Patchwork [2/2] Write OpenScop format.

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Submitter Sebastian Pop
Date July 29, 2010, 8:21 p.m.
Message ID <1280434877-24563-3-git-send-email-sebpop@gmail.com>
Download mbox | patch
Permalink /patch/60314/
State New
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Sebastian Pop - July 29, 2010, 8:21 p.m.
2010-07-29  Riyadh Baghdadi <baghdadi.mr@gmail.com>

	* graphite-cloog-util.c (openscop_print_cloog_matrix): New.
	(openscop_print_polyhedron_matrix): New.
	* graphite-cloog-util.h (openscop_print_polyhedron_matrix): Declared.
	* graphite-poly.c (openscop_print_pdr_polyhedron): Same.
	(openscop_print_pdr_powerset): New.
	(openscop_print_powerset_matrix): New.
	(openscop_print_scattering_function_1): New.
	(print_scattering_function): Add support for scattering names and
	OpenScop format.
	(graphite_write_transforms): Remove.
	(apply_poly_transforms): Updated to call print_scop.
	(print_pdr_access_layout): Updated to support OpenScop format.
	(print_pdr): Same.
	(openscop_print_pbb_domain): New.
	(print_pbb_body): Added a parameter to allow indicating that pbb_body is
	not provided.
	(print_pbb): Updated to call the new print_pbb_body.
	(openscop_print_scop_context): New.
	(print_scop_header): New.
	(print_scop): Updated to call print_scop_header.
	* graphite-poly.h: Document OpenScop format.
---
 gcc/ChangeLog.graphite    |   24 ++++
 gcc/graphite-cloog-util.c |   39 ++++++
 gcc/graphite-cloog-util.h |    2 +
 gcc/graphite-poly.c       |  313 ++++++++++++++++++++++++++++++++++++++++-----
 gcc/graphite-poly.h       |   49 +++++++-
 5 files changed, 394 insertions(+), 33 deletions(-)

Patch

diff --git a/gcc/ChangeLog.graphite b/gcc/ChangeLog.graphite
index e040d6e..2b3310d 100644
--- a/gcc/ChangeLog.graphite
+++ b/gcc/ChangeLog.graphite
@@ -1,3 +1,27 @@ 
+2010-07-29  Riyadh Baghdadi <baghdadi.mr@gmail.com>
+
+	* graphite-cloog-util.c (openscop_print_cloog_matrix): New.
+	(openscop_print_polyhedron_matrix): New.
+	* graphite-cloog-util.h (openscop_print_polyhedron_matrix): Declared.
+	* graphite-poly.c (openscop_print_pdr_polyhedron): Same.
+	(openscop_print_pdr_powerset): New.
+	(openscop_print_powerset_matrix): New.
+	(openscop_print_scattering_function_1): New.
+	(print_scattering_function): Add support for scattering names and
+	OpenScop format.
+	(graphite_write_transforms): Remove.
+	(apply_poly_transforms): Updated to call print_scop.
+	(print_pdr_access_layout): Updated to support OpenScop format.
+	(print_pdr): Same.
+	(openscop_print_pbb_domain): New.
+	(print_pbb_body): Added a parameter to allow indicating that pbb_body is
+	not provided.
+	(print_pbb): Updated to call the new print_pbb_body.
+	(openscop_print_scop_context): New.
+	(print_scop_header): New.
+	(print_scop): Updated to call print_scop_header.
+	* graphite-poly.h: Document OpenScop format.
+
 2010-07-29  Sebastian Pop  <sebastian.pop@amd.com>
 
 	* graphite-sese-to-poly.c (rewrite_close_phi_out_of_ssa): Add back
diff --git a/gcc/graphite-cloog-util.c b/gcc/graphite-cloog-util.c
index 5ea7c3c..97ef73d 100644
--- a/gcc/graphite-cloog-util.c
+++ b/gcc/graphite-cloog-util.c
@@ -296,4 +296,43 @@  new_Cloog_Domain_from_ppl_Pointset_Powerset
 
