On Mon, 1 May 2006 11:04, Joe Neeman wrote:
> On Mon, 1 May 2006 10:04, Han-Wen Nienhuys wrote:
> > If you have checked that the regtest document
> > looks ok, please apply the spacing patch too.
>
> I have a couple regressions that may be caused by my spacing patch (or
> maybe by some of my other changes). But I'll hold off on commiting until I
> have figured out where they come from.
>
I fixed all the regressions that I found. I attach just the diff of 
simple-spacer.cc because there were only extremely minor changes in any of 
the other files since my last patch. If you want to see the full patch again, 
though, I can send it. ChangeLog is the same as before.

Col_desc is now Column_desc -- I assume this is OK since you didn't complain 
about Rod_desc. Both names are local to the bottom half simple-spacer.cc and 
"description" is such a long word... ;)

2006-05-04  Joe Neeman <[EMAIL PROTECTED]>

        * lily/simple-spacer.cc: Remove class Simple_spacer_wrapper.
        Replace it with functions get_line_forces and get_line_configuration.
        (class Simple_spacer): Make data private.
        Rewrite compression algorithm to be faster and simpler.

        * lily/simple-spacer-scheme.cc (ly_solve_rod_and_spring_problem):
        * lily/gourlay-breaking.cc (solve):
        * lily/constrained_breaking.cc (space_line):
        Change it to the new simple-spacer code.

        * lily/paper-score.cc (get_paper_systems):
        (Paper_score):
        (process):
        Delay breaking the systems until they are requested.
        (find_break_indices):
        Use vsize for indices.
        (calc_breaking):
        Move the "Calculating line breaks" message here.

        * lily/system.cc (pre_processing):
        Move the "Calculating line breaks" message away from here.
        (break_into_pieces):
        Allow multiple calls to this function in sequence (with touching-but-
        not-overlapping breakpoints).

        * lily/constrained-breaking.cc:
        Replace most of the get_XXXX functions with get_line_details.
        Only calculate the force for each line. Calculate configurations only
        for the lines we will actually use.
        Replace cols_ with lines_.
Index: lily/simple-spacer.cc
===================================================================
RCS file: /sources/lilypond/lilypond/lily/simple-spacer.cc,v
retrieving revision 1.96
diff -u -r1.96 simple-spacer.cc
--- lily/simple-spacer.cc	11 Feb 2006 11:35:17 -0000	1.96
+++ lily/simple-spacer.cc	4 May 2006 01:06:08 -0000
@@ -59,14 +59,29 @@
 
 Simple_spacer::Simple_spacer ()
 {
-  /*
-    Give an extra penalty for compression. Needed to avoid compressing
-    tightly spaced lines.
-  */
-  active_count_ = 0;
   force_ = 0.;
-  indent_ = 0.0;
-  default_space_ = 20 PT;
+  fits_ = true;
+}
+
+Real
+Simple_spacer::force ()
+{
+  return force_;
+}
+
+bool
+Simple_spacer::fits ()
+{
+  return fits_;
+}
+
+Real
+Simple_spacer::rod_force (int l, int r, Real dist)
+{
+  Real c = range_stiffness (l, r);
+  Real d = range_ideal_len (l, r);
+  Real block_stretch = dist - d;
+  return c * block_stretch;
 }
 
 void
@@ -78,30 +93,18 @@
       return;
     }
 
-  Real c = range_stiffness (l, r);
-  if (isinf (c))
-    {
-      /*
-	If a spring is fixed, we have to do something here:
-	we let the rod override the spring.
-      */
-      Real total_dist = 0.;
-      for (int i = l; i < r; i++)
-	total_dist += springs_[i].ideal_;
+  Real block_force = rod_force (l, r, dist);
 
-      if (total_dist < dist)
+  if (isinf (block_force))
+    {
+      Real spring_dist = range_ideal_len (l, r);
+      if (spring_dist < dist)
 	for (int i = l; i < r; i++)
-	  springs_[i].ideal_ *= dist / total_dist;
+	  springs_[i].ideal_ *= dist / spring_dist;
 
       return;
     }
-
-  Real d = range_ideal_len (l, r);
-  Real block_stretch = dist - d;
-
-  Real block_force = c * block_stretch;
   force_ = max (force_, block_force);
-
   for (int i = l; i < r; i++)
     springs_[i].block_force_ = max (block_force, springs_[i].block_force_);
 }
@@ -120,122 +123,121 @@
 {
   Real den = 0.0;
   for (int i = l; i < r; i++)
-    {
-      if (springs_[i].is_active_)
-	den += 1 * springs_[i].inverse_hooke_;
-    }
+    den += springs_[i].inverse_hooke_;
 
