diff --git a/gcc/graphite-clast-to-gimple.c b/gcc/graphite-clast-to-gimple.c
index bb0f4c8..9a9effa 100644
--- a/gcc/graphite-clast-to-gimple.c
+++ b/gcc/graphite-clast-to-gimple.c
@@ -24,6 +24,11 @@ along with GCC; see the file COPYING3.  If not see
 #include <isl/set.h>
 #include <isl/map.h>
 #include <isl/union_map.h>
+#include <isl/list.h>
+#include <isl/constraint.h>
+#include <isl/div.h>
+#include <isl/ilp.h>
+#include <isl/aff.h>
 #include <cloog/cloog.h>
 #include <cloog/isl/domain.h>
 #endif
@@ -768,16 +773,19 @@ graphite_create_new_guard (edge entry_edge, struct clast_guard *stmt,
 static void
 compute_bounds_for_param (scop_p scop, int param, mpz_t low, mpz_t up)
 {
-  ppl_Linear_Expression_t le;
-
-  /* Prepare the linear expression corresponding to the parameter that
-     we want to maximize/minimize.  */
-  ppl_new_Linear_Expression_with_dimension (&le, scop_nb_params (scop));
-  ppl_set_coef (le, param, 1);
-
-  ppl_max_for_le_pointset (SCOP_CONTEXT (scop), le, up);
-  ppl_min_for_le_pointset (SCOP_CONTEXT (scop), le, low);
-  ppl_delete_Linear_Expression (le);
+  isl_int v;
+  isl_aff *aff = isl_aff_zero
+    (isl_local_space_from_dim (isl_set_get_dim (scop->context)));
+
+  aff = isl_aff_add_coefficient_si (aff, isl_dim_param, param, 1);
+
+  isl_int_init (v);
+  isl_set_min (scop->context, aff, &v);
+  isl_int_get_gmp (v, low);
+  isl_set_max (scop->context, aff, &v);
+  isl_int_get_gmp (v, up);
+  isl_int_clear (v);
+  isl_aff_free (aff);
 }
 
 /* Compute the lower bound LOW and upper bound UP for the induction
@@ -1357,7 +1365,6 @@ build_cloog_union_domain (scop_p scop)
 {
   int i;
   poly_bb_p pbb;
-
   CloogUnionDomain *union_domain =
     cloog_union_domain_alloc (scop_nb_params (scop));
 
@@ -1460,8 +1467,30 @@ generate_cloog_input (scop_p scop, htab_t params_index)
   union_domain = add_names_to_union_domain (scop, union_domain,
 					    nb_scattering_dims,
 					    params_index);
-  context = new_Cloog_Domain_from_ppl_Pointset_Powerset
-    (SCOP_CONTEXT (scop), scop_nb_params (scop), cloog_state);
+
+  if (1)
+    {
+      /* For now remove the isl_id's from the context before
+	 translating to CLooG: this code will be removed when the
+	 domain will also contain isl_id's.  */
+      isl_set *ct = isl_set_project_out (isl_set_copy (scop->context),
+					 isl_dim_set, 0, number_of_loops ());
+      isl_printer *p = isl_printer_to_str (scop->ctx);
+      char *str;
+
+      p = isl_printer_set_output_format (p, ISL_FORMAT_EXT_POLYLIB);
+      p = isl_printer_print_set (p, ct);
+      isl_set_free (ct);
+
+      str = isl_printer_get_str (p);
+      ct = isl_set_read_from_str (scop->ctx, str,
+				  scop_nb_params (scop));
+      free (str);
+      isl_printer_free (p);
+      context = cloog_domain_from_isl_set (ct);
+    }
+  else
+    context = cloog_domain_from_isl_set (isl_set_copy (scop->context));
 
   cloog_input = cloog_input_alloc (context, union_domain);
 
diff --git a/gcc/graphite-cloog-util.c b/gcc/graphite-cloog-util.c
index 82a49a1..6086864 100644
--- a/gcc/graphite-cloog-util.c
+++ b/gcc/graphite-cloog-util.c
@@ -25,6 +25,7 @@ along with GCC; see the file COPYING3.  If not see
 #include <isl/set.h>
 #include <isl/map.h>
 #include <isl/union_map.h>
+#include <isl/aff.h>
 #include <cloog/cloog.h>
 #include <cloog/isl/domain.h>
 #endif
diff --git a/gcc/graphite-poly.c b/gcc/graphite-poly.c
index af40d20..fd2703b 100644
--- a/gcc/graphite-poly.c
+++ b/gcc/graphite-poly.c
@@ -1012,6 +1012,7 @@ new_scop (void *region)
   scop_p scop = XNEW (struct scop);
 
