Initial checkin of GCC 4.9.0 from trunk (r208799).

Change-Id: I48a3c08bb98542aa215912a75f03c0890e497dba

1 files changed, 3179 insertions, 0 deletions

diff --git a/gcc-4.9/gcc/graphite-sese-to-poly.c b/gcc-4.9/gcc/graphite-sese-to-poly.c
new file mode 100644
index 000000000..d4a1bb2df
--- /dev/null
+++ b/gcc-4.9/gcc/graphite-sese-to-poly.c
@@ -0,0 +1,3179 @@
+/* Conversion of SESE regions to Polyhedra.
+   Copyright (C) 2009-2014 Free Software Foundation, Inc.
+   Contributed by Sebastian Pop <sebastian.pop@amd.com>.
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3, or (at your option)
+any later version.
+
+GCC is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with GCC; see the file COPYING3.  If not see
+<http://www.gnu.org/licenses/>.  */
+
+#include "config.h"
+
+#ifdef HAVE_cloog
+#include <isl/set.h>
+#include <isl/map.h>
+#include <isl/union_map.h>
+#include <isl/constraint.h>
+#include <isl/aff.h>
+#include <cloog/cloog.h>
+#include <cloog/cloog.h>
+#include <cloog/isl/domain.h>
+#endif
+
+#include "system.h"
+#include "coretypes.h"
+#include "tree.h"
+#include "basic-block.h"
+#include "tree-ssa-alias.h"
+#include "internal-fn.h"
+#include "gimple-expr.h"
+#include "is-a.h"
+#include "gimple.h"
+#include "gimple-iterator.h"
+#include "gimplify.h"
+#include "gimplify-me.h"
+#include "gimple-ssa.h"
+#include "tree-cfg.h"
+#include "tree-phinodes.h"
+#include "ssa-iterators.h"
+#include "stringpool.h"
+#include "tree-ssanames.h"
+#include "tree-ssa-loop-manip.h"
+#include "tree-ssa-loop-niter.h"
+#include "tree-ssa-loop.h"
+#include "tree-into-ssa.h"
+#include "tree-pass.h"
+#include "cfgloop.h"
+#include "tree-chrec.h"
+#include "tree-data-ref.h"
+#include "tree-scalar-evolution.h"
+#include "domwalk.h"
+#include "sese.h"
+#include "tree-ssa-propagate.h"
+
+#ifdef HAVE_cloog
+#include "expr.h"
+#include "graphite-poly.h"
+#include "graphite-sese-to-poly.h"
+
+
+/* Assigns to RES the value of the INTEGER_CST T.  */
+
+static inline void
+tree_int_to_gmp (tree t, mpz_t res)
+{
+  double_int di = tree_to_double_int (t);
+  mpz_set_double_int (res, di, TYPE_UNSIGNED (TREE_TYPE (t)));
+}
+
+/* Returns the index of the PHI argument defined in the outermost
+   loop.  */
+
+static size_t
+phi_arg_in_outermost_loop (gimple phi)
+{
+  loop_p loop = gimple_bb (phi)->loop_father;
+  size_t i, res = 0;
+
+  for (i = 0; i < gimple_phi_num_args (phi); i++)
+    if (!flow_bb_inside_loop_p (loop, gimple_phi_arg_edge (phi, i)->src))
+      {
+	loop = gimple_phi_arg_edge (phi, i)->src->loop_father;
+	res = i;
+      }
+
+  return res;
+}
+
+/* Removes a simple copy phi node "RES = phi (INIT, RES)" at position
+   PSI by inserting on the loop ENTRY edge assignment "RES = INIT".  */
+
+static void
+remove_simple_copy_phi (gimple_stmt_iterator *psi)
+{
+  gimple phi = gsi_stmt (*psi);
+  tree res = gimple_phi_result (phi);
+  size_t entry = phi_arg_in_outermost_loop (phi);
+  tree init = gimple_phi_arg_def (phi, entry);
+  gimple stmt = gimple_build_assign (res, init);
+  edge e = gimple_phi_arg_edge (phi, entry);
+
+  remove_phi_node (psi, false);
+  gsi_insert_on_edge_immediate (e, stmt);
+}
+
+/* Removes an invariant phi node at position PSI by inserting on the
+   loop ENTRY edge the assignment RES = INIT.  */
+
+static void
+remove_invariant_phi (sese region, gimple_stmt_iterator *psi)
+{
+  gimple phi = gsi_stmt (*psi);
+  loop_p loop = loop_containing_stmt (phi);
+  tree res = gimple_phi_result (phi);
+  tree scev = scalar_evolution_in_region (region, loop, res);
+  size_t entry = phi_arg_in_outermost_loop (phi);
+  edge e = gimple_phi_arg_edge (phi, entry);
+  tree var;
+  gimple stmt;
+  gimple_seq stmts = NULL;
+
+  if (tree_contains_chrecs (scev, NULL))
+    scev = gimple_phi_arg_def (phi, entry);
+
+  var = force_gimple_operand (scev, &stmts, true, NULL_TREE);
+  stmt = gimple_build_assign (res, var);
+  remove_phi_node (psi, false);
+
+  gimple_seq_add_stmt (&stmts, stmt);
+  gsi_insert_seq_on_edge (e, stmts);
+  gsi_commit_edge_inserts ();
+  SSA_NAME_DEF_STMT (res) = stmt;
+}
+
+/* Returns true when the phi node at PSI is of the form "a = phi (a, x)".  */
+
+static inline bool
+simple_copy_phi_p (gimple phi)
+{
+  tree res;
+
+  if (gimple_phi_num_args (phi) != 2)
+    return false;
+
+  res = gimple_phi_result (phi);
+  return (res == gimple_phi_arg_def (phi, 0)
+	  || res == gimple_phi_arg_def (phi, 1));
+}
+
+/* Returns true when the phi node at position PSI is a reduction phi
+   node in REGION.  Otherwise moves the pointer PSI to the next phi to
+   be considered.  */
+
+static bool
+reduction_phi_p (sese region, gimple_stmt_iterator *psi)
+{
+  loop_p loop;
+  gimple phi = gsi_stmt (*psi);
+  tree res = gimple_phi_result (phi);
+
+  loop = loop_containing_stmt (phi);
+
+  if (simple_copy_phi_p (phi))
+    {
+      /* PRE introduces phi nodes like these, for an example,
+	 see id-5.f in the fortran graphite testsuite:
+
+	 # prephitmp.85_265 = PHI <prephitmp.85_258(33), prephitmp.85_265(18)>
+      */
+      remove_simple_copy_phi (psi);
+      return false;
+    }
+
+  if (scev_analyzable_p (res, region))
+    {
+      tree scev = scalar_evolution_in_region (region, loop, res);
+
+      if (evolution_function_is_invariant_p (scev, loop->num))
+	remove_invariant_phi (region, psi);
+      else
+	gsi_next (psi);
+
+      return false;
+    }
+
+  /* All the other cases are considered reductions.  */
+  return true;
+}
+
+/* Store the GRAPHITE representation of BB.  */
+
+static gimple_bb_p
+new_gimple_bb (basic_block bb, vec<data_reference_p> drs)
+{
+  struct gimple_bb *gbb;
+
+  gbb = XNEW (struct gimple_bb);
+  bb->aux = gbb;
+  GBB_BB (gbb) = bb;
+  GBB_DATA_REFS (gbb) = drs;
+  GBB_CONDITIONS (gbb).create (0);
+  GBB_CONDITION_CASES (gbb).create (0);
+
+  return gbb;
+}
+
+static void
+free_data_refs_aux (vec<data_reference_p> datarefs)
+{
+  unsigned int i;
+  struct data_reference *dr;
+
+  FOR_EACH_VEC_ELT (datarefs, i, dr)
+    if (dr->aux)
+      {
+	base_alias_pair *bap = (base_alias_pair *)(dr->aux);
+
+	free (bap->alias_set);
+
+	free (bap);
+	dr->aux = NULL;
+      }
+}
+/* Frees GBB.  */
+
+static void
+free_gimple_bb (struct gimple_bb *gbb)
+{
+  free_data_refs_aux (GBB_DATA_REFS (gbb));
+  free_data_refs (GBB_DATA_REFS (gbb));
+
+  GBB_CONDITIONS (gbb).release ();
+  GBB_CONDITION_CASES (gbb).release ();
+  GBB_BB (gbb)->aux = 0;
+  XDELETE (gbb);
+}
+
+/* Deletes all gimple bbs in SCOP.  */
+
+static void
+remove_gbbs_in_scop (scop_p scop)
+{
+  int i;
+  poly_bb_p pbb;
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    free_gimple_bb (PBB_BLACK_BOX (pbb));
+}
+
+/* Deletes all scops in SCOPS.  */
+
+void
+free_scops (vec<scop_p> scops)
+{
+  int i;
+  scop_p scop;
+
+  FOR_EACH_VEC_ELT (scops, i, scop)
+    {
+      remove_gbbs_in_scop (scop);
+      free_sese (SCOP_REGION (scop));
+      free_scop (scop);
+    }
+
+  scops.release ();
+}
+
+/* Same as outermost_loop_in_sese, returns the outermost loop
+   containing BB in REGION, but makes sure that the returned loop
+   belongs to the REGION, and so this returns the first loop in the
+   REGION when the loop containing BB does not belong to REGION.  */
+
+static loop_p
+outermost_loop_in_sese_1 (sese region, basic_block bb)
+{
+  loop_p nest = outermost_loop_in_sese (region, bb);
+
+  if (loop_in_sese_p (nest, region))
+    return nest;
+
+  /* When the basic block BB does not belong to a loop in the region,
+     return the first loop in the region.  */
+  nest = nest->inner;
+  while (nest)
+    if (loop_in_sese_p (nest, region))
+      break;
+    else
+      nest = nest->next;
+
+  gcc_assert (nest);
+  return nest;
+}
+
+/* Generates a polyhedral black box only if the bb contains interesting
+   information.  */
+
+static gimple_bb_p
+try_generate_gimple_bb (scop_p scop, basic_block bb)
+{
+  vec<data_reference_p> drs;
+  drs.create (5);
+  sese region = SCOP_REGION (scop);
+  loop_p nest = outermost_loop_in_sese_1 (region, bb);
+  gimple_stmt_iterator gsi;
+
+  for (gsi = gsi_start_bb (bb); !gsi_end_p (gsi); gsi_next (&gsi))
+    {
+      gimple stmt = gsi_stmt (gsi);
+      loop_p loop;
+
+      if (is_gimple_debug (stmt))
+	continue;
+
+      loop = loop_containing_stmt (stmt);
+      if (!loop_in_sese_p (loop, region))
+	loop = nest;
+
+      graphite_find_data_references_in_stmt (nest, loop, stmt, &drs);
+    }
+
+  return new_gimple_bb (bb, drs);
+}
+
+/* Returns true if all predecessors of BB, that are not dominated by BB, are
+   marked in MAP.  The predecessors dominated by BB are loop latches and will
+   be handled after BB.  */
+
+static bool
+all_non_dominated_preds_marked_p (basic_block bb, sbitmap map)
+{
+  edge e;
+  edge_iterator ei;
+
+  FOR_EACH_EDGE (e, ei, bb->preds)
+    if (!bitmap_bit_p (map, e->src->index)
+	&& !dominated_by_p (CDI_DOMINATORS, e->src, bb))
+	return false;
+
+  return true;
+}
+
+/* Compare the depth of two basic_block's P1 and P2.  */
+
+static int
+compare_bb_depths (const void *p1, const void *p2)
+{
+  const_basic_block const bb1 = *(const_basic_block const*)p1;
+  const_basic_block const bb2 = *(const_basic_block const*)p2;
+  int d1 = loop_depth (bb1->loop_father);
+  int d2 = loop_depth (bb2->loop_father);
+
+  if (d1 < d2)
+    return 1;
+
+  if (d1 > d2)
+    return -1;
+
+  return 0;
+}
+
+/* Sort the basic blocks from DOM such that the first are the ones at
+   a deepest loop level.  */
+
+static void
+graphite_sort_dominated_info (vec<basic_block> dom)
+{
+  dom.qsort (compare_bb_depths);
+}
+
+/* Recursive helper function for build_scops_bbs.  */
+
+static void
+build_scop_bbs_1 (scop_p scop, sbitmap visited, basic_block bb)
+{
+  sese region = SCOP_REGION (scop);
+  vec<basic_block> dom;
+  poly_bb_p pbb;
+
+  if (bitmap_bit_p (visited, bb->index)
+      || !bb_in_sese_p (bb, region))
+    return;
+
+  pbb = new_poly_bb (scop, try_generate_gimple_bb (scop, bb));
+  SCOP_BBS (scop).safe_push (pbb);
+  bitmap_set_bit (visited, bb->index);
+
+  dom = get_dominated_by (CDI_DOMINATORS, bb);
+
+  if (!dom.exists ())
+    return;
+
+  graphite_sort_dominated_info (dom);
+
+  while (!dom.is_empty ())
+    {
+      int i;
+      basic_block dom_bb;
+
+      FOR_EACH_VEC_ELT (dom, i, dom_bb)
+	if (all_non_dominated_preds_marked_p (dom_bb, visited))
+	  {
+	    build_scop_bbs_1 (scop, visited, dom_bb);
+	    dom.unordered_remove (i);
+	    break;
+	  }
+    }
+
+  dom.release ();
+}
+
+/* Gather the basic blocks belonging to the SCOP.  */
+
+static void
+build_scop_bbs (scop_p scop)
+{
+  sbitmap visited = sbitmap_alloc (last_basic_block_for_fn (cfun));
+  sese region = SCOP_REGION (scop);
+
+  bitmap_clear (visited);
+  build_scop_bbs_1 (scop, visited, SESE_ENTRY_BB (region));
+  sbitmap_free (visited);
+}
+
+/* Return an ISL identifier for the polyhedral basic block PBB.  */
+
+static isl_id *
+isl_id_for_pbb (scop_p s, poly_bb_p pbb)
+{
+  char name[50];
+  snprintf (name, sizeof (name), "S_%d", pbb_index (pbb));
+  return isl_id_alloc (s->ctx, name, pbb);
+}
+
+/* Converts the STATIC_SCHEDULE of PBB into a scattering polyhedron.