   return 1 / den;
 }
 
 Real
-Simple_spacer::active_blocking_force () const
+Simple_spacer::configuration_length () const
 {
-  Real bf = -infinity_f;
+  Real l = 0.;
   for (vsize i = 0; i < springs_.size (); i++)
-    if (springs_[i].is_active_)
-      bf = max (bf, springs_[i].block_force_);
-  return bf;
-}
-
-Real
-Simple_spacer::active_springs_stiffness () const
-{
-  Real stiff = range_stiffness (0, springs_.size ());
-  if (isinf (stiff))
-    {
-      /*
-	all springs are inactive. Take the stiffness of the
-	latest spring to block.
-      */
-
-      Real max_block_force = -infinity_f;
-      int max_i = -1;
-      for (vsize i = 0; i < springs_.size (); i++)
-	{
-	  if (springs_[i].block_force_ > max_block_force)
-	    {
-	      max_i = i;
-	      max_block_force = springs_[i].block_force_;
-	    }
-	}
+    l += springs_[i].length (force_);
 
-      stiff = 1/springs_[max_i].inverse_hooke_;
-    }
-  return stiff;
+  return l;
 }
 
 void
-Simple_spacer::set_active_states ()
+Simple_spacer::solve (Real line_len, bool ragged)
 {
-  /* float comparison is safe, since force is only copied.  */
-  for (vsize i = 0; i < springs_.size (); i++)
-    if (springs_[i].is_active_
-	&& springs_[i].block_force_ >= force_)
-      {
-	springs_[i].is_active_ = false;
-	active_count_--;
-      }
+  Real conf = configuration_length ();
+
+  ragged_ = ragged;
+  line_len_ = line_len;
+  if (ragged)
+    {
+      force_ = 0;
+      fits_ = configuration_length () <= line_len_;
+      /* we need to calculate a force here to prevent a bunch of short lines */
+      if (fits_)
+	force_ = expand_line ();
+    }
+  else if (conf < line_len_)
+    force_ = expand_line ();
+  else if (conf > line_len_)
+    force_ = compress_line ();
 }
 
 Real
-Simple_spacer::configuration_length () const
+Simple_spacer::expand_line ()
 {
-  Real l = 0.;
-  for (vsize i = 0; i < springs_.size (); i++)
-    l += springs_[i].length (force_);
+  double inv_hooke = 0;
+  double cur_len = configuration_length ();
 
-  return l;
-}
+  fits_ = true;
+  for (vsize i=0; i < springs_.size (); i++)
+    inv_hooke += springs_[i].inverse_hooke_;
 
-bool
-Simple_spacer::is_active () const
-{
-  return active_count_;
+  assert (cur_len <= line_len_);
+  return (line_len_ - cur_len) / inv_hooke + force_;
 }
 
-void
-Simple_spacer::my_solve_linelen ()
+Real
+Simple_spacer::compress_line ()
 {
-  while (is_active ())
+  double inv_hooke = 0;
+  double cur_len = configuration_length ();
+  double cur_force = force_;
+
+  fits_ = true;
+  for (vsize i=0; i < springs_.size (); i++)
+    inv_hooke += springs_[i].inverse_hooke_;
+
+  assert (line_len_ <= cur_len);
+
+  vector<Spring_description> sorted_springs = springs_;
+  sort (sorted_springs.begin (), sorted_springs.end (), greater<Spring_description> ());
+  for (vsize i = 0; i < sorted_springs.size (); i++)
     {
-      force_ = active_blocking_force ();
-      Real conf = configuration_length ();
+      Spring_description sp = sorted_springs[i];
 
-      if (conf < line_len_)
-	{
-	  force_ += (line_len_ - conf) * active_springs_stiffness ();
-	  break;
-	}
-      else
-	set_active_states ();
+      assert (sp.block_force_ <= cur_force);
+      if (isinf (sp.block_force_))
+	break;
+
+      double block_dist = (cur_force - sp.block_force_) * inv_hooke;
+      if (cur_len - block_dist <= line_len_)
+	return cur_force + (line_len_ - cur_len) / inv_hooke;
+      cur_len -= block_dist;
+      inv_hooke -= sp.inverse_hooke_;
+      cur_force = sp.block_force_;
     }
+
+  fits_ = false;
+  return cur_force;
 }
 
 void
-Simple_spacer::my_solve_natural_len ()
+Simple_spacer::add_spring (Real ideal, Real inverse_hooke)
 {
-  Real line_len_force = 0.0;
+  Spring_description desc;
 
