Re: [GRAPHITE, PATCH] Loop unroll and jam optimization

[Mircea Namolaru <mircea dot namolaru at inria dot fr>]

A small modification of the patch + extended comment for the
mapping used for computing the separating class. The code didn't
contained an adjustment of the stride with 1 (but the comment yes),
that was temporary removed and forget to insert it back.

The code generated now is:

ISL AST generated by ISL: 
{
  for (int c0 = 0; c0 < HEIGHT - 3; c0 += 4)
    for (int c1 = 0; c1 < LENGTH - 3; c1 += 1)
      for (int c2 = c0; c2 <= c0 + 3; c2 += 1)
        S_4(c2, c1);
  if ((HEIGHT - 1) % 4 <= 2)
    for (int c1 = 0; c1 < LENGTH - 3; c1 += 1)
      for (int c2 = -((HEIGHT - 1) % 4) + HEIGHT - 1; c2 < HEIGHT; c2 += 1)
        S_4(c2, c1);
}

The previous code was correct too (after all the code set an option for AST
but the transformation is preserved), but slightly less optimal in the case
when N was a multiple of the stride.

Mircea





----- Original Message -----
> From: "Sven Verdoolaege" <skimo@kotnet.org>
> To: "Mircea Namolaru" <mircea.namolaru@inria.fr>
> Cc: gcc-patches@gcc.gnu.org, "Tobias Grosser" <tobias@grosser.es>, "Richard Biener" <richard.guenther@gmail.com>,
> "Albert Cohen" <albert.cohen@inria.fr>
> Sent: Wednesday, November 12, 2014 12:24:40 AM
> Subject: Re: [GRAPHITE, PATCH] Loop unroll and jam optimization
> 
> On Tue, Nov 11, 2014 at 04:05:57PM +0100, Mircea Namolaru wrote:
> > > I'm not sure if Tobi or Albert have told you, but the separation_class
> > > option
> > > is going to be phased out since its design is fundamentally flawed.
> > > If you can't wait until isl-0.15, then I guess you have no choice but
> > > to use this option, but you should realize that it will remain frozen
> > > in its current broken state (until it is removed at some point).
> > > 
> > 
> > No, didn't know about the phase out of separation_class option. Anyway, for
> > the time
> > being is the best solution available. My understanding is that this option
> > should
> > always generate correct code, of course as long as the scheduling is
> > correct, but
> > think that had some cases when setting the separating_class leads to
> > incorrect code.
> > 
> > For isl_0.15, do you intend to provide some option with a similar
> > functionality ?
> 
> Yes.
> 
> > > > +      /* Extract the original and auxiliar maps from pbb->transformed.
> > > > +         Set pbb->transformed to the original map. */
> > > > +      psmap = &smap;
> > > > +      psmap->n = 0;
> > > > +      res = isl_map_foreach_basic_map (pbb->transformed, separate_map,
> > > > (void *)psmap);
> > > > +      gcc_assert (res == 0);
> > > > +
> > > > +      isl_map_free(pbb->transformed);
> > > > +      pbb->transformed = isl_map_copy(psmap->map_arr[0]);
> > > > +
> > > 
> > > I have no idea what this pbb->transformed is supposed to represent,
> > > but you appear to be assuming that it has exactly two disjuncts and that
> > > they appear in some order.  Now, perhaps you have explicitly
> > > checked that this map has two disjuncts, but then you should
> > > probably bring the check closer since any operation on sets that
> > > you perform could change the internal representation (even of
> > > other sets).  However, in no way can you assume that
> > > isl_map_foreach_basic_map will iterate over these disjuncts
> > > in any specific order.
> > >
> > 
> > At this point pbb->transformed has two basic maps, one is the mapping for
> > unroll and jam,
> > and one for the full tile for the striped dimension. Introduce a check that
> > differentiate
> > between them as the image of one maps should be included in the other.
> 
> I didn't do a full review (and I won't have time for it either),
> but at a quick glance,
> you still seem to be assuming that if you take the union of two
> basic maps, that you can extract the original two basic maps from the union.
> In general, you can't.  At least you shouldn't assume that you can.
> Besides, your updated code is also pretty convoluted,
> with very little documentation.
> 
> skimo
>

