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imported gcc-4.6.4 source tree from verified upstream tarball.

downloading a git-generated archive based on the 'upstream' tag
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1 files changed, 934 insertions, 0 deletions

diff --git a/gcc/graphite-dependences.c b/gcc/graphite-dependences.c
new file mode 100644
index 000000000..b9b1d1b58
--- /dev/null
+++ b/gcc/graphite-dependences.c
@@ -0,0 +1,934 @@
+/* Data dependence analysis for Graphite.
+   Copyright (C) 2009, 2010 Free Software Foundation, Inc.
+   Contributed by Sebastian Pop <sebastian.pop@amd.com> and
+   Konrad Trifunovic <konrad.trifunovic@inria.fr>.
+
+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"
+#include "system.h"
+#include "coretypes.h"
+#include "tree-flow.h"
+#include "tree-dump.h"
+#include "cfgloop.h"
+#include "tree-chrec.h"
+#include "tree-data-ref.h"
+#include "tree-scalar-evolution.h"
+#include "sese.h"
+
+#ifdef HAVE_cloog
+#include "ppl_c.h"
+#include "graphite-ppl.h"
+#include "graphite-poly.h"
+#include "graphite-dependences.h"
+#include "graphite-cloog-util.h"
+
+/* Comparison function for poly_ddr hash table.  */
+
+int
+eq_poly_ddr_p (const void *pddr1, const void *pddr2)
+{
+  const struct poly_ddr *p1 = (const struct poly_ddr *) pddr1;
+  const struct poly_ddr *p2 = (const struct poly_ddr *) pddr2;
+
+  return (PDDR_SOURCE (p1) == PDDR_SOURCE (p2)
+          && PDDR_SINK (p1) == PDDR_SINK (p2));
+}
+
+/* Hash function for poly_ddr hashtable.  */
+
+hashval_t
+hash_poly_ddr_p (const void *pddr)
+{
+  const struct poly_ddr *p = (const struct poly_ddr *) pddr;
+
+  return (hashval_t) ((long) PDDR_SOURCE (p) + (long) PDDR_SINK (p));
+}
+
+/* Returns true when PDDR has no dependence.  */
+
+static bool
+pddr_is_empty (poly_ddr_p pddr)
+{
+  if (!pddr)
+    return true;
+
+  gcc_assert (PDDR_KIND (pddr) != unknown_dependence);
+
+  return PDDR_KIND (pddr) == no_dependence ? true : false;
+}
+
+/* Prints to FILE the layout of the dependence polyhedron of PDDR:
+
+   T1|I1|T2|I2|S1|S2|G
+
+   with
+   | T1 and T2 the scattering dimensions for PDDR_SOURCE and PDDR_SINK
+   | I1 and I2 the iteration domains
+   | S1 and S2 the subscripts
+   | G the global parameters.  */
+
+static void
+print_dependence_polyhedron_layout (FILE *file, poly_ddr_p pddr)
+{
+  poly_dr_p pdr1 = PDDR_SOURCE (pddr);
+  poly_dr_p pdr2 = PDDR_SINK (pddr);
+  poly_bb_p pbb1 = PDR_PBB (pdr1);
+  poly_bb_p pbb2 = PDR_PBB (pdr2);
+
+  graphite_dim_t i;
+  graphite_dim_t tdim1 = PDDR_ORIGINAL_SCATTERING_P (pddr) ?
+    pbb_nb_scattering_orig (pbb1) : pbb_nb_scattering_transform (pbb1);
+  graphite_dim_t tdim2 = PDDR_ORIGINAL_SCATTERING_P (pddr) ?
