path: root/gcc/tree-ssa-structalias.c

/* Tree based points-to analysis
   Copyright (C) 2005 Free Software Foundation, Inc.
   Contributed by Daniel Berlin <dberlin@dberlin.org>

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify
under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, 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; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "ggc.h"
#include "obstack.h"
#include "bitmap.h"
#include "tree-ssa-structalias.h"
#include "flags.h"
#include "rtl.h"
#include "tm_p.h"
#include "hard-reg-set.h"
#include "basic-block.h"
#include "output.h"
#include "errors.h"
#include "expr.h"
#include "diagnostic.h"
#include "tree.h"
#include "c-common.h"
#include "tree-flow.h"
#include "tree-inline.h"
#include "varray.h"
#include "c-tree.h"
#include "tree-gimple.h"
#include "hashtab.h"
#include "function.h"
#include "cgraph.h"
#include "tree-pass.h"
#include "timevar.h"
#include "alloc-pool.h"
#include "splay-tree.h"

/* The idea behind this analyzer is to generate set constraints from the
   program, then solve the resulting constraints in order to generate the
   points-to sets. 

   Set constraints are a way of modeling program analysis problems that
   involve sets.  They consist of an inclusion constraint language,
   describing the variables (each variable is a set) and operations that
   are involved on the variables, and a set of rules that derive facts
   from these operations.  To solve a system of set constraints, you derive
   all possible facts under the rules, which gives you the correct sets
   as a consequence.

   See  "Efficient Field-sensitive pointer analysis for C" by "David
   J. Pearce and Paul H. J. Kelly and Chris Hankin, at
   http://citeseer.ist.psu.edu/pearce04efficient.html

   Also see "Ultra-fast Aliasing Analysis using CLA: A Million Lines
   of C Code in a Second" by ""Nevin Heintze and Olivier Tardieu" at
   http://citeseer.ist.psu.edu/heintze01ultrafast.html 

   There are three types of constraint expressions, DEREF, ADDRESSOF, and
   SCALAR.  Each constraint expression consists of a constraint type,
   a variable, and an offset.  
   
   SCALAR is a constraint expression type used to represent x, whether
   it appears on the LHS or the RHS of a statement.
   DEREF is a constraint expression type used to represent *x, whether
   it appears on the LHS or the RHS of a statement. 
   ADDRESSOF is a constraint expression used to represent &x, whether
   it apepars on the LHS or the RHS of a statement.
   
   Each pointer variable in the program is assigned an integer id, and
   each field of a structure variable is assigned an integer id as well.
   
   Structure variables are linked to their list of fields through a "next
   field" in each variable that points to the next field in offset
   order.  
   Each variable for a structure field has 

   1. "size", that tells the size in bits of that field.
   2. "fullsize, that tells the size in bits of the entire structure.
   3. "offset", that tells the offset in bits from the beginning of the
   structure to this field.

   Thus, 
   struct f
   {
     int a;
     int b;
   } foo;
   int *bar;

   looks like

   foo.a -> id 1, size 32, offset 0, fullsize 64, next foo.b
   foo.b -> id 2, size 32, offset 32, fullsize 64, next NULL
   bar -> id 3, size 32, offset 0, fullsize 32, next NULL

   
  In order to solve the system of set constraints, the following is
  done:

  1. Each constraint variable x has a solution set associated with it,
  Sol(x).
  
  2. Constraints are separated into direct, copy, and complex.
  Direct constraints are ADDRESSOF constraints that require no extra
  processing, such as P = &Q
  Copy constraints are those of the form P = Q.
  Complex constraints are all the constraints involving dereferences.
  
  3. All direct constraints of the form P = &Q are processed, such
  that Q is added to Sol(P) 

  4. All complex constraints for a given constraint variable are stored in a
  linked list attached to that variable's node.  

  5. A directed graph is built out of the copy constraints. Each
  constraint variable is a node in the graph, and an edge from 
  Q to P is added for each copy constraint of the form P = Q
  
  6. The graph is then walked, and solution sets are
  propagated along the copy edges, such that an edge from Q to P
  causes Sol(P) <- Sol(P) union Sol(Q).
  
  7.  As we visit each node, all complex constraints associated with
  that node are processed by adding approriate copy edges to the graph, or the
  approriate variables to the solution set.  

  8. The process of walking the graph is iterated until no solution
  sets change.

  Prior to walking the graph in steps 6 and 7, We perform static
  cycle elimination on the constraint graph, as well 
  as off-line variable substitution.
  
  TODO: Adding offsets to pointer-to-structures can be handled (IE not punted
  on and turned into anything), but isn't.  You can just see what offset
  inside the pointed-to struct it's going to access.
  
  TODO: Constant bounded arrays can be handled as if they were structs of the
  same number of elements. 

  TODO: Modeling heap and incoming pointers becomes much better if we
  add fields to them as we discover them, which we could do.

  TODO: We could handle unions, but to be honest, it's probably not
  worth the pain or slowdown.  */

static bool use_field_sensitive = true;
static unsigned int create_variable_info_for (tree, const char *);
static struct constraint_expr get_constraint_for (tree);
static void build_constraint_graph (void);

static bitmap_obstack ptabitmap_obstack;
static bitmap_obstack iteration_obstack;
DEF_VEC_P(constraint_t);
DEF_VEC_ALLOC_P(constraint_t,gc);

static struct constraint_stats
{
  unsigned int total_vars;
  unsigned int collapsed_vars;
  unsigned int unified_vars_static;
  unsigned int unified_vars_dynamic;
  unsigned int iterations;
} stats;

struct variable_info
{
  /* ID of this variable  */
  unsigned int id;

  /* Name of this variable */
  const char *name;

  /* Tree that this variable is associated with.  */
  tree decl;

  /* Offset of this variable, in bits, from the base variable  */
  unsigned HOST_WIDE_INT offset;  

  /* Size of the variable, in bits.  */
  unsigned HOST_WIDE_INT size;

  /* Full size of the base variable, in bits.  */
  unsigned HOST_WIDE_INT fullsize;

  /* A link to the variable for the next field in this structure.  */
  struct variable_info *next;

  /* Node in the graph that represents the constraints and points-to
     solution for the variable.  */
  unsigned int node;

  /* True if the address of this variable is taken.  Needed for
     variable substitution.  */
  unsigned int address_taken:1;

  /* True if this variable is the target of a dereference.  Needed for
     variable substitution.  */
  unsigned int indirect_target:1;

  /* True if this is a variable created by the constraint analysis, such as
     heap variables and constraints we had to break up.  */
  unsigned int is_artificial_var:1;

  /* True for variables whose size is not known or variable.  */
  unsigned int is_unknown_size_var:1;  

  /* True for variables that have unions somewhere in them.  */
  unsigned int has_union:1;

  /* Points-to set for this variable.  */
  bitmap solution;

  /* Variable ids represented by this node.  */
  bitmap variables;

  /* Vector of complex constraints for this node.  Complex
     constraints are those involving dereferences.  */
  VEC(constraint_t,gc) *complex;
};
typedef struct variable_info *varinfo_t;

static varinfo_t first_vi_for_offset (varinfo_t, unsigned HOST_WIDE_INT);

/* Pool of variable info structures.  */
static alloc_pool variable_info_pool;

DEF_VEC_P(varinfo_t);

DEF_VEC_ALLOC_P(varinfo_t, gc);

/* Table of variable info structures for constraint variables.  Indexed direcly
   by variable info id.  */
static VEC(varinfo_t,gc) *varmap;
#define get_varinfo(n) VEC_index(varinfo_t, varmap, n)

/* Variable that represents the unknown pointer.  */
static varinfo_t var_anything;
static tree anything_tree;
static unsigned int anything_id;

/* Variable that represents the NULL pointer.  */
static varinfo_t var_nothing;
static tree nothing_tree;
static unsigned int nothing_id;

/* Variable that represents read only memory.  */
static varinfo_t var_readonly;
static tree readonly_tree;
static unsigned int readonly_id;

/* Variable that represents integers.  This is used for when people do things
   like &0->a.b.  */
static varinfo_t var_integer;
static tree integer_tree;
static unsigned int integer_id;


/* Return a new variable info structure consisting for a variable
   named NAME, and using constraint graph node NODE.  */

static varinfo_t
new_var_info (tree t, unsigned int id, const char *name, unsigned int node)
{
  varinfo_t ret = pool_alloc (variable_info_pool);

  ret->id = id;
  ret->name = name;
  ret->decl = t;
  ret->node = node;
  ret->address_taken = false;
  ret->indirect_target = false;
  ret->is_artificial_var = false;
  ret->is_unknown_size_var = false;
  ret->solution = BITMAP_ALLOC (&ptabitmap_obstack);
  bitmap_clear (ret->solution);
  ret->variables = BITMAP_ALLOC (&ptabitmap_obstack);
  bitmap_clear (ret->variables);
  ret->complex = NULL;
  ret->next = NULL;
  return ret;
}

typedef enum {SCALAR, DEREF, ADDRESSOF} constraint_expr_type;

/* An expression that appears in a constraint.  */

struct constraint_expr 
{
  /* Constraint type.  */
  constraint_expr_type type;

  /* Variable we are referring to in the constraint.  */
  unsigned int var;

  /* Offset, in bits, of this constraint from the beginning of
     variables it ends up referring to.

     IOW, in a deref constraint, we would deref, get the result set,
     then add OFFSET to each member.   */
  unsigned HOST_WIDE_INT offset;
};

static struct constraint_expr do_deref (struct constraint_expr);

/* Our set constraints are made up of two constraint expressions, one
   LHS, and one RHS.  

   As described in the introduction, our set constraints each represent an
   operation between set valued variables.
*/
struct constraint
{
  struct constraint_expr lhs;
  struct constraint_expr rhs;
};

/* List of constraints that we use to build the constraint graph from.  */

static VEC(constraint_t,gc) *constraints;
static alloc_pool constraint_pool;

/* An edge in the constraint graph.  We technically have no use for
   the src, since it will always be the same node that we are indexing
   into the pred/succ arrays with, but it's nice for checking
   purposes.  The edges are weighted, with a bit set in weights for
   each edge from src to dest with that weight.  */

struct constraint_edge
{
  unsigned int src;
  unsigned int dest;
  bitmap weights;
};

typedef struct constraint_edge *constraint_edge_t;
static alloc_pool constraint_edge_pool;

/* Return a new constraint edge from SRC to DEST.  */

static constraint_edge_t
new_constraint_edge (unsigned int src, unsigned int dest)
{
  constraint_edge_t ret = pool_alloc (constraint_edge_pool);
  ret->src = src;
  ret->dest = dest;
  ret->weights = NULL;
  return ret;
}

DEF_VEC_P(constraint_edge_t);
DEF_VEC_ALLOC_P(constraint_edge_t,gc);


/* The constraint graph is simply a set of adjacency vectors, one per
   variable. succs[x] is the vector of successors for variable x, and preds[x]
   is the vector of predecessors for variable x. 
   IOW, all edges are "forward" edges, which is not like our CFG.  
   So remember that
   preds[x]->src == x, and
   succs[x]->src == x*/

struct constraint_graph
{
  VEC(constraint_edge_t,gc) **succs;
  VEC(constraint_edge_t,gc) **preds;
};

typedef struct constraint_graph *constraint_graph_t;

static constraint_graph_t graph;

/* Create a new constraint consisting of LHS and RHS expressions.  */

static constraint_t 
new_constraint (const struct constraint_expr lhs,
		const struct constraint_expr rhs)
{
  constraint_t ret = pool_alloc (constraint_pool);
  ret->lhs = lhs;
  ret->rhs = rhs;
  return ret;
}

/* Print out constraint C to FILE.  */

void
dump_constraint (FILE *file, constraint_t c)
{
  if (c->lhs.type == ADDRESSOF)
    fprintf (file, "&");
  else if (c->lhs.type == DEREF)
    fprintf (file, "*");  
  fprintf (file, "%s", get_varinfo (c->lhs.var)->name);
  if (c->lhs.offset != 0)
    fprintf (file, " + " HOST_WIDE_INT_PRINT_DEC, c->lhs.offset);
  fprintf (file, " = ");
  if (c->rhs.type == ADDRESSOF)
    fprintf (file, "&");
  else if (c->rhs.type == DEREF)
    fprintf (file, "*");
  fprintf (file, "%s", get_varinfo (c->rhs.var)->name);
  if (c->rhs.offset != 0)
    fprintf (file, " + " HOST_WIDE_INT_PRINT_DEC, c->rhs.offset);
  fprintf (file, "\n");
}

/* Print out constraint C to stderr.  */

void
debug_constraint (constraint_t c)
{
  dump_constraint (stderr, c);
}

/* Print out all constraints to FILE */

void
dump_constraints (FILE *file)
{
  int i;
  constraint_t c;
  for (i = 0; VEC_iterate (constraint_t, constraints, i, c); i++)
    dump_constraint (file, c);
}

/* Print out all constraints to stderr.  */

void
debug_constraints (void)
{
  dump_constraints (stderr);
}

/* SOLVER FUNCTIONS 

   The solver is a simple worklist solver, that works on the following
   algorithm:
   
   sbitmap changed_nodes = all ones;
   changed_count = number of nodes;
   For each node that was already collapsed:
       changed_count--;


   while (changed_count > 0)
   {
     compute topological ordering for constraint graph
  
     find and collapse cycles in the constraint graph (updating
     changed if necessary)
     
     for each node (n) in the graph in topological order:
       changed_count--;

       Process each complex constraint associated with the node,
       updating changed if necessary.