   SCOP_CONTEXT (scop) = NULL;
+  scop->context = NULL;
   scop_set_region (scop, region);
   SCOP_BBS (scop) = VEC_alloc (poly_bb_p, heap, 3);
   SCOP_ORIGINAL_PDDRS (scop) = htab_create (10, hash_poly_ddr_p,
@@ -1040,6 +1041,7 @@ free_scop (scop_p scop)
   if (SCOP_CONTEXT (scop))
     ppl_delete_Pointset_Powerset_C_Polyhedron (SCOP_CONTEXT (scop));
 
+  isl_set_free (scop->context);
   htab_delete (SCOP_ORIGINAL_PDDRS (scop));
   free_lst (SCOP_ORIGINAL_SCHEDULE (scop));
   free_lst (SCOP_TRANSFORMED_SCHEDULE (scop));
@@ -1401,6 +1403,12 @@ print_scop_context (FILE *file, scop_p scop, int verbosity)
   else
     fprintf (file, "0 %d\n", (int) scop_nb_params (scop) + 2);
 
+  if (scop->context)
+    {
+      isl_printer *p = isl_printer_to_file (scop->ctx, file);
+      isl_printer_print_set (p, scop->context);
+    }
+
   if (verbosity > 0)
     fprintf (file, "# )\n");
 }
diff --git a/gcc/graphite-poly.h b/gcc/graphite-poly.h
index 72e9530..bb8771d 100644
--- a/gcc/graphite-poly.h
+++ b/gcc/graphite-poly.h
@@ -1409,6 +1409,9 @@ struct scop
   ppl_Pointset_Powerset_C_Polyhedron_t _context;
   isl_set *context;
 
+  /* The context used internally by ISL.  */
+  isl_ctx *ctx;
+
   /* A hashtable of the data dependence relations for the original
      scattering.  */
   htab_t original_pddrs;
diff --git a/gcc/graphite-sese-to-poly.c b/gcc/graphite-sese-to-poly.c
index b7efe41..69392a9 100644
--- a/gcc/graphite-sese-to-poly.c
+++ b/gcc/graphite-sese-to-poly.c
@@ -24,6 +24,8 @@ along with GCC; see the file COPYING3.  If not see
 #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>
@@ -595,6 +597,216 @@ build_scop_scattering (scop_p scop)
   ppl_delete_Linear_Expression (static_schedule);
 }
 