+    pbb_nb_scattering_orig (pbb2) : pbb_nb_scattering_transform (pbb2);
+  graphite_dim_t idim1 = pbb_dim_iter_domain (pbb1);
+  graphite_dim_t idim2 = pbb_dim_iter_domain (pbb2);
+  graphite_dim_t sdim1 = PDR_NB_SUBSCRIPTS (pdr1) + 1;
+  graphite_dim_t sdim2 = PDR_NB_SUBSCRIPTS (pdr2) + 1;
+  graphite_dim_t gdim = scop_nb_params (PBB_SCOP (pbb1));
+
+  fprintf (file, "#  eq");
+
+  for (i = 0; i < tdim1; i++)
+    fprintf (file, "   t1_%d", (int) i);
+  for (i = 0; i < idim1; i++)
+    fprintf (file, "   i1_%d", (int) i);
+  for (i = 0; i < tdim2; i++)
+    fprintf (file, "   t2_%d", (int) i);
+  for (i = 0; i < idim2; i++)
+    fprintf (file, "   i2_%d", (int) i);
+  for (i = 0; i < sdim1; i++)
+    fprintf (file, "   s1_%d", (int) i);
+  for (i = 0; i < sdim2; i++)
+    fprintf (file, "   s2_%d", (int) i);
+  for (i = 0; i < gdim; i++)
+    fprintf (file, "    g_%d", (int) i);
+
+  fprintf (file, "    cst\n");
+}
+
+/* Prints to FILE the poly_ddr_p PDDR.  */
+
+void
+print_pddr (FILE *file, poly_ddr_p pddr)
+{
+  fprintf (file, "pddr (kind: ");
+
+  if (PDDR_KIND (pddr) == unknown_dependence)
+    fprintf (file, "unknown_dependence");
+  else if (PDDR_KIND (pddr) == no_dependence)
+    fprintf (file, "no_dependence");
+  else if (PDDR_KIND (pddr) == has_dependence)
+    fprintf (file, "has_dependence");
+
+  fprintf (file, "\n  source ");
+  print_pdr (file, PDDR_SOURCE (pddr), 2);
+
+  fprintf (file, "\n  sink ");
+  print_pdr (file, PDDR_SINK (pddr), 2);
+
+  if (PDDR_KIND (pddr) == has_dependence)
+    {
+      fprintf (file, "\n  dependence polyhedron (\n");
+      print_dependence_polyhedron_layout (file, pddr);
+      ppl_print_powerset_matrix (file, PDDR_DDP (pddr));
+      ppl_io_fprint_Pointset_Powerset_C_Polyhedron (file, PDDR_DDP (pddr));
+      fprintf (file, ")\n");
+    }
+
+  fprintf (file, ")\n");
+}
+
+/* Prints to STDERR the poly_ddr_p PDDR.  */
+
+DEBUG_FUNCTION void
+debug_pddr (poly_ddr_p pddr)
+{
+  print_pddr (stderr, pddr);
+}
+
+
+/* Remove all the dimensions except alias information at dimension
+   ALIAS_DIM.  */
+
+static void
+build_alias_set_powerset (ppl_Pointset_Powerset_C_Polyhedron_t alias_powerset,
+			  ppl_dimension_type alias_dim)
+{
+  ppl_dimension_type *ds;
+  ppl_dimension_type access_dim;
+  unsigned i, pos = 0;
+
+  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (alias_powerset,
+						      &access_dim);
+  ds = XNEWVEC (ppl_dimension_type, access_dim-1);
+  for (i = 0; i < access_dim; i++)
+    {
+      if (i == alias_dim)
+	continue;
+
+      ds[pos] = i;
+      pos++;
+    }
+
+  ppl_Pointset_Powerset_C_Polyhedron_remove_space_dimensions (alias_powerset,
+							      ds,
+							      access_dim - 1);
+  free (ds);
+}
+
+/* Return true when PDR1 and PDR2 may alias.  */
+
+static bool
+poly_drs_may_alias_p (poly_dr_p pdr1, poly_dr_p pdr2)
+{
+  ppl_Pointset_Powerset_C_Polyhedron_t alias_powerset1, alias_powerset2;
+  ppl_Pointset_Powerset_C_Polyhedron_t accesses1 = PDR_ACCESSES (pdr1);
+  ppl_Pointset_Powerset_C_Polyhedron_t accesses2 = PDR_ACCESSES (pdr2);
+  ppl_dimension_type alias_dim1 = pdr_alias_set_dim (pdr1);
+  ppl_dimension_type alias_dim2 = pdr_alias_set_dim (pdr2);
+  int empty_p;
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
+    (&alias_powerset1, accesses1);
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
+    (&alias_powerset2, accesses2);
+
+  build_alias_set_powerset (alias_powerset1, alias_dim1);
+  build_alias_set_powerset (alias_powerset2, alias_dim2);
+
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign
+    (alias_powerset1, alias_powerset2);
+
+  empty_p = ppl_Pointset_Powerset_C_Polyhedron_is_empty (alias_powerset1);
+
+  ppl_delete_Pointset_Powerset_C_Polyhedron (alias_powerset1);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (alias_powerset2);
+
+  return !empty_p;
+}
+
+/* Swap [cut0, ..., cut1] to the end of DR: "a CUT0 b CUT1 c" is