       For each outgoing edge from n, propagate the solution from n to
       the destination of the edge, updating changed as necessary.

   }  */

/* Return true if two constraint expressions A and B are equal.  */

static bool
constraint_expr_equal (struct constraint_expr a, struct constraint_expr b)
{
  return a.type == b.type
    && a.var == b.var
    && a.offset == b.offset;
}

/* Return true if constraint expression A is less than constraint expression
   B.  This is just arbitrary, but consistent, in order to give them an
   ordering.  */

static bool
constraint_expr_less (struct constraint_expr a, struct constraint_expr b)
{
  if (a.type == b.type)
    {
      if (a.var == b.var)
	return a.offset < b.offset;
      else
	return a.var < b.var;
    }
  else
    return a.type < b.type;
}

/* Return true if constraint A is less than constraint B.  This is just
   arbitrary, but consistent, in order to give them an ordering.  */

static bool
constraint_less (const constraint_t a, const constraint_t b)
{
  if (constraint_expr_less (a->lhs, b->lhs))
    return true;
  else if (constraint_expr_less (b->lhs, a->lhs))
    return false;
  else
    return constraint_expr_less (a->rhs, b->rhs);
}

/* Return true if two constraints A and B are equal.  */
  
static bool
constraint_equal (struct constraint a, struct constraint b)
{
  return constraint_expr_equal (a.lhs, b.lhs) 
    && constraint_expr_equal (a.rhs, b.rhs);
}


/* Find a constraint LOOKFOR in the sorted constraint vector VEC */

static constraint_t
constraint_vec_find (VEC(constraint_t,gc) *vec,
		     struct constraint lookfor)
{
  unsigned int place;  
  constraint_t found;

  if (vec == NULL)
    return NULL;

  place = VEC_lower_bound (constraint_t, vec, &lookfor, constraint_less);
  if (place >= VEC_length (constraint_t, vec))
    return NULL;
  found = VEC_index (constraint_t, vec, place);
  if (!constraint_equal (*found, lookfor))
    return NULL;
  return found;
}

/* Union two constraint vectors, TO and FROM.  Put the result in TO.  */

static void
constraint_set_union (VEC(constraint_t,gc) **to,
		      VEC(constraint_t,gc) **from)
{
  int i;
  constraint_t c;

  for (i = 0; VEC_iterate (constraint_t, *from, i, c); i++)
    {
      if (constraint_vec_find (*to, *c) == NULL)
	{
	  unsigned int place = VEC_lower_bound (constraint_t, *to, c,
						constraint_less);
	  VEC_safe_insert (constraint_t, gc, *to, place, c);
	}
    }
}

/* Take a solution set SET, add OFFSET to each member of the set, and
   overwrite SET with the result when done.  */

static void
solution_set_add (bitmap set, unsigned HOST_WIDE_INT offset)
{
  bitmap result = BITMAP_ALLOC (&iteration_obstack);
  unsigned int i;
  bitmap_iterator bi;

  EXECUTE_IF_SET_IN_BITMAP (set, 0, i, bi)
    {
      /* If this is a properly sized variable, only add offset if it's
	 less than end.  Otherwise, it is globbed to a single
	 variable.  */
      
      if ((get_varinfo (i)->offset + offset) < get_varinfo (i)->fullsize)
	{
	  unsigned HOST_WIDE_INT fieldoffset = get_varinfo (i)->offset + offset;
	  varinfo_t v = first_vi_for_offset (get_varinfo (i), fieldoffset);
	  bitmap_set_bit (result, v->id);
	}
      else if (get_varinfo (i)->is_artificial_var 
	       || get_varinfo (i)->is_unknown_size_var)
	{
	  bitmap_set_bit (result, i);
	}
    }
  
  bitmap_copy (set, result);  
  BITMAP_FREE (result);
}

/* Union solution sets TO and FROM, and add INC to each member of FROM in the
   process.  */

static bool
set_union_with_increment  (bitmap to, bitmap from, unsigned HOST_WIDE_INT inc)
{
  if (inc == 0)
    return bitmap_ior_into (to, from);
  else
    {
      bitmap tmp;
      bool res;

      tmp = BITMAP_ALLOC (&iteration_obstack);
      bitmap_copy (tmp, from);
      solution_set_add (tmp, inc);
      res = bitmap_ior_into (to, tmp);
      BITMAP_FREE (tmp);
      return res;
    }
}

/* Insert constraint C into the list of complex constraints for VAR.  */

static void
insert_into_complex (unsigned int var, constraint_t c)
{
  varinfo_t vi = get_varinfo (var);
  unsigned int place = VEC_lower_bound (constraint_t, vi->complex, c,
					constraint_less);
  VEC_safe_insert (constraint_t, gc, vi->complex, place, c);
}


/* Compare two constraint edges A and B, return true if they are equal.  */

static bool
constraint_edge_equal (struct constraint_edge a, struct constraint_edge b)
{
  return a.src == b.src && a.dest == b.dest;
}

/* Compare two constraint edges, return true if A is less than B */

static bool
constraint_edge_less (const constraint_edge_t a, const constraint_edge_t b)
{
  if (a->dest < b->dest)
    return true;
  else if (a->dest == b->dest)
    return a->src < b->src;
  else
    return false;
}

/* Find the constraint edge that matches LOOKFOR, in VEC.
   Return the edge, if found, NULL otherwise.  */

static constraint_edge_t 
constraint_edge_vec_find (VEC(constraint_edge_t,gc) *vec, 
			  struct constraint_edge lookfor)
{
  unsigned int place;  
  constraint_edge_t edge;

  place = VEC_lower_bound (constraint_edge_t, vec, &lookfor, 
			   constraint_edge_less);
  edge = VEC_index (constraint_edge_t, vec, place);
  if (!constraint_edge_equal (*edge, lookfor))
    return NULL;
  return edge;
}

/* Condense two variable nodes into a single variable node, by moving
   all associated info from SRC to TO.  */

static void 
condense_varmap_nodes (unsigned int to, unsigned int src)
{
  varinfo_t tovi = get_varinfo (to);
  varinfo_t srcvi = get_varinfo (src);
  unsigned int i;
  constraint_t c;
  bitmap_iterator bi;
  
  /* the src node, and all its variables, are now the to node.  */
  srcvi->node = to;
  EXECUTE_IF_SET_IN_BITMAP (srcvi->variables, 0, i, bi)
    get_varinfo (i)->node = to;
  
  /* Merge the src node variables and the to node variables.  */
  bitmap_set_bit (tovi->variables, src);
  bitmap_ior_into (tovi->variables, srcvi->variables);
  bitmap_clear (srcvi->variables);
  
  /* Move all complex constraints from src node into to node  */
  for (i = 0; VEC_iterate (constraint_t, srcvi->complex, i, c); i++)
    {
      /* In complex constraints for node src, we may have either
	 a = *src, and *src = a.  */
      
      if (c->rhs.type == DEREF)
	c->rhs.var = to;
      else
	c->lhs.var = to;
    }
  constraint_set_union (&tovi->complex, &srcvi->complex);
  srcvi->complex = NULL;
}

/* Erase EDGE from GRAPH.  This routine only handles self-edges
   (e.g. an edge from a to a).  */

static void
erase_graph_self_edge (constraint_graph_t graph, struct constraint_edge edge)
{
  VEC(constraint_edge_t,gc) *predvec = graph->preds[edge.src];
  VEC(constraint_edge_t,gc) *succvec = graph->succs[edge.dest];
  unsigned int place;
  gcc_assert (edge.src == edge.dest);

  /* Remove from the successors.  */
  place = VEC_lower_bound (constraint_edge_t, succvec, &edge, 
			   constraint_edge_less);
  
  /* Make sure we found the edge.  */
#ifdef ENABLE_CHECKING
  {
    constraint_edge_t tmp = VEC_index (constraint_edge_t, succvec, place);
    gcc_assert (constraint_edge_equal (*tmp, edge));
  }
#endif
  VEC_ordered_remove (constraint_edge_t, succvec, place);

  /* Remove from the predecessors.  */
  place = VEC_lower_bound (constraint_edge_t, predvec, &edge,
			   constraint_edge_less);

  /* Make sure we found the edge.  */
#ifdef ENABLE_CHECKING
  {
    constraint_edge_t tmp = VEC_index (constraint_edge_t, predvec, place);
    gcc_assert (constraint_edge_equal (*tmp, edge));
  }
#endif
  VEC_ordered_remove (constraint_edge_t, predvec, place);
}

/* Remove edges involving NODE from GRAPH.  */

static void
clear_edges_for_node (constraint_graph_t graph, unsigned int node)
{
  VEC(constraint_edge_t,gc) *succvec = graph->succs[node];
  VEC(constraint_edge_t,gc) *predvec = graph->preds[node];
  constraint_edge_t c;
  int i;
  
  /* Walk the successors, erase the associated preds.  */
  for (i = 0; VEC_iterate (constraint_edge_t, succvec, i, c); i++)
    if (c->dest != node)
      {
	unsigned int place;
	struct constraint_edge lookfor;
	lookfor.src = c->dest;
	lookfor.dest = node;
	place = VEC_lower_bound (constraint_edge_t, graph->preds[c->dest], 
				 &lookfor, constraint_edge_less);
	VEC_ordered_remove (constraint_edge_t, graph->preds[c->dest], place);
      }
  /* Walk the preds, erase the associated succs.  */
  for (i =0; VEC_iterate (constraint_edge_t, predvec, i, c); i++)
    if (c->dest != node)
      {
	unsigned int place;
	struct constraint_edge lookfor;
	lookfor.src = c->dest;
	lookfor.dest = node;
	place = VEC_lower_bound (constraint_edge_t, graph->succs[c->dest],
				 &lookfor, constraint_edge_less);
	VEC_ordered_remove (constraint_edge_t, graph->succs[c->dest], place);
      }    
  
  graph->preds[node] = NULL;
  graph->succs[node] = NULL;
}

static bool edge_added = false;
  
/* Add edge NEWE to the graph.  */

static bool
add_graph_edge (constraint_graph_t graph, struct constraint_edge newe)
{
  unsigned int place;
  unsigned int src = newe.src;
  unsigned int dest = newe.dest;
  VEC(constraint_edge_t,gc) *vec;

  vec = graph->preds[src];
  place = VEC_lower_bound (constraint_edge_t, vec, &newe, 
			   constraint_edge_less);
  if (place == VEC_length (constraint_edge_t, vec)
      || VEC_index (constraint_edge_t, vec, place)->dest != dest)
    {
      constraint_edge_t edge = new_constraint_edge (src, dest);
      bitmap weightbitmap;

      weightbitmap = BITMAP_ALLOC (&ptabitmap_obstack);
      edge->weights = weightbitmap;
      VEC_safe_insert (constraint_edge_t, gc, graph->preds[edge->src], 
		       place, edge);
      edge = new_constraint_edge (dest, src);
      edge->weights = weightbitmap;
      place = VEC_lower_bound (constraint_edge_t, graph->succs[edge->src],
			       edge, constraint_edge_less);
      VEC_safe_insert (constraint_edge_t, gc, graph->succs[edge->src], 
		       place, edge);
      edge_added = true;
      return true;
    }
  else
    return false;
}