+   We generate SCATTERING_DIMENSIONS scattering dimensions.
+
+   CLooG 0.15.0 and previous versions require, that all
+   scattering functions of one CloogProgram have the same number of
+   scattering dimensions, therefore we allow to specify it.  This
+   should be removed in future versions of CLooG.
+
+   The scattering polyhedron consists of these dimensions: scattering,
+   loop_iterators, parameters.
+
+   Example:
+
+   | scattering_dimensions = 5
+   | used_scattering_dimensions = 3
+   | nb_iterators = 1
+   | scop_nb_params = 2
+   |
+   | Schedule:
+   |   i
+   | 4 5
+   |
+   | Scattering polyhedron:
+   |
+   | scattering: {s1, s2, s3, s4, s5}
+   | loop_iterators: {i}
+   | parameters: {p1, p2}
+   |
+   | s1  s2  s3  s4  s5  i   p1  p2  1
+   | 1   0   0   0   0   0   0   0  -4  = 0
+   | 0   1   0   0   0  -1   0   0   0  = 0
+   | 0   0   1   0   0   0   0   0  -5  = 0  */
+
+static void
+build_pbb_scattering_polyhedrons (isl_aff *static_sched,
+				  poly_bb_p pbb, int scattering_dimensions)
+{
+  int i;
+  int nb_iterators = pbb_dim_iter_domain (pbb);
+  int used_scattering_dimensions = nb_iterators * 2 + 1;
+  isl_int val;
+  isl_space *dc, *dm;
+
+  gcc_assert (scattering_dimensions >= used_scattering_dimensions);
+
+  isl_int_init (val);
+
+  dc = isl_set_get_space (pbb->domain);
+  dm = isl_space_add_dims (isl_space_from_domain (dc),
+			   isl_dim_out, scattering_dimensions);
+  pbb->schedule = isl_map_universe (dm);
+
+  for (i = 0; i < scattering_dimensions; i++)
+    {
+      /* Textual order inside this loop.  */
+      if ((i % 2) == 0)
+	{
+	  isl_constraint *c = isl_equality_alloc
+	      (isl_local_space_from_space (isl_map_get_space (pbb->schedule)));
+
+	  if (0 != isl_aff_get_coefficient (static_sched, isl_dim_in,
+					    i / 2, &val))
+	    gcc_unreachable ();
+
+	  isl_int_neg (val, val);
+	  c = isl_constraint_set_constant (c, val);
+	  c = isl_constraint_set_coefficient_si (c, isl_dim_out, i, 1);
+	  pbb->schedule = isl_map_add_constraint (pbb->schedule, c);
+	}
+
+      /* Iterations of this loop.  */
+      else /* if ((i % 2) == 1) */
+	{
+	  int loop = (i - 1) / 2;
+	  pbb->schedule = isl_map_equate (pbb->schedule, isl_dim_in, loop,
+					  isl_dim_out, i);
+	}
+    }
+
+  isl_int_clear (val);
+
+  pbb->transformed = isl_map_copy (pbb->schedule);
+}
+
+/* Build for BB the static schedule.
+
+   The static schedule is a Dewey numbering of the abstract syntax
+   tree: http://en.wikipedia.org/wiki/Dewey_Decimal_Classification
+
+   The following example informally defines the static schedule:
+
+   A
+   for (i: ...)
+     {
+       for (j: ...)
+         {
+           B
+           C
+         }
+
+       for (k: ...)
+         {
+           D
+           E
+         }
+     }
+   F
+
+   Static schedules for A to F:
+
+     DEPTH
+     0 1 2
+   A 0
+   B 1 0 0
+   C 1 0 1
+   D 1 1 0
+   E 1 1 1
+   F 2
+*/
+
+static void
+build_scop_scattering (scop_p scop)
+{
+  int i;
+  poly_bb_p pbb;
+  gimple_bb_p previous_gbb = NULL;
+  isl_space *dc = isl_set_get_space (scop->context);
+  isl_aff *static_sched;
+
+  dc = isl_space_add_dims (dc, isl_dim_set, number_of_loops (cfun));
+  static_sched = isl_aff_zero_on_domain (isl_local_space_from_space (dc));
+
+  /* We have to start schedules at 0 on the first component and
+     because we cannot compare_prefix_loops against a previous loop,
+     prefix will be equal to zero, and that index will be
+     incremented before copying.  */
+  static_sched = isl_aff_add_coefficient_si (static_sched, isl_dim_in, 0, -1);
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    {
+      gimple_bb_p gbb = PBB_BLACK_BOX (pbb);
+      int prefix;
+      int nb_scat_dims = pbb_dim_iter_domain (pbb) * 2 + 1;
+
+      if (previous_gbb)
+	prefix = nb_common_loops (SCOP_REGION (scop), previous_gbb, gbb);
+      else
+	prefix = 0;
+
+      previous_gbb = gbb;
+
+      static_sched = isl_aff_add_coefficient_si (static_sched, isl_dim_in,
+						 prefix, 1);
+      build_pbb_scattering_polyhedrons (static_sched, pbb, nb_scat_dims);
+    }
+
+  isl_aff_free (static_sched);
+}
+
+static isl_pw_aff *extract_affine (scop_p, tree, __isl_take isl_space *space);
+
+/* Extract an affine expression from the chain of recurrence E.  */
+
+static isl_pw_aff *
+extract_affine_chrec (scop_p s, tree e, __isl_take isl_space *space)
+{
+  isl_pw_aff *lhs = extract_affine (s, CHREC_LEFT (e), isl_space_copy (space));
+  isl_pw_aff *rhs = extract_affine (s, CHREC_RIGHT (e), isl_space_copy (space));
+  isl_local_space *ls = isl_local_space_from_space (space);
+  unsigned pos = sese_loop_depth ((sese) s->region, get_chrec_loop (e)) - 1;
+  isl_aff *loop = isl_aff_set_coefficient_si
+    (isl_aff_zero_on_domain (ls), isl_dim_in, pos, 1);
+  isl_pw_aff *l = isl_pw_aff_from_aff (loop);
+
+  /* Before multiplying, make sure that the result is affine.  */
+  gcc_assert (isl_pw_aff_is_cst (rhs)
+	      || isl_pw_aff_is_cst (l));
+
+  return isl_pw_aff_add (lhs, isl_pw_aff_mul (rhs, l));
+}
+
+/* Extract an affine expression from the mult_expr E.  */
+
+static isl_pw_aff *
+extract_affine_mul (scop_p s, tree e, __isl_take isl_space *space)
+{
+  isl_pw_aff *lhs = extract_affine (s, TREE_OPERAND (e, 0),
+				    isl_space_copy (space));
+  isl_pw_aff *rhs = extract_affine (s, TREE_OPERAND (e, 1), space);
+
+  if (!isl_pw_aff_is_cst (lhs)
+      && !isl_pw_aff_is_cst (rhs))
+    {
+      isl_pw_aff_free (lhs);
+      isl_pw_aff_free (rhs);
+      return NULL;
+    }
+
+  return isl_pw_aff_mul (lhs, rhs);
+}
+
+/* Return an ISL identifier from the name of the ssa_name E.  */
+
+static isl_id *
+isl_id_for_ssa_name (scop_p s, tree e)
+{
+  const char *name = get_name (e);
+  isl_id *id;
+
+  if (name)
+    id = isl_id_alloc (s->ctx, name, e);
+  else
+    {
+      char name1[50];
+      snprintf (name1, sizeof (name1), "P_%d", SSA_NAME_VERSION (e));
+      id = isl_id_alloc (s->ctx, name1, e);
+    }
+
+  return id;
+}
+
+/* Return an ISL identifier for the data reference DR.  */
+
+static isl_id *
+isl_id_for_dr (scop_p s, data_reference_p dr ATTRIBUTE_UNUSED)
+{
+  /* Data references all get the same isl_id.  They need to be comparable
+     and are distinguished through the first dimension, which contains the
+     alias set number.  */
+  return isl_id_alloc (s->ctx, "", 0);
+}
+
+/* Extract an affine expression from the ssa_name E.  */
+
+static isl_pw_aff *
+extract_affine_name (scop_p s, tree e, __isl_take isl_space *space)
+{
+  isl_aff *aff;
+  isl_set *dom;
+  isl_id *id;
+  int dimension;
+
+  id = isl_id_for_ssa_name (s, e);
+  dimension = isl_space_find_dim_by_id (space, isl_dim_param, id);
+  isl_id_free (id);
+  dom = isl_set_universe (isl_space_copy (space));
+  aff = isl_aff_zero_on_domain (isl_local_space_from_space (space));
+  aff = isl_aff_add_coefficient_si (aff, isl_dim_param, dimension, 1);
+  return isl_pw_aff_alloc (dom, aff);
+}
+
+/* Extract an affine expression from the gmp constant G.  */
+
+static isl_pw_aff *
+extract_affine_gmp (mpz_t g, __isl_take isl_space *space)
+{
+  isl_local_space *ls = isl_local_space_from_space (isl_space_copy (space));
+  isl_aff *aff = isl_aff_zero_on_domain (ls);
+  isl_set *dom = isl_set_universe (space);
+  isl_int v;
+
+  isl_int_init (v);
+  isl_int_set_gmp (v, g);
+  aff = isl_aff_add_constant (aff, v);
+  isl_int_clear (v);
+
+  return isl_pw_aff_alloc (dom, aff);
+}
+
+/* Extract an affine expression from the integer_cst E.  */
+
+static isl_pw_aff *
+extract_affine_int (tree e, __isl_take isl_space *space)
+{
+  isl_pw_aff *res;
+  mpz_t g;
+
+  mpz_init (g);
+  tree_int_to_gmp (e, g);
+  res = extract_affine_gmp (g, space);
+  mpz_clear (g);
+
+  return res;
+}
+
+/* Compute pwaff mod 2^width.  */
+
+static isl_pw_aff *
+wrap (isl_pw_aff *pwaff, unsigned width)
+{
+  isl_int mod;
+
+  isl_int_init (mod);
+  isl_int_set_si (mod, 1);
+  isl_int_mul_2exp (mod, mod, width);
+
+  pwaff = isl_pw_aff_mod (pwaff, mod);
+
+  isl_int_clear (mod);
+
+  return pwaff;
+}
+
+/* When parameter NAME is in REGION, returns its index in SESE_PARAMS.