-  while (is_active ())
+  desc.ideal_ = ideal;
+  desc.inverse_hooke_ = inverse_hooke;
+  if (!desc.is_sane ())
     {
-      force_ = max (active_blocking_force (), 0.0);
-      Real conf = configuration_length ();
+      programming_error ("insane spring found, setting to unit");
 
-      if (conf < line_len_)
-	{
-	  line_len_force = force_
-	    + (line_len_ - conf)
-	    * active_springs_stiffness ();
-	}
+      desc.inverse_hooke_ = 1.0;
+      desc.ideal_ = 1.0;
+    }
 
-      if (force_ < 1e-8) // ugh.,
-	break;
+  desc.block_force_ = -desc.ideal_ / desc.inverse_hooke_;
+  // block at distance 0
 
-      set_active_states ();
-    }
+  springs_.push_back (desc);
+}
 
-  force_ = line_len_force;
+vector<Real>
+Simple_spacer::spring_positions () const
+{
+  vector<Real> ret;
+  ret.push_back (0.);
+
+  for (vsize i = 0; i < springs_.size (); i++)
+    ret.push_back (ret.back () + springs_[i].length (ragged_ ? 0.0 : force_));
+  return ret;
 }
 
 /****************************************************************/
@@ -244,7 +246,6 @@
 {
   ideal_ = 0.0;
   inverse_hooke_ = 0.0;
-  is_active_ = true;
   block_force_ = 0.0;
 }
 
@@ -259,10 +260,9 @@
 Real
 Spring_description::length (Real f) const
 {
-  if (!is_active_)
-    f = block_force_;
-  return ideal_ + f * inverse_hooke_;
+  return ideal_ + max (f, block_force_) * inverse_hooke_;
 }
+
 /****************************************************************/
 
 /*
@@ -278,174 +278,263 @@
   The ## forces the notes apart; we shouldn't allow the O's to touch
   this closely.
 */
-void
-Simple_spacer_wrapper::solve (Column_x_positions *positions, bool ragged)
+
+struct Rod_desc
 {
-  if (ragged)
-    spacer_->my_solve_natural_len ();
-  else
-    spacer_->my_solve_linelen ();
+  vsize r_;
+  Real dist_;
 
-  positions->force_ = spacer_->force_;
+  bool operator< (const Rod_desc r)
+  {
+    return r_ < r.r_;
+  }
 
-  /*
-    We used to have a penalty for compression, no matter what, but that
-    fucked up wtk1-fugue2 (taking 3 full pages.)
-  */
-  positions->config_.push_back (spacer_->indent_);
-  for (vsize i = 0; i < spacer_->springs_.size (); i++)
-    {
-      Real l = spacer_->springs_[i].length ((ragged) ? 0.0 : spacer_->force_);
-      positions->config_.push_back (positions->config_.back () + l);
-      /*
-	we have l>= 0 here, up to rounding errors
-      */
-    }
+  Rod_desc () {}
+  Rod_desc (vsize r, Real d)
+  {
+    r_ = r;
+    dist_ = d;
+  }
+};
 
-  /*
-    For raggedright, we must have a measure of music density: this is
-    to prevent lots of short lines (which all have force = 0).
-  */
-  if (ragged)
-    {
-      positions->satisfies_constraints_
-	= positions->config_.back () < spacer_->line_len_;
-    }
-  else
-    positions->satisfies_constraints_ = spacer_->is_active ();
+struct Column_desc
+{
+  vector<Rod_desc> rods_;
+  vector<Rod_desc> end_rods_;   /* use these if they end at the last column of the line */
+  Real ideal_;
+  Real inverse_hooke_;
+  Real end_ideal_;
+  Real end_inverse_hooke_;
+  Interval keep_inside_line_;
+};
 
-  positions->cols_ = spaced_cols_;
-  positions->loose_cols_ = loose_cols_;
+static int compare_paper_column_rank (Grob *const &a, Grob *const &b);
 