Attachment: Change.txt
Description: Text document

Index: gcc/graphite-poly.h
===================================================================
--- gcc/graphite-poly.h	(revision 217013)
+++ gcc/graphite-poly.h	(working copy)
@@ -349,6 +349,9 @@
   poly_scattering_p _saved;
   isl_map *saved;
 
+  /* For tiling, the map for computing the separating class.  */
+  isl_map *map_sepclass;
+
   /* True when this PBB contains only a reduction statement.  */
   bool is_reduction;
 };
Index: gcc/graphite.c
===================================================================
--- gcc/graphite.c	(revision 217013)
+++ gcc/graphite.c	(working copy)
@@ -383,7 +383,8 @@
       || flag_loop_strip_mine
       || flag_graphite_identity
       || flag_loop_parallelize_all
-      || flag_loop_optimize_isl)
+      || flag_loop_optimize_isl
+      || flag_loop_unroll_jam)
     flag_graphite = 1;
 
   return flag_graphite != 0;
Index: gcc/common.opt
===================================================================
--- gcc/common.opt	(revision 217013)
+++ gcc/common.opt	(working copy)
@@ -1328,6 +1328,10 @@
 Common Report Var(flag_loop_block) Optimization
 Enable Loop Blocking transformation
 
+floop-unroll-and-jam
+Common Report Var(flag_loop_unroll_jam) Optimization
+Enable Loop Unroll Jam transformation
+ 
 fgnu-tm
 Common Report Var(flag_tm)
 Enable support for GNU transactional memory
Index: gcc/graphite-optimize-isl.c
===================================================================
--- gcc/graphite-optimize-isl.c	(revision 217013)
+++ gcc/graphite-optimize-isl.c	(working copy)
@@ -186,7 +186,7 @@
   PartialSchedule = isl_band_get_partial_schedule (Band);
   *Dimensions = isl_band_n_member (Band);
 
-  if (DisableTiling)
+  if (DisableTiling || flag_loop_unroll_jam)
     return PartialSchedule;
 
   /* It does not make any sense to tile a band with just one dimension.  */
@@ -241,7 +241,9 @@
    constant number of iterations, if the number of loop iterations at
    DimToVectorize can be devided by VectorWidth. The default VectorWidth is
    currently constant and not yet target specific. This function does not reason
-   about parallelism.  */
+   about parallelism.
+
+  */
 static isl_map *
 getPrevectorMap (isl_ctx *ctx, int DimToVectorize,
 		 int ScheduleDimensions,
@@ -305,8 +307,98 @@
   isl_constraint_set_constant_si (c, VectorWidth - 1);
   TilingMap = isl_map_add_constraint (TilingMap, c);
 