+   Otherwise returns -1.  */
+
+static inline int
+parameter_index_in_region_1 (tree name, sese region)
+{
+  int i;
+  tree p;
+
+  gcc_assert (TREE_CODE (name) == SSA_NAME);
+
+  FOR_EACH_VEC_ELT (SESE_PARAMS (region), i, p)
+    if (p == name)
+      return i;
+
+  return -1;
+}
+
+/* When the parameter NAME is in REGION, returns its index in
+   SESE_PARAMS.  Otherwise this function inserts NAME in SESE_PARAMS
+   and returns the index of NAME.  */
+
+static int
+parameter_index_in_region (tree name, sese region)
+{
+  int i;
+
+  gcc_assert (TREE_CODE (name) == SSA_NAME);
+
+  i = parameter_index_in_region_1 (name, region);
+  if (i != -1)
+    return i;
+
+  gcc_assert (SESE_ADD_PARAMS (region));
+
+  i = SESE_PARAMS (region).length ();
+  SESE_PARAMS (region).safe_push (name);
+  return i;
+}
+
+/* Extract an affine expression from the tree E in the scop S.  */
+
+static isl_pw_aff *
+extract_affine (scop_p s, tree e, __isl_take isl_space *space)
+{
+  isl_pw_aff *lhs, *rhs, *res;
+  tree type;
+
+  if (e == chrec_dont_know) {
+    isl_space_free (space);
+    return NULL;
+  }
+
+  switch (TREE_CODE (e))
+    {
+    case POLYNOMIAL_CHREC:
+      res = extract_affine_chrec (s, e, space);
+      break;
+
+    case MULT_EXPR:
+      res = extract_affine_mul (s, e, space);
+      break;
+
+    case PLUS_EXPR:
+    case POINTER_PLUS_EXPR:
+      lhs = extract_affine (s, TREE_OPERAND (e, 0), isl_space_copy (space));
+      rhs = extract_affine (s, TREE_OPERAND (e, 1), space);
+      res = isl_pw_aff_add (lhs, rhs);
+      break;
+
+    case MINUS_EXPR:
+      lhs = extract_affine (s, TREE_OPERAND (e, 0), isl_space_copy (space));
+      rhs = extract_affine (s, TREE_OPERAND (e, 1), space);
+      res = isl_pw_aff_sub (lhs, rhs);
+      break;
+
+    case NEGATE_EXPR:
+    case BIT_NOT_EXPR:
+      lhs = extract_affine (s, TREE_OPERAND (e, 0), isl_space_copy (space));
+      rhs = extract_affine (s, integer_minus_one_node, space);
+      res = isl_pw_aff_mul (lhs, rhs);
+      break;
+
+    case SSA_NAME:
+      gcc_assert (-1 != parameter_index_in_region_1 (e, SCOP_REGION (s)));
+      res = extract_affine_name (s, e, space);
+      break;
+
+    case INTEGER_CST:
+      res = extract_affine_int (e, space);
+      /* No need to wrap a single integer.  */
+      return res;
+
+    CASE_CONVERT:
+    case NON_LVALUE_EXPR:
+      res = extract_affine (s, TREE_OPERAND (e, 0), space);
+      break;
+
+    default:
+      gcc_unreachable ();
+      break;
+    }
+
+  type = TREE_TYPE (e);
+  if (TYPE_UNSIGNED (type))
+    res = wrap (res, TYPE_PRECISION (type));
+
+  return res;
+}
+
+/* In the context of sese S, scan the expression E and translate it to
+   a linear expression C.  When parsing a symbolic multiplication, K
+   represents the constant multiplier of an expression containing
+   parameters.  */
+
+static void
+scan_tree_for_params (sese s, tree e)
+{
+  if (e == chrec_dont_know)
+    return;
+
+  switch (TREE_CODE (e))
+    {
+    case POLYNOMIAL_CHREC:
+      scan_tree_for_params (s, CHREC_LEFT (e));
+      break;
+
+    case MULT_EXPR:
+      if (chrec_contains_symbols (TREE_OPERAND (e, 0)))
+	scan_tree_for_params (s, TREE_OPERAND (e, 0));
+      else
+	scan_tree_for_params (s, TREE_OPERAND (e, 1));
+      break;
+
+    case PLUS_EXPR:
+    case POINTER_PLUS_EXPR:
+    case MINUS_EXPR:
+      scan_tree_for_params (s, TREE_OPERAND (e, 0));
+      scan_tree_for_params (s, TREE_OPERAND (e, 1));
+      break;
+
+    case NEGATE_EXPR:
+    case BIT_NOT_EXPR:
+    CASE_CONVERT:
+    case NON_LVALUE_EXPR:
+      scan_tree_for_params (s, TREE_OPERAND (e, 0));
+      break;
+
+    case SSA_NAME:
+      parameter_index_in_region (e, s);
+      break;
+
+    case INTEGER_CST:
+    case ADDR_EXPR:
+      break;
+
+   default:
+      gcc_unreachable ();
+      break;
+    }
+}
+
+/* Find parameters with respect to REGION in BB. We are looking in memory
+   access functions, conditions and loop bounds.  */
+
+static void
+find_params_in_bb (sese region, gimple_bb_p gbb)
+{
+  int i;
+  unsigned j;
+  data_reference_p dr;
+  gimple stmt;
+  loop_p loop = GBB_BB (gbb)->loop_father;
+
+  /* Find parameters in the access functions of data references.  */
+  FOR_EACH_VEC_ELT (GBB_DATA_REFS (gbb), i, dr)
+    for (j = 0; j < DR_NUM_DIMENSIONS (dr); j++)
+      scan_tree_for_params (region, DR_ACCESS_FN (dr, j));
+
+  /* Find parameters in conditional statements.  */
+  FOR_EACH_VEC_ELT (GBB_CONDITIONS (gbb), i, stmt)
+    {
+      tree lhs = scalar_evolution_in_region (region, loop,
+					     gimple_cond_lhs (stmt));
+      tree rhs = scalar_evolution_in_region (region, loop,
+					     gimple_cond_rhs (stmt));
+
+      scan_tree_for_params (region, lhs);
+      scan_tree_for_params (region, rhs);
+    }
+}
+
+/* Record the parameters used in the SCOP.  A variable is a parameter
+   in a scop if it does not vary during the execution of that scop.  */
+
+static void
+find_scop_parameters (scop_p scop)
+{
+  poly_bb_p pbb;
+  unsigned i;
+  sese region = SCOP_REGION (scop);
+  struct loop *loop;
+  int nbp;
+
+  /* Find the parameters used in the loop bounds.  */
+  FOR_EACH_VEC_ELT (SESE_LOOP_NEST (region), i, loop)
+    {
+      tree nb_iters = number_of_latch_executions (loop);
+
+      if (!chrec_contains_symbols (nb_iters))
+	continue;
+
+      nb_iters = scalar_evolution_in_region (region, loop, nb_iters);
+      scan_tree_for_params (region, nb_iters);
+    }
+
+  /* Find the parameters used in data accesses.  */
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    find_params_in_bb (region, PBB_BLACK_BOX (pbb));
+
+  nbp = sese_nb_params (region);
+  scop_set_nb_params (scop, nbp);
+  SESE_ADD_PARAMS (region) = false;
+
+  {
+    tree e;
+    isl_space *space = isl_space_set_alloc (scop->ctx, nbp, 0);
+
+    FOR_EACH_VEC_ELT (SESE_PARAMS (region), i, e)
+      space = isl_space_set_dim_id (space, isl_dim_param, i,
+				    isl_id_for_ssa_name (scop, e));
+
+    scop->context = isl_set_universe (space);
+  }
+}
+
+/* Builds the constraint polyhedra for LOOP in SCOP.  OUTER_PH gives
+   the constraints for the surrounding loops.  */
+
+static void
+build_loop_iteration_domains (scop_p scop, struct loop *loop,
+                              int nb,
+			      isl_set *outer, isl_set **doms)
+{
+  tree nb_iters = number_of_latch_executions (loop);
+  sese region = SCOP_REGION (scop);
+
+  isl_set *inner = isl_set_copy (outer);
+  isl_space *space;
+  isl_constraint *c;
+  int pos = isl_set_dim (outer, isl_dim_set);
+  isl_int v;
+  mpz_t g;
+
+  mpz_init (g);
+  isl_int_init (v);
+
+  inner = isl_set_add_dims (inner, isl_dim_set, 1);
+  space = isl_set_get_space (inner);
+
+  /* 0 <= loop_i */
+  c = isl_inequality_alloc
+      (isl_local_space_from_space (isl_space_copy (space)));
+  c = isl_constraint_set_coefficient_si (c, isl_dim_set, pos, 1);
+  inner = isl_set_add_constraint (inner, c);
+
+  /* loop_i <= cst_nb_iters */
+  if (TREE_CODE (nb_iters) == INTEGER_CST)
+    {
+      c = isl_inequality_alloc
+	  (isl_local_space_from_space (isl_space_copy (space)));
+      c = isl_constraint_set_coefficient_si (c, isl_dim_set, pos, -1);
+      tree_int_to_gmp (nb_iters, g);
+      isl_int_set_gmp (v, g);
+      c = isl_constraint_set_constant (c, v);
+      inner = isl_set_add_constraint (inner, c);
+    }
+
+  /* loop_i <= expr_nb_iters */
+  else if (!chrec_contains_undetermined (nb_iters))
+    {
+      double_int nit;
+      isl_pw_aff *aff;
+      isl_set *valid;
+      isl_local_space *ls;
+      isl_aff *al;
+      isl_set *le;
+
+      nb_iters = scalar_evolution_in_region (region, loop, nb_iters);
+
+      aff = extract_affine (scop, nb_iters, isl_set_get_space (inner));
+      valid = isl_pw_aff_nonneg_set (isl_pw_aff_copy (aff));
+      valid = isl_set_project_out (valid, isl_dim_set, 0,
+				   isl_set_dim (valid, isl_dim_set));
+      scop->context = isl_set_intersect (scop->context, valid);
+
+      ls = isl_local_space_from_space (isl_space_copy (space));
+      al = isl_aff_set_coefficient_si (isl_aff_zero_on_domain (ls),
+				       isl_dim_in, pos, 1);
+      le = isl_pw_aff_le_set (isl_pw_aff_from_aff (al),
+			      isl_pw_aff_copy (aff));
+      inner = isl_set_intersect (inner, le);
+
+      if (max_stmt_executions (loop, &nit))
+	{
+	  /* Insert in the context the constraints from the
+	     estimation of the number of iterations NIT and the
+	     symbolic number of iterations (involving parameter
+	     names) NB_ITERS.  First, build the affine expression
+	     "NIT - NB_ITERS" and then say that it is positive,
+	     i.e., NIT approximates NB_ITERS: "NIT >= NB_ITERS".  */
+	  isl_pw_aff *approx;
+	  mpz_t g;
+	  isl_set *x;
+	  isl_constraint *c;
+
+	  mpz_init (g);
+	  mpz_set_double_int (g, nit, false);
+	  mpz_sub_ui (g, g, 1);
+	  approx = extract_affine_gmp (g, isl_set_get_space (inner));
+	  x = isl_pw_aff_ge_set (approx, aff);
+	  x = isl_set_project_out (x, isl_dim_set, 0,
+				   isl_set_dim (x, isl_dim_set));
+	  scop->context = isl_set_intersect (scop->context, x);
+
+	  c = isl_inequality_alloc
+	      (isl_local_space_from_space (isl_space_copy (space)));
+	  c = isl_constraint_set_coefficient_si (c, isl_dim_set, pos, -1);
+	  isl_int_set_gmp (v, g);
+	  mpz_clear (g);
+	  c = isl_constraint_set_constant (c, v);
+	  inner = isl_set_add_constraint (inner, c);
+	}
+      else
+	isl_pw_aff_free (aff);
+    }
+  else
+    gcc_unreachable ();
+
+  if (loop->inner && loop_in_sese_p (loop->inner, region))
+    build_loop_iteration_domains (scop, loop->inner, nb + 1,
+				  isl_set_copy (inner), doms);
+
+  if (nb != 0
+      && loop->next
+      && loop_in_sese_p (loop->next, region))
+    build_loop_iteration_domains (scop, loop->next, nb,
+				  isl_set_copy (outer), doms);
+
+  doms[loop->num] = inner;
+
+  isl_set_free (outer);
+  isl_space_free (space);
+  isl_int_clear (v);
+  mpz_clear (g);
+}
+
+/* Returns a linear expression for tree T evaluated in PBB.  */
+
+static isl_pw_aff *
+create_pw_aff_from_tree (poly_bb_p pbb, tree t)
+{
+  scop_p scop = PBB_SCOP (pbb);
+
+  t = scalar_evolution_in_region (SCOP_REGION (scop), pbb_loop (pbb), t);
+  gcc_assert (!automatically_generated_chrec_p (t));
+
+  return extract_affine (scop, t, isl_set_get_space (pbb->domain));
+}
+
+/* Add conditional statement STMT to pbb.  CODE is used as the comparison
+   operator.  This allows us to invert the condition or to handle
+   inequalities.  */
+
+static void
+add_condition_to_pbb (poly_bb_p pbb, gimple stmt, enum tree_code code)
+{
+  isl_pw_aff *lhs = create_pw_aff_from_tree (pbb, gimple_cond_lhs (stmt));
+  isl_pw_aff *rhs = create_pw_aff_from_tree (pbb, gimple_cond_rhs (stmt));
+  isl_set *cond;
+
+  switch (code)
+    {
+      case LT_EXPR:
+	cond = isl_pw_aff_lt_set (lhs, rhs);
+	break;
+
+      case GT_EXPR:
+	cond = isl_pw_aff_gt_set (lhs, rhs);
+	break;
+
+      case LE_EXPR:
+	cond = isl_pw_aff_le_set (lhs, rhs);
