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sdcc-gas/src/SDCCtree_dec.hpp

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// Philipp Klaus Krause, philipp@informatik.uni-frankfurt.de, pkk@spth.de, 2010 - 2011
//
// (c) 2010-2011 Goethe-Universität Frankfurt
//
// This program 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.
//
// This program 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 this program; if not, write to the Free Software
// Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
//
//
// Some routines for tree-decompositions.
//
// A tree decomposition is a graph that has a set of vertex indices as bundled property, e.g.:
//
// struct tree_dec_node
// {
// std::set<unsigned int> bag;
// };
// typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::bidirectionalS, tree_dec_node> tree_dec_t;
//
// The following are the routines that are most likely to be interesting for outside use:
//
// void nicify(T_t &T)
// Transforms a tree decomposition T into a nice tree decomposition
//
// void thorup_tree_decomposition(T_t &tree_decomposition, const G_t &cfg)
// Creates a tree decomposition T from a graph cfg using Thorup's heuristic.
//
// void tree_decomposition_from_elimination_ordering(T_t &T, std::list<unsigned int>& l, const G_t &G)
// Creates a tree decomposition T of a graph G from an elimination ordering l.
//
// void thorup_elimination_ordering(l_t &l, const J_t &J)
// Creates an elimination ordering l of a graph J using Thorup's heuristic.
//
#include <map>
#include <vector>
#include <set>
#include <stack>
#include <list>
#include <boost/tuple/tuple_io.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/graph_utility.hpp>
#include <boost/graph/properties.hpp>
#include <boost/graph/copy.hpp>
#include <boost/graph/adjacency_list.hpp>
#undef RANGE
#undef BLOCK
struct forget_properties
{
template<class T1, class T2>
void operator()(const T1&, const T2&) const
{
}
};
// Thorup algorithm D.
// The use of the multimap makes the complexity of this O(|I|log|I|), which could be reduced to O(|I|).
template <class l_t>
void thorup_D(l_t &l, const std::multimap<unsigned int, unsigned int> &MJ, const std::multimap<unsigned int, unsigned int> &MS, const unsigned int n)
{
std::map<unsigned int, unsigned int> m;
l.clear();
unsigned int i = 0;
for (unsigned int j = n; j > 0;)
{
j--;
if (m.find(j) == m.end())
m[j] = i++;
std::multimap<unsigned int, unsigned int>::const_iterator k, k_end;
for (boost::tie(k, k_end) = MS.equal_range(j); k != k_end; ++k)
if (m.find(k->second) == m.end())
m[k->second] = i++;
for (boost::tie(k, k_end) = MJ.equal_range(j); k != k_end; ++k)
if (m.find(k->second) == m.end())
m[k->second] = i++;
}
std::vector<unsigned int> v(n);
std::map<unsigned int, unsigned int>::iterator mi;
for (mi = m.begin(); mi != m.end(); ++mi)
v[mi->second] = mi->first;
for (i = 0; i < n; i++)
l.push_back(v[i]);
}
// Thorup algorithm E.
// The use of the multimap makes the complexity of this O(|I|log|I|), which could be reduced to O(|I|).
template <class I_t>
void thorup_E(std::multimap<unsigned int, unsigned int> &M, const I_t &I)
{
typedef typename boost::graph_traits<I_t>::adjacency_iterator adjacency_iter_t;
typedef typename boost::property_map<I_t, boost::vertex_index_t>::type index_map;
index_map index = boost::get(boost::vertex_index, I);
std::stack<std::pair<int, unsigned int> > s;
M.clear();
s.push(std::pair<int, unsigned int>(-1, boost::num_vertices(I)));
for (unsigned int i = 0; i < boost::num_vertices(I); i++)
{
unsigned int j = i;
adjacency_iter_t j_curr, j_end;
for (boost::tie(j_curr, j_end) = boost::adjacent_vertices(i, I); j_curr != j_end; ++j_curr)
if (index[*j_curr] > j)
j = index[*j_curr];
if (j == i)
continue;
while (s.top().second <= i)
{
M.insert(std::pair<unsigned int, unsigned int>(s.top().second, s.top().first));
s.pop();
}
unsigned int i2 = i;
while (j >= s.top().second && s.top().second > i2)
{
i2 = s.top().first;
s.pop();
}
s.push(std::pair<int, unsigned int>(i2, j));
}
// Thorup forgot this in his paper. Without it, some maximal chains are omitted.
while(s.size() > 1)
{
M.insert(std::pair<unsigned int, unsigned int>(s.top().second, s.top().first));
s.pop();
}
}
// Heuristically give an elimination ordering for a directed graph.