+   transformed into "a CUT0 c CUT1' b"
+
+   Add NB0 zeros before "a":  "00...0 a CUT0 c CUT1' b"
+   Add NB1 zeros between "a" and "c":  "00...0 a 00...0 c CUT1' b"
+   Add DIM - NB0 - NB1 - PDIM zeros between "c" and "b":
+   "00...0 a 00...0 c 00...0 b".  */
+
+static ppl_Pointset_Powerset_C_Polyhedron_t
+map_dr_into_dep_poly (graphite_dim_t dim,
+		      ppl_Pointset_Powerset_C_Polyhedron_t dr,
+		      graphite_dim_t cut0, graphite_dim_t cut1,
+		      graphite_dim_t nb0, graphite_dim_t nb1)
+{
+  ppl_dimension_type pdim;
+  ppl_dimension_type *map;
+  ppl_Pointset_Powerset_C_Polyhedron_t res;
+  ppl_dimension_type i;
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
+    (&res, dr);
+  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (res, &pdim);
+
+  map = (ppl_dimension_type *) XNEWVEC (ppl_dimension_type, pdim);
+
+  /* First mapping: move 'g' vector to right position.  */
+  for (i = 0; i < cut0; i++)
+    map[i] = i;
+
+  for (i = cut0; i < cut1; i++)
+    map[i] = pdim - cut1 + i;
+
+  for (i = cut1; i < pdim; i++)
+    map[i] = cut0 + i - cut1;
+
+  ppl_Pointset_Powerset_C_Polyhedron_map_space_dimensions (res, map, pdim);
+  free (map);
+
+  /* After swapping 's' and 'g' vectors, we have to update a new cut.  */
+  cut1 = pdim - cut1 + cut0;
+
+  ppl_insert_dimensions_pointset (res, 0, nb0);
+  ppl_insert_dimensions_pointset (res, nb0 + cut0, nb1);
+  ppl_insert_dimensions_pointset (res, nb0 + nb1 + cut1,
+				  dim - nb0 - nb1 - pdim);
+
+  return res;
+}
+
+/* Builds subscript equality constraints.  */
+
+static ppl_Pointset_Powerset_C_Polyhedron_t
+dr_equality_constraints (graphite_dim_t dim,
+		         graphite_dim_t pos, graphite_dim_t nb_subscripts)
+{
+  ppl_Polyhedron_t eqs;
+  ppl_Pointset_Powerset_C_Polyhedron_t res;
+  graphite_dim_t i;
+
+  ppl_new_C_Polyhedron_from_space_dimension (&eqs, dim, 0);
+
+  for (i = 0; i < nb_subscripts; i++)
+    {
+      ppl_Constraint_t cstr
+	= ppl_build_relation (dim, pos + i, pos + i + nb_subscripts,
+			      0, PPL_CONSTRAINT_TYPE_EQUAL);
+      ppl_Polyhedron_add_constraint (eqs, cstr);
+      ppl_delete_Constraint (cstr);
+    }
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron (&res, eqs);
+  ppl_delete_Polyhedron (eqs);
+  return res;
+}
+
+/* Builds scheduling inequality constraints: when DIRECTION is
+   1 builds a GE constraint,
+   0 builds an EQ constraint,
+   -1 builds a LE constraint.
+   DIM is the dimension of the scheduling space.
+   POS and POS + OFFSET are the dimensions that are related.  */
+
+static ppl_Pointset_Powerset_C_Polyhedron_t
+build_pairwise_scheduling (graphite_dim_t dim,
+			   graphite_dim_t pos,
+			   graphite_dim_t offset,
+			   int direction)
+{
+  ppl_Pointset_Powerset_C_Polyhedron_t res;
+  ppl_Polyhedron_t equalities;
+  ppl_Constraint_t cstr;
+  graphite_dim_t a = pos;
+  graphite_dim_t b = pos + offset;
+
+  ppl_new_C_Polyhedron_from_space_dimension (&equalities, dim, 0);
+
+  switch (direction)
+    {
+    case 1:
+      /* Builds "a + 1 <= b.  */
+      cstr = ppl_build_relation (dim, a, b, 1,
+				 PPL_CONSTRAINT_TYPE_LESS_OR_EQUAL);
+      break;
+
+    case 0:
+      /* Builds "a = b.  */
+      cstr = ppl_build_relation (dim, a, b, 0,
+				 PPL_CONSTRAINT_TYPE_EQUAL);
+      break;
+
+    case -1:
+      /* Builds "a >= b + 1.  */
+      cstr = ppl_build_relation (dim, a, b, -1,
+				 PPL_CONSTRAINT_TYPE_GREATER_OR_EQUAL);
+      break;
+
+    default:
+      gcc_unreachable ();
+    }
+
+  ppl_Polyhedron_add_constraint (equalities, cstr);
+  ppl_delete_Constraint (cstr);
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron (&res, equalities);
+  ppl_delete_Polyhedron (equalities);
+  return res;
+}
+
+/* Add to a non empty polyhedron BAG the precedence constraints for
+   the lexicographical comparison of time vectors in BAG following the
+   lexicographical order.  DIM is the dimension of the polyhedron BAG.