-  isl_map_dump (TilingMap);
+  return TilingMap;
+}
 
+/* Compute an auxiliary map to getPrevectorMap, for computing the separating 
+   class defined by full tiles.  Used in graphite_isl_ast_to_gimple.c to set the 
+   corresponding option for AST build.
+
+   The map (for VectorWidth=4):
+
+   [i,j] -> [it,j,ip] : it % 4 = 0 and it <= ip <= it + 3 and it + 3 = i and
+                        ip >= 0
+
+   The image of this map is the separation class. The range of this map includes
+   all the i that are multiple of 4 in the domain beside the greater one. 
+    
+ */ 
+static isl_map *
+getPrevectorMap_full (isl_ctx *ctx, int DimToVectorize,
+		 int ScheduleDimensions,
+		 int VectorWidth)
+{
+  isl_space *Space;
+  isl_local_space *LocalSpace, *LocalSpaceRange;
+  isl_set *Modulo;
+  isl_map *TilingMap;
+  isl_constraint *c;
+  isl_aff *Aff;
+  int PointDimension; /* ip */
+  int TileDimension;  /* it */
+  isl_val *VectorWidthMP;
+  int i;
+
+  /* assert (0 <= DimToVectorize && DimToVectorize < ScheduleDimensions);*/
+
+  Space = isl_space_alloc (ctx, 0, ScheduleDimensions, ScheduleDimensions + 1);
+  TilingMap = isl_map_universe (isl_space_copy (Space));
+  LocalSpace = isl_local_space_from_space (Space);
+  PointDimension = ScheduleDimensions;
+  TileDimension = DimToVectorize;
+
+  /* Create an identity map for everything except DimToVectorize and the 
+     point loop. */
+  for (i = 0; i < ScheduleDimensions; i++)
+    {
+      if (i == DimToVectorize)
+        continue;
+
+      c = isl_equality_alloc (isl_local_space_copy (LocalSpace));
+
+      isl_constraint_set_coefficient_si (c, isl_dim_in, i, -1);
+      isl_constraint_set_coefficient_si (c, isl_dim_out, i, 1);
+
+      TilingMap = isl_map_add_constraint (TilingMap, c);
+    }
+
+  /* it % 'VectorWidth' = 0  */
+  LocalSpaceRange = isl_local_space_range (isl_local_space_copy (LocalSpace));
+  Aff = isl_aff_zero_on_domain (LocalSpaceRange);
+  Aff = isl_aff_set_constant_si (Aff, VectorWidth);
+  Aff = isl_aff_set_coefficient_si (Aff, isl_dim_in, TileDimension, 1);
+
+  VectorWidthMP = isl_val_int_from_si (ctx, VectorWidth);
+  Aff = isl_aff_mod_val (Aff, VectorWidthMP);
+  Modulo = isl_pw_aff_zero_set (isl_pw_aff_from_aff (Aff));
+  TilingMap = isl_map_intersect_range (TilingMap, Modulo);
+
+  /* it + ('VectorWidth' - 1) = i0  */
+  c = isl_equality_alloc (isl_local_space_copy(LocalSpace));
+  isl_constraint_set_coefficient_si (c, isl_dim_out, TileDimension,-1);
+  isl_constraint_set_coefficient_si (c, isl_dim_in, TileDimension, 1);
+  isl_constraint_set_constant_si (c, -VectorWidth + 1);
+  TilingMap = isl_map_add_constraint (TilingMap, c);
+
+  /* ip >= 0 */
+  c = isl_inequality_alloc (isl_local_space_copy (LocalSpace));
+  isl_constraint_set_coefficient_si (c, isl_dim_out, PointDimension, 1);
+  isl_constraint_set_constant_si (c, 0);
+  TilingMap = isl_map_add_constraint (TilingMap, c);
+
+  /* it <= ip */
+  c = isl_inequality_alloc (isl_local_space_copy (LocalSpace));
+  isl_constraint_set_coefficient_si (c, isl_dim_out, TileDimension, -1);
+  isl_constraint_set_coefficient_si (c, isl_dim_out, PointDimension, 1);
+  TilingMap = isl_map_add_constraint (TilingMap, c);
+
+  /* ip <= it + ('VectorWidth' - 1) */
+  c = isl_inequality_alloc (LocalSpace);
+  isl_constraint_set_coefficient_si (c, isl_dim_out, TileDimension, 1);
+  isl_constraint_set_coefficient_si (c, isl_dim_out, PointDimension, -1);
+  isl_constraint_set_constant_si (c, VectorWidth - 1);
+  TilingMap = isl_map_add_constraint (TilingMap, c);
+
   return TilingMap;
 }
 
@@ -316,9 +408,11 @@
     
    We walk recursively the forest of bands to combine the schedules of the
    individual bands to the overall schedule. In case tiling is requested,
-   the individual bands are tiled.  */
+   the individual bands are tiled.
+   For unroll and jam the map the schedule for full tiles of the unrolled
+   dimnesion is computed.  */
 static isl_union_map *
-getScheduleForBandList (isl_band_list *BandList)
+getScheduleForBandList (isl_band_list *BandList, isl_union_map **map_sepcl)
 {
   int NumBands, i;
   isl_union_map *Schedule;
@@ -335,55 +429,87 @@
       int ScheduleDimensions;
       isl_space *Space;
 
+      isl_union_map *PartialSchedule_f;
+
       Band = isl_band_list_get_band (BandList, i);
       PartialSchedule = getScheduleForBand (Band, &ScheduleDimensions);
       Space = isl_union_map_get_space (PartialSchedule);
 
+      PartialSchedule_f = NULL;
+
       if (isl_band_has_children (Band))
 	{
 	  isl_band_list *Children;
 	  isl_union_map *SuffixSchedule;
 