/* Return the bitmap representing the weights of edge LOOKFOR */

static bitmap
get_graph_weights (constraint_graph_t graph, struct constraint_edge lookfor)
{
  constraint_edge_t edge;
  unsigned int src = lookfor.src;
  VEC(constraint_edge_t,gc) *vec;
  vec = graph->preds[src];
  edge = constraint_edge_vec_find (vec, lookfor);
  gcc_assert (edge != NULL);
  return edge->weights;
}


/* Merge GRAPH nodes FROM and TO into node TO.  */

static void
merge_graph_nodes (constraint_graph_t graph, unsigned int to, 
		   unsigned int from)
{
  VEC(constraint_edge_t,gc) *succvec = graph->succs[from];
  VEC(constraint_edge_t,gc) *predvec = graph->preds[from];
  int i;
  constraint_edge_t c;
  
  /* Merge all the predecessor edges.  */

  for (i = 0; VEC_iterate (constraint_edge_t, predvec, i, c); i++)
    {
      unsigned int d = c->dest;
      struct constraint_edge olde;
      struct constraint_edge newe;
      bitmap temp;
      bitmap weights;
      if (c->dest == from)
	d = to;
      newe.src = to;
      newe.dest = d;
      add_graph_edge (graph, newe);
      olde.src = from;
      olde.dest = c->dest;
      temp = get_graph_weights (graph, olde);
      weights = get_graph_weights (graph, newe);
      bitmap_ior_into (weights, temp);
    }
  
  /* Merge all the successor edges.  */
  for (i = 0; VEC_iterate (constraint_edge_t, succvec, i, c); i++)
    {
      unsigned int d = c->dest;
      struct constraint_edge olde;
      struct constraint_edge newe;
      bitmap temp;
      bitmap weights;
      if (c->dest == from)
	d = to;
      newe.src = d;
      newe.dest = to;
      add_graph_edge (graph, newe);
      olde.src = c->dest;
      olde.dest = from;
      temp = get_graph_weights (graph, olde);
      weights = get_graph_weights (graph, newe);
      bitmap_ior_into (weights, temp);
    }
  clear_edges_for_node (graph, from);
}

/* Add a graph edge to GRAPH, going from TO to FROM, with WEIGHT, if
   it doesn't exist in the graph already.
   Return false if the edge already existed, true otherwise.  */

static bool
int_add_graph_edge (constraint_graph_t graph, unsigned int to, 
		    unsigned int from, unsigned HOST_WIDE_INT weight)
{
  if (to == from && weight == 0)
    {
      return false;
    }
  else
    {
      bool r;
      struct constraint_edge edge;
      edge.src = to;
      edge.dest = from;
      r = add_graph_edge (graph, edge);
      r |= !bitmap_bit_p (get_graph_weights (graph, edge), weight);
      bitmap_set_bit (get_graph_weights (graph, edge), weight);
      return r;
    }
}


/* Return true if LOOKFOR is an existing graph edge.  */

static bool
valid_graph_edge (constraint_graph_t graph, struct constraint_edge lookfor)
{
  return constraint_edge_vec_find (graph->preds[lookfor.src], lookfor) != NULL;
}


/* Build the constraint graph.  */

static void
build_constraint_graph (void)
{
  int i = 0;
  constraint_t c;

  graph = ggc_alloc (sizeof (struct constraint_graph));
  graph->succs = ggc_alloc_cleared (VEC_length (varinfo_t, varmap) * sizeof (*graph->succs));
  graph->preds = ggc_alloc_cleared (VEC_length (varinfo_t, varmap) * sizeof (*graph->preds));
  for (i = 0; VEC_iterate (constraint_t, constraints, i, c); i++)
    {
      struct constraint_expr lhs = c->lhs;
      struct constraint_expr rhs = c->rhs;
      if (lhs.type == DEREF)
	{
	  /* *x = y or *x = &y (complex) */
	  if (rhs.type == ADDRESSOF || rhs.var > anything_id)
	    insert_into_complex (lhs.var, c);
	}
      else if (rhs.type == DEREF)
	{
	  /* !ANYTHING = *y */
	  if (lhs.var > anything_id) 
	    insert_into_complex (rhs.var, c);
	}
      else if (rhs.type == ADDRESSOF)
	{
	  /* x = &y */
	  bitmap_set_bit (get_varinfo (lhs.var)->solution, rhs.var);
	}
      else if (rhs.var > anything_id && lhs.var > anything_id)
	{
	  /* Ignore 0 weighted self edges, as they can't possibly contribute
	     anything */
	  if (lhs.var != rhs.var || rhs.offset != 0 || lhs.offset != 0)
	    {
	      
	      struct constraint_edge edge;
	      edge.src = lhs.var;
	      edge.dest = rhs.var;
	      /* x = y (simple) */
	      add_graph_edge (graph, edge);
	      bitmap_set_bit (get_graph_weights (graph, edge),
			      rhs.offset);
	    }
	  
	}
    }
}
/* Changed variables on the last iteration.  */
static unsigned int changed_count;
static sbitmap changed;

DEF_VEC_I(uint);
DEF_VEC_ALLOC_I(uint,heap);


/* Strongly Connected Component visitation info.  */

struct scc_info
{
  sbitmap visited;
  sbitmap in_component;
  int current_index;
  unsigned int *visited_index;
  VEC(uint,heap) *scc_stack;
  VEC(uint,heap) *unification_queue;
};


/* Recursive routine to find strongly connected components in GRAPH.
   SI is the SCC info to store the information in, and N is the id of current
   graph node we are processing.
   
   This is Tarjan's strongly connected component finding algorithm, as
   modified by Nuutila to keep only non-root nodes on the stack.  
   The algorithm can be found in "On finding the strongly connected
   connected components in a directed graph" by Esko Nuutila and Eljas
   Soisalon-Soininen, in Information Processing Letters volume 49,
   number 1, pages 9-14.  */

static void
scc_visit (constraint_graph_t graph, struct scc_info *si, unsigned int n)
{
  constraint_edge_t c;
  int i;

  gcc_assert (get_varinfo (n)->node == n);
  SET_BIT (si->visited, n);
  RESET_BIT (si->in_component, n);
  si->visited_index[n] = si->current_index ++;
  
  /* Visit all the successors.  */
  for (i = 0; VEC_iterate (constraint_edge_t, graph->succs[n], i, c); i++)
    {
      /* We only want to find and collapse the zero weight edges. */
      if (bitmap_bit_p (c->weights, 0))
	{
	  unsigned int w = c->dest;
	  if (!TEST_BIT (si->visited, w))
	    scc_visit (graph, si, w);
	  if (!TEST_BIT (si->in_component, w))
	    {
	      unsigned int t = get_varinfo (w)->node;
	      unsigned int nnode = get_varinfo (n)->node;
	      if (si->visited_index[t] < si->visited_index[nnode])
		get_varinfo (n)->node = t;
	    }
	}
    }
  
  /* See if any components have been identified.  */
  if (get_varinfo (n)->node == n)
    {
      unsigned int t = si->visited_index[n];
      SET_BIT (si->in_component, n);
      while (VEC_length (uint, si->scc_stack) != 0 
	     && t < si->visited_index[VEC_last (uint, si->scc_stack)])
	{
	  unsigned int w = VEC_pop (uint, si->scc_stack);
	  get_varinfo (w)->node = n;
	  SET_BIT (si->in_component, w);
	  /* Mark this node for collapsing.  */
	  VEC_safe_push (uint, heap, si->unification_queue, w);
	} 
    }
  else
    VEC_safe_push (uint, heap, si->scc_stack, n);
}


/* Collapse two variables into one variable.  */

static void
collapse_nodes (constraint_graph_t graph, unsigned int to, unsigned int from)
{
  bitmap tosol, fromsol;
  struct constraint_edge edge;


  condense_varmap_nodes (to, from);
  tosol = get_varinfo (to)->solution;
  fromsol = get_varinfo (from)->solution;
  bitmap_ior_into (tosol, fromsol);
  merge_graph_nodes (graph, to, from);
  edge.src = to;
  edge.dest = to;
  if (valid_graph_edge (graph, edge))
    {
      bitmap weights = get_graph_weights (graph, edge);
      bitmap_clear_bit (weights, 0);
      if (bitmap_empty_p (weights))
	erase_graph_self_edge (graph, edge);
    }
  bitmap_clear (fromsol);
  get_varinfo (to)->address_taken |= get_varinfo (from)->address_taken;
  get_varinfo (to)->indirect_target |= get_varinfo (from)->indirect_target;
}


/* Unify nodes in GRAPH that we have found to be part of a cycle.
   SI is the Strongly Connected Components information structure that tells us
   what components to unify.
   UPDATE_CHANGED should be set to true if the changed sbitmap and changed
   count should be updated to reflect the unification.  */

static void
process_unification_queue (constraint_graph_t graph, struct scc_info *si,
			   bool update_changed)
{
  size_t i = 0;
  bitmap tmp = BITMAP_ALLOC (update_changed ? &iteration_obstack : NULL);
  bitmap_clear (tmp);

  /* We proceed as follows:

     For each component in the queue (components are delineated by
     when current_queue_element->node != next_queue_element->node):

        rep = representative node for component

        For each node (tounify) to be unified in the component,
           merge the solution for tounify into tmp bitmap

           clear solution for tounify

           merge edges from tounify into rep

	   merge complex constraints from tounify into rep

	   update changed count to note that tounify will never change
	   again

	Merge tmp into solution for rep, marking rep changed if this
	changed rep's solution.
	
	Delete any 0 weighted self-edges we now have for rep.  */
  while (i != VEC_length (uint, si->unification_queue))
    {
      unsigned int tounify = VEC_index (uint, si->unification_queue, i);
      unsigned int n = get_varinfo (tounify)->node;

      if (dump_file && (dump_flags & TDF_DETAILS))
	fprintf (dump_file, "Unifying %s to %s\n", 
		 get_varinfo (tounify)->name,
		 get_varinfo (n)->name);
      if (update_changed)
	stats.unified_vars_dynamic++;
      else
	stats.unified_vars_static++;
      bitmap_ior_into (tmp, get_varinfo (tounify)->solution);
      merge_graph_nodes (graph, n, tounify);
      condense_varmap_nodes (n, tounify);
      
      if (update_changed && TEST_BIT (changed, tounify))
	{
	  RESET_BIT (changed, tounify);
	  if (!TEST_BIT (changed, n))
	    SET_BIT (changed, n);
	  else
	    {
	      gcc_assert (changed_count > 0);
	      changed_count--;
	    }
	}

      bitmap_clear (get_varinfo (tounify)->solution);
      ++i;

      /* If we've either finished processing the entire queue, or
	 finished processing all nodes for component n, update the solution for
	 n.  */
      if (i == VEC_length (uint, si->unification_queue)
	  || get_varinfo (VEC_index (uint, si->unification_queue, i))->node != n)
	{
	  struct constraint_edge edge;

	  /* If the solution changes because of the merging, we need to mark
	     the variable as changed.  */
	  if (bitmap_ior_into (get_varinfo (n)->solution, tmp))
	    {
	      if (update_changed && !TEST_BIT (changed, n))
		{
		  SET_BIT (changed, n);
		  changed_count++;
		}
	    }
	  bitmap_clear (tmp);
	  edge.src = n;
	  edge.dest = n;
	  if (valid_graph_edge (graph, edge))
	    {
	      bitmap weights = get_graph_weights (graph, edge);
	      bitmap_clear_bit (weights, 0);
	      if (bitmap_empty_p (weights))
		erase_graph_self_edge (graph, edge);
	    }
	}
    }
  BITMAP_FREE (tmp);
}


/* Information needed to compute the topological ordering of a graph.  */

struct topo_info
{
  /* sbitmap of visited nodes.  */
  sbitmap visited;
  /* Array that stores the topological order of the graph, *in
     reverse*.  */
  VEC(uint,heap) *topo_order;
};


/* Initialize and return a topological info structure.  */

static struct topo_info *
init_topo_info (void)
{
  size_t size = VEC_length (varinfo_t, varmap);
  struct topo_info *ti = xmalloc (sizeof (struct topo_info));
  ti->visited = sbitmap_alloc (size);
  sbitmap_zero (ti->visited);
  ti->topo_order = VEC_alloc (uint, heap, 1);
  return ti;
}