+   TDIM is the number of loops common to the two statements that are
+   compared lexicographically, i.e. the number of loops containing
+   both statements.  OFFSET is the number of dimensions needed to
+   represent the first statement, i.e. dimT1 + dimI1 in the layout of
+   the BAG polyhedron: T1|I1|T2|I2|S1|S2|G.  When DIRECTION is set to
+   1, compute the direct dependence from PDR1 to PDR2, and when
+   DIRECTION is -1, compute the reversed dependence relation, from
+   PDR2 to PDR1.  */
+
+static ppl_Pointset_Powerset_C_Polyhedron_t
+build_lexicographical_constraint (ppl_Pointset_Powerset_C_Polyhedron_t bag,
+				  graphite_dim_t dim,
+				  graphite_dim_t tdim,
+				  graphite_dim_t offset,
+				  int direction)
+{
+  graphite_dim_t i;
+  ppl_Pointset_Powerset_C_Polyhedron_t res, lex;
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension (&res, dim, 1);
+
+  lex = build_pairwise_scheduling (dim, 0, offset, direction);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (lex, bag);
+
+  if (!ppl_powerset_is_empty (lex))
+    ppl_Pointset_Powerset_C_Polyhedron_upper_bound_assign (res, lex);
+
+  ppl_delete_Pointset_Powerset_C_Polyhedron (lex);
+
+  for (i = 0; i < tdim - 1; i++)
+    {
+      ppl_Pointset_Powerset_C_Polyhedron_t sceq;
+
+      sceq = build_pairwise_scheduling (dim, i, offset, 0);
+      ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (bag, sceq);
+      ppl_delete_Pointset_Powerset_C_Polyhedron (sceq);
+
+      if (ppl_powerset_is_empty (bag))
+	break;
+
+      lex = build_pairwise_scheduling (dim, i + 1, offset, direction);
+      ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (lex, bag);
+
+      if (!ppl_powerset_is_empty (lex))
+	ppl_Pointset_Powerset_C_Polyhedron_upper_bound_assign (res, lex);
+
+      ppl_delete_Pointset_Powerset_C_Polyhedron (lex);
+    }
+
+  return res;
+}
+
+/* Build the dependence polyhedron for data references PDR1 and PDR2.
+   The layout of the dependence polyhedron is:
+
+   T1|I1|T2|I2|S1|S2|G
+
+   with
+   | T1 and T2 the scattering dimensions for PDR1 and PDR2
+   | I1 and I2 the iteration domains
+   | S1 and S2 the subscripts
+   | G the global parameters.
+
+   When DIRECTION is set to 1, compute the direct dependence from PDR1
+   to PDR2, and when DIRECTION is -1, compute the reversed dependence
+   relation, from PDR2 to PDR1.  */
+
+static ppl_Pointset_Powerset_C_Polyhedron_t
+dependence_polyhedron (poly_dr_p pdr1, poly_dr_p pdr2,
+		       int direction, bool original_scattering_p)
+{
+  poly_bb_p pbb1 = PDR_PBB (pdr1);
+  poly_bb_p pbb2 = PDR_PBB (pdr2);
+  scop_p scop = PBB_SCOP (pbb1);
+  graphite_dim_t tdim1 = original_scattering_p ?
+    pbb_nb_scattering_orig (pbb1) : pbb_nb_scattering_transform (pbb1);
+  graphite_dim_t tdim2 = original_scattering_p ?