 	  Children = isl_band_get_children (Band);
-	  SuffixSchedule = getScheduleForBandList (Children);
+	  SuffixSchedule = getScheduleForBandList (Children, map_sepcl);
 	  PartialSchedule = isl_union_map_flat_range_product (PartialSchedule,
 							      SuffixSchedule);
 	  isl_band_list_free (Children);
 	}
-      else if (EnablePollyVector)
+      else if (EnablePollyVector || flag_loop_unroll_jam)
 	{
+	  int i;
+	  int depth;
+ 
+ 	  depth = PARAM_VALUE (PARAM_LOOP_UNROLL_JAM_DEPTH);
+  
 	  for (i = ScheduleDimensions - 1 ;  i >= 0 ; i--)
 	    {
+	      if (flag_loop_unroll_jam && (i != (ScheduleDimensions - depth)))
+		continue;
+
 	      if (isl_band_member_is_zero_distance (Band, i))
 		{
 		  isl_map *TileMap;
 		  isl_union_map *TileUMap;
+		  int stride;
 
-		  TileMap = getPrevectorMap (ctx, i, ScheduleDimensions, 4);
+                  stride = PARAM_VALUE (PARAM_LOOP_UNROLL_JAM_SIZE);    
+
+		  TileMap = getPrevectorMap_full (ctx, i, ScheduleDimensions, 
+						  stride); 
+ 		  TileUMap = isl_union_map_from_map (TileMap);
+		  TileUMap = isl_union_map_align_params
+		    (TileUMap, isl_space_copy (Space));
+		  PartialSchedule_f = isl_union_map_apply_range
+		    (isl_union_map_copy (PartialSchedule), TileUMap);
+
+		  TileMap = getPrevectorMap (ctx, i, ScheduleDimensions, stride);
 		  TileUMap = isl_union_map_from_map (TileMap);
 		  TileUMap = isl_union_map_align_params
 		    (TileUMap, isl_space_copy (Space));
 		  PartialSchedule = isl_union_map_apply_range
 		    (PartialSchedule, TileUMap);
 		  break;
-		}
+		}	
 	    }
 	}
-
       Schedule = isl_union_map_union (Schedule, PartialSchedule);
 
       isl_band_free (Band);
       isl_space_free (Space);
+
+      if (!flag_loop_unroll_jam)
+	continue;
+
+      if (PartialSchedule_f)
+	*map_sepcl = isl_union_map_union (*map_sepcl, 
+					  PartialSchedule_f);
+      else
+        *map_sepcl = isl_union_map_union (*map_sepcl, 
+         				  isl_union_map_copy (PartialSchedule));
     }
 
   return Schedule;
 }
 
 static isl_union_map *
-getScheduleMap (isl_schedule *Schedule)
+getScheduleMap (isl_schedule *Schedule, isl_union_map **map_sepcl)
 {
   isl_band_list *BandList = isl_schedule_get_band_forest (Schedule);
-  isl_union_map *ScheduleMap = getScheduleForBandList (BandList);
+  isl_union_map *ScheduleMap = getScheduleForBandList (BandList, map_sepcl);
   isl_band_list_free (BandList);
   return ScheduleMap;
 }
@@ -398,7 +524,7 @@
 }
 
 static void
-apply_schedule_map_to_scop (scop_p scop, isl_union_map *schedule_map)
+apply_schedule_map_to_scop (scop_p scop, isl_union_map *schedule_map, bool sepcl)
 {
   int i;
   poly_bb_p pbb;
@@ -413,8 +539,15 @@
 	(isl_union_map_copy (schedule_map),
 	 isl_union_set_from_set (domain));
       isl_union_map_foreach_map (stmtBand, getSingleMap, &stmtSchedule);
-      isl_map_free (pbb->transformed);
-      pbb->transformed = stmtSchedule;
+
+      if (!sepcl)
+	{
+	  isl_map_free (pbb->transformed);
+	  pbb->transformed = stmtSchedule;
+	}
+      else
+	  pbb->map_sepclass = stmtSchedule;
+
       isl_union_map_free (stmtBand);
     }
 }
@@ -429,6 +562,7 @@
   isl_union_set *domain;
   isl_union_map *validity, *proximity, *dependences;
   isl_union_map *schedule_map;
+  isl_union_map *schedule_map_f;
 
   domain = scop_get_domains (scop);
   dependences = scop_get_dependences (scop);
@@ -450,9 +584,13 @@
   if (!schedule)
     return false;
 