+static isl_pw_aff *extract_affine (scop_p, tree);
+
+/* Extract an affine expression from the chain of recurrence E.  */
+
+static isl_pw_aff *
+extract_affine_chrec (scop_p s, tree e)
+{
+  isl_pw_aff *lhs = extract_affine (s, CHREC_LEFT (e));
+  isl_pw_aff *rhs = extract_affine (s, CHREC_RIGHT (e));
+  isl_dim *dim = isl_dim_set_alloc (s->ctx, 0, number_of_loops ());
+  isl_local_space *ls = isl_local_space_from_dim (dim);
+  isl_aff *loop = isl_aff_set_coefficient_si
+    (isl_aff_zero (ls), isl_dim_set, CHREC_VARIABLE (e), 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_pw_aff *lhs = extract_affine (s, TREE_OPERAND (e, 0));
+  isl_pw_aff *rhs = extract_affine (s, TREE_OPERAND (e, 1));
+
+  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 from the loop L.  */
+
+static isl_id *
+isl_id_for_loop (scop_p s, loop_p l)
+{
+  isl_id *id;
+  char name[50];
+
+  snprintf (name, sizeof (name), "L_%d", l ? l->num : -1);
+  id = isl_id_alloc (s->ctx, name, l);
+
+  return id;
+}
+
+/* Extract an affine expression from the ssa_name E.  */
+
+static isl_pw_aff *
+extract_affine_name (scop_p s, tree e)
+{
+  isl_aff *aff;
+  isl_set *dom;
+  isl_dim *dim = isl_dim_set_alloc (s->ctx, 1, number_of_loops ());
+
+  dim = isl_dim_set_dim_id (dim, isl_dim_param, 0, isl_id_for_ssa_name (s, e));
+  dom = isl_set_universe (isl_dim_copy (dim));
+  aff = isl_aff_zero (isl_local_space_from_dim (dim));
+  aff = isl_aff_add_coefficient_si (aff, isl_dim_param, 0, 1);
+  return isl_pw_aff_alloc (dom, aff);
+}
+
+/* Extract an affine expression from the gmp constant G.  */
+
+static isl_pw_aff *
+extract_affine_gmp (scop_p s, mpz_t g)
+{
+  isl_dim *dim = isl_dim_set_alloc (s->ctx, 0, number_of_loops ());
+  isl_local_space *ls = isl_local_space_from_dim (isl_dim_copy (dim));
+  isl_aff *aff = isl_aff_zero (ls);
+  isl_set *dom = isl_set_universe (dim);
+  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 (scop_p s, tree e)
+{
+  isl_pw_aff *res;
+  mpz_t g;
+
+  mpz_init (g);
+  tree_int_to_gmp (e, g);
+  res = extract_affine_gmp (s, g);
+  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;
+}
+
+/* Extract an affine expression from the tree E in the scop S.  */
+
+static isl_pw_aff *
+extract_affine (scop_p s, tree e)
+{
+  isl_pw_aff *lhs, *rhs, *res;
+  tree type;
+
+  if (e == chrec_dont_know)
+    return NULL;
+
+  switch (TREE_CODE (e))
+    {
+    case POLYNOMIAL_CHREC:
+      res = extract_affine_chrec (s, e);
+      break;
+
+    case MULT_EXPR:
+      res = extract_affine_mul (s, e);
+      break;
+
+    case PLUS_EXPR:
+    case POINTER_PLUS_EXPR:
+      lhs = extract_affine (s, TREE_OPERAND (e, 0));
+      rhs = extract_affine (s, TREE_OPERAND (e, 1));
+      res = isl_pw_aff_add (lhs, rhs);
+      break;
+
+    case MINUS_EXPR:
+      lhs = extract_affine (s, TREE_OPERAND (e, 0));
+      rhs = extract_affine (s, TREE_OPERAND (e, 1));
+      res = isl_pw_aff_sub (lhs, rhs);
+      break;
+
+    case NEGATE_EXPR:
+    case BIT_NOT_EXPR:
+      lhs = extract_affine (s, TREE_OPERAND (e, 0));
+      rhs = extract_affine (s, integer_minus_one_node);
+      res = isl_pw_aff_mul (lhs, rhs);
+      break;
+
+    case SSA_NAME:
+      res = extract_affine_name (s, e);
+      break;
+
+    case INTEGER_CST:
+      res = extract_affine_int (s, e);
+      break;
+
+    CASE_CONVERT:
+    case NON_LVALUE_EXPR:
+      res = extract_affine (s, TREE_OPERAND (e, 0));
+      break;
+
+    default:
+      gcc_unreachable ();
+      break;
+    }
+
+  type = TREE_TYPE (e);
+  if (TYPE_UNSIGNED (type))
+    res = wrap (res, TYPE_PRECISION (type));
+
+  return res;
+}
+
 /* Add the value K to the dimension D of the linear expression EXPR.  */
 
 static void
@@ -931,6 +1143,7 @@ find_scop_parameters (scop_p scop)
   sese region = SCOP_REGION (scop);
   struct loop *loop;
   mpz_t one;
+  int nbp;
 
   mpz_init (one);
   mpz_set_si (one, 1);
@@ -953,11 +1166,28 @@ find_scop_parameters (scop_p scop)
   FOR_EACH_VEC_ELT (poly_bb_p, SCOP_BBS (scop), i, pbb)
     find_params_in_bb (region, PBB_BLACK_BOX (pbb));
 
-  scop_set_nb_params (scop, sese_nb_params (region));
+  nbp = sese_nb_params (region);
+  scop_set_nb_params (scop, nbp);
   SESE_ADD_PARAMS (region) = false;
 
   ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension
-    (&SCOP_CONTEXT (scop), scop_nb_params (scop), 0);
+    (&SCOP_CONTEXT (scop), nbp, 0);
+
+  {
+    tree e;
+    unsigned nbl = number_of_loops ();
+    isl_dim *dim = isl_dim_set_alloc (scop->ctx, nbp, nbl);
+
+    FOR_EACH_VEC_ELT (tree, SESE_PARAMS (region), i, e)
+      dim = isl_dim_set_dim_id (dim, isl_dim_param, i,
+				isl_id_for_ssa_name (scop, e));
+
+    for (i = 0; i < nbl; i++)
+      dim = isl_dim_set_dim_id (dim, isl_dim_set, i,
+				isl_id_for_loop (scop, get_loop (i)));
+
+    scop->context = isl_set_universe (dim);
+  }
 }
 