+    pbb_nb_scattering_orig (pbb2) : pbb_nb_scattering_transform (pbb2);
+  graphite_dim_t ddim1 = pbb_dim_iter_domain (pbb1);
+  graphite_dim_t ddim2 = pbb_dim_iter_domain (pbb2);
+  graphite_dim_t sdim1 = PDR_NB_SUBSCRIPTS (pdr1) + 1;
+  graphite_dim_t sdim2 = PDR_NB_SUBSCRIPTS (pdr2) + 1;
+  graphite_dim_t gdim = scop_nb_params (scop);
+  graphite_dim_t dim1 = pdr_dim (pdr1);
+  graphite_dim_t dim2 = pdr_dim (pdr2);
+  graphite_dim_t dim = tdim1 + tdim2 + dim1 + dim2 - gdim;
+  ppl_Pointset_Powerset_C_Polyhedron_t res;
+  ppl_Pointset_Powerset_C_Polyhedron_t idr1, idr2;
+  ppl_Pointset_Powerset_C_Polyhedron_t sc1, sc2, dreq;
+  ppl_Pointset_Powerset_C_Polyhedron_t lex;
+
+  gcc_assert (PBB_SCOP (pbb1) == PBB_SCOP (pbb2));
+
+  combine_context_id_scat (&sc1, pbb1, original_scattering_p);
+  combine_context_id_scat (&sc2, pbb2, original_scattering_p);
+
+  ppl_insert_dimensions_pointset (sc1, tdim1 + ddim1,
+				  tdim2 + ddim2 + sdim1 + sdim2);
+
+  ppl_insert_dimensions_pointset (sc2, 0, tdim1 + ddim1);
+  ppl_insert_dimensions_pointset (sc2, tdim1 + ddim1 + tdim2 + ddim2,
+				  sdim1 + sdim2);
+
+  idr1 = map_dr_into_dep_poly (dim, PDR_ACCESSES (pdr1), ddim1, ddim1 + gdim,
+			       tdim1, tdim2 + ddim2);
+  idr2 = map_dr_into_dep_poly (dim, PDR_ACCESSES (pdr2), ddim2, ddim2 + gdim,
+			       tdim1 + ddim1 + tdim2, sdim1);
+
+  /* Now add the subscript equalities.  */
+  dreq = dr_equality_constraints (dim, tdim1 + ddim1 + tdim2 + ddim2, sdim1);
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension (&res, dim, 0);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, sc1);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, sc2);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, idr1);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, idr2);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, dreq);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (sc1);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (sc2);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (idr1);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (idr2);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (dreq);
+
+  if (ppl_powerset_is_empty (res))
+    return NULL;
+
+  lex = build_lexicographical_constraint (res, dim, MIN (tdim1, tdim2),
+					  tdim1 + ddim1, direction);
+  ppl_delete_Pointset_Powerset_C_Polyhedron (res);
+
+  return lex;
+}
+
+/* Build the dependence polyhedron for data references PDR1 and PDR2.
+   If possible use already cached information.
+
+   When DIRECTION is set to 1, compute the direct dependence from PDR1
+   to PDR2, and when DIRECTION is -1, compute the reversed dependence
+   relation, from PDR2 to PDR1.  */
+
+static poly_ddr_p
+new_poly_ddr (poly_dr_p pdr1, poly_dr_p pdr2,
+	      int direction, bool original_scattering_p)
+{
+  PTR *x = NULL;
+  poly_ddr_p res;
+  bool may_alias;
+
+  /* Return the PDDR from the cache if it already has been computed.  */
+  if (original_scattering_p)
+    {
+      struct poly_ddr tmp;
+      scop_p scop = PBB_SCOP (PDR_PBB (pdr1));
+
+      tmp.source = pdr1;
+      tmp.sink = pdr2;
+      x = htab_find_slot (SCOP_ORIGINAL_PDDRS (scop),
+                          &tmp, INSERT);
+
+      if (x && *x)
+	return (poly_ddr_p) *x;
+    }
+
+  res = XNEW (struct poly_ddr);
+  PDDR_SOURCE (res) = pdr1;
+  PDDR_SINK (res) = pdr2;
+  PDDR_DDP (res) = NULL;
+  PDDR_ORIGINAL_SCATTERING_P (res) = original_scattering_p;
+  PDDR_KIND (res) = unknown_dependence;
+
+  may_alias = poly_drs_may_alias_p (pdr1, pdr2);
+
+  if (!(pdr_read_p (pdr1) && pdr_read_p (pdr2))
+      && PDR_BASE_OBJECT_SET (pdr1) != PDR_BASE_OBJECT_SET (pdr2)
+      && may_alias)