-  /*
-    Check if breaking constraints are met.
-  */
-  bool break_satisfy = true;
-  int sz = positions->cols_.size ();
-  for (int i = sz; i--;)
-    {
-      SCM p = positions->cols_[i]->get_property ("penalty");
-      if (scm_is_number (p))
-	{
-	  if (scm_to_double (p) < -9999)
-	    break_satisfy = break_satisfy && (i == 0 || i == sz -1);
-	  if (scm_to_double (p) > 9999)
-	    break_satisfy = break_satisfy && ! (i == 0 || i == sz -1);
-	}
-    }
+static bool
+is_loose (Grob *g)
+{
+  return (scm_is_pair (g->get_object ("between-cols")));
+}
 
-  positions->satisfies_constraints_
-    = positions->satisfies_constraints_ && break_satisfy;
+static Grob*
+maybe_find_prebroken_piece (Grob *g, Direction d)
+{
+  Grob *ret = dynamic_cast<Item*> (g)->find_prebroken_piece (d);
+  if (ret)
+    return ret;
+  return g;
 }
 
-void
-Simple_spacer::add_spring (Real ideal, Real inverse_hooke)
+static Grob*
+next_spaceable_column (vector<Grob*> const &list, vsize starting)
 {
-  Spring_description desc;
+  for (vsize i = starting+1; i < list.size (); i++)
+    if (!is_loose (list[i]))
+      return list[i];
+  return 0;
+}
 
-  desc.ideal_ = ideal;
-  desc.inverse_hooke_ = inverse_hooke;
-  if (!desc.is_sane ())
-    {
-      programming_error ("insane spring found, setting to unit");
+/* this only returns non-NULL if the line-ending column is the next
+   spaceable-or-breakable column */
+static Grob*
+next_line_ending_column (vector<Grob*> const &list, vsize starting)
+{
+  vsize i = starting + 1;
+  for (; i < list.size ()
+	 && is_loose (list[i])
+	 && !Item::is_breakable (list[i]);
+       i++)
+    ;
+  return dynamic_cast<Item*> (list[i])->find_prebroken_piece (LEFT);
+}
 
-      desc.inverse_hooke_ = 1.0;
-      desc.ideal_ = 1.0;
-    }
+static void
+get_column_spring (Grob *this_col, Grob *next_col, Real *ideal, Real *inv_hooke)
+{
+  Spring_smob *spring = 0;
 
-  if (!inverse_hooke)
-    desc.is_active_ = false;
-  else
-    {
-      /*
-	desc.is_active_ ?
-      */
-      desc.block_force_ = -desc.ideal_ / desc.inverse_hooke_;
-      // block at distance 0
+  for (SCM s = this_col->get_object ("ideal-distances");
+       !spring && scm_is_pair (s);
+       s = scm_cdr (s))
+    {
+      Spring_smob *sp = unsmob_spring (scm_car (s));
 
-      active_count_++;
+      if (sp->other_ == next_col)
+	spring = sp;
     }
-  springs_.push_back (desc);
-}
 
-static int
-compare_paper_column_rank (Grob *const &a,
-			   Grob *const &b)
-{
-  return Paper_column::get_rank (a) - Paper_column::get_rank (b);
+  if (!spring)
+    programming_error (_f ("No spring between column %d and next one",
+			   Paper_column::get_rank (this_col)));
+
+  *ideal = (spring) ? spring->distance_ : 5.0;
+  *inv_hooke = (spring) ? spring->inverse_strength_ : 1.0;
 }
 
-void
-Simple_spacer_wrapper::add_columns (vector<Grob*> const &icols)
+static Column_desc
+get_column_desc (vector<Grob*> const &cols, vsize col_index, bool line_starter)
 {
-  vector<Grob*> cols (icols);
-  cols.clear ();
+  Grob *col = cols[col_index];
+  if (line_starter)
+    col = maybe_find_prebroken_piece (col, RIGHT);
 
-  for (vsize i = 0; i < icols.size (); i++)
-    if (scm_is_pair (icols[i]->get_object ("between-cols")))
-      loose_cols_.push_back (icols[i]);
-    else
-      cols.push_back (icols[i]);
+  Column_desc desc;
+  Grob *next_col = next_spaceable_column (cols, col_index);
+  if (next_col)
+    get_column_spring (col, next_col, &desc.ideal_, &desc.inverse_hooke_);
+  Grob *end_col = next_line_ending_column (cols, col_index);
+  if (end_col)
+    get_column_spring (col, end_col, &desc.end_ideal_, &desc.end_inverse_hooke_);
 