   return res;
 }
+
+/* Print to FILE the matrix MAT in OpenScop format.  OUTPUT is the number
+   of output dimensions, INPUT is the number of input dimensions, LOCALS
+   is the number of existentially quantified variables and PARAMS is the
+   number of parameters.  */
+
+static void
+openscop_print_cloog_matrix (FILE *file, CloogMatrix *mat,
+			     int output, int input, int locals,
+			     int params)
+{
+  int i, j;
+
+  fprintf (file, "%d %d %d %d %d %d \n", cloog_matrix_nrows (mat),
+	   cloog_matrix_ncolumns (mat), output, input, locals, params);
+
+  for (i = 0; i < cloog_matrix_nrows (mat); i++)
+    {
+      for (j = 0; j < cloog_matrix_ncolumns (mat); j++)
+	fprintf (file, "%6ld ", mpz_get_si (mat->p[i][j]));
+      fprintf (file, "\n");
+    }
+}
+
+/* Print to FILE the polyhedron PH in OpenScop format.  OUTPUT is the number
+   of output dimensions, INPUT is the number of input dimensions, LOCALS is
+   the number of existentially quantified variables and PARAMS is the number
+   of parameters.  */
+
+void
+openscop_print_polyhedron_matrix (FILE *file, ppl_const_Polyhedron_t ph,
+				  int output, int input, int locals,
+				  int params)
+{
+  CloogMatrix *mat = new_Cloog_Matrix_from_ppl_Polyhedron (ph);
+  openscop_print_cloog_matrix (file, mat, output, input, locals, params);
+  cloog_matrix_free (mat);
+}
+
 #endif
diff --git a/gcc/graphite-cloog-util.h b/gcc/graphite-cloog-util.h
index d7758ce..62e2f94 100644
--- a/gcc/graphite-cloog-util.h
+++ b/gcc/graphite-cloog-util.h
@@ -32,5 +32,7 @@  CloogScattering *new_Cloog_Scattering_from_ppl_Polyhedron
 CloogDomain * new_Cloog_Domain_from_ppl_Pointset_Powerset
   (ppl_Pointset_Powerset_C_Polyhedron_t, int, CloogState *);
 void new_C_Polyhedron_from_Cloog_Matrix (ppl_Polyhedron_t *, CloogMatrix *);
+void openscop_print_polyhedron_matrix (FILE *, ppl_const_Polyhedron_t, int,
+				       int, int, int);
 
 #endif /* GRAPHITE_CLOOG_UTIL_H */
diff --git a/gcc/graphite-poly.c b/gcc/graphite-poly.c
index 8718973..c1ac69e 100644
--- a/gcc/graphite-poly.c
+++ b/gcc/graphite-poly.c
@@ -44,6 +44,7 @@  along with GCC; see the file COPYING3.  If not see
 #include "pointer-set.h"
 #include "gimple.h"
 #include "params.h"
+#include "graphite-cloog-util.h"
 
 #ifdef HAVE_cloog
 #include "ppl_c.h"
@@ -136,6 +137,159 @@  unify_scattering_dimensions (scop_p scop)
   return max_scattering;
 }
 