+	break;
+
+      case GE_EXPR:
+	cond = isl_pw_aff_ge_set (lhs, rhs);
+	break;
+
+      case EQ_EXPR:
+	cond = isl_pw_aff_eq_set (lhs, rhs);
+	break;
+
+      case NE_EXPR:
+	cond = isl_pw_aff_ne_set (lhs, rhs);
+	break;
+
+      default:
+	isl_pw_aff_free (lhs);
+	isl_pw_aff_free (rhs);
+	return;
+    }
+
+  cond = isl_set_coalesce (cond);
+  cond = isl_set_set_tuple_id (cond, isl_set_get_tuple_id (pbb->domain));
+  pbb->domain = isl_set_intersect (pbb->domain, cond);
+}
+
+/* Add conditions to the domain of PBB.  */
+
+static void
+add_conditions_to_domain (poly_bb_p pbb)
+{
+  unsigned int i;
+  gimple stmt;
+  gimple_bb_p gbb = PBB_BLACK_BOX (pbb);
+
+  if (GBB_CONDITIONS (gbb).is_empty ())
+    return;
+
+  FOR_EACH_VEC_ELT (GBB_CONDITIONS (gbb), i, stmt)
+    switch (gimple_code (stmt))
+      {
+      case GIMPLE_COND:
+	  {
+	    enum tree_code code = gimple_cond_code (stmt);
+
+	    /* The conditions for ELSE-branches are inverted.  */
+	    if (!GBB_CONDITION_CASES (gbb)[i])
+	      code = invert_tree_comparison (code, false);
+
+	    add_condition_to_pbb (pbb, stmt, code);
+	    break;
+	  }
+
+      case GIMPLE_SWITCH:
+	/* Switch statements are not supported right now - fall through.  */
+
+      default:
+	gcc_unreachable ();
+	break;
+      }
+}
+
+/* Traverses all the GBBs of the SCOP and add their constraints to the
+   iteration domains.  */
+
+static void
+add_conditions_to_constraints (scop_p scop)
+{
+  int i;
+  poly_bb_p pbb;
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    add_conditions_to_domain (pbb);
+}
+
+/* Returns a COND_EXPR statement when BB has a single predecessor, the
+   edge between BB and its predecessor is not a loop exit edge, and
+   the last statement of the single predecessor is a COND_EXPR.  */
+
+static gimple
+single_pred_cond_non_loop_exit (basic_block bb)
+{
+  if (single_pred_p (bb))
+    {
+      edge e = single_pred_edge (bb);
+      basic_block pred = e->src;
+      gimple stmt;
+
+      if (loop_depth (pred->loop_father) > loop_depth (bb->loop_father))
+	return NULL;
+
+      stmt = last_stmt (pred);
+
+      if (stmt && gimple_code (stmt) == GIMPLE_COND)
+	return stmt;
+    }
+
+  return NULL;
+}
+
+class sese_dom_walker : public dom_walker
+{
+public:
+  sese_dom_walker (cdi_direction, sese);
+
+  virtual void before_dom_children (basic_block);
+  virtual void after_dom_children (basic_block);
+
+private:
+  auto_vec<gimple, 3> m_conditions, m_cases;
+  sese m_region;
+};
+
+sese_dom_walker::sese_dom_walker (cdi_direction direction, sese region)
+  : dom_walker (direction), m_region (region)
+{
+}
+
+/* Call-back for dom_walk executed before visiting the dominated
+   blocks.  */
+
+void
+sese_dom_walker::before_dom_children (basic_block bb)
+{
+  gimple_bb_p gbb;
+  gimple stmt;
+
+  if (!bb_in_sese_p (bb, m_region))
+    return;
+
+  stmt = single_pred_cond_non_loop_exit (bb);
+
+  if (stmt)
+    {
+      edge e = single_pred_edge (bb);
+
+      m_conditions.safe_push (stmt);
+
+      if (e->flags & EDGE_TRUE_VALUE)
+	m_cases.safe_push (stmt);
+      else
+	m_cases.safe_push (NULL);
+    }
+
+  gbb = gbb_from_bb (bb);
+
+  if (gbb)
+    {
+      GBB_CONDITIONS (gbb) = m_conditions.copy ();
+      GBB_CONDITION_CASES (gbb) = m_cases.copy ();
+    }
+}
+
+/* Call-back for dom_walk executed after visiting the dominated
+   blocks.  */
+
+void
+sese_dom_walker::after_dom_children (basic_block bb)
+{
+  if (!bb_in_sese_p (bb, m_region))
+    return;
+
+  if (single_pred_cond_non_loop_exit (bb))
+    {
+      m_conditions.pop ();
+      m_cases.pop ();
+    }
+}
+
+/* Add constraints on the possible values of parameter P from the type
+   of P.  */
+
+static void
+add_param_constraints (scop_p scop, graphite_dim_t p)
+{
+  tree parameter = SESE_PARAMS (SCOP_REGION (scop))[p];
+  tree type = TREE_TYPE (parameter);
+  tree lb = NULL_TREE;
+  tree ub = NULL_TREE;
+
+  if (POINTER_TYPE_P (type) || !TYPE_MIN_VALUE (type))
+    lb = lower_bound_in_type (type, type);
+  else
+    lb = TYPE_MIN_VALUE (type);
+
+  if (POINTER_TYPE_P (type) || !TYPE_MAX_VALUE (type))
+    ub = upper_bound_in_type (type, type);
+  else
+    ub = TYPE_MAX_VALUE (type);
+
+  if (lb)
+    {
+      isl_space *space = isl_set_get_space (scop->context);
+      isl_constraint *c;
+      mpz_t g;
+      isl_int v;
+
+      c = isl_inequality_alloc (isl_local_space_from_space (space));
+      mpz_init (g);
+      isl_int_init (v);
+      tree_int_to_gmp (lb, g);
+      isl_int_set_gmp (v, g);
+      isl_int_neg (v, v);
+      mpz_clear (g);
+      c = isl_constraint_set_constant (c, v);
+      isl_int_clear (v);
+      c = isl_constraint_set_coefficient_si (c, isl_dim_param, p, 1);
+
+      scop->context = isl_set_add_constraint (scop->context, c);
+    }
+
+  if (ub)
+    {
+      isl_space *space = isl_set_get_space (scop->context);
+      isl_constraint *c;
+      mpz_t g;
+      isl_int v;
+
+      c = isl_inequality_alloc (isl_local_space_from_space (space));
+
+      mpz_init (g);
+      isl_int_init (v);
+      tree_int_to_gmp (ub, g);
+      isl_int_set_gmp (v, g);
+      mpz_clear (g);
+      c = isl_constraint_set_constant (c, v);
+      isl_int_clear (v);
+      c = isl_constraint_set_coefficient_si (c, isl_dim_param, p, -1);
+
+      scop->context = isl_set_add_constraint (scop->context, c);
+    }
+}
+
+/* Build the context of the SCOP.  The context usually contains extra
+   constraints that are added to the iteration domains that constrain
+   some parameters.  */
+
+static void
+build_scop_context (scop_p scop)
+{
+  graphite_dim_t p, n = scop_nb_params (scop);
+
+  for (p = 0; p < n; p++)
+    add_param_constraints (scop, p);
+}
+
+/* Build the iteration domains: the loops belonging to the current
+   SCOP, and that vary for the execution of the current basic block.
+   Returns false if there is no loop in SCOP.  */
+
+static void
+build_scop_iteration_domain (scop_p scop)
+{
+  struct loop *loop;
+  sese region = SCOP_REGION (scop);
+  int i;
+  poly_bb_p pbb;
+  int nb_loops = number_of_loops (cfun);
+  isl_set **doms = XCNEWVEC (isl_set *, nb_loops);
+
+  FOR_EACH_VEC_ELT (SESE_LOOP_NEST (region), i, loop)
+    if (!loop_in_sese_p (loop_outer (loop), region))
+      build_loop_iteration_domains (scop, loop, 0,
+				    isl_set_copy (scop->context), doms);
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    {
+      loop = pbb_loop (pbb);
+
+      if (doms[loop->num])
+	pbb->domain = isl_set_copy (doms[loop->num]);
+      else
+	pbb->domain = isl_set_copy (scop->context);
+
+      pbb->domain = isl_set_set_tuple_id (pbb->domain,
+					  isl_id_for_pbb (scop, pbb));
+    }
+
+  for (i = 0; i < nb_loops; i++)
+    if (doms[i])
+      isl_set_free (doms[i]);
+
+  free (doms);
+}
+
+/* Add a constrain to the ACCESSES polyhedron for the alias set of
+   data reference DR.  ACCESSP_NB_DIMS is the dimension of the
+   ACCESSES polyhedron, DOM_NB_DIMS is the dimension of the iteration
+   domain.  */
+
+static isl_map *
+pdr_add_alias_set (isl_map *acc, data_reference_p dr)
+{
+  isl_constraint *c;
+  int alias_set_num = 0;
+  base_alias_pair *bap = (base_alias_pair *)(dr->aux);
+
+  if (bap && bap->alias_set)
+    alias_set_num = *(bap->alias_set);
+
+  c = isl_equality_alloc
+      (isl_local_space_from_space (isl_map_get_space (acc)));
+  c = isl_constraint_set_constant_si (c, -alias_set_num);
+  c = isl_constraint_set_coefficient_si (c, isl_dim_out, 0, 1);
+
+  return isl_map_add_constraint (acc, c);
+}
+
+/* Assign the affine expression INDEX to the output dimension POS of
+   MAP and return the result.  */
+
+static isl_map *
+set_index (isl_map *map, int pos, isl_pw_aff *index)
+{
+  isl_map *index_map;
+  int len = isl_map_dim (map, isl_dim_out);
+  isl_id *id;
+
+  index_map = isl_map_from_pw_aff (index);
+  index_map = isl_map_insert_dims (index_map, isl_dim_out, 0, pos);
+  index_map = isl_map_add_dims (index_map, isl_dim_out, len - pos - 1);
+
+  id = isl_map_get_tuple_id (map, isl_dim_out);
+  index_map = isl_map_set_tuple_id (index_map, isl_dim_out, id);
+  id = isl_map_get_tuple_id (map, isl_dim_in);
+  index_map = isl_map_set_tuple_id (index_map, isl_dim_in, id);
+
+  return isl_map_intersect (map, index_map);
+}
+
+/* Add to ACCESSES polyhedron equalities defining the access functions
+   to the memory.  ACCESSP_NB_DIMS is the dimension of the ACCESSES
+   polyhedron, DOM_NB_DIMS is the dimension of the iteration domain.
+   PBB is the poly_bb_p that contains the data reference DR.  */
+
+static isl_map *
+pdr_add_memory_accesses (isl_map *acc, data_reference_p dr, poly_bb_p pbb)
+{
+  int i, nb_subscripts = DR_NUM_DIMENSIONS (dr);
+  scop_p scop = PBB_SCOP (pbb);
+
+  for (i = 0; i < nb_subscripts; i++)
+    {
+      isl_pw_aff *aff;
+      tree afn = DR_ACCESS_FN (dr, nb_subscripts - 1 - i);
+
+      aff = extract_affine (scop, afn,
+			    isl_space_domain (isl_map_get_space (acc)));
+      acc = set_index (acc, i + 1, aff);
+    }
+
+  return acc;
+}
+
+/* Add constrains representing the size of the accessed data to the
+   ACCESSES polyhedron.  ACCESSP_NB_DIMS is the dimension of the
+   ACCESSES polyhedron, DOM_NB_DIMS is the dimension of the iteration
+   domain.  */
+
+static isl_set *
+pdr_add_data_dimensions (isl_set *extent, scop_p scop, data_reference_p dr)
+{
+  tree ref = DR_REF (dr);
+  int i, nb_subscripts = DR_NUM_DIMENSIONS (dr);
+
+  for (i = nb_subscripts - 1; i >= 0; i--, ref = TREE_OPERAND (ref, 0))
+    {
+      tree low, high;
+
+      if (TREE_CODE (ref) != ARRAY_REF)
+	break;
+
+      low = array_ref_low_bound (ref);
+      high = array_ref_up_bound (ref);
+
+      /* XXX The PPL code dealt separately with
+         subscript - low >= 0 and high - subscript >= 0 in case one of
+	 the two bounds isn't known.  Do the same here?  */
+
+      if (tree_fits_shwi_p (low)
+	  && high
+	  && tree_fits_shwi_p (high)
+	  /* 1-element arrays at end of structures may extend over
+	     their declared size.  */
+	  && !(array_at_struct_end_p (ref)
+	       && operand_equal_p (low, high, 0)))
+	{
+	  isl_id *id;
+	  isl_aff *aff;
+	  isl_set *univ, *lbs, *ubs;
+	  isl_pw_aff *index;
+	  isl_space *space;
+	  isl_set *valid;
+	  isl_pw_aff *lb = extract_affine_int (low, isl_set_get_space (extent));
+	  isl_pw_aff *ub = extract_affine_int (high, isl_set_get_space (extent));
+
+	  /* high >= 0 */
+	  valid = isl_pw_aff_nonneg_set (isl_pw_aff_copy (ub));
+	  valid = isl_set_project_out (valid, isl_dim_set, 0,
+				       isl_set_dim (valid, isl_dim_set));
+	  scop->context = isl_set_intersect (scop->context, valid);
+
+	  space = isl_set_get_space (extent);
+	  aff = isl_aff_zero_on_domain (isl_local_space_from_space (space));
+	  aff = isl_aff_add_coefficient_si (aff, isl_dim_in, i + 1, 1);
+	  univ = isl_set_universe (isl_space_domain (isl_aff_get_space (aff)));
+	  index = isl_pw_aff_alloc (univ, aff);
+
+	  id = isl_set_get_tuple_id (extent);