+    PDDR_KIND (res) = unknown_dependence;
+
+  else if (!(pdr_read_p (pdr1) && pdr_read_p (pdr2))
+	   && same_pdr_p (pdr1, pdr2)
+	   && may_alias)
+    {
+      PDDR_DDP (res) = dependence_polyhedron (pdr1, pdr2, direction,
+					      original_scattering_p);
+      if (PDDR_DDP (res))
+	PDDR_KIND (res) = has_dependence;
+      else
+	PDDR_KIND (res) = no_dependence;
+    }
+  else
+    PDDR_KIND (res) = no_dependence;
+
+  if (original_scattering_p)
+    *x = res;
+
+  return res;
+}
+
+/* Free the data dependence relation poly_ddr_p P.  */
+
+void
+free_poly_ddr (void *p)
+{
+  poly_ddr_p pddr = (poly_ddr_p) p;
+  ppl_delete_Pointset_Powerset_C_Polyhedron (PDDR_DDP (pddr));
+  free (pddr);
+}
+
+/* Return true when the data dependence relation between the data
+   references PDR1 belonging to PBB1 and PDR2 is part of a
+   reduction.  */
+
+static inline bool
+reduction_dr_1 (poly_bb_p pbb1, poly_dr_p pdr1, poly_dr_p pdr2)
+{
+  int i;
+  poly_dr_p pdr;
+
+  FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb1), i, pdr)
+    if (PDR_TYPE (pdr) == PDR_WRITE
+	&& same_pdr_p (pdr, pdr1) && same_pdr_p (pdr, pdr2))
+      return true;
+
+  return false;
+}
+
+/* Return true when the data dependence relation between the data
+   references PDR1 belonging to PBB1 and PDR2 belonging to PBB2 is
+   part of a reduction.  */
+
+static inline bool
+reduction_dr_p (poly_dr_p pdr1, poly_dr_p pdr2)
+{
+  poly_bb_p pbb1 = PDR_PBB (pdr1);
+  poly_bb_p pbb2 = PDR_PBB (pdr2);
+
+  if (PBB_IS_REDUCTION (pbb1))
+    return reduction_dr_1 (pbb1, pdr1, pdr2);
+
+  if (PBB_IS_REDUCTION (pbb2))
+    return reduction_dr_1 (pbb2, pdr2, pdr1);
+
+  return false;
+}
+
+/* Returns true when the PBB_TRANSFORMED_SCATTERING functions of PBB1
+   and PBB2 respect the data dependences of PBB_ORIGINAL_SCATTERING
+   functions.  */
+
+static bool
+graphite_legal_transform_dr (poly_dr_p pdr1, poly_dr_p pdr2)
+{
+  ppl_Pointset_Powerset_C_Polyhedron_t po, pt;
+  graphite_dim_t ddim1, otdim1, otdim2, ttdim1, ttdim2;
+  ppl_Pointset_Powerset_C_Polyhedron_t po_temp;
+  ppl_dimension_type pdim;
+  bool is_empty_p;
+  poly_ddr_p opddr, tpddr;
+  poly_bb_p pbb1, pbb2;
+
+  if (reduction_dr_p (pdr1, pdr2))
+    return true;
+
+  /* We build the reverse dependence relation for the transformed
+     scattering, such that when we intersect it with the original PO,
+     we get an empty intersection when the transform is legal:
+     i.e. the transform should reverse no dependences, and so PT, the
+     reversed transformed PDDR, should have no constraint from PO.  */
+  opddr = new_poly_ddr (pdr1, pdr2, 1, true);
+
+  if (PDDR_KIND (opddr) == unknown_dependence)
+    return false;
+
+    /* There are no dependences between PDR1 and PDR2 in the original
+       version of the program, or after the transform, so the
+       transform is legal.  */
+  if (pddr_is_empty (opddr))
+    return true;
+
+  tpddr = new_poly_ddr (pdr1, pdr2, -1, false);
+
+  if (PDDR_KIND (tpddr) == unknown_dependence)
+    {
+      free_poly_ddr (tpddr);
+      return false;
+    }
+
+  if (pddr_is_empty (tpddr))
+    {
+      free_poly_ddr (tpddr);
+      return true;
+    }
+
+  po = PDDR_DDP (opddr);
+  pt = PDDR_DDP (tpddr);
+
+  /* Copy PO into PO_TEMP, such that PO is not destroyed.  PO is
+     stored in a cache and should not be modified or freed.  */
+  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (po, &pdim);
+  ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension (&po_temp,
+							       pdim, 0);
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (po_temp, po);
+
+  /* Extend PO and PT to have the same dimensions.  */
+  pbb1 = PDR_PBB (pdr1);
+  pbb2 = PDR_PBB (pdr2);