+/* Print to FILE the pdr PH in OpenScop format.  NB_SUBSCRIPTS is the number
+   of subscripts in PH, ALIAS_SET_DIM is the dimension of the alias set and
+   NB_PARAMS is the number of parameters in PH.  */
+
+static void
+openscop_print_pdr_polyhedron (FILE *file, ppl_const_Polyhedron_t ph,
+			       int nb_subscripts, int alias_set_dimension,
+			       int nb_params)
+{
+  int input, locals, output;
+  ppl_dimension_type alias_set_dim = (ppl_dimension_type) alias_set_dimension;
+  ppl_dimension_type sub_dim_last = alias_set_dim + nb_subscripts;
+  ppl_dimension_type *map, i, ph_space_dim = sub_dim_last + 1;
+  ppl_Polyhedron_t pph;
+
+  ppl_new_C_Polyhedron_from_C_Polyhedron (&pph,ph);
+
+  map = (ppl_dimension_type *) XNEWVEC (ppl_dimension_type, ph_space_dim);
+
+  for (i = 0; i < alias_set_dim - 1; i++)
+    map[i] = nb_subscripts + 1 + i;
+
+  for (i = alias_set_dim - 1; i < sub_dim_last; i++)
+    map[i] = i - alias_set_dim + 1;
+
+  ppl_Polyhedron_map_space_dimensions (pph, map, ph_space_dim - 1);
+
+  locals = 0;
+  input = alias_set_dim - nb_params - 1;
+
+  /* According to OpenScop specification, the alias set column is a part of
+     the output columns.  */
+  output = nb_subscripts + 1;
+
+  openscop_print_polyhedron_matrix (file, ph, output, input, locals, nb_params);
+}
+
+/* Print to FILE the powerset PDR.  NB_SUBSCRIPTS is the number of subscripts
+   in PDR, ALIAS_SET_DIM is the dimension of the alias set in PDR and
+   NB_PARAMS is the number of parameters in PDR.  */
+
+static void
+openscop_print_pdr_powerset (FILE *file,
+			     ppl_Pointset_Powerset_C_Polyhedron_t ps,
+			     int nb_subscripts,
+			     int alias_set_dim,
+			     int nb_params)
+{
+  size_t nb_disjuncts;
+  ppl_Pointset_Powerset_C_Polyhedron_iterator_t it, end;
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_iterator (&it);
+  ppl_new_Pointset_Powerset_C_Polyhedron_iterator (&end);
+
+  ppl_Pointset_Powerset_C_Polyhedron_size (ps, &nb_disjuncts);
+  fprintf (file, "%d\n", (int) nb_disjuncts);
+
+  for (ppl_Pointset_Powerset_C_Polyhedron_iterator_begin (ps, it),
+       ppl_Pointset_Powerset_C_Polyhedron_iterator_end (ps, end);
+       !ppl_Pointset_Powerset_C_Polyhedron_iterator_equal_test (it, end);
+       ppl_Pointset_Powerset_C_Polyhedron_iterator_increment (it))
+    {
+      ppl_const_Polyhedron_t ph;
+
+      ppl_Pointset_Powerset_C_Polyhedron_iterator_dereference (it, &ph);
+      openscop_print_pdr_polyhedron (file, ph, nb_subscripts, alias_set_dim,
+				     nb_params);
+    }
+
+  ppl_delete_Pointset_Powerset_C_Polyhedron_iterator (it);
+  ppl_delete_Pointset_Powerset_C_Polyhedron_iterator (end);
+}
+
+/* Print to FILE the powerset PS in its OpenScop matrix form.  */
+
+static void
+openscop_print_powerset_matrix (FILE *file,
+				ppl_Pointset_Powerset_C_Polyhedron_t ps,
+				int output, int input, int locals,
+				int params)
+{
+  size_t nb_disjuncts;
+  ppl_Pointset_Powerset_C_Polyhedron_iterator_t it, end;
+
+  ppl_new_Pointset_Powerset_C_Polyhedron_iterator (&it);
+  ppl_new_Pointset_Powerset_C_Polyhedron_iterator (&end);
+
+  ppl_Pointset_Powerset_C_Polyhedron_size (ps, &nb_disjuncts);
+  fprintf (file, "%d\n", (int) nb_disjuncts);
+
+  for (ppl_Pointset_Powerset_C_Polyhedron_iterator_begin (ps, it),
+       ppl_Pointset_Powerset_C_Polyhedron_iterator_end (ps, end);
+       !ppl_Pointset_Powerset_C_Polyhedron_iterator_equal_test (it, end);
+       ppl_Pointset_Powerset_C_Polyhedron_iterator_increment (it))
+    {
+      ppl_const_Polyhedron_t ph;
+
+      ppl_Pointset_Powerset_C_Polyhedron_iterator_dereference (it, &ph);
+      openscop_print_polyhedron_matrix (file, ph, output, input, locals,
+				        params);
+    }
+
+  ppl_delete_Pointset_Powerset_C_Polyhedron_iterator (it);
+  ppl_delete_Pointset_Powerset_C_Polyhedron_iterator (end);
+}
+
+/* Prints to FILE the scattering function of PBB in OpenScop format, at some
+   VERBOSITY level.  */
+
+static void
+openscop_print_scattering_function_1 (FILE *file, poly_bb_p pbb, int verbosity)
+{
+  graphite_dim_t i;
+  ppl_const_Polyhedron_t ph;
+
+  if (verbosity > 0)
+    {
+      fprintf (file, "# scattering bb_%d (\n", pbb_index (pbb));
+      fprintf (file, "#  eq");
+
+      for (i = 0; i < pbb_nb_scattering_transform (pbb); i++)
+	fprintf (file, "     s%d", (int) i);
+
+      for (i = 0; i < pbb_nb_local_vars (pbb); i++)
+	fprintf (file, "    lv%d", (int) i);
+
+      for (i = 0; i < pbb_dim_iter_domain (pbb); i++)
+	fprintf (file, "     i%d", (int) i);
+
+      for (i = 0; i < pbb_nb_params (pbb); i++)
+	fprintf (file, "     p%d", (int) i);
+
+      fprintf (file, "    cst\n");
+    }
+
+  /* Number of disjunct components.  Remove this when
+     PBB_TRANSFORMED_SCATTERING will be a pointset_powerset.  */
+  fprintf (file, "1\n");
+
+  ph = PBB_TRANSFORMED_SCATTERING (pbb)
+    ? PBB_TRANSFORMED_SCATTERING (pbb)
+    : PBB_ORIGINAL_SCATTERING (pbb);
+
+  openscop_print_polyhedron_matrix (file, ph,
+				    pbb_nb_scattering_transform (pbb),
+				    pbb_dim_iter_domain (pbb),
+				    pbb_nb_local_vars (pbb),
+				    pbb_nb_params (pbb));
+
+  if (verbosity > 0)
+    fprintf (file, "#)\n");
+}
+
 /* Prints to FILE the scattering function of PBB, at some VERBOSITY
    level.  */
 