-  schedule_map = getScheduleMap (schedule);
+  schedule_map_f = isl_union_map_empty (isl_space_params_alloc (scop->ctx, 0));
+  schedule_map = getScheduleMap (schedule, &schedule_map_f);
 
-  apply_schedule_map_to_scop (scop, schedule_map);
+  apply_schedule_map_to_scop (scop, schedule_map, false);
+  if (!isl_union_map_is_empty (schedule_map_f))
+    apply_schedule_map_to_scop (scop, schedule_map_f, true);
+  isl_union_map_free (schedule_map_f);
 
   isl_schedule_free (schedule);
   isl_union_map_free (schedule_map);
Index: gcc/graphite-isl-ast-to-gimple.c
===================================================================
--- gcc/graphite-isl-ast-to-gimple.c	(revision 217013)
+++ gcc/graphite-isl-ast-to-gimple.c	(working copy)
@@ -831,6 +831,92 @@
   return schedule;
 }
 
+/* Set the separation_class option for unroll and jam. */
+
+static __isl_give isl_union_map *
+generate_luj_sepclass_opt (scop_p scop, __isl_take isl_union_set *domain, 
+			int dim, int cl)
+{
+  isl_map  *map;
+  isl_space *space, *space_sep;
+  isl_ctx *ctx;
+  isl_union_map *mapu;
+  int nsched = get_max_schedule_dimensions (scop);
+ 
+  ctx = scop->ctx;
+  space_sep = isl_space_alloc (ctx, 0, 1, 1);
+  space_sep = isl_space_wrap (space_sep);
+  space_sep = isl_space_set_tuple_name (space_sep, isl_dim_set,
+				        "separation_class");
+  space = isl_set_get_space (scop->context);
+  space_sep = isl_space_align_params (space_sep, isl_space_copy(space));
+  space = isl_space_map_from_domain_and_range (space, space_sep);
+  space = isl_space_add_dims (space,isl_dim_in, nsched);
+  map = isl_map_universe (space);
+  isl_map_fix_si (map,isl_dim_out,0,dim);
+  isl_map_fix_si (map,isl_dim_out,1,cl);
+
+  mapu = isl_union_map_intersect_domain (isl_union_map_from_map (map), 
+					 domain);
+  return (mapu);
+}
+
+/* Compute the separation class for loop unroll and jam.  */
+
+static __isl_give isl_union_set *
+generate_luj_sepclass (scop_p scop)
+{
+  int i;
+  poly_bb_p pbb;
+  isl_union_set *domain_isl;
+
+  domain_isl = isl_union_set_empty (isl_set_get_space (scop->context));
+
+  FOR_EACH_VEC_ELT (SCOP_BBS (scop), i, pbb)
+    {
+      isl_set *bb_domain;
+      isl_set *bb_domain_s;
+
+      if (pbb->map_sepclass == NULL)
+	continue;
+
+      if (isl_set_is_empty (pbb->domain))
+	continue;
+
+      bb_domain = isl_set_copy (pbb->domain);
+      bb_domain_s = isl_set_apply (bb_domain, pbb->map_sepclass);
+      pbb->map_sepclass = NULL;
+
+      domain_isl =
+	isl_union_set_union (domain_isl, isl_union_set_from_set (bb_domain_s));
+    }
+
+  return domain_isl;
+}
+
+/* Set the AST built options for loop unroll and jam. */
+ 
+static __isl_give isl_union_map *
+generate_luj_options (scop_p scop)
+{
+  isl_union_set *domain_isl;
+  isl_union_map *options_isl_ss;
+  isl_union_map *options_isl =
+    isl_union_map_empty (isl_set_get_space (scop->context));
+  int dim = get_max_schedule_dimensions (scop) - 1;
+  int dim1 = dim - PARAM_VALUE (PARAM_LOOP_UNROLL_JAM_DEPTH);
+
+  if (!flag_loop_unroll_jam)
+    return options_isl;
+
+  domain_isl = generate_luj_sepclass (scop);
+
+  options_isl_ss = generate_luj_sepclass_opt (scop, domain_isl, dim1, 0);
+  options_isl = isl_union_map_union (options_isl, options_isl_ss);
+
+  return options_isl;
+}
+
 /* Generates a schedule, which specifies an order used to
    visit elements in a domain.  */
 