+	  lb = isl_pw_aff_set_tuple_id (lb, isl_dim_in, isl_id_copy (id));
+	  ub = isl_pw_aff_set_tuple_id (ub, isl_dim_in, id);
+
+	  /* low <= sub_i <= high */
+	  lbs = isl_pw_aff_ge_set (isl_pw_aff_copy (index), lb);
+	  ubs = isl_pw_aff_le_set (index, ub);
+	  extent = isl_set_intersect (extent, lbs);
+	  extent = isl_set_intersect (extent, ubs);
+	}
+    }
+
+  return extent;
+}
+
+/* Build data accesses for DR in PBB.  */
+
+static void
+build_poly_dr (data_reference_p dr, poly_bb_p pbb)
+{
+  int dr_base_object_set;
+  isl_map *acc;
+  isl_set *extent;
+  scop_p scop = PBB_SCOP (pbb);
+
+  {
+    isl_space *dc = isl_set_get_space (pbb->domain);
+    int nb_out = 1 + DR_NUM_DIMENSIONS (dr);
+    isl_space *space = isl_space_add_dims (isl_space_from_domain (dc),
+					   isl_dim_out, nb_out);
+
+    acc = isl_map_universe (space);
+    acc = isl_map_set_tuple_id (acc, isl_dim_out, isl_id_for_dr (scop, dr));
+  }
+
+  acc = pdr_add_alias_set (acc, dr);
+  acc = pdr_add_memory_accesses (acc, dr, pbb);
+
+  {
+    isl_id *id = isl_id_for_dr (scop, dr);
+    int nb = 1 + DR_NUM_DIMENSIONS (dr);
+    isl_space *space = isl_space_set_alloc (scop->ctx, 0, nb);
+    int alias_set_num = 0;
+    base_alias_pair *bap = (base_alias_pair *)(dr->aux);
+
+    if (bap && bap->alias_set)
+      alias_set_num = *(bap->alias_set);
+
+    space = isl_space_set_tuple_id (space, isl_dim_set, id);
+    extent = isl_set_nat_universe (space);
+    extent = isl_set_fix_si (extent, isl_dim_set, 0, alias_set_num);
+    extent = pdr_add_data_dimensions (extent, scop, dr);
+  }
+
+  gcc_assert (dr->aux);
+  dr_base_object_set = ((base_alias_pair *)(dr->aux))->base_obj_set;
+
+  new_poly_dr (pbb, dr_base_object_set,
+	       DR_IS_READ (dr) ? PDR_READ : PDR_WRITE,
+	       dr, DR_NUM_DIMENSIONS (dr), acc, extent);
+}
+
+/* Write to FILE the alias graph of data references in DIMACS format.  */
+
+static inline bool
+write_alias_graph_to_ascii_dimacs (FILE *file, char *comment,
+				   vec<data_reference_p> drs)
+{
+  int num_vertex = drs.length ();
+  int edge_num = 0;
+  data_reference_p dr1, dr2;
+  int i, j;
+
+  if (num_vertex == 0)
+    return true;
+
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    for (j = i + 1; drs.iterate (j, &dr2); j++)
+      if (dr_may_alias_p (dr1, dr2, true))
+	edge_num++;
+
+  fprintf (file, "$\n");
+
+  if (comment)
+    fprintf (file, "c %s\n", comment);
+
+  fprintf (file, "p edge %d %d\n", num_vertex, edge_num);
+
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    for (j = i + 1; drs.iterate (j, &dr2); j++)
+      if (dr_may_alias_p (dr1, dr2, true))
+	fprintf (file, "e %d %d\n", i + 1, j + 1);
+
+  return true;
+}
+
+/* Write to FILE the alias graph of data references in DOT format.  */
+
+static inline bool
+write_alias_graph_to_ascii_dot (FILE *file, char *comment,
+				vec<data_reference_p> drs)
+{
+  int num_vertex = drs.length ();
+  data_reference_p dr1, dr2;
+  int i, j;
+
+  if (num_vertex == 0)
+    return true;
+
+  fprintf (file, "$\n");
+
+  if (comment)
+    fprintf (file, "c %s\n", comment);
+
+  /* First print all the vertices.  */
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    fprintf (file, "n%d;\n", i);
+
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    for (j = i + 1; drs.iterate (j, &dr2); j++)
+      if (dr_may_alias_p (dr1, dr2, true))
+	fprintf (file, "n%d n%d\n", i, j);
+
+  return true;
+}
+
+/* Write to FILE the alias graph of data references in ECC format.  */
+
+static inline bool
+write_alias_graph_to_ascii_ecc (FILE *file, char *comment,
+				vec<data_reference_p> drs)
+{
+  int num_vertex = drs.length ();
+  data_reference_p dr1, dr2;
+  int i, j;
+
+  if (num_vertex == 0)
+    return true;
+
+  fprintf (file, "$\n");
+
+  if (comment)
+    fprintf (file, "c %s\n", comment);
+
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    for (j = i + 1; drs.iterate (j, &dr2); j++)
+      if (dr_may_alias_p (dr1, dr2, true))
+	fprintf (file, "%d %d\n", i, j);
+
+  return true;
+}
+
+/* Check if DR1 and DR2 are in the same object set.  */
+
+static bool
+dr_same_base_object_p (const struct data_reference *dr1,
+		       const struct data_reference *dr2)
+{
+  return operand_equal_p (DR_BASE_OBJECT (dr1), DR_BASE_OBJECT (dr2), 0);
+}
+
+/* Uses DFS component number as representative of alias-sets. Also tests for
+   optimality by verifying if every connected component is a clique. Returns
+   true (1) if the above test is true, and false (0) otherwise.  */
+
+static int
+build_alias_set_optimal_p (vec<data_reference_p> drs)
+{
+  int num_vertices = drs.length ();
+  struct graph *g = new_graph (num_vertices);
+  data_reference_p dr1, dr2;
+  int i, j;
+  int num_connected_components;
+  int v_indx1, v_indx2, num_vertices_in_component;
+  int *all_vertices;
+  int *vertices;
+  struct graph_edge *e;
+  int this_component_is_clique;
+  int all_components_are_cliques = 1;
+
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    for (j = i+1; drs.iterate (j, &dr2); j++)
+      if (dr_may_alias_p (dr1, dr2, true))
+	{
+	  add_edge (g, i, j);
+	  add_edge (g, j, i);
+	}
+
+  all_vertices = XNEWVEC (int, num_vertices);
+  vertices = XNEWVEC (int, num_vertices);
+  for (i = 0; i < num_vertices; i++)
+    all_vertices[i] = i;
+
+  num_connected_components = graphds_dfs (g, all_vertices, num_vertices,
+					  NULL, true, NULL);
+  for (i = 0; i < g->n_vertices; i++)
+    {
+      data_reference_p dr = drs[i];
+      base_alias_pair *bap;
+
+      gcc_assert (dr->aux);
+      bap = (base_alias_pair *)(dr->aux);
+
+      bap->alias_set = XNEW (int);
+      *(bap->alias_set) = g->vertices[i].component + 1;
+    }
+
+  /* Verify if the DFS numbering results in optimal solution.  */
+  for (i = 0; i < num_connected_components; i++)
+    {
+      num_vertices_in_component = 0;
+      /* Get all vertices whose DFS component number is the same as i.  */
+      for (j = 0; j < num_vertices; j++)
+	if (g->vertices[j].component == i)
+	  vertices[num_vertices_in_component++] = j;
+
+      /* Now test if the vertices in 'vertices' form a clique, by testing
+	 for edges among each pair.  */
+      this_component_is_clique = 1;
+      for (v_indx1 = 0; v_indx1 < num_vertices_in_component; v_indx1++)
+	{
+	  for (v_indx2 = v_indx1+1; v_indx2 < num_vertices_in_component; v_indx2++)
+	    {
+	      /* Check if the two vertices are connected by iterating
+		 through all the edges which have one of these are source.  */
+	      e = g->vertices[vertices[v_indx2]].pred;
+	      while (e)
+		{
+		  if (e->src == vertices[v_indx1])
+		    break;
+		  e = e->pred_next;
+		}
+	      if (!e)
+		{
+		  this_component_is_clique = 0;
+		  break;
+		}
+	    }
+	  if (!this_component_is_clique)
+	    all_components_are_cliques = 0;
+	}
+    }
+
+  free (all_vertices);
+  free (vertices);
+  free_graph (g);
+  return all_components_are_cliques;
+}
+
+/* Group each data reference in DRS with its base object set num.  */
+
+static void
+build_base_obj_set_for_drs (vec<data_reference_p> drs)
+{
+  int num_vertex = drs.length ();
+  struct graph *g = new_graph (num_vertex);
+  data_reference_p dr1, dr2;
+  int i, j;
+  int *queue;
+
+  FOR_EACH_VEC_ELT (drs, i, dr1)
+    for (j = i + 1; drs.iterate (j, &dr2); j++)
+      if (dr_same_base_object_p (dr1, dr2))
+	{
+	  add_edge (g, i, j);
+	  add_edge (g, j, i);
+	}
+
+  queue = XNEWVEC (int, num_vertex);
+  for (i = 0; i < num_vertex; i++)
+    queue[i] = i;
+
+  graphds_dfs (g, queue, num_vertex, NULL, true, NULL);
+
+  for (i = 0; i < g->n_vertices; i++)
+    {
+      data_reference_p dr = drs[i];
+      base_alias_pair *bap;
+
+      gcc_assert (dr->aux);
+      bap = (base_alias_pair *)(dr->aux);
+
+      bap->base_obj_set = g->vertices[i].component + 1;
+    }
+
+  free (queue);
+  free_graph (g);
+}
+
+/* Build the data references for PBB.  */
+
+static void
+build_pbb_drs (poly_bb_p pbb)
+{
+  int j;
+  data_reference_p dr;
+  vec<data_reference_p> gbb_drs = GBB_DATA_REFS (PBB_BLACK_BOX (pbb));
+
+  FOR_EACH_VEC_ELT (gbb_drs, j, dr)
+    build_poly_dr (dr, pbb);
+}
+
+/* Dump to file the alias graphs for the data references in DRS.  */
+
+static void
+dump_alias_graphs (vec<data_reference_p> drs)
+{
+  char comment[100];
+  FILE *file_dimacs, *file_ecc, *file_dot;
+
+  file_dimacs = fopen ("/tmp/dr_alias_graph_dimacs", "ab");
+  if (file_dimacs)
+    {
+      snprintf (comment, sizeof (comment), "%s %s", main_input_filename,
+		current_function_name ());
+      write_alias_graph_to_ascii_dimacs (file_dimacs, comment, drs);
+      fclose (file_dimacs);
+    }
+
+  file_ecc = fopen ("/tmp/dr_alias_graph_ecc", "ab");
+  if (file_ecc)
+    {
+      snprintf (comment, sizeof (comment), "%s %s", main_input_filename,
+		current_function_name ());
+      write_alias_graph_to_ascii_ecc (file_ecc, comment, drs);
+      fclose (file_ecc);
+    }
+
+  file_dot = fopen ("/tmp/dr_alias_graph_dot", "ab");
+  if (file_dot)
+    {
+      snprintf (comment, sizeof (comment), "%s %s", main_input_filename,
+		current_function_name ());
+      write_alias_graph_to_ascii_dot (file_dot, comment, drs);
+      fclose (file_dot);
+    }
+}
+
+/* Build data references in SCOP.  */
+
+static void
+build_scop_drs (scop_p scop)
+{
+  int i, j;
+  poly_bb_p pbb;
+  data_reference_p dr;
+  auto_vec<data_reference_p, 3> drs;
+
+  /* Remove all the PBBs that do not have data references: these basic
+     blocks are not handled in the polyhedral representation.  */
+  for (i = 0; SCOP_BBS (scop).iterate (i, &pbb); i++)
+    if (GBB_DATA_REFS (PBB_BLACK_BOX (pbb)).is_empty ())
+      {
+	free_gimple_bb (PBB_BLACK_BOX (pbb));
+	free_poly_bb (pbb);
+	SCOP_BBS (scop).ordered_remove (i);
+	i--;
+      }
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    for (j = 0; GBB_DATA_REFS (PBB_BLACK_BOX (pbb)).iterate (j, &dr); j++)
+      drs.safe_push (dr);
+
+  FOR_EACH_VEC_ELT (drs, i, dr)
+    dr->aux = XNEW (base_alias_pair);
+
+  if (!build_alias_set_optimal_p (drs))
+    {
+      /* TODO: Add support when building alias set is not optimal.  */
+      ;
+    }
+
+  build_base_obj_set_for_drs (drs);
+
+  /* When debugging, enable the following code.  This cannot be used
+     in production compilers.  */
+  if (0)
+    dump_alias_graphs (drs);
+
+  drs.release ();
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    build_pbb_drs (pbb);
+}
+
+/* Return a gsi at the position of the phi node STMT.  */
+
+static gimple_stmt_iterator
+gsi_for_phi_node (gimple stmt)
+{
+  gimple_stmt_iterator psi;
+  basic_block bb = gimple_bb (stmt);
+
+  for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
+    if (stmt == gsi_stmt (psi))
+      return psi;
+
+  gcc_unreachable ();
+  return psi;
+}
+
+/* Analyze all the data references of STMTS and add them to the
+   GBB_DATA_REFS vector of BB.  */
+
+static void
+analyze_drs_in_stmts (scop_p scop, basic_block bb, vec<gimple> stmts)
+{
+  loop_p nest;