/* Free the topological sort info pointed to by TI.  */

static void
free_topo_info (struct topo_info *ti)
{
  sbitmap_free (ti->visited);
  VEC_free (uint, heap, ti->topo_order);
  free (ti);
}

/* Visit the graph in topological order, and store the order in the
   topo_info structure.  */

static void
topo_visit (constraint_graph_t graph, struct topo_info *ti,
	    unsigned int n)
{
  VEC(constraint_edge_t,gc) *succs = graph->succs[n];
  constraint_edge_t c;
  int i;
  SET_BIT (ti->visited, n);
  for (i = 0; VEC_iterate (constraint_edge_t, succs, i, c); i++)
    {
      if (!TEST_BIT (ti->visited, c->dest))
	topo_visit (graph, ti, c->dest);
    }
  VEC_safe_push (uint, heap, ti->topo_order, n);
}

/* Return true if variable N + OFFSET is a legal field of N.  */

static bool 
type_safe (unsigned int n, unsigned HOST_WIDE_INT *offset)
{
  varinfo_t ninfo = get_varinfo (n);

  /* For things we've globbed to single variables, any offset into the
     variable acts like the entire variable, so that it becomes offset
     0.  */
  if (n == anything_id
      || ninfo->is_artificial_var
      || ninfo->is_unknown_size_var)
    {
      *offset = 0;
      return true;
    }
  return n > anything_id 
    && (get_varinfo (n)->offset + *offset) < get_varinfo (n)->fullsize;
}

/* Process a constraint C that represents *x = &y.  */

static void
do_da_constraint (constraint_graph_t graph ATTRIBUTE_UNUSED,
		  constraint_t c, bitmap delta)
{
  unsigned int rhs = c->rhs.var;
  unsigned HOST_WIDE_INT offset = c->lhs.offset;
  unsigned int j;
  bitmap_iterator bi;

  /* For each member j of Delta (Sol(x)), add x to Sol(j)  */
  EXECUTE_IF_SET_IN_BITMAP (delta, 0, j, bi)
    {
      if (type_safe (j, &offset))
	{
	/* *x != NULL && *x != ANYTHING*/
	  varinfo_t v;
	  unsigned int t;
	  bitmap sol;
	  unsigned HOST_WIDE_INT fieldoffset = get_varinfo (j)->offset + offset;
	  v = first_vi_for_offset (get_varinfo (j), fieldoffset);
	  t = v->node;
	  sol = get_varinfo (t)->solution;
	  if (!bitmap_bit_p (sol, rhs))
	    {		  
	      bitmap_set_bit (sol, rhs);
	      if (!TEST_BIT (changed, t))
		{
		  SET_BIT (changed, t);
		  changed_count++;
		}
	    }
	}
      else if (dump_file)
	fprintf (dump_file, "Untypesafe usage in do_da_constraint.\n");
      
    }
}

/* Process a constraint C that represents x = *y, using DELTA as the
   starting solution.  */

static void
do_sd_constraint (constraint_graph_t graph, constraint_t c,
		  bitmap delta)
{
  unsigned int lhs = get_varinfo (c->lhs.var)->node;
  unsigned HOST_WIDE_INT roffset = c->rhs.offset;
  bool flag = false;
  bitmap sol = get_varinfo (lhs)->solution;
  unsigned int j;
  bitmap_iterator bi;
  
  /* For each variable j in delta (Sol(y)), add    
     an edge in the graph from j to x, and union Sol(j) into Sol(x).  */
  EXECUTE_IF_SET_IN_BITMAP (delta, 0, j, bi)
    {
      if (type_safe (j, &roffset))
	{
	  varinfo_t v;
	  unsigned HOST_WIDE_INT fieldoffset = get_varinfo (j)->offset + roffset;
	  unsigned int t;

	  v = first_vi_for_offset (get_varinfo (j), fieldoffset);	  
	  t = v->node;
	  if (int_add_graph_edge (graph, lhs, t, 0))
	    flag |= bitmap_ior_into (sol, get_varinfo (t)->solution);	  
	}
      else if (dump_file)
	fprintf (dump_file, "Untypesafe usage in do_sd_constraint\n");
      
    }

  /* If the LHS solution changed, mark the var as changed.  */
  if (flag)
    {
      get_varinfo (lhs)->solution = sol;
      if (!TEST_BIT (changed, lhs))
	{
	  SET_BIT (changed, lhs);
	  changed_count++;
	}
    }    
}

/* Process a constraint C that represents *x = y.  */

static void
do_ds_constraint (constraint_graph_t graph, constraint_t c, bitmap delta)
{
  unsigned int rhs = get_varinfo (c->rhs.var)->node;
  unsigned HOST_WIDE_INT loff = c->lhs.offset;
  unsigned HOST_WIDE_INT roff = c->rhs.offset;
  bitmap sol = get_varinfo (rhs)->solution;
  unsigned int j;
  bitmap_iterator bi;

  /* For each member j of delta (Sol(x)), add an edge from y to j and
     union Sol(y) into Sol(j) */
  EXECUTE_IF_SET_IN_BITMAP (delta, 0, j, bi)
    {
      if (type_safe (j, &loff))
	{
	  varinfo_t v;
	  unsigned int t;
	  unsigned HOST_WIDE_INT fieldoffset = get_varinfo (j)->offset + loff;

	  v = first_vi_for_offset (get_varinfo (j), fieldoffset);
	  t = v->node;
	  if (int_add_graph_edge (graph, t, rhs, roff))
	    {
	      bitmap tmp = get_varinfo (t)->solution;
	      if (set_union_with_increment (tmp, sol, roff))
		{
		  get_varinfo (t)->solution = tmp;
		  if (t == rhs)
		    {
		      sol = get_varinfo (rhs)->solution;
		    }
		  if (!TEST_BIT (changed, t))
		    {
		      SET_BIT (changed, t);
		      changed_count++;
		    }
		}
	    }
	}    
      else if (dump_file)
	fprintf (dump_file, "Untypesafe usage in do_ds_constraint\n");
    }
}

/* Handle a non-simple (simple meaning requires no iteration), non-copy
   constraint (IE *x = &y, x = *y, and *x = y).  */
   
static void
do_complex_constraint (constraint_graph_t graph, constraint_t c, bitmap delta)
{
  if (c->lhs.type == DEREF)
    {
      if (c->rhs.type == ADDRESSOF)
	{
	  /* *x = &y */
	  do_da_constraint (graph, c, delta);
	}
      else
	{
	  /* *x = y */
	  do_ds_constraint (graph, c, delta);
	}
    }
  else
    {
      /* x = *y */
      do_sd_constraint (graph, c, delta);
    }
}

/* Initialize and return a new SCC info structure.  */

static struct scc_info *
init_scc_info (void)
{
  struct scc_info *si = xmalloc (sizeof (struct scc_info));
  size_t size = VEC_length (varinfo_t, varmap);

  si->current_index = 0;
  si->visited = sbitmap_alloc (size);
  sbitmap_zero (si->visited);
  si->in_component = sbitmap_alloc (size);
  sbitmap_ones (si->in_component);
  si->visited_index = xcalloc (sizeof (unsigned int), size + 1);
  si->scc_stack = VEC_alloc (uint, heap, 1);
  si->unification_queue = VEC_alloc (uint, heap, 1);
  return si;
}

/* Free an SCC info structure pointed to by SI */

static void
free_scc_info (struct scc_info *si)
{  
  sbitmap_free (si->visited);
  sbitmap_free (si->in_component);
  free (si->visited_index);
  VEC_free (uint, heap, si->scc_stack);
  VEC_free (uint, heap, si->unification_queue);
  free(si); 
}


/* Find cycles in GRAPH that occur, using strongly connected components, and
   collapse the cycles into a single representative node.  if UPDATE_CHANGED
   is true, then update the changed sbitmap to note those nodes whose
   solutions have changed as a result of collapsing.  */

static void
find_and_collapse_graph_cycles (constraint_graph_t graph, bool update_changed)
{
  unsigned int i;
  unsigned int size = VEC_length (varinfo_t, varmap);
  struct scc_info *si = init_scc_info ();

  for (i = 0; i != size; ++i)
    if (!TEST_BIT (si->visited, i) && get_varinfo (i)->node == i)
      scc_visit (graph, si, i);
  process_unification_queue (graph, si, update_changed);
  free_scc_info (si);
}

/* Compute a topological ordering for GRAPH, and store the result in the
   topo_info structure TI.  */

static void 
compute_topo_order (constraint_graph_t graph,
		    struct topo_info *ti)
{
  unsigned int i;
  unsigned int size = VEC_length (varinfo_t, varmap);
  
  for (i = 0; i != size; ++i)
    if (!TEST_BIT (ti->visited, i) && get_varinfo (i)->node == i)
      topo_visit (graph, ti, i);
}

/* Return true if bitmap B is empty, or a bitmap other than bit 0 is set. */

static bool
bitmap_other_than_zero_bit_set (bitmap b)
{
  unsigned int i;
  bitmap_iterator bi;

  if (bitmap_empty_p (b))
    return false;
  EXECUTE_IF_SET_IN_BITMAP (b, 1, i, bi)
    return true;
  return false;
}

/* Perform offline variable substitution.
   
   This is a linear time way of identifying variables that must have
   equivalent points-to sets, including those caused by static cycles,
   and single entry subgraphs, in the constraint graph.

   The technique is described in "Off-line variable substitution for
   scaling points-to analysis" by Atanas Rountev and Satish Chandra,
   in "ACM SIGPLAN Notices" volume 35, number 5, pages 47-56.  */

static void
perform_var_substitution (constraint_graph_t graph)
{
  struct topo_info *ti = init_topo_info ();
 
  /* Compute the topological ordering of the graph, then visit each
     node in topological order.  */
  compute_topo_order (graph, ti);
 
  while (VEC_length (uint, ti->topo_order) != 0)
    {
      unsigned int i = VEC_pop (uint, ti->topo_order);
      unsigned int pred;
      varinfo_t vi = get_varinfo (i);
      bool okay_to_elim = false;
      unsigned int root = VEC_length (varinfo_t, varmap);
      VEC(constraint_edge_t,gc) *predvec = graph->preds[i];
      constraint_edge_t ce;
      bitmap tmp;

      /* We can't eliminate things whose address is taken, or which is
	 the target of a dereference.  */
      if (vi->address_taken || vi->indirect_target)
	continue;

      /* See if all predecessors of I are ripe for elimination */
      for (pred = 0; VEC_iterate (constraint_edge_t, predvec, pred, ce); pred++)
	{
	  bitmap weight;
	  unsigned int w;
	  weight = get_graph_weights (graph, *ce);
	
	  /* We can't eliminate variables that have non-zero weighted
	     edges between them.  */
	  if (bitmap_other_than_zero_bit_set (weight))
	    {
	      okay_to_elim = false;
	      break;
	    }
	  w = get_varinfo (ce->dest)->node;

	  /* We can't eliminate the node if one of the predecessors is
	     part of a different strongly connected component.  */
	  if (!okay_to_elim)
	    {
	      root = w;
	      okay_to_elim = true;
	    }
	  else if (w != root)
	    {
	      okay_to_elim = false;
	      break;
	    }

	  /* Theorem 4 in Rountev and Chandra: If i is a direct node,
	     then Solution(i) is a subset of Solution (w), where w is a
	     predecessor in the graph.  
	     Corrolary: If all predecessors of i have the same
	     points-to set, then i has that same points-to set as
	     those predecessors.  */
	  tmp = BITMAP_ALLOC (NULL);
	  bitmap_and_compl (tmp, get_varinfo (i)->solution,
			    get_varinfo (w)->solution);
	  if (!bitmap_empty_p (tmp))
	    {
	      okay_to_elim = false;
	      BITMAP_FREE (tmp);
	      break;
	    }
	  BITMAP_FREE (tmp);
	}