@@ -201,7 +355,13 @@  print_scattering_function (FILE *file, poly_bb_p pbb, int verbosity)
       return;
     }
 
-  print_scattering_function_1 (file, pbb, verbosity);
+  openscop_print_scattering_function_1 (file, pbb, verbosity);
+
+  if (verbosity > 0)
+    fprintf (file, "# Scattering names are not provided\n");
+
+  fprintf (file, "0\n");
+
 }
 
 /* Prints to FILE the iteration domain of PBB, at some VERBOSITY
@@ -274,14 +434,6 @@  debug_iteration_domains (scop_p scop, int verbosity)
   print_iteration_domains (stderr, scop, verbosity);
 }
 
-/* Write to file_name.graphite the transforms for SCOP.  */
-
-static void
-graphite_write_transforms (scop_p scop)
-{
-  print_scattering_functions (graphite_out_file, scop, 0);
-}
-
 /* Read transforms from file_name.graphite and set the transforms on
    SCOP.  */
 
@@ -338,7 +490,7 @@  apply_poly_transforms (scop_p scop)
     }
 
   if (flag_graphite_write)
-    graphite_write_transforms (scop);
+    print_scop (graphite_out_file, scop, 1);
 
   return transform_done;
 }
@@ -466,23 +618,23 @@  free_poly_bb (poly_bb_p pbb)
 }
 
 static void
-print_pdr_access_layout (FILE *file, poly_dr_p pdr)
+print_pdr_access_layout (FILE *file, poly_bb_p pbb, poly_dr_p pdr)
 {
   graphite_dim_t i;
 
   fprintf (file, "#  eq");
 
-  for (i = 0; i < pdr_dim_iter_domain (pdr); i++)
-    fprintf (file, "     i%d", (int) i);
-
-  for (i = 0; i < pdr_nb_params (pdr); i++)
-    fprintf (file, "     p%d", (int) i);
-
-  fprintf (file, "  alias");
+  fprintf (file, "   alias");
 
   for (i = 0; i < PDR_NB_SUBSCRIPTS (pdr); i++)
     fprintf (file, "   sub%d", (int) i);
 
+  for (i = 0; i < pbb_dim_iter_domain (pbb); i++)
+    fprintf (file, "     i%d", (int) i);
+
+  for (i = 0; i < pbb_nb_params (pbb); i++)
+    fprintf (file, "     p%d", (int) i);
+
   fprintf (file, "    cst\n");
 }
 
@@ -492,6 +644,8 @@  print_pdr_access_layout (FILE *file, poly_dr_p pdr)
 void
 print_pdr (FILE *file, poly_dr_p pdr, int verbosity)
 {
+  int alias_set_dim;
+
   if (verbosity > 1)
     {
       fprintf (file, "# pdr_%d (", PDR_ID (pdr));
@@ -520,10 +674,16 @@  print_pdr (FILE *file, poly_dr_p pdr, int verbosity)
   if (verbosity > 0)
     {
       fprintf (file, "# data accesses (\n");
-      print_pdr_access_layout (file, pdr);
+      print_pdr_access_layout (file, PDR_PBB (pdr), pdr);
     }
 
-  ppl_print_powerset_matrix (file, PDR_ACCESSES (pdr));
+  alias_set_dim = pdr_alias_set_dim (pdr) + 1;
+
+  openscop_print_pdr_powerset (file,
+			       PDR_ACCESSES (pdr),
+			       PDR_NB_SUBSCRIPTS (pdr),
+			       alias_set_dim,
+			       pbb_nb_params (PDR_PBB (pdr)));
 
   if (verbosity > 0)
     fprintf (file, "#)\n");
@@ -584,6 +744,45 @@  free_scop (scop_p scop)
   XDELETE (scop);
 }
 