+  gimple_bb_p gbb;
+  gimple stmt;
+  int i;
+  sese region = SCOP_REGION (scop);
+
+  if (!bb_in_sese_p (bb, region))
+    return;
+
+  nest = outermost_loop_in_sese_1 (region, bb);
+  gbb = gbb_from_bb (bb);
+
+  FOR_EACH_VEC_ELT (stmts, i, stmt)
+    {
+      loop_p loop;
+
+      if (is_gimple_debug (stmt))
+	continue;
+
+      loop = loop_containing_stmt (stmt);
+      if (!loop_in_sese_p (loop, region))
+	loop = nest;
+
+      graphite_find_data_references_in_stmt (nest, loop, stmt,
+					     &GBB_DATA_REFS (gbb));
+    }
+}
+
+/* Insert STMT at the end of the STMTS sequence and then insert the
+   statements from STMTS at INSERT_GSI and call analyze_drs_in_stmts
+   on STMTS.  */
+
+static void
+insert_stmts (scop_p scop, gimple stmt, gimple_seq stmts,
+	      gimple_stmt_iterator insert_gsi)
+{
+  gimple_stmt_iterator gsi;
+  auto_vec<gimple, 3> x;
+
+  gimple_seq_add_stmt (&stmts, stmt);
+  for (gsi = gsi_start (stmts); !gsi_end_p (gsi); gsi_next (&gsi))
+    x.safe_push (gsi_stmt (gsi));
+
+  gsi_insert_seq_before (&insert_gsi, stmts, GSI_SAME_STMT);
+  analyze_drs_in_stmts (scop, gsi_bb (insert_gsi), x);
+}
+
+/* Insert the assignment "RES := EXPR" just after AFTER_STMT.  */
+
+static void
+insert_out_of_ssa_copy (scop_p scop, tree res, tree expr, gimple after_stmt)
+{
+  gimple_seq stmts;
+  gimple_stmt_iterator gsi;
+  tree var = force_gimple_operand (expr, &stmts, true, NULL_TREE);
+  gimple stmt = gimple_build_assign (unshare_expr (res), var);
+  auto_vec<gimple, 3> x;
+
+  gimple_seq_add_stmt (&stmts, stmt);
+  for (gsi = gsi_start (stmts); !gsi_end_p (gsi); gsi_next (&gsi))
+    x.safe_push (gsi_stmt (gsi));
+
+  if (gimple_code (after_stmt) == GIMPLE_PHI)
+    {
+      gsi = gsi_after_labels (gimple_bb (after_stmt));
+      gsi_insert_seq_before (&gsi, stmts, GSI_NEW_STMT);
+    }
+  else
+    {
+      gsi = gsi_for_stmt (after_stmt);
+      gsi_insert_seq_after (&gsi, stmts, GSI_NEW_STMT);
+    }
+
+  analyze_drs_in_stmts (scop, gimple_bb (after_stmt), x);
+}
+
+/* Creates a poly_bb_p for basic_block BB from the existing PBB.  */
+
+static void
+new_pbb_from_pbb (scop_p scop, poly_bb_p pbb, basic_block bb)
+{
+  vec<data_reference_p> drs;
+  drs.create (3);
+  gimple_bb_p gbb = PBB_BLACK_BOX (pbb);
+  gimple_bb_p gbb1 = new_gimple_bb (bb, drs);
+  poly_bb_p pbb1 = new_poly_bb (scop, gbb1);
+  int index, n = SCOP_BBS (scop).length ();
+
+  /* The INDEX of PBB in SCOP_BBS.  */
+  for (index = 0; index < n; index++)
+    if (SCOP_BBS (scop)[index] == pbb)
+      break;
+
+  pbb1->domain = isl_set_copy (pbb->domain);
+
+  GBB_PBB (gbb1) = pbb1;
+  GBB_CONDITIONS (gbb1) = GBB_CONDITIONS (gbb).copy ();
+  GBB_CONDITION_CASES (gbb1) = GBB_CONDITION_CASES (gbb).copy ();
+  SCOP_BBS (scop).safe_insert (index + 1, pbb1);
+}
+
+/* Insert on edge E the assignment "RES := EXPR".  */
+
+static void
+insert_out_of_ssa_copy_on_edge (scop_p scop, edge e, tree res, tree expr)
+{
+  gimple_stmt_iterator gsi;
+  gimple_seq stmts = NULL;
+  tree var = force_gimple_operand (expr, &stmts, true, NULL_TREE);
+  gimple stmt = gimple_build_assign (unshare_expr (res), var);
+  basic_block bb;
+  auto_vec<gimple, 3> x;
+
+  gimple_seq_add_stmt (&stmts, stmt);
+  for (gsi = gsi_start (stmts); !gsi_end_p (gsi); gsi_next (&gsi))
+    x.safe_push (gsi_stmt (gsi));
+
+  gsi_insert_seq_on_edge (e, stmts);
+  gsi_commit_edge_inserts ();
+  bb = gimple_bb (stmt);
+
+  if (!bb_in_sese_p (bb, SCOP_REGION (scop)))
+    return;
+
+  if (!gbb_from_bb (bb))
+    new_pbb_from_pbb (scop, pbb_from_bb (e->src), bb);
+
+  analyze_drs_in_stmts (scop, bb, x);
+}
+
+/* Creates a zero dimension array of the same type as VAR.  */
+
+static tree
+create_zero_dim_array (tree var, const char *base_name)
+{
+  tree index_type = build_index_type (integer_zero_node);
+  tree elt_type = TREE_TYPE (var);
+  tree array_type = build_array_type (elt_type, index_type);
+  tree base = create_tmp_var (array_type, base_name);
+
+  return build4 (ARRAY_REF, elt_type, base, integer_zero_node, NULL_TREE,
+		 NULL_TREE);
+}
+
+/* Returns true when PHI is a loop close phi node.  */
+
+static bool
+scalar_close_phi_node_p (gimple phi)
+{
+  if (gimple_code (phi) != GIMPLE_PHI
+      || virtual_operand_p (gimple_phi_result (phi)))
+    return false;
+
+  /* Note that loop close phi nodes should have a single argument
+     because we translated the representation into a canonical form
+     before Graphite: see canonicalize_loop_closed_ssa_form.  */
+  return (gimple_phi_num_args (phi) == 1);
+}
+
+/* For a definition DEF in REGION, propagates the expression EXPR in
+   all the uses of DEF outside REGION.  */
+
+static void
+propagate_expr_outside_region (tree def, tree expr, sese region)
+{
+  imm_use_iterator imm_iter;
+  gimple use_stmt;
+  gimple_seq stmts;
+  bool replaced_once = false;
+
+  gcc_assert (TREE_CODE (def) == SSA_NAME);
+
+  expr = force_gimple_operand (unshare_expr (expr), &stmts, true,
+			       NULL_TREE);
+
+  FOR_EACH_IMM_USE_STMT (use_stmt, imm_iter, def)
+    if (!is_gimple_debug (use_stmt)
+	&& !bb_in_sese_p (gimple_bb (use_stmt), region))
+      {
+	ssa_op_iter iter;
+	use_operand_p use_p;
+
+	FOR_EACH_PHI_OR_STMT_USE (use_p, use_stmt, iter, SSA_OP_ALL_USES)
+	  if (operand_equal_p (def, USE_FROM_PTR (use_p), 0)
+	      && (replaced_once = true))
+	    replace_exp (use_p, expr);
+
+	update_stmt (use_stmt);
+      }
+
+  if (replaced_once)
+    {
+      gsi_insert_seq_on_edge (SESE_ENTRY (region), stmts);
+      gsi_commit_edge_inserts ();
+    }
+}
+
+/* Rewrite out of SSA the reduction phi node at PSI by creating a zero
+   dimension array for it.  */
+
+static void
+rewrite_close_phi_out_of_ssa (scop_p scop, gimple_stmt_iterator *psi)
+{
+  sese region = SCOP_REGION (scop);
+  gimple phi = gsi_stmt (*psi);
+  tree res = gimple_phi_result (phi);
+  basic_block bb = gimple_bb (phi);
+  gimple_stmt_iterator gsi = gsi_after_labels (bb);
+  tree arg = gimple_phi_arg_def (phi, 0);
+  gimple stmt;
+
+  /* Note that loop close phi nodes should have a single argument
+     because we translated the representation into a canonical form
+     before Graphite: see canonicalize_loop_closed_ssa_form.  */
+  gcc_assert (gimple_phi_num_args (phi) == 1);
+
+  /* The phi node can be a non close phi node, when its argument is
+     invariant, or a default definition.  */
+  if (is_gimple_min_invariant (arg)
+      || SSA_NAME_IS_DEFAULT_DEF (arg))
+    {
+      propagate_expr_outside_region (res, arg, region);
+      gsi_next (psi);
+      return;
+    }
+
+  else if (gimple_bb (SSA_NAME_DEF_STMT (arg))->loop_father == bb->loop_father)
+    {
+      propagate_expr_outside_region (res, arg, region);
+      stmt = gimple_build_assign (res, arg);
+      remove_phi_node (psi, false);
+      gsi_insert_before (&gsi, stmt, GSI_NEW_STMT);
+      return;
+    }
+
+  /* If res is scev analyzable and is not a scalar value, it is safe
+     to ignore the close phi node: it will be code generated in the
+     out of Graphite pass.  */
+  else if (scev_analyzable_p (res, region))
+    {
+      loop_p loop = loop_containing_stmt (SSA_NAME_DEF_STMT (res));
+      tree scev;
+
+      if (!loop_in_sese_p (loop, region))
+	{
+	  loop = loop_containing_stmt (SSA_NAME_DEF_STMT (arg));
+	  scev = scalar_evolution_in_region (region, loop, arg);
+	  scev = compute_overall_effect_of_inner_loop (loop, scev);
+	}
+      else
+	scev = scalar_evolution_in_region (region, loop, res);
+
+      if (tree_does_not_contain_chrecs (scev))
+	propagate_expr_outside_region (res, scev, region);
+
+      gsi_next (psi);
+      return;
+    }
+  else
+    {
+      tree zero_dim_array = create_zero_dim_array (res, "Close_Phi");
+
+      stmt = gimple_build_assign (res, unshare_expr (zero_dim_array));
+
+      if (TREE_CODE (arg) == SSA_NAME)
+	insert_out_of_ssa_copy (scop, zero_dim_array, arg,
+				SSA_NAME_DEF_STMT (arg));
+      else
+	insert_out_of_ssa_copy_on_edge (scop, single_pred_edge (bb),
+					zero_dim_array, arg);
+    }
+
+  remove_phi_node (psi, false);
+  SSA_NAME_DEF_STMT (res) = stmt;
+
+  insert_stmts (scop, stmt, NULL, gsi_after_labels (bb));
+}
+
+/* Rewrite out of SSA the reduction phi node at PSI by creating a zero
+   dimension array for it.  */
+
+static void
+rewrite_phi_out_of_ssa (scop_p scop, gimple_stmt_iterator *psi)
+{
+  size_t i;
+  gimple phi = gsi_stmt (*psi);
+  basic_block bb = gimple_bb (phi);
+  tree res = gimple_phi_result (phi);
+  tree zero_dim_array = create_zero_dim_array (res, "phi_out_of_ssa");
+  gimple stmt;
+
+  for (i = 0; i < gimple_phi_num_args (phi); i++)
+    {
+      tree arg = gimple_phi_arg_def (phi, i);
+      edge e = gimple_phi_arg_edge (phi, i);
+
+      /* Avoid the insertion of code in the loop latch to please the
+	 pattern matching of the vectorizer.  */
+      if (TREE_CODE (arg) == SSA_NAME
+	  && e->src == bb->loop_father->latch)
+	insert_out_of_ssa_copy (scop, zero_dim_array, arg,
+				SSA_NAME_DEF_STMT (arg));
+      else
+	insert_out_of_ssa_copy_on_edge (scop, e, zero_dim_array, arg);
+    }
+
+  stmt = gimple_build_assign (res, unshare_expr (zero_dim_array));
+  remove_phi_node (psi, false);
+  insert_stmts (scop, stmt, NULL, gsi_after_labels (bb));
+}
+
+/* Rewrite the degenerate phi node at position PSI from the degenerate
+   form "x = phi (y, y, ..., y)" to "x = y".  */
+
+static void
+rewrite_degenerate_phi (gimple_stmt_iterator *psi)
+{
+  tree rhs;
+  gimple stmt;
+  gimple_stmt_iterator gsi;
+  gimple phi = gsi_stmt (*psi);
+  tree res = gimple_phi_result (phi);
+  basic_block bb;
+
+  bb = gimple_bb (phi);
+  rhs = degenerate_phi_result (phi);
+  gcc_assert (rhs);
+
+  stmt = gimple_build_assign (res, rhs);
+  remove_phi_node (psi, false);
+
+  gsi = gsi_after_labels (bb);
+  gsi_insert_before (&gsi, stmt, GSI_NEW_STMT);
+}
+
+/* Rewrite out of SSA all the reduction phi nodes of SCOP.  */
+
+static void
+rewrite_reductions_out_of_ssa (scop_p scop)
+{
+  basic_block bb;
+  gimple_stmt_iterator psi;
+  sese region = SCOP_REGION (scop);
+
+  FOR_EACH_BB_FN (bb, cfun)
+    if (bb_in_sese_p (bb, region))
+      for (psi = gsi_start_phis (bb); !gsi_end_p (psi);)
+	{
+	  gimple phi = gsi_stmt (psi);
+
+	  if (virtual_operand_p (gimple_phi_result (phi)))
+	    {
+	      gsi_next (&psi);
+	      continue;
+	    }
+
+	  if (gimple_phi_num_args (phi) > 1
+	      && degenerate_phi_result (phi))
+	    rewrite_degenerate_phi (&psi);
+
+	  else if (scalar_close_phi_node_p (phi))
+	    rewrite_close_phi_out_of_ssa (scop, &psi);
+
+	  else if (reduction_phi_p (region, &psi))
+	    rewrite_phi_out_of_ssa (scop, &psi);
+	}
+
+  update_ssa (TODO_update_ssa);
+#ifdef ENABLE_CHECKING
+  verify_loop_closed_ssa (true);
+#endif
+}
+
+/* Rewrite the scalar dependence of DEF used in USE_STMT with a memory
+   read from ZERO_DIM_ARRAY.  */
+
+static void
+rewrite_cross_bb_scalar_dependence (scop_p scop, tree zero_dim_array,
+				    tree def, gimple use_stmt)
+{