      /* See if the root is different than the original node. 
	 If so, we've found an equivalence.  */
      if (root != get_varinfo (i)->node && okay_to_elim)
	{
	  /* Found an equivalence */
	  get_varinfo (i)->node = root;
	  collapse_nodes (graph, root, i);
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    fprintf (dump_file, "Collapsing %s into %s\n",
		     get_varinfo (i)->name,
		     get_varinfo (root)->name);
	  stats.collapsed_vars++;
	}
    }

  free_topo_info (ti);
}


/* Solve the constraint graph GRAPH using our worklist solver.
   This is based on the PW* family of solvers from the "Efficient Field
   Sensitive Pointer Analysis for C" paper.
   It works by iterating over all the graph nodes, processing the complex
   constraints and propagating the copy constraints, until everything stops
   changed.  This corresponds to steps 6-8 in the solving list given above.  */

static void
solve_graph (constraint_graph_t graph)
{
  unsigned int size = VEC_length (varinfo_t, varmap);
  unsigned int i;

  changed_count = size;
  changed = sbitmap_alloc (size);
  sbitmap_ones (changed);
  
  /* The already collapsed/unreachable nodes will never change, so we
     need to  account for them in changed_count.  */
  for (i = 0; i < size; i++)
    if (get_varinfo (i)->node != i)
      changed_count--;
  
  while (changed_count > 0)
    {
      unsigned int i;
      struct topo_info *ti = init_topo_info ();
      stats.iterations++;
      
      bitmap_obstack_initialize (&iteration_obstack);
      
      if (edge_added)
	{
	  /* We already did cycle elimination once, when we did
	     variable substitution, so we don't need it again for the
	     first iteration.  */
	  if (stats.iterations > 1)
	    find_and_collapse_graph_cycles (graph, true);
	  
	  edge_added = false;
	}

      compute_topo_order (graph, ti);

      while (VEC_length (uint, ti->topo_order) != 0)
	{
	  i = VEC_pop (uint, ti->topo_order);
	  gcc_assert (get_varinfo (i)->node == i);

	  /* If the node has changed, we need to process the
	     complex constraints and outgoing edges again.  */
	  if (TEST_BIT (changed, i))
	    {
	      unsigned int j;
	      constraint_t c;
	      constraint_edge_t e;
	      bitmap solution;
	      VEC(constraint_t,gc) *complex = get_varinfo (i)->complex;
	      VEC(constraint_edge_t,gc) *succs;

	      RESET_BIT (changed, i);
	      changed_count--;

	      /* Process the complex constraints */
	      solution = get_varinfo (i)->solution;
	      for (j = 0; VEC_iterate (constraint_t, complex, j, c); j++)
		do_complex_constraint (graph, c, solution);

	      /* Propagate solution to all successors.  */
	      succs = graph->succs[i];
	      for (j = 0; VEC_iterate (constraint_edge_t, succs, j, e); j++)
		{
		  bitmap tmp = get_varinfo (e->dest)->solution;
		  bool flag = false;
		  unsigned int k;
		  bitmap weights = e->weights;
		  bitmap_iterator bi;

		  gcc_assert (!bitmap_empty_p (weights));
		  EXECUTE_IF_SET_IN_BITMAP (weights, 0, k, bi)
		    flag |= set_union_with_increment (tmp, solution, k);

		  if (flag)
		    {
		      get_varinfo (e->dest)->solution = tmp;		    
		      if (!TEST_BIT (changed, e->dest))
			{
			  SET_BIT (changed, e->dest);
			  changed_count++;
			}
		    }
		}
	    }
	}
      free_topo_info (ti);
      bitmap_obstack_release (&iteration_obstack);
    }

  sbitmap_free (changed);
}


/* CONSTRAINT AND VARIABLE GENERATION FUNCTIONS */

/* Map from trees to variable ids.  */    
static htab_t id_for_tree;

typedef struct tree_id
{
  tree t;
  unsigned int id;
} *tree_id_t;

/* Hash a tree id structure.  */

static hashval_t 
tree_id_hash (const void *p)
{
  const tree_id_t ta = (tree_id_t) p;
  return htab_hash_pointer (ta->t);
}

/* Return true if the tree in P1 and the tree in P2 are the same.  */

static int
tree_id_eq (const void *p1, const void *p2)
{
  const tree_id_t ta1 = (tree_id_t) p1;
  const tree_id_t ta2 = (tree_id_t) p2;
  return ta1->t == ta2->t;
}

/* Insert ID as the variable id for tree T in the hashtable.  */

static void 
insert_id_for_tree (tree t, int id)
{
  void **slot;
  struct tree_id finder;
  tree_id_t new_pair;
  
  finder.t = t;
  slot = htab_find_slot (id_for_tree, &finder, INSERT);
  gcc_assert (*slot == NULL);
  new_pair = xmalloc (sizeof (struct tree_id));
  new_pair->t = t;
  new_pair->id = id;
  *slot = (void *)new_pair;
}

/* Find the variable id for tree T in ID_FOR_TREE.  If T does not
   exist in the hash table, return false, otherwise, return true and
   set *ID to the id we found.  */

static bool
lookup_id_for_tree (tree t, unsigned int *id)
{
  tree_id_t pair;
  struct tree_id finder;

  finder.t = t;
  pair = htab_find (id_for_tree,  &finder);
  if (pair == NULL)
    return false;
  *id = pair->id;
  return true;
}

/* Return a printable name for DECL  */

static const char *
alias_get_name (tree decl)
{
  const char *res = get_name (decl);
  char *temp;
  int num_printed = 0;

  if (res != NULL)
    return res;

  res = "NULL";
  if (TREE_CODE (decl) == SSA_NAME)
    {
      num_printed = asprintf (&temp, "%s_%u", 
			      alias_get_name (SSA_NAME_VAR (decl)),
			      SSA_NAME_VERSION (decl));
    }
  else if (DECL_P (decl))
    {
      num_printed = asprintf (&temp, "D.%u", DECL_UID (decl));
    }
  if (num_printed > 0)
    {
      res = ggc_strdup (temp);
      free (temp);
    }
  return res;
}

/* Find the variable id for tree T in the hashtable.
   If T doesn't exist in the hash table, create an entry for it.  */

static unsigned int
get_id_for_tree (tree t)
{
  tree_id_t pair;
  struct tree_id finder;

  finder.t = t;
  pair = htab_find (id_for_tree,  &finder);
  if (pair == NULL)
    return create_variable_info_for (t, alias_get_name (t));
  
  return pair->id;
}

/* Get a constraint expression from an SSA_VAR_P node.  */

static struct constraint_expr
get_constraint_exp_from_ssa_var (tree t)
{
  struct constraint_expr cexpr;

  gcc_assert (SSA_VAR_P (t) || DECL_P (t));

  /* For parameters, get at the points-to set for the actual parm
     decl.  */
  if (TREE_CODE (t) == SSA_NAME 
      && TREE_CODE (SSA_NAME_VAR (t)) == PARM_DECL 
      && default_def (SSA_NAME_VAR (t)) == t)
    return get_constraint_exp_from_ssa_var (SSA_NAME_VAR (t));

  cexpr.type = SCALAR;
  
  if (TREE_READONLY (t))
    {
      cexpr.type = ADDRESSOF;
      cexpr.var = readonly_id;
    }
  else
    cexpr.var = get_id_for_tree (t);    
    
  cexpr.offset = 0;
  return cexpr;
}

/* Process a completed constraint T, and add it to the constraint
   list.  */

static void
process_constraint (constraint_t t)
{
  struct constraint_expr rhs = t->rhs;
  struct constraint_expr lhs = t->lhs;
  
  gcc_assert (rhs.var < VEC_length (varinfo_t, varmap));
  gcc_assert (lhs.var < VEC_length (varinfo_t, varmap));

  /* ANYTHING == ANYTHING is pointless.  */
  if (lhs.var == anything_id && rhs.var == anything_id)
    return;

  /* If we have &ANYTHING = something, convert to SOMETHING = &ANYTHING) */
  else if (lhs.var == anything_id && lhs.type == ADDRESSOF)
    {
      rhs = t->lhs;
      t->lhs = t->rhs;
      t->rhs = rhs;
      process_constraint (t);
    }   
  /* This can happen in our IR with things like n->a = *p */
  else if (rhs.type == DEREF && lhs.type == DEREF && rhs.var != anything_id)
    {
      /* Split into tmp = *rhs, *lhs = tmp */
      tree rhsdecl = get_varinfo (rhs.var)->decl;
      tree pointertype = TREE_TYPE (rhsdecl);
      tree pointedtotype = TREE_TYPE (pointertype);
      tree tmpvar = create_tmp_var_raw (pointedtotype, "doubledereftmp");
      struct constraint_expr tmplhs = get_constraint_exp_from_ssa_var (tmpvar);
      
      /* If this is an aggregate of known size, we should have passed
	 this off to do_structure_copy, and it should have broken it
	 up.  */
      gcc_assert (!AGGREGATE_TYPE_P (pointedtotype) 
		  || get_varinfo (rhs.var)->is_unknown_size_var);
      
      process_constraint (new_constraint (tmplhs, rhs));
      process_constraint (new_constraint (lhs, tmplhs));
    }
  else if (rhs.type == ADDRESSOF)
    {
      varinfo_t vi;
      gcc_assert (rhs.offset == 0);
      
      for (vi = get_varinfo (rhs.var); vi != NULL; vi = vi->next)
	vi->address_taken = true;

      VEC_safe_push (constraint_t, gc, constraints, t);
    }
  else
    {
      if (lhs.type != DEREF && rhs.type == DEREF)
	get_varinfo (lhs.var)->indirect_target = true;
      VEC_safe_push (constraint_t, gc, constraints, t);
    }
}


/* Return the position, in bits, of FIELD_DECL from the beginning of its
   structure.  */

static unsigned HOST_WIDE_INT
bitpos_of_field (const tree fdecl)
{

  if (TREE_CODE (DECL_FIELD_OFFSET (fdecl)) != INTEGER_CST
      || TREE_CODE (DECL_FIELD_BIT_OFFSET (fdecl)) != INTEGER_CST)
    return -1;
  
  return (tree_low_cst (DECL_FIELD_OFFSET (fdecl), 1) * 8) 
         + tree_low_cst (DECL_FIELD_BIT_OFFSET (fdecl), 1);
}


/* Given a COMPONENT_REF T, return the constraint_expr for it.  */

static struct constraint_expr
get_constraint_for_component_ref (tree t)
{
  struct constraint_expr result;
  HOST_WIDE_INT bitsize;
  HOST_WIDE_INT bitpos;
  tree offset;
  enum machine_mode mode;
  int unsignedp;
  int volatilep;
  tree forzero;
  
  result.offset = 0;
  result.type = SCALAR;
  result.var = 0;

  /* Some people like to do cute things like take the address of
     &0->a.b */
  forzero = t;
  while (!SSA_VAR_P (forzero) && !CONSTANT_CLASS_P (forzero))
      forzero = TREE_OPERAND (forzero, 0);

  if (CONSTANT_CLASS_P (forzero) && integer_zerop (forzero)) 
    {
      result.offset = 0;
      result.var = integer_id;
      result.type = SCALAR;
      return result;
    }
 
  t = get_inner_reference (t, &bitsize, &bitpos, &offset, &mode,
			   &unsignedp, &volatilep, false);
  result = get_constraint_for (t);

  /* This can also happen due to weird offsetof type macros.  */
  if (TREE_CODE (t) != ADDR_EXPR && result.type == ADDRESSOF)
    result.type = SCALAR;
  
  /* If we know where this goes, then yay. Otherwise, booo. */

  if (offset == NULL && bitsize != -1)
    {
      result.offset = bitpos;
    }	
  else
    {
      result.var = anything_id;
      result.offset = 0;      
    }

  if (result.type == SCALAR)
    {
      /* In languages like C, you can access one past the end of an
	 array.  You aren't allowed to dereference it, so we can
	 ignore this constraint. When we handle pointer subtraction,
	 we may have to do something cute here.  */
      
      if (result.offset < get_varinfo (result.var)->fullsize)	
	result.var = first_vi_for_offset (get_varinfo (result.var), 
					  result.offset)->id;
      else
	if (dump_file && (dump_flags & TDF_DETAILS))
	  fprintf (dump_file, "Access to past the end of variable, ignoring\n");

      result.offset = 0;
    }
  
  return result;
}


/* Dereference the constraint expression CONS, and return the result.
   DEREF (ADDRESSOF) = SCALAR
   DEREF (SCALAR) = DEREF
   DEREF (DEREF) = (temp = DEREF1; result = DEREF(temp))
   This is needed so that we can handle dereferencing DEREF constraints.  */

static struct constraint_expr
do_deref (struct constraint_expr cons)
{
  if (cons.type == SCALAR)
    {
      cons.type = DEREF;
      return cons;
    }
  else if (cons.type == ADDRESSOF)
    {
      cons.type = SCALAR;
      return cons;
    }
  else if (cons.type == DEREF)
    {
      tree tmpvar = create_tmp_var_raw (ptr_type_node, "derefmp");
      struct constraint_expr tmplhs = get_constraint_exp_from_ssa_var (tmpvar);
      process_constraint (new_constraint (tmplhs, cons));
      cons.var = tmplhs.var;
      return cons;
    }
  gcc_unreachable ();
}