@@ -879,11 +965,13 @@
 }
 
 /* Set the separate option for all dimensions.
-   This helps to reduce control overhead.  */
+   This helps to reduce control overhead.
+   Set the options for unroll and jam.  */
 
 static __isl_give isl_ast_build *
 set_options (__isl_take isl_ast_build *control,
-	     __isl_keep isl_union_map *schedule)
+	     __isl_keep isl_union_map *schedule,
+	     __isl_take isl_union_map *opt_luj)
 {
   isl_ctx *ctx = isl_union_map_get_ctx (schedule);
   isl_space *range_space = isl_space_set_alloc (ctx, 0, 1);
@@ -894,6 +982,9 @@
   isl_union_set *domain = isl_union_map_range (isl_union_map_copy (schedule));
   domain = isl_union_set_universe (domain);
   isl_union_map *options = isl_union_map_from_domain_and_range (domain, range);
+
+  options = isl_union_map_union (options, opt_luj);
+
   return isl_ast_build_set_options (control, options);
 }
 
@@ -907,9 +998,14 @@
   isl_options_set_ast_build_atomic_upper_bound (scop->ctx, true);
 
   add_parameters_to_ivs_params (scop, ip);
+
+  isl_union_map *options_luj = generate_luj_options (scop);
+
   isl_union_map *schedule_isl = generate_isl_schedule (scop);
   isl_ast_build *context_isl = generate_isl_context (scop);
-  context_isl = set_options (context_isl, schedule_isl);
+
+  context_isl = set_options (context_isl, schedule_isl, options_luj);
+
   isl_union_map *dependences = NULL;
   if (flag_loop_parallelize_all)
   {
Index: gcc/toplev.c
===================================================================
--- gcc/toplev.c	(revision 217013)
+++ gcc/toplev.c	(working copy)
@@ -1302,11 +1302,12 @@
       || flag_loop_block
       || flag_loop_interchange
       || flag_loop_strip_mine
-      || flag_loop_parallelize_all)
+      || flag_loop_parallelize_all
+      || flag_loop_unroll_jam)
     sorry ("Graphite loop optimizations cannot be used (ISL is not available)" 
 	   "(-fgraphite, -fgraphite-identity, -floop-block, "
 	   "-floop-interchange, -floop-strip-mine, -floop-parallelize-all, "
-	   "and -ftree-loop-linear)");
+	   "-floop-unroll-and-jam, and -ftree-loop-linear)");
 #endif
 
   /* One region RA really helps to decrease the code size.  */
Index: gcc/params.def
===================================================================
--- gcc/params.def	(revision 217013)
+++ gcc/params.def	(working copy)
@@ -847,6 +847,21 @@
 	  "size of tiles for loop blocking",
 	  51, 0, 0)
 
+/* Size of unrolling factor for unroll-and-jam.  */
+ 
+DEFPARAM (PARAM_LOOP_UNROLL_JAM_SIZE,
+ 	  "loop-unroll-jam-size",
+ 	  "size of unrolling factor for unroll-and-jam",
+ 	  4, 0, 0)
+
+/* Size of the band formed by the strip mined dimension and the most inner one for unroll-and-jam.  */
+ 
+DEFPARAM (PARAM_LOOP_UNROLL_JAM_DEPTH,
+ 	  "loop-unroll-jam-depth",
+ 	  "depth of unrolled loop for unroll-and-jam",
+ 	  2, 0, 0)
+
+
 /* Maximal number of parameters that we allow in a SCoP.  */
 
 DEFPARAM (PARAM_GRAPHITE_MAX_NB_SCOP_PARAMS,
Index: gcc/graphite-poly.c
===================================================================
--- gcc/graphite-poly.c	(revision 217013)
+++ gcc/graphite-poly.c	(working copy)
@@ -276,7 +276,7 @@
 
   /* This pass needs to be run at the final stage, as it does not
      update the lst.  */
-  if (flag_loop_optimize_isl)
+  if (flag_loop_optimize_isl || flag_loop_unroll_jam)
     transform_done |= optimize_isl (scop);
 
   return transform_done;
@@ -327,6 +327,7 @@
   pbb->schedule = NULL;
   pbb->transformed = NULL;
   pbb->saved = NULL;
+  pbb->map_sepclass = NULL;
   PBB_SCOP (pbb) = scop;
   pbb_set_black_box (pbb, black_box);
   PBB_TRANSFORMED (pbb) = NULL;