 /* Insert in the SCOP context constraints from the estimation of the
@@ -1094,6 +1324,7 @@ build_loop_iteration_domains (scop_p scop, struct loop *loop,
       ppl_Constraint_t ub;
       ppl_Linear_Expression_t ub_expr;
       double_int nit;
+      isl_pw_aff *aff;
 
       mpz_init (one);
       mpz_set_si (one, 1);
@@ -1102,8 +1333,33 @@ build_loop_iteration_domains (scop_p scop, struct loop *loop,
       scan_tree_for_params (SCOP_REGION (scop), nb_iters, ub_expr, one);
       mpz_clear (one);
 
+      aff = extract_affine (scop, nb_iters);
+      scop->context = isl_set_intersect
+	(scop->context, isl_pw_aff_nonneg_set (isl_pw_aff_copy (aff)));
+
       if (max_stmt_executions (loop, true, &nit))
-	add_upper_bounds_from_estimated_nit (scop, nit, dim, ub_expr);
+	{
+	  add_upper_bounds_from_estimated_nit (scop, nit, dim, ub_expr);
+
+	  {
+	    /* 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;
+
+	    mpz_init (g);
+	    mpz_set_double_int (g, nit, false);
+	    approx = extract_affine_gmp (scop, g);
+	    mpz_clear (g);
+	    x = isl_pw_aff_ge_set (approx, aff);
+	    scop->context = isl_set_intersect (scop->context, x);
+	  }
+	}
 
       /* loop_i <= expr_nb_iters */
       ppl_set_coef (ub_expr, nb, -1);
@@ -1463,6 +1719,26 @@ add_param_constraints (scop_p scop, ppl_Polyhedron_t context, graphite_dim_t p)
       ppl_Polyhedron_add_constraint (context, cstr);
       ppl_delete_Linear_Expression (le);
       ppl_delete_Constraint (cstr);
+
+      {
+	isl_dim *dim = isl_set_get_dim (scop->context);
+	isl_constraint *c = isl_inequality_alloc (dim);
+	mpz_t g;
+	isl_int v;
+
+	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);
+	isl_constraint_set_constant (c, v);
+	isl_int_set_si (v, 1);
+	isl_constraint_set_coefficient (c, isl_dim_param, p, v);
+	isl_int_clear (v);
+
+	scop->context = isl_set_add_constraint (scop->context, c);
+      }
     }
 
   if (ub)
@@ -1474,6 +1750,25 @@ add_param_constraints (scop_p scop, ppl_Polyhedron_t context, graphite_dim_t p)
       ppl_Polyhedron_add_constraint (context, cstr);
       ppl_delete_Linear_Expression (le);
       ppl_delete_Constraint (cstr);
+
+      {
+	isl_dim *dim = isl_set_get_dim (scop->context);
+	isl_constraint *c = isl_inequality_alloc (dim);
+	mpz_t g;
+	isl_int v;
+
+	mpz_init (g);
+	isl_int_init (v);
+	tree_int_to_gmp (ub, g);
+	isl_int_set_gmp (v, g);
+	mpz_clear (g);
+	isl_constraint_set_constant (c, v);
+	isl_int_set_si (v, -1);
+	isl_constraint_set_coefficient (c, isl_dim_param, p, v);
+	isl_int_clear (v);
+
+	scop->context = isl_set_add_constraint (scop->context, c);
+      }
     }
 }
 
diff --git a/gcc/graphite.c b/gcc/graphite.c
index 8f6d8a1..b2cf7c6 100644
--- a/gcc/graphite.c
+++ b/gcc/graphite.c
@@ -260,10 +260,12 @@ graphite_transform_loops (void)
   bool need_cfg_cleanup_p = false;
   VEC (scop_p, heap) *scops = NULL;
   htab_t bb_pbb_mapping;
+  isl_ctx *ctx;
 
   if (!graphite_initialize ())
     return;
 
+  ctx = isl_ctx_alloc ();
   build_scops (&scops);
 
   if (dump_file && (dump_flags & TDF_DETAILS))
@@ -277,6 +279,7 @@ graphite_transform_loops (void)
   FOR_EACH_VEC_ELT (scop_p, scops, i, scop)
     if (dbg_cnt (graphite_scop))
       {
+	scop->ctx = ctx;
 	build_poly_scop (scop);
 
 	if (POLY_SCOP_P (scop)
@@ -288,6 +291,7 @@ graphite_transform_loops (void)
   htab_delete (bb_pbb_mapping);
   free_scops (scops);
   graphite_finalize (need_cfg_cleanup_p);
+  isl_ctx_free (ctx);
 }
 
 #else /* If Cloog is not available: #ifndef HAVE_cloog.  */