/* Given a tree T, return the constraint expression for it.  */

static struct constraint_expr
get_constraint_for (tree t)
{
  struct constraint_expr temp;

  /* x = integer is all glommed to a single variable, which doesn't
     point to anything by itself.  That is, of course, unless it is an
     integer constant being treated as a pointer, in which case, we
     will return that this is really the addressof anything.  This
     happens below, since it will fall into the default case. The only
     case we know something about an integer treated like a pointer is
     when it is the NULL pointer, and then we just say it points to
     NULL.  */
  if (TREE_CODE (t) == INTEGER_CST
      && !POINTER_TYPE_P (TREE_TYPE (t)))
    {
      temp.var = integer_id;
      temp.type = SCALAR;
      temp.offset = 0;
      return temp;
    }
  else if (TREE_CODE (t) == INTEGER_CST
	   && integer_zerop (t))
    {
      temp.var = nothing_id;
      temp.type = ADDRESSOF;
      temp.offset = 0;
      return temp;
    }

  switch (TREE_CODE_CLASS (TREE_CODE (t)))
    {
    case tcc_expression:
      {
	switch (TREE_CODE (t))
	  {
	  case ADDR_EXPR:
	    {
	      temp = get_constraint_for (TREE_OPERAND (t, 0));
	       if (temp.type == DEREF)
		 temp.type = SCALAR;
	       else
		 temp.type = ADDRESSOF;
	      return temp;
	    }
	    break;
	  case CALL_EXPR:
	    
	    /* XXX: In interprocedural mode, if we didn't have the
	       body, we would need to do *each pointer argument =
	       &ANYTHING added.  */
	    if (call_expr_flags (t) & (ECF_MALLOC | ECF_MAY_BE_ALLOCA))
	      {
		tree heapvar = create_tmp_var_raw (ptr_type_node, "HEAP");
		temp.var = create_variable_info_for (heapvar,
						     alias_get_name (heapvar));
		
		get_varinfo (temp.var)->is_artificial_var = 1;
		temp.type = ADDRESSOF;
		temp.offset = 0;
		return temp;
	      }
	    /* FALLTHRU */
	  default:
	    {
	      temp.type = ADDRESSOF;
	      temp.var = anything_id;
	      temp.offset = 0;
	      return temp;
	    }
	  }
      }
    case tcc_reference:
      {
	switch (TREE_CODE (t))
	  {
	  case INDIRECT_REF:
	    {
	      temp = get_constraint_for (TREE_OPERAND (t, 0));
	      temp = do_deref (temp);
	      return temp;
	    }
	  case ARRAY_REF:
	  case COMPONENT_REF:
	    temp = get_constraint_for_component_ref (t);
	    return temp;
	  default:
	    {
	      temp.type = ADDRESSOF;
	      temp.var = anything_id;
	      temp.offset = 0;
	      return temp;
	    }
	  }
      }
    case tcc_unary:
      {
	switch (TREE_CODE (t))
	  {
	  case NOP_EXPR:
	  case CONVERT_EXPR:
	  case NON_LVALUE_EXPR:
	    {
	      tree op = TREE_OPERAND (t, 0);
	      
	      /* Cast from non-pointer to pointers are bad news for us.
		 Anything else, we see through */
	      if (!(POINTER_TYPE_P (TREE_TYPE (t))  &&
		    ! POINTER_TYPE_P (TREE_TYPE (op))))
		return get_constraint_for (op);
	    }
	  default:
	    {
	      temp.type = ADDRESSOF;
	      temp.var = anything_id;
	      temp.offset = 0;
	      return temp;
	    }
	  }
      }
    case tcc_exceptional:
      {
	switch (TREE_CODE (t))
	  {
	  case PHI_NODE:	   
	    return get_constraint_for (PHI_RESULT (t));
	  case SSA_NAME:
	    return get_constraint_exp_from_ssa_var (t);
	  default:
	    {
	      temp.type = ADDRESSOF;
	      temp.var = anything_id;
	      temp.offset = 0;
	      return temp;
	    }
	  }
      }
    case tcc_declaration:
      return get_constraint_exp_from_ssa_var (t);
    default:
      {
	temp.type = ADDRESSOF;
	temp.var = anything_id;
	temp.offset = 0;
	return temp;
      }
    }
}


/* Handle the structure copy case where we have a simple structure copy
   between LHS and RHS that is of SIZE (in bits) 
  
   For each field of the lhs variable (lhsfield)
     For each field of the rhs variable at lhsfield.offset (rhsfield)
       add the constraint lhsfield = rhsfield
*/

static void
do_simple_structure_copy (const struct constraint_expr lhs,
			  const struct constraint_expr rhs,
			  const unsigned HOST_WIDE_INT size)
{
  varinfo_t p = get_varinfo (lhs.var);
  unsigned HOST_WIDE_INT pstart,last;

  pstart = p->offset;
  last = p->offset + size;
  for (; p && p->offset < last; p = p->next)
    {
      varinfo_t q;
      struct constraint_expr templhs = lhs;
      struct constraint_expr temprhs = rhs;
      unsigned HOST_WIDE_INT fieldoffset;

      templhs.var = p->id;            
      q = get_varinfo (temprhs.var);
      fieldoffset = p->offset - pstart;
      q = first_vi_for_offset (q, q->offset + fieldoffset);
      temprhs.var = q->id;
      process_constraint (new_constraint (templhs, temprhs));
    }
}


/* Handle the structure copy case where we have a  structure copy between a
   aggregate on the LHS and a dereference of a pointer on the RHS
   that is of SIZE (in bits) 
  
   For each field of the lhs variable (lhsfield)
       rhs.offset = lhsfield->offset
       add the constraint lhsfield = rhs
*/

static void
do_rhs_deref_structure_copy (const struct constraint_expr lhs,
			     const struct constraint_expr rhs,
			     const unsigned HOST_WIDE_INT size)
{
  varinfo_t p = get_varinfo (lhs.var);
  unsigned HOST_WIDE_INT pstart,last;
  pstart = p->offset;
  last = p->offset + size;

  for (; p && p->offset < last; p = p->next)
    {
      varinfo_t q;
      struct constraint_expr templhs = lhs;
      struct constraint_expr temprhs = rhs;
      unsigned HOST_WIDE_INT fieldoffset;


      if (templhs.type == SCALAR)
	templhs.var = p->id;      
      else
	templhs.offset = p->offset;
      
      q = get_varinfo (temprhs.var);
      fieldoffset = p->offset - pstart;      
      temprhs.offset += fieldoffset;
      process_constraint (new_constraint (templhs, temprhs));
    }
}

/* Handle the structure copy case where we have a structure copy
   between a aggregate on the RHS and a dereference of a pointer on
   the LHS that is of SIZE (in bits) 

   For each field of the rhs variable (rhsfield)
       lhs.offset = rhsfield->offset
       add the constraint lhs = rhsfield
*/

static void
do_lhs_deref_structure_copy (const struct constraint_expr lhs,
			     const struct constraint_expr rhs,
			     const unsigned HOST_WIDE_INT size)
{
  varinfo_t p = get_varinfo (rhs.var);
  unsigned HOST_WIDE_INT pstart,last;
  pstart = p->offset;
  last = p->offset + size;

  for (; p && p->offset < last; p = p->next)
    {
      varinfo_t q;
      struct constraint_expr templhs = lhs;
      struct constraint_expr temprhs = rhs;
      unsigned HOST_WIDE_INT fieldoffset;


      if (temprhs.type == SCALAR)
	temprhs.var = p->id;      
      else
	temprhs.offset = p->offset;
      
      q = get_varinfo (templhs.var);
      fieldoffset = p->offset - pstart;      
      templhs.offset += fieldoffset;
      process_constraint (new_constraint (templhs, temprhs));
    }
}


/* Handle aggregate copies by expanding into copies of the respective
   fields of the structures.  */

static void
do_structure_copy (tree lhsop, tree rhsop)
{
  struct constraint_expr lhs, rhs, tmp;
  varinfo_t p;
  unsigned HOST_WIDE_INT lhssize;
  unsigned HOST_WIDE_INT rhssize;

  lhssize = TREE_INT_CST_LOW (TYPE_SIZE (TREE_TYPE (lhsop)));
  rhssize = TREE_INT_CST_LOW (TYPE_SIZE (TREE_TYPE (rhsop)));
  lhs = get_constraint_for (lhsop);  
  rhs = get_constraint_for (rhsop);
  
  /* If we have special var = x, swap it around.  */
  if (lhs.var <= integer_id && rhs.var > integer_id)
    {
      tmp = lhs;
      lhs = rhs;
      rhs = tmp;
    }
  
  /* If the RHS is a special var, set all the LHS fields to that
     special var.  */
  if (rhs.var <= integer_id)
    {
      for (p = get_varinfo (lhs.var); p; p = p->next)
	{
	  struct constraint_expr templhs = lhs;
	  struct constraint_expr temprhs = rhs;
	  if (templhs.type == SCALAR )
	    templhs.var = p->id;
	  else
	    templhs.offset += p->offset;
	  process_constraint (new_constraint (templhs, temprhs));
	}
    }
  else
    {
      if (rhs.type == SCALAR && lhs.type == SCALAR)  
	do_simple_structure_copy (lhs, rhs, MIN (lhssize, rhssize));
      else if (lhs.type != DEREF && rhs.type == DEREF)
	do_rhs_deref_structure_copy (lhs, rhs, MIN (lhssize, rhssize));
      else if (lhs.type == DEREF && rhs.type != DEREF)
	do_lhs_deref_structure_copy (lhs, rhs, MIN (lhssize, rhssize));
      else
	{
	  tree rhsdecl = get_varinfo (rhs.var)->decl;
	  tree pointertype = TREE_TYPE (rhsdecl);
	  tree pointedtotype = TREE_TYPE (pointertype);
	  tree tmpvar;
	  gcc_assert (rhs.type == DEREF && lhs.type == DEREF);
	  tmpvar = create_tmp_var_raw (pointedtotype, "structcopydereftmp");
	  lhs = get_constraint_for (tmpvar);
	  do_rhs_deref_structure_copy (lhs, rhs, MIN (lhssize, rhssize));
	  rhs = lhs;
	  lhs = get_constraint_for (lhsop);
	  do_lhs_deref_structure_copy (lhs, rhs, MIN (lhssize, rhssize));
	}
    }
}


/* Return true if REF, a COMPONENT_REF, has an INDIRECT_REF somewhere
   in it.  */

static inline bool
ref_contains_indirect_ref (tree ref)
{
  while (handled_component_p (ref))
    {
      if (TREE_CODE (ref) == INDIRECT_REF)
	return true;
      ref = TREE_OPERAND (ref, 0);
    }
  return false;
}


/*  Tree walker that is the heart of the aliasing infrastructure.
    TP is a pointer to the current tree.
    WALK_SUBTREES specifies whether to continue traversing subtrees or
    not.
    Returns NULL_TREE when we should stop.
    
