}
if (b == en_block)
k1 = di->dfs_order[n_basic_blocks];
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;
}
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]];
}
/* Convert the information about immediate dominators (in DI) to sets of all
dominators (in DOMINATORS). */
static void
idoms_to_doms (di, dominators)
struct dom_info *di;
sbitmap *dominators;
{
TBB i, e_index;
int bb, bb_idom;
sbitmap_vector_zero (dominators, n_basic_blocks);
/* We have to be careful, to not include the ENTRY_BLOCK or EXIT_BLOCK
in the list of (post)-doms, so remember that in e_index. */
e_index = di->dfs_order[n_basic_blocks];
for (i = 1; i <= di->nodes; i++)
{
if (i == e_index)
continue;
bb = di->dfs_to_bb[i]->index;
if (di->dom[i] && (di->dom[i] != e_index))
{
bb_idom = di->dfs_to_bb[di->dom[i]]->index;
sbitmap_copy (dominators[bb], dominators[bb_idom]);
}
else
{
/* It has no immediate dom or only ENTRY_BLOCK or EXIT_BLOCK.
If it is a child of ENTRY_BLOCK that's OK, and it's only
dominated by itself; if it's _not_ a child of ENTRY_BLOCK, it
means, it is unreachable. That case has been disallowed in the
building of the DFS tree, so we are save here. For the reverse
flow graph it means, it has no children, so, to be compatible
with the old code, we set the post_dominators to all one. */
if (!di->dom[i])
{
sbitmap_ones (dominators[bb]);
}
}
SET_BIT (dominators[bb], bb);
}
}
/* The main entry point into this module. IDOM is an integer array with room
for n_basic_blocks integers, DOMS is a preallocated sbitmap array having
room for n_basic_blocks^2 bits, and POST is true if the caller wants to
know post-dominators.
On return IDOM[i] will be the BB->index of the immediate (post) dominator
of basic block i, and DOMS[i] will have set bit j if basic block j is a
(post)dominator for block i.
Either IDOM or DOMS may be NULL (meaning the caller is not interested in
immediate resp. all dominators). */
void
calculate_dominance_info (idom, doms, reverse)
int *idom;
sbitmap *doms;
enum cdi_direction reverse;
{
struct dom_info di;
if (!doms && !idom)
return;
init_dom_info (&di);
calc_dfs_tree (&di, reverse);
calc_idoms (&di, reverse);
if (idom)
{
int i;
for (i = 0; i < n_basic_blocks; i++)
{
basic_block b = BASIC_BLOCK (i);
TBB d = di.dom[di.dfs_order[b->index]];
/* The old code didn't modify array elements of nodes having only
itself as dominator (d==0) or only ENTRY_BLOCK (resp. EXIT_BLOCK)
(d==1). */
if (d > 1)
idom[i] = di.dfs_to_bb[d]->index;
}
}
if (doms)
idoms_to_doms (&di, doms);
free_dom_info (&di);
}