+  gimple name_stmt;
+  tree name;
+  ssa_op_iter iter;
+  use_operand_p use_p;
+
+  gcc_assert (gimple_code (use_stmt) != GIMPLE_PHI);
+
+  name = copy_ssa_name (def, NULL);
+  name_stmt = gimple_build_assign (name, zero_dim_array);
+
+  gimple_assign_set_lhs (name_stmt, name);
+  insert_stmts (scop, name_stmt, NULL, gsi_for_stmt (use_stmt));
+
+  FOR_EACH_SSA_USE_OPERAND (use_p, use_stmt, iter, SSA_OP_ALL_USES)
+    if (operand_equal_p (def, USE_FROM_PTR (use_p), 0))
+      replace_exp (use_p, name);
+
+  update_stmt (use_stmt);
+}
+
+/* For every definition DEF in the SCOP that is used outside the scop,
+   insert a closing-scop definition in the basic block just after this
+   SCOP.  */
+
+static void
+handle_scalar_deps_crossing_scop_limits (scop_p scop, tree def, gimple stmt)
+{
+  tree var = create_tmp_reg (TREE_TYPE (def), NULL);
+  tree new_name = make_ssa_name (var, stmt);
+  bool needs_copy = false;
+  use_operand_p use_p;
+  imm_use_iterator imm_iter;
+  gimple use_stmt;
+  sese region = SCOP_REGION (scop);
+
+  FOR_EACH_IMM_USE_STMT (use_stmt, imm_iter, def)
+    {
+      if (!bb_in_sese_p (gimple_bb (use_stmt), region))
+	{
+	  FOR_EACH_IMM_USE_ON_STMT (use_p, imm_iter)
+	    {
+	      SET_USE (use_p, new_name);
+	    }
+	  update_stmt (use_stmt);
+	  needs_copy = true;
+	}
+    }
+
+  /* Insert in the empty BB just after the scop a use of DEF such
+     that the rewrite of cross_bb_scalar_dependences won't insert
+     arrays everywhere else.  */
+  if (needs_copy)
+    {
+      gimple assign = gimple_build_assign (new_name, def);
+      gimple_stmt_iterator psi = gsi_after_labels (SESE_EXIT (region)->dest);
+
+      update_stmt (assign);
+      gsi_insert_before (&psi, assign, GSI_SAME_STMT);
+    }
+}
+
+/* Rewrite the scalar dependences crossing the boundary of the BB
+   containing STMT with an array.  Return true when something has been
+   changed.  */
+
+static bool
+rewrite_cross_bb_scalar_deps (scop_p scop, gimple_stmt_iterator *gsi)
+{
+  sese region = SCOP_REGION (scop);
+  gimple stmt = gsi_stmt (*gsi);
+  imm_use_iterator imm_iter;
+  tree def;
+  basic_block def_bb;
+  tree zero_dim_array = NULL_TREE;
+  gimple use_stmt;
+  bool res = false;
+
+  switch (gimple_code (stmt))
+    {
+    case GIMPLE_ASSIGN:
+      def = gimple_assign_lhs (stmt);
+      break;
+
+    case GIMPLE_CALL:
+      def = gimple_call_lhs (stmt);
+      break;
+
+    default:
+      return false;
+    }
+
+  if (!def
+      || !is_gimple_reg (def))
+    return false;
+
+  if (scev_analyzable_p (def, region))
+    {
+      loop_p loop = loop_containing_stmt (SSA_NAME_DEF_STMT (def));
+      tree scev = scalar_evolution_in_region (region, loop, def);
+
+      if (tree_contains_chrecs (scev, NULL))
+	return false;
+
+      propagate_expr_outside_region (def, scev, region);
+      return true;
+    }
+
+  def_bb = gimple_bb (stmt);
+
+  handle_scalar_deps_crossing_scop_limits (scop, def, stmt);
+
+  FOR_EACH_IMM_USE_STMT (use_stmt, imm_iter, def)
+    if (gimple_code (use_stmt) == GIMPLE_PHI
+	&& (res = true))
+      {
+	gimple_stmt_iterator psi = gsi_for_stmt (use_stmt);
+
+	if (scalar_close_phi_node_p (gsi_stmt (psi)))
+	  rewrite_close_phi_out_of_ssa (scop, &psi);
+	else
+	  rewrite_phi_out_of_ssa (scop, &psi);
+      }
+
+  FOR_EACH_IMM_USE_STMT (use_stmt, imm_iter, def)
+    if (gimple_code (use_stmt) != GIMPLE_PHI
+	&& def_bb != gimple_bb (use_stmt)
+	&& !is_gimple_debug (use_stmt)
+	&& (res = true))
+      {
+	if (!zero_dim_array)
+	  {
+	    zero_dim_array = create_zero_dim_array
+	      (def, "Cross_BB_scalar_dependence");
+	    insert_out_of_ssa_copy (scop, zero_dim_array, def,
+				    SSA_NAME_DEF_STMT (def));
+	    gsi_next (gsi);
+	  }
+
+	rewrite_cross_bb_scalar_dependence (scop, zero_dim_array,
+					    def, use_stmt);
+      }
+
+  return res;
+}
+
+/* Rewrite out of SSA all the reduction phi nodes of SCOP.  */
+
+static void
+rewrite_cross_bb_scalar_deps_out_of_ssa (scop_p scop)
+{
+  basic_block bb;
+  gimple_stmt_iterator psi;
+  sese region = SCOP_REGION (scop);
+  bool changed = false;
+
+  /* Create an extra empty BB after the scop.  */
+  split_edge (SESE_EXIT (region));
+
+  FOR_EACH_BB_FN (bb, cfun)
+    if (bb_in_sese_p (bb, region))
+      for (psi = gsi_start_bb (bb); !gsi_end_p (psi); gsi_next (&psi))
+	changed |= rewrite_cross_bb_scalar_deps (scop, &psi);
+
+  if (changed)
+    {
+      scev_reset_htab ();
+      update_ssa (TODO_update_ssa);
+#ifdef ENABLE_CHECKING
+      verify_loop_closed_ssa (true);
+#endif
+    }
+}
+
+/* Returns the number of pbbs that are in loops contained in SCOP.  */
+
+static int
+nb_pbbs_in_loops (scop_p scop)
+{
+  int i;
+  poly_bb_p pbb;
+  int res = 0;
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    if (loop_in_sese_p (gbb_loop (PBB_BLACK_BOX (pbb)), SCOP_REGION (scop)))
+      res++;
+
+  return res;
+}
+
+/* Return the number of data references in BB that write in
+   memory.  */
+
+static int
+nb_data_writes_in_bb (basic_block bb)
+{
+  int res = 0;
+  gimple_stmt_iterator gsi;
+
+  for (gsi = gsi_start_bb (bb); !gsi_end_p (gsi); gsi_next (&gsi))
+    if (gimple_vdef (gsi_stmt (gsi)))
+      res++;
+
+  return res;
+}
+
+/* Splits at STMT the basic block BB represented as PBB in the
+   polyhedral form.  */
+
+static edge
+split_pbb (scop_p scop, poly_bb_p pbb, basic_block bb, gimple stmt)
+{
+  edge e1 = split_block (bb, stmt);
+  new_pbb_from_pbb (scop, pbb, e1->dest);
+  return e1;
+}
+
+/* Splits STMT out of its current BB.  This is done for reduction
+   statements for which we want to ignore data dependences.  */
+
+static basic_block
+split_reduction_stmt (scop_p scop, gimple stmt)
+{
+  basic_block bb = gimple_bb (stmt);
+  poly_bb_p pbb = pbb_from_bb (bb);
+  gimple_bb_p gbb = gbb_from_bb (bb);
+  edge e1;
+  int i;
+  data_reference_p dr;
+
+  /* Do not split basic blocks with no writes to memory: the reduction
+     will be the only write to memory.  */
+  if (nb_data_writes_in_bb (bb) == 0
+      /* Or if we have already marked BB as a reduction.  */
+      || PBB_IS_REDUCTION (pbb_from_bb (bb)))
+    return bb;
+
+  e1 = split_pbb (scop, pbb, bb, stmt);
+
+  /* Split once more only when the reduction stmt is not the only one
+     left in the original BB.  */
+  if (!gsi_one_before_end_p (gsi_start_nondebug_bb (bb)))
+    {
+      gimple_stmt_iterator gsi = gsi_last_bb (bb);
+      gsi_prev (&gsi);
+      e1 = split_pbb (scop, pbb, bb, gsi_stmt (gsi));
+    }
+
+  /* A part of the data references will end in a different basic block
+     after the split: move the DRs from the original GBB to the newly
+     created GBB1.  */
+  FOR_EACH_VEC_ELT (GBB_DATA_REFS (gbb), i, dr)
+    {
+      basic_block bb1 = gimple_bb (DR_STMT (dr));
+
+      if (bb1 != bb)
+	{
+	  gimple_bb_p gbb1 = gbb_from_bb (bb1);
+	  GBB_DATA_REFS (gbb1).safe_push (dr);
+	  GBB_DATA_REFS (gbb).ordered_remove (i);
+	  i--;
+	}
+    }
+
+  return e1->dest;
+}
+
+/* Return true when stmt is a reduction operation.  */
+
+static inline bool
+is_reduction_operation_p (gimple stmt)
+{
+  enum tree_code code;
+
+  gcc_assert (is_gimple_assign (stmt));
+  code = gimple_assign_rhs_code (stmt);
+
+  return flag_associative_math
+    && commutative_tree_code (code)
+    && associative_tree_code (code);
+}
+
+/* Returns true when PHI contains an argument ARG.  */
+
+static bool
+phi_contains_arg (gimple phi, tree arg)
+{
+  size_t i;
+
+  for (i = 0; i < gimple_phi_num_args (phi); i++)
+    if (operand_equal_p (arg, gimple_phi_arg_def (phi, i), 0))
+      return true;
+
+  return false;
+}
+
+/* Return a loop phi node that corresponds to a reduction containing LHS.  */
+
+static gimple
+follow_ssa_with_commutative_ops (tree arg, tree lhs)
+{
+  gimple stmt;
+
+  if (TREE_CODE (arg) != SSA_NAME)
+    return NULL;
+
+  stmt = SSA_NAME_DEF_STMT (arg);
+
+  if (gimple_code (stmt) == GIMPLE_NOP
+      || gimple_code (stmt) == GIMPLE_CALL)
+    return NULL;
+
+  if (gimple_code (stmt) == GIMPLE_PHI)
+    {
+      if (phi_contains_arg (stmt, lhs))
+	return stmt;
+      return NULL;
+    }
+
+  if (!is_gimple_assign (stmt))
+    return NULL;
+
+  if (gimple_num_ops (stmt) == 2)
+    return follow_ssa_with_commutative_ops (gimple_assign_rhs1 (stmt), lhs);
+
+  if (is_reduction_operation_p (stmt))
+    {
+      gimple res = follow_ssa_with_commutative_ops (gimple_assign_rhs1 (stmt), lhs);
+
+      return res ? res :
+	follow_ssa_with_commutative_ops (gimple_assign_rhs2 (stmt), lhs);
+    }
+
+  return NULL;
+}
+
+/* Detect commutative and associative scalar reductions starting at
+   the STMT.  Return the phi node of the reduction cycle, or NULL.  */
+
+static gimple
+detect_commutative_reduction_arg (tree lhs, gimple stmt, tree arg,
+				  vec<gimple> *in,
+				  vec<gimple> *out)
+{
+  gimple phi = follow_ssa_with_commutative_ops (arg, lhs);
+
+  if (!phi)
+    return NULL;
+
+  in->safe_push (stmt);
+  out->safe_push (stmt);
+  return phi;
+}
+
+/* Detect commutative and associative scalar reductions starting at
+   STMT.  Return the phi node of the reduction cycle, or NULL.  */
+
+static gimple
+detect_commutative_reduction_assign (gimple stmt, vec<gimple> *in,
+				     vec<gimple> *out)
+{
+  tree lhs = gimple_assign_lhs (stmt);
+
+  if (gimple_num_ops (stmt) == 2)
+    return detect_commutative_reduction_arg (lhs, stmt,
+					     gimple_assign_rhs1 (stmt),
+					     in, out);
+
+  if (is_reduction_operation_p (stmt))
+    {
+      gimple res = detect_commutative_reduction_arg (lhs, stmt,
+						     gimple_assign_rhs1 (stmt),
+						     in, out);
+      return res ? res
+	: detect_commutative_reduction_arg (lhs, stmt,
+					    gimple_assign_rhs2 (stmt),
+					    in, out);
+    }
+
+  return NULL;
+}
+
+/* Return a loop phi node that corresponds to a reduction containing LHS.  */
+
+static gimple
+follow_inital_value_to_phi (tree arg, tree lhs)
+{
+  gimple stmt;
+
+  if (!arg || TREE_CODE (arg) != SSA_NAME)
+    return NULL;
+
+  stmt = SSA_NAME_DEF_STMT (arg);
+
+  if (gimple_code (stmt) == GIMPLE_PHI
+      && phi_contains_arg (stmt, lhs))
+    return stmt;
+
+  return NULL;
+}
+
+
+/* Return the argument of the loop PHI that is the initial value coming
+   from outside the loop.  */
+
+static edge
+edge_initial_value_for_loop_phi (gimple phi)
+{
+  size_t i;
+
+  for (i = 0; i < gimple_phi_num_args (phi); i++)
+    {
+      edge e = gimple_phi_arg_edge (phi, i);
+
+      if (loop_depth (e->src->loop_father)
+	  < loop_depth (e->dest->loop_father))
+	return e;
+    }
+
+  return NULL;
+}
+
+/* Return the argument of the loop PHI that is the initial value coming
+   from outside the loop.  */
+
+static tree
+initial_value_for_loop_phi (gimple phi)
+{
+  size_t i;
+
+  for (i = 0; i < gimple_phi_num_args (phi); i++)
+    {
+      edge e = gimple_phi_arg_edge (phi, i);
+
+      if (loop_depth (e->src->loop_father)
+	  < loop_depth (e->dest->loop_father))
+	return gimple_phi_arg_def (phi, i);