    This function is the main part of the constraint builder. It
    walks the trees, calling the appropriate building functions
    to process various statements.  */

static void
find_func_aliases (tree t)
{
  struct constraint_expr lhs, rhs;
  switch (TREE_CODE (t))
    {      
    case PHI_NODE:
      {
	int i;

	/* Only care about pointers and structures containing
	   pointers.  */
	if (POINTER_TYPE_P (TREE_TYPE (PHI_RESULT (t)))
	    || AGGREGATE_TYPE_P (TREE_TYPE (PHI_RESULT (t))))
	  {
	    lhs = get_constraint_for (PHI_RESULT (t));
	    for (i = 0; i < PHI_NUM_ARGS (t); i++)
	      {
		rhs = get_constraint_for (PHI_ARG_DEF (t, i));
		process_constraint (new_constraint (lhs, rhs));
	      }
	  }
      }
      break;

    case MODIFY_EXPR:
      {
	tree lhsop = TREE_OPERAND (t, 0);
	tree rhsop = TREE_OPERAND (t, 1);
	int i;	

	if (AGGREGATE_TYPE_P (TREE_TYPE (lhsop)) 
	    && AGGREGATE_TYPE_P (TREE_TYPE (rhsop)))
	  {
	    do_structure_copy (lhsop, rhsop);
	  }
	else
	  {
	    /* Only care about operations with pointers, structures
	       containing pointers, dereferences, and call
	       expressions.  */
	    if (POINTER_TYPE_P (TREE_TYPE (lhsop))
		|| AGGREGATE_TYPE_P (TREE_TYPE (lhsop))
		|| ref_contains_indirect_ref (lhsop)
		|| TREE_CODE (rhsop) == CALL_EXPR)
	      {
		lhs = get_constraint_for (lhsop);
		switch (TREE_CODE_CLASS (TREE_CODE (rhsop)))
		  {
		    /* RHS that consist of unary operations,
		       exceptional types, or bare decls/constants, get
		       handled directly by get_constraint_for.  */ 
		  case tcc_reference:
		  case tcc_declaration:
		  case tcc_constant:
		  case tcc_exceptional:
		  case tcc_expression:
		  case tcc_unary:
		    {
		      rhs = get_constraint_for (rhsop);
		      process_constraint (new_constraint (lhs, rhs));
		    }
		    break;

		    /* Otherwise, walk each operand.  */
		  default:
		    for (i = 0; i < TREE_CODE_LENGTH (TREE_CODE (rhsop)); i++)
		      {
			tree op = TREE_OPERAND (rhsop, i);
			rhs = get_constraint_for (op);
			process_constraint (new_constraint (lhs, rhs));
		      }
		  }      
	      }
	  }
      }
      break;

    default:
      break;
    }
}


/* Find the first varinfo in the same variable as START that overlaps with
   OFFSET.
   Effectively, walk the chain of fields for the variable START to find the
   first field that overlaps with OFFSET.
   Abort if we can't find one.  */

static varinfo_t 
first_vi_for_offset (varinfo_t start, unsigned HOST_WIDE_INT offset)
{
  varinfo_t curr = start;
  while (curr)
    {
      /* We may not find a variable in the field list with the actual
	 offset when when we have glommed a structure to a variable.
	 In that case, however, offset should still be within the size
	 of the variable. */
      if (offset >= curr->offset && offset < (curr->offset +  curr->size))
	return curr;
      curr = curr->next;
    }

  gcc_unreachable ();
}


/* Insert the varinfo FIELD into the field list for BASE, ordered by
   offset.  */

static void
insert_into_field_list (varinfo_t base, varinfo_t field)
{
  varinfo_t prev = base;
  varinfo_t curr = base->next;
  
  if (curr == NULL)
    {
      prev->next = field;
      field->next = NULL;
    }
  else
    {
      while (curr)
	{
	  if (field->offset <= curr->offset)
	    break;
	  prev = curr;
	  curr = curr->next;
	}
      field->next = prev->next;
      prev->next = field;
    }
}

/* qsort comparison function for two fieldoff's PA and PB */

static int 
fieldoff_compare (const void *pa, const void *pb)
{
  const fieldoff_s *foa = (const fieldoff_s *)pa;
  const fieldoff_s *fob = (const fieldoff_s *)pb;
  HOST_WIDE_INT foasize, fobsize;
  
  if (foa->offset != fob->offset)
    return foa->offset - fob->offset;

  foasize = TREE_INT_CST_LOW (DECL_SIZE (foa->field));
  fobsize = TREE_INT_CST_LOW (DECL_SIZE (fob->field));
  return foasize - fobsize;
}

/* Sort a fieldstack according to the field offset and sizes.  */
void sort_fieldstack (VEC(fieldoff_s,heap) *fieldstack)
{
  qsort (VEC_address (fieldoff_s, fieldstack), 
	 VEC_length (fieldoff_s, fieldstack), 
	 sizeof (fieldoff_s),
	 fieldoff_compare);
}

/* Given a TYPE, and a vector of field offsets FIELDSTACK, push all the fields
   of TYPE onto fieldstack, recording their offsets along the way.
   OFFSET is used to keep track of the offset in this entire structure, rather
   than just the immediately containing structure.  Returns the number
   of fields pushed.
   HAS_UNION is set to true if we find a union type as a field of
   TYPE.  */

int
push_fields_onto_fieldstack (tree type, VEC(fieldoff_s,heap) **fieldstack, 
			     HOST_WIDE_INT offset, bool *has_union)
{
  tree field;
  int count = 0;

  for (field = TYPE_FIELDS (type); field; field = TREE_CHAIN (field))
    if (TREE_CODE (field) == FIELD_DECL)
      {
	bool push = false;
	
	if (has_union 
	    && (TREE_CODE (TREE_TYPE (field)) == QUAL_UNION_TYPE
		|| TREE_CODE (TREE_TYPE (field)) == UNION_TYPE))
	  *has_union = true;
	
	if (!var_can_have_subvars (field))
	  push = true;
	else if (!(push_fields_onto_fieldstack
		   (TREE_TYPE (field), fieldstack,
		    offset + bitpos_of_field (field), has_union))
		 && DECL_SIZE (field)
		 && !integer_zerop (DECL_SIZE (field)))
	  /* Empty structures may have actual size, like in C++. So
	     see if we didn't push any subfields and the size is
	     nonzero, push the field onto the stack */
	  push = true;
	
	if (push)
	  {
	    fieldoff_s *pair;

	    pair = VEC_safe_push (fieldoff_s, heap, *fieldstack, NULL);
	    pair->field = field;
	    pair->offset = offset + bitpos_of_field (field);
	    count++;
	  }
      }

  return count;
}

static void
make_constraint_to_anything (varinfo_t vi)
{
  struct constraint_expr lhs, rhs;
  
  lhs.var = vi->id;
  lhs.offset = 0;
  lhs.type = SCALAR;
  
  rhs.var = anything_id;
  rhs.offset =0 ;
  rhs.type = ADDRESSOF;
  process_constraint (new_constraint (lhs, rhs));
}

/* Create a varinfo structure for NAME and DECL, and add it to VARMAP.
   This will also create any varinfo structures necessary for fields
   of DECL.  */

static unsigned int
create_variable_info_for (tree decl, const char *name)
{
  unsigned int index = VEC_length (varinfo_t, varmap);
  varinfo_t vi;
  tree decltype = TREE_TYPE (decl);
  bool notokay = false;
  bool hasunion;
  subvar_t svars;
  bool is_global = DECL_P (decl) ? is_global_var (decl) : false;
  VEC (fieldoff_s,heap) *fieldstack = NULL;
  

  hasunion = TREE_CODE (decltype) == UNION_TYPE || TREE_CODE (decltype) == QUAL_UNION_TYPE;
  if (var_can_have_subvars (decl) && use_field_sensitive && !hasunion)
    {
      push_fields_onto_fieldstack (decltype, &fieldstack, 0, &hasunion);
      if (hasunion)
	{
	  VEC_free (fieldoff_s, heap, fieldstack);
	  notokay = true;
	}	 
    }

  /* If this variable already has subvars, just create the variables for the
     subvars and we are done.
     NOTE: This assumes things haven't generated uses of previously
     unused structure fields.  */
  if (use_field_sensitive 
      && !notokay 
      && var_can_have_subvars (decl) 
      && var_ann (decl)      
      && (svars = get_subvars_for_var (decl)))
    {
      subvar_t sv;
      varinfo_t base = NULL;
      unsigned int firstindex = index;

      for (sv = svars; sv; sv = sv->next)
	{
	  /* For debugging purposes, this will print the names of the
	     fields as "<var>.<offset>.<size>"
	     This is only for debugging purposes.  */
#define PRINT_LONG_NAMES
#ifdef PRINT_LONG_NAMES
	  char *tempname;
	  const char *newname;

	  asprintf (&tempname,
	            "%s." HOST_WIDE_INT_PRINT_DEC "." HOST_WIDE_INT_PRINT_DEC,
		    alias_get_name (decl), sv->offset, sv->size);
	  newname = ggc_strdup (tempname);
	  free (tempname);
	  vi = new_var_info (sv->var, index, newname, index);
#else
	  vi = new_var_info (sv->var, index, alias_get_name (sv->var), index);
#endif
	  vi->decl = sv->var;
	  vi->fullsize = TREE_INT_CST_LOW (TYPE_SIZE (decltype));
	  vi->size = sv->size;
	  vi->offset = sv->offset;
	  if (!base)
	    {
	      base = vi;
	      insert_id_for_tree (decl, index);
	    }
	  else
	    {
	      insert_into_field_list (base, vi);
	    }
	  insert_id_for_tree (sv->var, index);  
	  VEC_safe_push (varinfo_t, gc, varmap, vi);
	  if (is_global)
	    make_constraint_to_anything (vi);
	  index++;
	  
	}
      return firstindex;
    }
  

  /* If the variable doesn't have subvars, we may end up needing to
     sort the field list and create fake variables for all the
     fields.  */
  vi = new_var_info (decl, index, name, index);
  vi->decl = decl;
  vi->offset = 0;
  vi->has_union = hasunion;
  if (!TYPE_SIZE (decltype) 
      || TREE_CODE (TYPE_SIZE  (decltype)) != INTEGER_CST
      || TREE_CODE (decltype) == ARRAY_TYPE
      || TREE_CODE (decltype) == UNION_TYPE
      || TREE_CODE (decltype) == QUAL_UNION_TYPE)
    {
      vi->is_unknown_size_var = true;
      vi->fullsize = ~0;
      vi->size = ~0;
    }
  else
    {
      vi->fullsize = TREE_INT_CST_LOW (TYPE_SIZE (decltype));
      vi->size = vi->fullsize;
    }
  
  insert_id_for_tree (vi->decl, index);  
  VEC_safe_push (varinfo_t, gc, varmap, vi);
  if (is_global)
    make_constraint_to_anything (vi);

  stats.total_vars++;
  if (use_field_sensitive 
      && !notokay 
      && !vi->is_unknown_size_var 
      && var_can_have_subvars (decl))
    {
      unsigned int newindex = VEC_length (varinfo_t, varmap);
      fieldoff_s *fo = NULL;
      unsigned int i;
      tree field;

      for (i = 0; !notokay && VEC_iterate (fieldoff_s, fieldstack, i, fo); i++)
	{
	  if (!DECL_SIZE (fo->field) 
	      || TREE_CODE (DECL_SIZE (fo->field)) != INTEGER_CST
	      || TREE_CODE (TREE_TYPE (fo->field)) == ARRAY_TYPE
	      || fo->offset < 0)
	    {
	      notokay = true;
	      break;
	    }
	}

      /* We can't sort them if we have a field with a variable sized type,
	 which will make notokay = true.  In that case, we are going to return
	 without creating varinfos for the fields anyway, so sorting them is a
	 waste to boot.  */
      if (!notokay)	
	sort_fieldstack (fieldstack);
      
      if (VEC_length (fieldoff_s, fieldstack) != 0)
	fo = VEC_index (fieldoff_s, fieldstack, 0);

      if (fo == NULL || notokay)
	{
	  vi->is_unknown_size_var = 1;
	  vi->fullsize = ~0;
	  vi->size = ~0;
	  VEC_free (fieldoff_s, heap, fieldstack);
	  return index;
	}
      
      field = fo->field;
      gcc_assert (bitpos_of_field (field) == 0);
      vi->size = TREE_INT_CST_LOW (DECL_SIZE (field));
      for (i = 1; VEC_iterate (fieldoff_s, fieldstack, i, fo); i++)
	{
	  varinfo_t newvi;
	  const char *newname;
	  char *tempname;

	  field = fo->field;
	  newindex = VEC_length (varinfo_t, varmap);
	  asprintf (&tempname, "%s.%s", vi->name, alias_get_name (field));
	  newname = ggc_strdup (tempname);
	  free (tempname);
	  newvi = new_var_info (decl, newindex, newname, newindex);
	  newvi->offset = fo->offset;
	  newvi->size = TREE_INT_CST_LOW (DECL_SIZE (field));
	  newvi->fullsize = vi->fullsize;
	  insert_into_field_list (vi, newvi);
	  VEC_safe_push (varinfo_t, gc, varmap, newvi);
	  if (is_global)
	    make_constraint_to_anything (newvi);

	  stats.total_vars++;	  
	}
      VEC_free (fieldoff_s, heap, fieldstack);
    }
  return index;
}