// For a description of this, including algorithms D and E, see
// Mikkel Thorup, "All Structured Programs have Small Tree-Width and Good Register Allocation", Appendix A.
// The use of the multimap makes the complexity of this O(|I|log|I|), could be reduced to O(|I|).
template <class l_t, class G_t>
void thorup_elimination_ordering(l_t &l, const G_t &G)
{
// Remove edges to immediately following instruction. By "each statement can have at most obne jump" in the last paragraph of Appendix A it is clear that Thorup does not consider the implicit next-instruction-edges as jumps.
boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS> J;
boost::copy_graph(G, J, boost::vertex_copy(forget_properties()).edge_copy(forget_properties()));
for (unsigned int i = 0; i < boost::num_vertices(J) - 1; i++)
remove_edge(i, i + 1, J);
// Todo: Implement a graph adaptor for boost that allows to treat directed graphs as undirected graphs.
boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS> S;
boost::copy_graph(J, S);
std::multimap<unsigned int, unsigned int> MJ, MS;
thorup_E(MJ, J);
thorup_E(MS, S);
thorup_D(l, MJ, MS, num_vertices(J));
}
// Finds a (the newest) bag that contains all vertices in X in the tree decomposition T.
template <class X_t, class T_t>
typename boost::graph_traits<T_t>::vertex_iterator find_bag(const X_t &X, const T_t &T)
{
typedef typename boost::graph_traits<T_t>::vertex_iterator T_vertex_iter_t;
typedef typename X_t::const_iterator vertex_index_iter_t;
T_vertex_iter_t t, t_end, t_found;
vertex_index_iter_t v;
for (boost::tie(t, t_end) = vertices(T), t_found = t_end; t != t_end; ++t)
{
for (v = X.begin(); v != X.end(); ++v)
if (T[*t].bag.find(*v) == T[*t].bag.end())
break;
if (v == X.end())
t_found = t;
}
if (t_found == t_end) // Todo: Better error handling (throw exception?)
{
std::cerr << "find_bag() failed.\n";
std::cerr.flush();
}
return(t_found);
}
// Add edges to make the vertices in X a clique in G.
template <class X_t, class G_t>
void make_clique(const X_t &X , G_t &G)
{
typename X_t::const_iterator n1, n2;
for (n1 = X.begin(); n1 != X.end(); n1++)
for (n2 = n1, ++n2; n2 != X.end(); ++n2)
add_edge(*n1, *n2, G);
}
template <class T_t, class v_t, class G_t>
void add_vertices_to_tree_decomposition(T_t &T, const v_t v, const v_t v_end, G_t &G, std::vector<bool> &active)
{
// Base case: Empty graph. Create an empty bag.
if (v == v_end)
{
boost::add_vertex(T);
return;
}
// Todo: A more elegant solution, e.g. using subgraphs or filtered graphs.
typedef typename boost::graph_traits<G_t>::adjacency_iterator adjacency_iter_t;
typedef typename boost::property_map<G_t, boost::vertex_index_t>::type index_map;
index_map index = boost::get(boost::vertex_index, G);
// Get the neigbours
adjacency_iter_t n, n_end;
decltype(T[0].bag) neighbours;
for (boost::tie(n, n_end) = boost::adjacent_vertices(*v, G); n != n_end; ++n)
if (active[index[*n]])
neighbours.insert(index[*n]);
// Recurse
active[*v] = false;
make_clique(neighbours, G);
v_t v_next = v;
add_vertices_to_tree_decomposition(T, ++v_next, v_end, G, active);
// Add new bag
typename boost::graph_traits<T_t>::vertex_iterator t;
typename boost::graph_traits<T_t>::vertex_descriptor s;
t = find_bag(neighbours, T);
s = boost::add_vertex(T);
boost::add_edge(*t, s, T);
T[s].bag = neighbours;
T[s].bag.insert(*v);
}
// Create a tree decomposition from an elimination ordering.