+  ddim1 = pbb_dim_iter_domain (pbb1);
+  otdim1 = pbb_nb_scattering_orig (pbb1);
+  otdim2 = pbb_nb_scattering_orig (pbb2);
+  ttdim1 = pbb_nb_scattering_transform (pbb1);
+  ttdim2 = pbb_nb_scattering_transform (pbb2);
+  ppl_insert_dimensions_pointset (po_temp, otdim1, ttdim1);
+  ppl_insert_dimensions_pointset (po_temp, otdim1 + ttdim1 + ddim1 + otdim2,
+				  ttdim2);
+  ppl_insert_dimensions_pointset (pt, 0, otdim1);
+  ppl_insert_dimensions_pointset (pt, otdim1 + ttdim1 + ddim1, otdim2);
+
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (po_temp, pt);
+  is_empty_p = ppl_powerset_is_empty (po_temp);
+
+  ppl_delete_Pointset_Powerset_C_Polyhedron (po_temp);
+  free_poly_ddr (tpddr);
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, "\nloop carries dependency.\n");
+
+  return is_empty_p;
+}
+
+/* Return true when the data dependence relation for PBB1 and PBB2 is
+   part of a reduction.  */
+
+static inline bool
+reduction_ddr_p (poly_bb_p pbb1, poly_bb_p pbb2)
+{
+  return pbb1 == pbb2 && PBB_IS_REDUCTION (pbb1);
+}
+
+/* Iterates over the data references of PBB1 and PBB2 and detect
+   whether the transformed schedule is correct.  */
+
+static bool
+graphite_legal_transform_bb (poly_bb_p pbb1, poly_bb_p pbb2)
+{
+  int i, j;
+  poly_dr_p pdr1, pdr2;
+
+  if (!PBB_PDR_DUPLICATES_REMOVED (pbb1))
+    pbb_remove_duplicate_pdrs (pbb1);
+
+  if (!PBB_PDR_DUPLICATES_REMOVED (pbb2))
+    pbb_remove_duplicate_pdrs (pbb2);
+
+  if (reduction_ddr_p (pbb1, pbb2))
+    return true;
+
+  FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb1), i, pdr1)
+    FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb2), j, pdr2)
+      if (!graphite_legal_transform_dr (pdr1, pdr2))
+	return false;
+
+  return true;
+}
+
+/* Iterates over the SCOP and detect whether the transformed schedule
+   is correct.  */
+
+bool
+graphite_legal_transform (scop_p scop)
+{
+  int i, j;
+  poly_bb_p pbb1, pbb2;
+
+  timevar_push (TV_GRAPHITE_DATA_DEPS);
+
+  FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), i, pbb1)
+    FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), j, pbb2)
+      if (!graphite_legal_transform_bb (pbb1, pbb2))
+	{
+	  timevar_pop (TV_GRAPHITE_DATA_DEPS);
+	  return false;
+	}
+
+  timevar_pop (TV_GRAPHITE_DATA_DEPS);
+  return true;
+}
+
+/* Returns TRUE when the dependence polyhedron between PDR1 and
+   PDR2 represents a loop carried dependence at level LEVEL.  */
+
+static bool
+graphite_carried_dependence_level_k (poly_dr_p pdr1, poly_dr_p pdr2,
+				     int level)
+{
+  ppl_Pointset_Powerset_C_Polyhedron_t po;
+  ppl_Pointset_Powerset_C_Polyhedron_t eqpp;
+  graphite_dim_t tdim1 = pbb_nb_scattering_transform (PDR_PBB (pdr1));
+  graphite_dim_t ddim1 = pbb_dim_iter_domain (PDR_PBB (pdr1));
+  ppl_dimension_type dim;
+  bool empty_p;
+  poly_ddr_p pddr = new_poly_ddr (pdr1, pdr2, 1, false);
+
+  if (PDDR_KIND (pddr) == unknown_dependence)
+    {
+      free_poly_ddr (pddr);
+      return true;
+    }
+
+  if (pddr_is_empty (pddr))
+    {
+      free_poly_ddr (pddr);
+      return false;
+    }
+
+  po = PDDR_DDP (pddr);
+  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (po, &dim);
+  eqpp = build_pairwise_scheduling (dim, level, tdim1 + ddim1, 1);
+
+  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (eqpp, po);
+  empty_p = ppl_powerset_is_empty (eqpp);
+
+  ppl_delete_Pointset_Powerset_C_Polyhedron (eqpp);
+  free_poly_ddr (pddr);
+
+  return !empty_p;
+}
+
+/* Check data dependency between PBB1 and PBB2 at level LEVEL.  */
+
+bool
+dependency_between_pbbs_p (poly_bb_p pbb1, poly_bb_p pbb2, int level)
+{
+  int i, j;
+  poly_dr_p pdr1, pdr2;
+
+  timevar_push (TV_GRAPHITE_DATA_DEPS);
+