/* Print out the points-to solution for VAR to FILE.  */

void
dump_solution_for_var (FILE *file, unsigned int var)
{
  varinfo_t vi = get_varinfo (var);
  unsigned int i;
  bitmap_iterator bi; 
  
  fprintf (file, "%s = {", vi->name);
  EXECUTE_IF_SET_IN_BITMAP (get_varinfo (vi->node)->solution, 0, i, bi)
    {
      fprintf (file, "%s,", get_varinfo (i)->name);
    }
  fprintf (file, "}\n");
}

/* Print the points-to solution for VAR to stdout.  */

void
debug_solution_for_var (unsigned int var)
{
  dump_solution_for_var (stdout, var);
}


/* Create varinfo structures for all of the variables in the
   function for intraprocedural mode.  */

static void
intra_create_variable_infos (void)
{
  tree t;

  /* For each incoming argument arg, ARG = &ANYTHING */
  for (t = DECL_ARGUMENTS (current_function_decl); t; t = TREE_CHAIN (t))
    {
      struct constraint_expr lhs;
      struct constraint_expr rhs;
      varinfo_t p;
      
      lhs.offset = 0;
      lhs.type = SCALAR;
      lhs.var  = create_variable_info_for (t, alias_get_name (t));
      
      get_varinfo (lhs.var)->is_artificial_var = true;
      rhs.var = anything_id;
      rhs.type = ADDRESSOF;
      rhs.offset = 0;

      for (p = get_varinfo (lhs.var); p; p = p->next)
	{
	  struct constraint_expr temp = lhs;
	  temp.var = p->id;
	  process_constraint (new_constraint (temp, rhs));
	}
    }	

}

/* Set bits in INTO corresponding to the variable uids in solution set
   FROM  */

static void
set_uids_in_ptset (bitmap into, bitmap from)
{
  unsigned int i;
  bitmap_iterator bi;

  EXECUTE_IF_SET_IN_BITMAP (from, 0, i, bi)
    {
      varinfo_t vi = get_varinfo (i);
      
      /* Variables containing unions may need to be converted to their 
	 SFT's, because SFT's can have unions and we cannot.  */
      if (vi->has_union && get_subvars_for_var (vi->decl) != NULL)
	{
	  subvar_t svars = get_subvars_for_var (vi->decl);
	  subvar_t sv;
	  for (sv = svars; sv; sv = sv->next)
	    bitmap_set_bit (into, var_ann (sv->var)->uid);    
	}
      /* We may end up with labels in the points-to set because people
	 take their address, and they are _DECL's.  */
      else if (TREE_CODE (vi->decl) == VAR_DECL 
	  || TREE_CODE (vi->decl) == PARM_DECL)
	bitmap_set_bit (into, var_ann (vi->decl)->uid);

	  
    }
}
static int have_alias_info = false;

/* Given a pointer variable P, fill in its points-to set, or return
   false if we can't.  */

bool
find_what_p_points_to (tree p)
{
  unsigned int id = 0;
  if (!have_alias_info)
    return false;
  if (lookup_id_for_tree (p, &id))
    {
      varinfo_t vi = get_varinfo (id);
      
      if (vi->is_artificial_var)
	return false;

      /* See if this is a field or a structure */
      if (vi->size != vi->fullsize)
	{
	  if (!var_can_have_subvars (vi->decl)
	      || get_subvars_for_var (vi->decl) == NULL)
	    return false;
	  /* Nothing currently asks about structure fields directly, but when
	     they do, we need code here to hand back the points-to set.  */
	} 
      else
	{
	  struct ptr_info_def *pi = get_ptr_info (p);
	  unsigned int i;
	  bitmap_iterator bi;

	  /* This variable may have been collapsed, let's get the real
	     variable.  */
	  vi = get_varinfo (vi->node);
	  
	  /* Make sure there aren't any artificial vars in the points to set.
             XXX: Note that we need to translate our heap variables to
             something.  */
	  EXECUTE_IF_SET_IN_BITMAP (vi->solution, 0, i, bi)
	    {
	      if (get_varinfo (i)->is_artificial_var)
		return false;
	    }
	  pi->pt_anything = false;
	  if (!pi->pt_vars)
	    pi->pt_vars = BITMAP_GGC_ALLOC ();
	  set_uids_in_ptset (pi->pt_vars, vi->solution);
	  return true;
	}
    }
  return false;
}

/* Initialize things necessary to perform PTA */

static void
init_alias_vars (void)
{
  bitmap_obstack_initialize (&ptabitmap_obstack);
}

/* Dump the points-to information to OUTFILE.  */

static void
dump_sa_points_to_info (FILE *outfile)
{
  
  unsigned int i;
  if (dump_flags & TDF_STATS)
    {
      fprintf (outfile, "Stats:\n");
      fprintf (outfile, "Total vars:%d\n", stats.total_vars);
      fprintf (outfile, "Statically unified vars:%d\n", stats.unified_vars_static);
      fprintf (outfile, "Collapsed vars:%d\n", stats.collapsed_vars);
      fprintf (outfile, "Dynamically unified vars:%d\n", stats.unified_vars_dynamic);
      fprintf (outfile, "Iterations:%d\n", stats.iterations);
    }
  for (i = 0; i < VEC_length (varinfo_t, varmap); i++)
    dump_solution_for_var (outfile, i);
}


/* Initialize the always-existing constraint variables for NULL
   ANYTHING, READONLY, and INTEGER */

static void
init_base_vars (void)
{
  struct constraint_expr lhs, rhs;

  /* Create the NULL variable, used to represent that a variable points
     to NULL.  */
  nothing_tree = create_tmp_var_raw (void_type_node, "NULL");
  var_nothing = new_var_info (nothing_tree, 0, "NULL", 0);
  insert_id_for_tree (nothing_tree, 0);
  var_nothing->is_artificial_var = 1;
  var_nothing->offset = 0;
  var_nothing->size = ~0;
  var_nothing->fullsize = ~0;
  nothing_id = 0;
  VEC_safe_push (varinfo_t, gc, varmap, var_nothing);

  /* Create the ANYTHING variable, used to represent that a variable
     points to some unknown piece of memory.  */
  anything_tree = create_tmp_var_raw (void_type_node, "ANYTHING");
  var_anything = new_var_info (anything_tree, 1, "ANYTHING", 1); 
  insert_id_for_tree (anything_tree, 1);
  var_anything->is_artificial_var = 1;
  var_anything->size = ~0;
  var_anything->offset = 0;
  var_anything->next = NULL;
  var_anything->fullsize = ~0;
  anything_id = 1;

  /* Anything points to anything.  This makes deref constraints just
     work in the presence of linked list and other p = *p type loops, 
     by saying that *ANYTHING = ANYTHING. */
  VEC_safe_push (varinfo_t, gc, varmap, var_anything);
  lhs.type = SCALAR;
  lhs.var = anything_id;
  lhs.offset = 0;
  rhs.type = ADDRESSOF;
  rhs.var = anything_id;
  rhs.offset = 0;
  var_anything->address_taken = true;
  process_constraint (new_constraint (lhs, rhs));

  
  /* Create the READONLY variable, used to represent that a variable
     points to readonly memory.  */
  readonly_tree = create_tmp_var_raw (void_type_node, "READONLY");
  var_readonly = new_var_info (readonly_tree, 2, "READONLY", 2);
  var_readonly->is_artificial_var = 1;
  var_readonly->offset = 0;
  var_readonly->size = ~0;
  var_readonly->fullsize = ~0;
  var_readonly->next = NULL;
  insert_id_for_tree (readonly_tree, 2);
  readonly_id = 2;
  VEC_safe_push (varinfo_t, gc, varmap, var_readonly);

  /* readonly memory points to anything, in order to make deref
     easier.  In reality, it points to anything the particular
     readonly variable can point to, but we don't track this
     seperately. */
  lhs.type = SCALAR;
  lhs.var = readonly_id;
  lhs.offset = 0;
  rhs.type = ADDRESSOF;
  rhs.var = anything_id;
  rhs.offset = 0;
  var_readonly->address_taken = true;
  
  process_constraint (new_constraint (lhs, rhs));
  
  /* Create the INTEGER variable, used to represent that a variable points
     to an INTEGER.  */
  integer_tree = create_tmp_var_raw (void_type_node, "INTEGER");
  var_integer = new_var_info (integer_tree, 3, "INTEGER", 3);
  insert_id_for_tree (integer_tree, 3);
  var_integer->is_artificial_var = 1;
  var_integer->size = ~0;
  var_integer->fullsize = ~0;
  var_integer->offset = 0;
  var_integer->next = NULL;
  integer_id = 3;
  VEC_safe_push (varinfo_t, gc, varmap, var_integer);
}  


/* Create points-to sets for the current function.  See the comments
   at the start of the file for an algorithmic overview.  */

static void
create_alias_vars (void)
{
  basic_block bb;

  
  init_alias_vars ();

  constraint_pool = create_alloc_pool ("Constraint pool", 
				       sizeof (struct constraint), 30);
  variable_info_pool = create_alloc_pool ("Variable info pool",
					  sizeof (struct variable_info), 30);
  constraint_edge_pool = create_alloc_pool ("Constraint edges",
					    sizeof (struct constraint_edge), 30);
  
  constraints = VEC_alloc (constraint_t, gc, 8);
  varmap = VEC_alloc (varinfo_t, gc, 8);
  id_for_tree = htab_create (10, tree_id_hash, tree_id_eq, free);
  memset (&stats, 0, sizeof (stats));
  
  init_base_vars ();

  intra_create_variable_infos ();

  /* Now walk all statements and derive aliases.  */
  FOR_EACH_BB (bb)
    {
      block_stmt_iterator bsi; 
      tree phi;

      for (phi = phi_nodes (bb); phi; phi = TREE_CHAIN (phi))
	if (is_gimple_reg (PHI_RESULT (phi)))
	  find_func_aliases (phi);

      for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
	find_func_aliases (bsi_stmt (bsi));
    }

  build_constraint_graph ();

  if (dump_file)
    {
      fprintf (dump_file, "Constraints:\n");
      dump_constraints (dump_file);
    }

  if (dump_file)
    fprintf (dump_file, "Collapsing static cycles and doing variable substitution:\n");

  find_and_collapse_graph_cycles (graph, false);
  perform_var_substitution (graph);

  if (dump_file)
    fprintf (dump_file, "Solving graph:\n");

  solve_graph (graph);

  if (dump_file)
    dump_sa_points_to_info (dump_file);
  
  have_alias_info = true;
}

struct tree_opt_pass pass_build_pta = 
{
  "pta",				/* name */
  NULL,					/* gate */
  create_alias_vars,			/* execute */
  NULL,					/* sub */
  NULL,					/* next */
  0,					/* static_pass_number */
  TV_TREE_PTA,				/* tv_id */
  PROP_cfg,				/* properties_required */
  PROP_pta,				/* properties_provided */
  0,					/* properties_destroyed */
  0,					/* todo_flags_start */
  0,                                    /* todo_flags_finish */
  0					/* letter */
};
 

/* Delete created points-to sets.  */

static void
delete_alias_vars (void)
{
  htab_delete (id_for_tree);
  free_alloc_pool (variable_info_pool);
  free_alloc_pool (constraint_pool); 
  free_alloc_pool (constraint_edge_pool);
  bitmap_obstack_release (&ptabitmap_obstack);
  have_alias_info = false;
}

struct tree_opt_pass pass_del_pta = 
{
  NULL,                                 /* name */
  NULL,					/* gate */
  delete_alias_vars,			/* execute */
  NULL,					/* sub */
  NULL,					/* next */
  0,					/* static_pass_number */
  TV_TREE_PTA,				/* tv_id */
  PROP_pta,				/* properties_required */
  0,					/* properties_provided */
  PROP_pta,				/* properties_destroyed */
  0,					/* todo_flags_start */
  0,                                    /* todo_flags_finish */
  0					/* letter */
};