template <class T_t, class G_t>
void tree_decomposition_from_elimination_ordering(T_t &T, const std::list<unsigned int>& l, const G_t &G)
{
std::list<unsigned int>::const_reverse_iterator v, v_end;
v = l.rbegin(), v_end = l.rend();
// Todo: Implement a graph adaptor for boost that allows to treat directed graphs as undirected graphs.
boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS> G_sym;
boost::copy_graph(G, G_sym, boost::vertex_copy(forget_properties()).edge_copy(forget_properties()));
std::vector<bool> active(boost::num_vertices(G), true);
add_vertices_to_tree_decomposition(T, v, v_end, G_sym, active);
}
template <class T_t, class G_t>
void thorup_tree_decomposition(T_t &tree_decomposition, const G_t &cfg)
{
std::list<unsigned int> elimination_ordering;
thorup_elimination_ordering(elimination_ordering, cfg);
tree_decomposition_from_elimination_ordering(tree_decomposition, elimination_ordering, cfg);
}
// Ensure that all joins are at proper join nodes: Each node that has two children has the same bag as its children.
// Complexity: Linear in the number of vertices of T.
template <class T_t>
void nicify_joins(T_t &T, typename boost::graph_traits<T_t>::vertex_descriptor t)
{
typedef typename boost::graph_traits<T_t>::adjacency_iterator adjacency_iter_t;
adjacency_iter_t c, c_end;
typename boost::graph_traits<T_t>::vertex_descriptor c0, c1;
boost::tie(c, c_end) = boost::adjacent_vertices(t, T);
switch (out_degree(t, T))
{
case 0:
return;
case 1:
nicify_joins(T, *c);
return;
case 2:
break;
default:
c0 = *c++;
c1 = *c;
typename boost::graph_traits<T_t>::vertex_descriptor d;
d = boost::add_vertex(T);
add_edge(d, c0, T);
add_edge(d, c1, T);
boost::remove_edge(t, c0, T);
boost::remove_edge(t, c1, T);
T[d].bag = T[t].bag;
boost::add_edge(t, d, T);
nicify_joins(T, t);
return;
}
c0 = *c++;
c1 = *c;
nicify_joins(T, c0);
if (T[t].bag != T[c0].bag)
{
typename boost::graph_traits<T_t>::vertex_descriptor d;
d = boost::add_vertex(T);
boost::add_edge(d, c0, T);
boost::remove_edge(t, c0, T);
T[d].bag = T[t].bag;
boost::add_edge(t, d, T);
}
nicify_joins(T, c1);
if (T[t].bag != T[c1].bag)
{
typename boost::graph_traits<T_t>::vertex_descriptor d = boost::add_vertex(T);
boost::add_edge(d, c1, T);
boost::remove_edge(t, c1, T);
T[d].bag = T[t].bag;
boost::add_edge(t, d, T);
}
}
// Ensure that all nodes' bags are either a subset or a superset of their successors'.
// Complexity: Linear in the number of vertices of T.
template <class T_t>
void nicify_diffs(T_t &T, typename boost::graph_traits<T_t>::vertex_descriptor t)
{
typedef typename boost::graph_traits<T_t>::adjacency_iterator adjacency_iter_t;
adjacency_iter_t c, c_end;
typename boost::graph_traits<T_t>::vertex_descriptor c0, c1;
boost::tie(c, c_end) = adjacent_vertices(t, T);
switch (boost::out_degree(t, T))
{
case 0:
if (T[t].bag.size())
boost::add_edge(t, boost::add_vertex(T), T);
return;
case 1:
break;
case 2:
c0 = *c++;
c1 = *c;
nicify_diffs(T, c0);
nicify_diffs(T, c1);
return;
default:
std::cerr << "nicify_diffs error.\n";
return;
}
c0 = *c;
nicify_diffs(T, c0);
// Redundant bags are isolated, and thus marked for later removal.