+  FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb1), i, pdr1)
+    FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb2), j, pdr2)
+      if (graphite_carried_dependence_level_k (pdr1, pdr2, level))
+	{
+	  timevar_pop (TV_GRAPHITE_DATA_DEPS);
+	  return true;
+	}
+
+  timevar_pop (TV_GRAPHITE_DATA_DEPS);
+  return false;
+}
+
+/* When ORIG is true, pretty print to FILE all the original data
+   dependences of SCoP in DOT format, otherwise print the transformed
+   data deps.  */
+
+static void
+dot_deps_stmt_2 (FILE *file, scop_p scop, bool orig)
+{
+  int i, j, k, l;
+  poly_bb_p pbb1, pbb2;
+  poly_dr_p pdr1, pdr2;
+
+  FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), i, pbb1)
+    FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), j, pbb2)
+      {
+	FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb1), k, pdr1)
+	  FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb2), l, pdr2)
+	    {
+	      poly_ddr_p pddr = new_poly_ddr (pdr1, pdr2, 1, orig);
+
+	      if (!pddr_is_empty (pddr))
+		{
+		  fprintf (file, orig ? "OS%d -> OS%d\n" : "TS%d -> TS%d\n",
+			   pbb_index (pbb1), pbb_index (pbb2));
+
+		  free_poly_ddr (pddr);
+		  goto done;
+		}
+
+	      free_poly_ddr (pddr);
+	    }
+      done:;
+      }
+}
+
+/* Pretty print to FILE all the data dependences of SCoP in DOT
+   format.  */
+
+static void
+dot_deps_stmt_1 (FILE *file, scop_p scop)
+{
+  fputs ("digraph all {\n", file);
+
+  dot_deps_stmt_2 (file, scop, true);
+  dot_deps_stmt_2 (file, scop, false);
+
+  fputs ("}\n\n", file);
+}
+
+/* When ORIG is true, pretty print to FILE all the original data
+   dependences of SCoP in DOT format, otherwise print the transformed
+   data deps.  */
+
+static void
+dot_deps_2 (FILE *file, scop_p scop, bool orig)
+{
+  int i, j, k, l;
+  poly_bb_p pbb1, pbb2;
+  poly_dr_p pdr1, pdr2;
+
+  FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), i, pbb1)
+    FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), j, pbb2)
+      FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb1), k, pdr1)
+	FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (pbb2), l, pdr2)
+          {
+	    poly_ddr_p pddr = new_poly_ddr (pdr1, pdr2, 1, orig);
+
+	    if (!pddr_is_empty (pddr))
+	      fprintf (file, orig
+		       ? "OS%d_D%d -> OS%d_D%d\n" : "TS%d_D%d -> TS%d_D%d\n",
+		       pbb_index (pbb1), PDR_ID (pdr1),
+		       pbb_index (pbb2), PDR_ID (pdr2));
+
+	    free_poly_ddr (pddr);
+	  }
+}
+
+/* Pretty print to FILE all the data dependences of SCoP in DOT
+   format.  */
+
+static void
+dot_deps_1 (FILE *file, scop_p scop)
+{
+  fputs ("digraph all {\n", file);
+
+  dot_deps_2 (file, scop, true);
+  dot_deps_2 (file, scop, false);
+
+  fputs ("}\n\n", file);
+}
+
+/* Display all the data dependences in SCoP using dotty.  */
+
+DEBUG_FUNCTION void
+dot_deps (scop_p scop)
+{
+  /* When debugging, enable the following code.  This cannot be used
+     in production compilers because it calls "system".  */
+#if 0
+  FILE *stream = fopen ("/tmp/scopdeps.dot", "w");
+  gcc_assert (stream);
+
+  dot_deps_1 (stream, scop);
+  fclose (stream);
+
+  system ("dotty /tmp/scopdeps.dot &");
+#else
+  dot_deps_1 (stderr, scop);
+#endif
+}
+
+/* Display all the statement dependences in SCoP using dotty.  */
+
+DEBUG_FUNCTION void
+dot_deps_stmt (scop_p scop)
+{
+  /* When debugging, enable the following code.  This cannot be used
+     in production compilers because it calls "system".  */
+#if 0
+  FILE *stream = fopen ("/tmp/scopdeps.dot", "w");
+  gcc_assert (stream);
+
+  dot_deps_stmt_1 (stream, scop);
+  fclose (stream);
+
+  system ("dotty /tmp/scopdeps.dot &");
+#else
+  dot_deps_stmt_1 (stderr, scop);
+#endif
+}
+
+#endif