+/* Print to FILE the domain of PBB in OpenScop format, at some VERBOSITY
+   level.  */
+
+static void
+openscop_print_pbb_domain (FILE *file, poly_bb_p pbb, int verbosity)
+{
+  graphite_dim_t i;
+  gimple_bb_p gbb = PBB_BLACK_BOX (pbb);
+
+  if (!PBB_DOMAIN (pbb))
+    return;
+
+  if (verbosity > 0)
+    {
+      fprintf (file, "\n# Iteration domain of bb_%d (\n", GBB_BB (gbb)->index);
+      fprintf (file, "#  eq");
+
+      for (i = 0; i < pbb_dim_iter_domain (pbb); i++)
+	fprintf (file, "     i%d", (int) i);
+
+      for (i = 0; i < pbb_nb_params (pbb); i++)
+	fprintf (file, "     p%d", (int) i);
+
+      fprintf (file, "    cst\n");
+    }
+
+  if (PBB_DOMAIN (pbb))
+    openscop_print_powerset_matrix (file, PBB_DOMAIN (pbb),
+				    pbb_dim_iter_domain (pbb),
+				    0,
+				    0,
+				    pbb_nb_params (pbb));
+  else
+    fprintf (file, "0\n");
+
+  if (verbosity > 0)
+    fprintf (file, "#)\n");
+}
+
 /* Print to FILE the domain of PBB, at some VERBOSITY level.  */
 
 void
@@ -744,14 +943,25 @@  debug_pdrs (poly_bb_p pbb, int verbosity)
   print_pdrs (stderr, pbb, verbosity);
 }
 
-/* Print to FILE the body of PBB, at some VERBOSITY level.  */
+/* Print to FILE the body of PBB, at some VERBOSITY level.
+   If statement_body_provided is false statement body is not printed.  */
 
 static void
-print_pbb_body (FILE *file, poly_bb_p pbb, int verbosity)
+print_pbb_body (FILE *file, poly_bb_p pbb, int verbosity,
+		bool statement_body_provided)
 {
   if (verbosity > 1)
     fprintf (file, "# Body (\n");
 
+  if (!statement_body_provided)
+  {
+    if (verbosity > 0)
+      fprintf (file, "# Statement body is not provided\n");
+
+   fprintf (file, "0\n");
+   return;
+  }
+
   if (verbosity > 0)
     fprintf (file, "# Statement body is provided\n");
   fprintf (file, "1\n");
@@ -783,10 +993,10 @@  print_pbb (FILE *file, poly_bb_p pbb, int verbosity)
       dump_gbb_cases (file, PBB_BLACK_BOX (pbb));
     }
 
-  print_pbb_domain (file, pbb, verbosity);
+  openscop_print_pbb_domain (file, pbb, verbosity);
   print_scattering_function (file, pbb, verbosity);
   print_pdrs (file, pbb, verbosity);
-  print_pbb_body (file, pbb, verbosity);
+  print_pbb_body (file, pbb, verbosity, false);
 
   if (verbosity > 1)
     fprintf (file, "#)\n");
@@ -832,6 +1042,36 @@  print_scop_params (FILE *file, scop_p scop, int verbosity)
     fprintf (file, "#)\n");
 }
 
+/* Print to FILE the context of SCoP in OpenScop format, at some VERBOSITY
+   level.  */
+
+static void
+openscop_print_scop_context (FILE *file, scop_p scop, int verbosity)
+{
+  graphite_dim_t i;
+
+  if (verbosity > 0)
+    {
+      fprintf (file, "# Context (\n");
+      fprintf (file, "#  eq");
+
+      for (i = 0; i < scop_nb_params (scop); i++)
+	fprintf (file, "     p%d", (int) i);
+
+      fprintf (file, "    cst\n");
+    }
+
+  if (SCOP_CONTEXT (scop))
+    openscop_print_powerset_matrix (file, SCOP_CONTEXT (scop), 0, 0, 0,
+				    scop_nb_params (scop));
+  else
+    fprintf (file, "0 %d 0 0 0 %d\n", (int) scop_nb_params (scop) + 2,
+	     (int) scop_nb_params (scop));
+
+  if (verbosity > 0)
+    fprintf (file, "# )\n");
+}
+
 /* Print to FILE the context of SCoP, at some VERBOSITY level.  */
 
 void
@@ -859,23 +1099,32 @@  print_scop_context (FILE *file, scop_p scop, int verbosity)
     fprintf (file, "# )\n");
 }
 