if (T[t].bag == T[c0].bag)
{
T[c0].bag.clear();
boost::remove_edge(t, c0, T);
adjacency_iter_t c, c_end;
for(boost::tie(c, c_end) = adjacent_vertices(c0, T); c != c_end; ++c)
boost::add_edge(t, *c, T);
boost::clear_vertex(c0, T);
}
if (std::includes(T[t].bag.begin(), T[t].bag.end(), T[c0].bag.begin(), T[c0].bag.end()) || std::includes(T[c0].bag.begin(), T[c0].bag.end(), T[t].bag.begin(), T[t].bag.end()))
return;
typename boost::graph_traits<T_t>::vertex_descriptor d = boost::add_vertex(T);
boost::add_edge(d, c0, T);
boost::remove_edge(t, c0, T);
std::set_intersection(T[t].bag.begin(), T[t].bag.end(), T[c0].bag.begin(), T[c0].bag.end(), std::inserter(T[d].bag, T[d].bag.begin()));
boost::add_edge(t, d, T);
}
// Ensure that all nodes' bags' sizes differ by at most one to their successors'.
template <class T_t>
void nicify_diffs_more(T_t &T, typename boost::graph_traits<T_t>::vertex_descriptor t)
{
typedef typename boost::graph_traits<T_t>::adjacency_iterator adjacency_iter_t;
adjacency_iter_t c, c_end;
typename boost::graph_traits<T_t>::vertex_descriptor c0, c1;
boost::tie(c, c_end) = adjacent_vertices(t, T);
switch (boost::out_degree(t, T))
{
case 0:
if (T[t].bag.size() > 1)
{
typename boost::graph_traits<T_t>::vertex_descriptor d = boost::add_vertex(T);
T[d].bag = T[t].bag;
T[d].bag.erase(T[d].bag.begin());
T[d].weight = 0;
boost::add_edge(t, d, T);
nicify_diffs_more(T, t);
}
else
T[t].weight = 0;
return;
case 1:
break;
case 2:
c0 = *c++;
c1 = *c;
nicify_diffs_more(T, c0);
nicify_diffs_more(T, c1);
{
const unsigned l = T[c0].weight;
const unsigned r = T[c1].weight;
T[t].weight = (l == r) ? l + 1 : std::max(l , r);
}
return;
default:
std::cerr << "nicify_diffs_more error.\n";
return;
}
c0 = *c;
size_t c0_size, t_size;
t_size = T[t].bag.size();
c0_size = T[c0].bag.size();
if (t_size <= c0_size + 1 && t_size + 1 >= c0_size)
{
nicify_diffs_more(T, c0);
T[t].weight = T[c0].weight;
return;
}
typename boost::graph_traits<T_t>::vertex_descriptor d = add_vertex(T);
boost::add_edge(d, c0, T);
boost::remove_edge(t, c0, T);
T[d].bag = T[t_size > c0_size ? t : c0].bag;
typename decltype(T[d].bag)::iterator i;
for (i = T[d].bag.begin(); T[t_size < c0_size ? t : c0].bag.find(*i) != T[t_size < c0_size ? t : c0].bag.end(); ++i);
T[d].bag.erase(i);
boost::add_edge(t, d, T);
nicify_diffs_more(T, t);
}
#ifdef HAVE_TREEDEC_COMBINATIONS_HPP
#include <treedec/treedec_traits.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/graph/graph_utility.hpp>
#include <treedec/nice_decomposition.hpp>
using treedec::find_root;
#else
// Find a root of an acyclic graph T
// Complexity: Linear in the number of vertices of T.
template <class T_t>
typename boost::graph_traits<T_t>::vertex_descriptor find_root(T_t &T)
{
typename boost::graph_traits<T_t>::vertex_descriptor t;
typename boost::graph_traits<T_t>::in_edge_iterator e, e_end;
t = *(boost::vertices(T).first);
for (boost::tie(e, e_end) = boost::in_edges(t, T); e != e_end; boost::tie(e, e_end) = boost::in_edges(t, T))
t = boost::source(*e, T);
return(t);
}
#endif
// Remove isolated vertices possibly introduced by nicify_diffs(). Complicated, since boost does not support removing more than one vertex at a time.
template <class T_t>
void remove_isolated_vertices(T_t &T)
{
bool change = true;
while(change)
{
change = false;
if(boost::num_vertices(T) <= 1)
return;
for (unsigned int i = 0; i < boost::num_vertices(T); i++)
if(!boost::out_degree(i, T) && !boost::in_degree(i, T))
{
remove_vertex(i, T);
change = true;
break;
}
}
}
// Transform a tree decomposition into a nice tree decomposition.