+    }
+
+  return NULL_TREE;
+}
+
+/* Returns true when DEF is used outside the reduction cycle of
+   LOOP_PHI.  */
+
+static bool
+used_outside_reduction (tree def, gimple loop_phi)
+{
+  use_operand_p use_p;
+  imm_use_iterator imm_iter;
+  loop_p loop = loop_containing_stmt (loop_phi);
+
+  /* In LOOP, DEF should be used only in LOOP_PHI.  */
+  FOR_EACH_IMM_USE_FAST (use_p, imm_iter, def)
+    {
+      gimple stmt = USE_STMT (use_p);
+
+      if (stmt != loop_phi
+	  && !is_gimple_debug (stmt)
+	  && flow_bb_inside_loop_p (loop, gimple_bb (stmt)))
+	return true;
+    }
+
+  return false;
+}
+
+/* Detect commutative and associative scalar reductions belonging to
+   the SCOP starting at the loop closed phi node STMT.  Return the phi
+   node of the reduction cycle, or NULL.  */
+
+static gimple
+detect_commutative_reduction (scop_p scop, gimple stmt, vec<gimple> *in,
+			      vec<gimple> *out)
+{
+  if (scalar_close_phi_node_p (stmt))
+    {
+      gimple def, loop_phi, phi, close_phi = stmt;
+      tree init, lhs, arg = gimple_phi_arg_def (close_phi, 0);
+
+      if (TREE_CODE (arg) != SSA_NAME)
+	return NULL;
+
+      /* Note that loop close phi nodes should have a single argument
+	 because we translated the representation into a canonical form
+	 before Graphite: see canonicalize_loop_closed_ssa_form.  */
+      gcc_assert (gimple_phi_num_args (close_phi) == 1);
+
+      def = SSA_NAME_DEF_STMT (arg);
+      if (!stmt_in_sese_p (def, SCOP_REGION (scop))
+	  || !(loop_phi = detect_commutative_reduction (scop, def, in, out)))
+	return NULL;
+
+      lhs = gimple_phi_result (close_phi);
+      init = initial_value_for_loop_phi (loop_phi);
+      phi = follow_inital_value_to_phi (init, lhs);
+
+      if (phi && (used_outside_reduction (lhs, phi)
+		  || !has_single_use (gimple_phi_result (phi))))
+	return NULL;
+
+      in->safe_push (loop_phi);
+      out->safe_push (close_phi);
+      return phi;
+    }
+
+  if (gimple_code (stmt) == GIMPLE_ASSIGN)
+    return detect_commutative_reduction_assign (stmt, in, out);
+
+  return NULL;
+}
+
+/* Translate the scalar reduction statement STMT to an array RED
+   knowing that its recursive phi node is LOOP_PHI.  */
+
+static void
+translate_scalar_reduction_to_array_for_stmt (scop_p scop, tree red,
+					      gimple stmt, gimple loop_phi)
+{
+  tree res = gimple_phi_result (loop_phi);
+  gimple assign = gimple_build_assign (res, unshare_expr (red));
+  gimple_stmt_iterator gsi;
+
+  insert_stmts (scop, assign, NULL, gsi_after_labels (gimple_bb (loop_phi)));
+
+  assign = gimple_build_assign (unshare_expr (red), gimple_assign_lhs (stmt));
+  gsi = gsi_for_stmt (stmt);
+  gsi_next (&gsi);
+  insert_stmts (scop, assign, NULL, gsi);
+}
+
+/* Removes the PHI node and resets all the debug stmts that are using
+   the PHI_RESULT.  */
+
+static void
+remove_phi (gimple phi)
+{
+  imm_use_iterator imm_iter;
+  tree def;
+  use_operand_p use_p;
+  gimple_stmt_iterator gsi;
+  auto_vec<gimple, 3> update;
+  unsigned int i;
+  gimple stmt;
+
+  def = PHI_RESULT (phi);
+  FOR_EACH_IMM_USE_FAST (use_p, imm_iter, def)
+    {
+      stmt = USE_STMT (use_p);
+
+      if (is_gimple_debug (stmt))
+	{
+	  gimple_debug_bind_reset_value (stmt);
+	  update.safe_push (stmt);
+	}
+    }
+
+  FOR_EACH_VEC_ELT (update, i, stmt)
+    update_stmt (stmt);
+
+  gsi = gsi_for_phi_node (phi);
+  remove_phi_node (&gsi, false);
+}
+
+/* Helper function for for_each_index.  For each INDEX of the data
+   reference REF, returns true when its indices are valid in the loop
+   nest LOOP passed in as DATA.  */
+
+static bool
+dr_indices_valid_in_loop (tree ref ATTRIBUTE_UNUSED, tree *index, void *data)
+{
+  loop_p loop;
+  basic_block header, def_bb;
+  gimple stmt;
+
+  if (TREE_CODE (*index) != SSA_NAME)
+    return true;
+
+  loop = *((loop_p *) data);
+  header = loop->header;
+  stmt = SSA_NAME_DEF_STMT (*index);
+
+  if (!stmt)
+    return true;
+
+  def_bb = gimple_bb (stmt);
+
+  if (!def_bb)
+    return true;
+
+  return dominated_by_p (CDI_DOMINATORS, header, def_bb);
+}
+
+/* When the result of a CLOSE_PHI is written to a memory location,
+   return a pointer to that memory reference, otherwise return
+   NULL_TREE.  */
+
+static tree
+close_phi_written_to_memory (gimple close_phi)
+{
+  imm_use_iterator imm_iter;
+  use_operand_p use_p;
+  gimple stmt;
+  tree res, def = gimple_phi_result (close_phi);
+
+  FOR_EACH_IMM_USE_FAST (use_p, imm_iter, def)
+    if ((stmt = USE_STMT (use_p))
+	&& gimple_code (stmt) == GIMPLE_ASSIGN
+	&& (res = gimple_assign_lhs (stmt)))
+      {
+	switch (TREE_CODE (res))
+	  {
+	  case VAR_DECL:
+	  case PARM_DECL:
+	  case RESULT_DECL:
+	    return res;
+
+	  case ARRAY_REF:
+	  case MEM_REF:
+	    {
+	      tree arg = gimple_phi_arg_def (close_phi, 0);
+	      loop_p nest = loop_containing_stmt (SSA_NAME_DEF_STMT (arg));
+
+	      /* FIXME: this restriction is for id-{24,25}.f and
+		 could be handled by duplicating the computation of
+		 array indices before the loop of the close_phi.  */
+	      if (for_each_index (&res, dr_indices_valid_in_loop, &nest))
+		return res;
+	    }
+	    /* Fallthru.  */
+
+	  default:
+	    continue;
+	  }
+      }
+  return NULL_TREE;
+}
+
+/* Rewrite out of SSA the reduction described by the loop phi nodes
+   IN, and the close phi nodes OUT.  IN and OUT are structured by loop
+   levels like this:
+
+   IN: stmt, loop_n, ..., loop_0
+   OUT: stmt, close_n, ..., close_0
+
+   the first element is the reduction statement, and the next elements
+   are the loop and close phi nodes of each of the outer loops.  */
+
+static void
+translate_scalar_reduction_to_array (scop_p scop,
+				     vec<gimple> in,
+				     vec<gimple> out)
+{
+  gimple loop_phi;
+  unsigned int i = out.length () - 1;
+  tree red = close_phi_written_to_memory (out[i]);
+
+  FOR_EACH_VEC_ELT (in, i, loop_phi)
+    {
+      gimple close_phi = out[i];
+
+      if (i == 0)
+	{
+	  gimple stmt = loop_phi;
+	  basic_block bb = split_reduction_stmt (scop, stmt);
+	  poly_bb_p pbb = pbb_from_bb (bb);
+	  PBB_IS_REDUCTION (pbb) = true;
+	  gcc_assert (close_phi == loop_phi);
+
+	  if (!red)
+	    red = create_zero_dim_array
+	      (gimple_assign_lhs (stmt), "Commutative_Associative_Reduction");
+
+	  translate_scalar_reduction_to_array_for_stmt (scop, red, stmt, in[1]);
+	  continue;
+	}
+
+      if (i == in.length () - 1)
+	{
+	  insert_out_of_ssa_copy (scop, gimple_phi_result (close_phi),
+				  unshare_expr (red), close_phi);
+	  insert_out_of_ssa_copy_on_edge
+	    (scop, edge_initial_value_for_loop_phi (loop_phi),
+	     unshare_expr (red), initial_value_for_loop_phi (loop_phi));
+	}
+
+      remove_phi (loop_phi);
+      remove_phi (close_phi);
+    }
+}
+
+/* Rewrites out of SSA a commutative reduction at CLOSE_PHI.  Returns
+   true when something has been changed.  */
+
+static bool
+rewrite_commutative_reductions_out_of_ssa_close_phi (scop_p scop,
+						     gimple close_phi)
+{
+  bool res;
+  auto_vec<gimple, 10> in;
+  auto_vec<gimple, 10> out;
+
+  detect_commutative_reduction (scop, close_phi, &in, &out);
+  res = in.length () > 1;
+  if (res)
+    translate_scalar_reduction_to_array (scop, in, out);
+
+  return res;
+}
+
+/* Rewrites all the commutative reductions from LOOP out of SSA.
+   Returns true when something has been changed.  */
+
+static bool
+rewrite_commutative_reductions_out_of_ssa_loop (scop_p scop,
+						loop_p loop)
+{
+  gimple_stmt_iterator gsi;
+  edge exit = single_exit (loop);
+  tree res;
+  bool changed = false;
+
+  if (!exit)
+    return false;
+
+  for (gsi = gsi_start_phis (exit->dest); !gsi_end_p (gsi); gsi_next (&gsi))
+    if ((res = gimple_phi_result (gsi_stmt (gsi)))
+	&& !virtual_operand_p (res)
+	&& !scev_analyzable_p (res, SCOP_REGION (scop)))
+      changed |= rewrite_commutative_reductions_out_of_ssa_close_phi
+	(scop, gsi_stmt (gsi));
+
+  return changed;
+}
+
+/* Rewrites all the commutative reductions from SCOP out of SSA.  */
+
+static void
+rewrite_commutative_reductions_out_of_ssa (scop_p scop)
+{
+  loop_p loop;
+  bool changed = false;
+  sese region = SCOP_REGION (scop);
+
+  FOR_EACH_LOOP (loop, 0)
+    if (loop_in_sese_p (loop, region))
+      changed |= rewrite_commutative_reductions_out_of_ssa_loop (scop, loop);
+
+  if (changed)
+    {
+      scev_reset_htab ();
+      gsi_commit_edge_inserts ();
+      update_ssa (TODO_update_ssa);
+#ifdef ENABLE_CHECKING
+      verify_loop_closed_ssa (true);
+#endif
+    }
+}
+
+/* Can all ivs be represented by a signed integer?
+   As CLooG might generate negative values in its expressions, signed loop ivs
+   are required in the backend. */
+
+static bool
+scop_ivs_can_be_represented (scop_p scop)
+{
+  loop_p loop;
+  gimple_stmt_iterator psi;
+  bool result = true;
+
+  FOR_EACH_LOOP (loop, 0)
+    {
+      if (!loop_in_sese_p (loop, SCOP_REGION (scop)))
+	continue;
+
+      for (psi = gsi_start_phis (loop->header);
+	   !gsi_end_p (psi); gsi_next (&psi))
+	{
+	  gimple phi = gsi_stmt (psi);
+	  tree res = PHI_RESULT (phi);
+	  tree type = TREE_TYPE (res);
+
+	  if (TYPE_UNSIGNED (type)
+	      && TYPE_PRECISION (type) >= TYPE_PRECISION (long_long_integer_type_node))
+	    {
+	      result = false;
+	      break;
+	    }
+	}
+      if (!result)
+	break;
+    }
+
+  return result;
+}
+
+/* Builds the polyhedral representation for a SESE region.  */
+
+void
+build_poly_scop (scop_p scop)
+{
+  sese region = SCOP_REGION (scop);
+  graphite_dim_t max_dim;
+
+  build_scop_bbs (scop);
+
+  /* FIXME: This restriction is needed to avoid a problem in CLooG.
+     Once CLooG is fixed, remove this guard.  Anyways, it makes no
+     sense to optimize a scop containing only PBBs that do not belong
+     to any loops.  */
+  if (nb_pbbs_in_loops (scop) == 0)
+    return;
+
+  if (!scop_ivs_can_be_represented (scop))
+    return;
+
+  if (flag_associative_math)
+    rewrite_commutative_reductions_out_of_ssa (scop);
+
+  build_sese_loop_nests (region);
+  /* Record all conditions in REGION.  */
+  sese_dom_walker (CDI_DOMINATORS, region).walk (cfun->cfg->x_entry_block_ptr);
+  find_scop_parameters (scop);
+
+  max_dim = PARAM_VALUE (PARAM_GRAPHITE_MAX_NB_SCOP_PARAMS);
+  if (scop_nb_params (scop) > max_dim)
+    return;
+
+  build_scop_iteration_domain (scop);
+  build_scop_context (scop);
+  add_conditions_to_constraints (scop);
+
+  /* Rewrite out of SSA only after having translated the
+     representation to the polyhedral representation to avoid scev
+     analysis failures.  That means that these functions will insert
+     new data references that they create in the right place.  */
+  rewrite_reductions_out_of_ssa (scop);
+  rewrite_cross_bb_scalar_deps_out_of_ssa (scop);
+
+  build_scop_drs (scop);
+  scop_to_lst (scop);
+  build_scop_scattering (scop);
+
+  /* This SCoP has been translated to the polyhedral
+     representation.  */
+  POLY_SCOP_P (scop) = true;
+}
+#endif