-/* Print to FILE the SCOP, at some VERBOSITY level.  */
+/* Print to FILE the SCOP header: context, parameters, and statements
+   number.  */
 
-void
-print_scop (FILE *file, scop_p scop, int verbosity)
+static void
+print_scop_header (FILE *file, scop_p scop, int verbosity)
 {
-  int i;
-  poly_bb_p pbb;
-
-  fprintf (file, "SCoP #(\n");
+  fprintf (file, "SCoP 1\n#(\n");
   fprintf (file, "# Language\nGimple\n");
-  print_scop_context (file, scop, verbosity);
+  openscop_print_scop_context (file, scop, verbosity);
   print_scop_params (file, scop, verbosity);
 
   if (verbosity > 0)
     fprintf (file, "# Number of statements\n");
 
   fprintf (file, "%d\n",VEC_length (poly_bb_p, SCOP_BBS (scop)));
+}
+
+/* Print to FILE the SCOP, at some VERBOSITY level.  */
+
+void
+print_scop (FILE *file, scop_p scop, int verbosity)
+{
+  int i;
+  poly_bb_p pbb;
+
+  print_scop_header (file, scop, verbosity);
 
   for (i = 0; VEC_iterate (poly_bb_p, SCOP_BBS (scop), i, pbb); i++)
     print_pbb (file, pbb, verbosity);
diff --git a/gcc/graphite-poly.h b/gcc/graphite-poly.h
index 5f858eb..0e1aa1f 100644
--- a/gcc/graphite-poly.h
+++ b/gcc/graphite-poly.h
@@ -132,7 +132,54 @@  struct poly_dr
      dimensions.
 
      | i   j   k   a   1
-     | 0   0   0  -1   15  = 0 */
+     | 0   0   0  -1   15  = 0
+
+     The difference between the graphite internal format for access data and
+     the OpenSop format is in the order of columns.
+     Instead of having:
+
+     | i   j   k   a  s0  s1   1
+     | 0   0   0   1   0   0  -5     =  0
+     |-1   0   0   0   1   0   0     =  0
+     | 0  -1  -1   0   0   1   0     =  0
+     | 0   0   0   0   1   0   0     >= 0  # The last four lines describe the
+     | 0   0   0   0   0   1   0     >= 0  # array size.
+     | 0   0   0   0  -1   0 1335    >= 0
+     | 0   0   0   0   0  -1 123     >= 0
+
+     In OpenScop we have:
+
+     | a  s0  s1   i   j   k   1
+     | 1   0   0   0   0   0  -5     =  0
+     | 0   1   0  -1   0   0   0     =  0
+     | 0   0   1   0  -1  -1   0     =  0
+     | 0   1   0   0   0   0   0     >= 0  # The last four lines describe the
+     | 0   0   1   0   0   0   0     >= 0  # array size.
+     | 0  -1   0   0   0   0 1335    >= 0
+     | 0   0  -1   0   0   0 123     >= 0
+
+     The OpenScop access function is printed as follows:
+
+     | 1  # The number of disjunct components in a union of access functions.
+     | R C O I L P  # Described bellow.
+     | a  s0  s1   i   j   k   1
+     | 1   0   0   0   0   0  -5     =  0
+     | 0   1   0  -1   0   0   0     =  0
+     | 0   0   1   0  -1  -1   0     =  0
+     | 0   1   0   0   0   0   0     >= 0  # The last four lines describe the
+     | 0   0   1   0   0   0   0     >= 0  # array size.
+     | 0  -1   0   0   0   0 1335    >= 0
+     | 0   0  -1   0   0   0 123     >= 0
+
+     Where:
+     - R: Number of rows.
+     - C: Number of columns.
+     - O: Number of output dimensions = alias set + number of subscripts.
+     - I: Number of input dimensions (iterators).
+     - L: Number of local (existentially quantified) dimensions.
+     - P: Number of parameters.
+
+     In the example, the vector "R C O I L P" is "7 7 3 2 0 1".  */
   ppl_Pointset_Powerset_C_Polyhedron_t accesses;
 
   /* Data reference's base object set number, we must assure 2 pdrs are in the