template <class T_t>
void nicify(T_t &T)
{
typename boost::graph_traits<T_t>::vertex_descriptor t;
t = find_root(T);
// Ensure we have an empty bag at the root.
if(T[t].bag.size())
{
typename boost::graph_traits<T_t>::vertex_descriptor d = t;
t = add_vertex(T);
boost::add_edge(t, d, T);
}
nicify_joins(T, t);
nicify_diffs(T, t);
nicify_diffs_more(T, t);
remove_isolated_vertices(T);
}
class cfg_titlewriter
{
public:
explicit cfg_titlewriter(const std::string& f, const std::string& p) : function(f), purpose(p)
{
}
void operator()(std::ostream& out) const
{
out << "graph [label=\"Control-flow-graph for " << purpose << " (function " << function << ")\"]\n";
}
private:
std::string function;
std::string purpose;
};
class dec_titlewriter
{
public:
explicit dec_titlewriter(unsigned int w, const std::string& f, const std::string& p) : function(f), purpose(p)
{
width = w;
}
void operator()(std::ostream& out) const
{
out << "graph [label=\"Tree-decomposition of width " << width << " for " << purpose << " (function " << function << ")\"]\n";
}
private:
unsigned int width;
std::string function;
std::string purpose;
};
#ifdef HAVE_TREEDEC_COMBINATIONS_HPP
#include <treedec/graph.hpp>
#include <treedec/preprocessing.hpp>
#include <boost/graph/copy.hpp>
#include <treedec/thorup.hpp>
#include <treedec/combinations.hpp>
#include <treedec/misc.hpp>
template <typename Gd_t, typename Gs_t>
void copy_undir(Gd_t &dst, const Gs_t &src)
{
for(unsigned i = 0; i < boost::num_vertices(src); i++)
boost::add_vertex(dst);
typename boost::graph_traits<Gs_t>::edge_iterator e, e_end;
for(boost::tie(e, e_end) = boost::edges(src); e != e_end; ++e)
{
wassert (boost::source(*e, src) != boost::target(*e, src));
if (!boost::edge(boost::source(*e, src), boost::target(*e, src), dst).second)
boost::add_edge(boost::source(*e, src), boost::target(*e, src), dst);
}
}
#endif
#undef USE_THORUP // Thorup's classic algorithm (default in SDCC pre-3.7.0). Substantially worse width than the others.
#define USE_PP_FI_TM 1 // A good trade-off between width and runtime
#undef USE_EX17 // Slightly better width than PP_FI_TM, but no polynomial runtime bound.
#undef USE_PP_MD // Slightly worse width than PP_FI_TM.
#undef USE_PP_FI // Slightly worse width than PP_FI_TM.
// Get a nice tree decomposition for a cfg.
template <class T_t, class G_t>
void get_nice_tree_decomposition(T_t &tree_dec, const G_t &cfg)
{
thorup_tree_decomposition(tree_dec, cfg);
#ifdef HAVE_TREEDEC_COMBINATIONS_HPP
#ifdef USE_THORUP
treedec::thorup<G_t> a2(cfg);
#else
typedef boost::adjacency_list<boost::setS, boost::vecS, boost::undirectedS> cfg2_t;
cfg2_t cfg2;
copy_undir(cfg2, cfg);
#if USE_PP_FI_TM
treedec::comb::PP_FI_TM<cfg2_t> a2(cfg2);
#elif USE_EX17
treedec::comb::ex17<cfg2_t> a2(cfg2);
#elif USE_PP_MD
treedec::comb::PP_MD<cfg2_t> a2(cfg2);
#elif USE_PP_FI
treedec::comb::PP_FI<cfg2_t> a2(cfg2);
#else
#error No algorithm selected
#endif
#endif
T_t tree_dec2;
a2.do_it();
a2.get_tree_decomposition(tree_dec2);
wassert(treedec::is_valid_treedecomposition(cfg, tree_dec2));
if (treedec::get_width(tree_dec2) < treedec::get_width(tree_dec))
std::swap(tree_dec, tree_dec2);
#endif
nicify(tree_dec);
#ifdef HAVE_TREEDEC_COMBINATIONS_HPP
wassert(treedec::is_valid_treedecomposition(cfg, tree_dec));
#endif
}
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