-  spaced_cols_ = cols;
-  for (vsize i = 0; i < cols.size () - 1; i++)
+  for (SCM s = Spaceable_grob::get_minimum_distances (col);
+       scm_is_pair (s); s = scm_cdr (s))
     {
-      Spring_smob *spring = 0;
-
-      for (SCM s = cols[i]->get_object ("ideal-distances");
-	   !spring && scm_is_pair (s);
-	   s = scm_cdr (s))
+      Grob *other = unsmob_grob (scm_caar (s));
+      vsize j = binary_search (cols, other, &compare_paper_column_rank, col_index);
+      if (j != VPOS)
 	{
-	  Spring_smob *sp = unsmob_spring (scm_car (s));
-
-	  if (sp->other_ == cols[i + 1])
-	    spring = sp;
+	  if (cols[j] == other)
+	    desc.rods_.push_back (Rod_desc (j, scm_to_double (scm_cdar (s))));
+	  else /* it must end at the LEFT prebroken_piece */
+	    desc.end_rods_.push_back (Rod_desc (j, scm_to_double (scm_cdar (s))));
 	}
-
-      if (!spring)
-	programming_error (_f ("No spring between column %d and next one",
-			       Paper_column::get_rank (cols[i])));
-
-      Real ideal = (spring) ? spring->distance_ : spacer_->default_space_;
-      Real inverse_hooke = (spring) ? spring->inverse_strength_ : 1.0;
-
-      spacer_->add_spring (ideal, inverse_hooke);
     }
+  if (!line_starter && to_boolean (col->get_property ("keep-inside-line")))
+    desc.keep_inside_line_ = col->extent (col, X_AXIS);
+  return desc;
+}
 
-  for (vsize i = 0; i < cols.size () - 1; i++)
+vector<Real>
+get_line_forces (vector<Grob*> const &icols, vector<vsize> breaks,
+		 Real line_len, Real indent, bool ragged)
+{
+  vector<Real> force;
+  force.resize (breaks.size () * breaks.size ());
+
+  vector<Column_desc> cols;
+  vsize b = 1;
+  cols.push_back (Column_desc ());
+  for (vsize i = 1; i < icols.size () - 1; i++)
     {
-      for (SCM s = Spaceable_grob::get_minimum_distances (cols[i]);
-	   scm_is_pair (s); s = scm_cdr (s))
+      if (b < breaks.size () && breaks[b] == i)
 	{
-	  Grob *other = unsmob_grob (scm_caar (s));
-	  vsize j = binary_search (cols, other, &compare_paper_column_rank);
-	  if (j != VPOS && cols[j] == other)
-	    spacer_->add_rod (i, j, scm_to_double (scm_cdar (s)));
+	  breaks[b] = cols.size ();
+	  b++;
 	}
+      if (!is_loose (icols[i]))
+	cols.push_back (get_column_desc (icols, i, false));
+    }
+  breaks.back () = cols.size () - 1;
 
-      if (i
-	  && to_boolean (cols[i]->get_property ("keep-inside-line")))
+  for (vsize b = 0; b < breaks.size () - 1; b++)
+    {
+      cols[breaks[b]] = get_column_desc (icols, breaks[b], true);
+      vsize st = breaks[b];
+
+      for (vsize c = b+1; c < breaks.size (); c++)
 	{
-	  Interval e = cols[i]->extent (cols[i], X_AXIS);
-	  if (!e.is_empty ())
+	  vsize end = breaks[c];
+	  Simple_spacer spacer;
+
+	  for (vsize i = breaks[b]; i < end - 1; i++)
+	    spacer.add_spring (cols[i].ideal_, cols[i].inverse_hooke_);
+	  spacer.add_spring (cols[end-1].end_ideal_, cols[end-1].inverse_hooke_);
+
+
+	  for (vsize i = breaks[b]; i < end; i++)
 	    {
-	      spacer_->add_rod (i, cols.size () - 1, e[RIGHT]);
-	      spacer_->add_rod (0, i, e[LEFT]);
+	      for (vsize r = 0; r < cols[i].rods_.size (); r++)
+		if (cols[i].rods_[r].r_ < end)
+		  spacer.add_rod (i - st, cols[i].rods_[r].r_ - st, cols[i].rods_[r].dist_);
+	      for (vsize r = 0; r < cols[i].end_rods_.size (); r++)
+		if (cols[i].end_rods_[r].r_ == end)
+		  spacer.add_rod (i - st, end - st, cols[i].end_rods_[r].dist_);
+	      if (!cols[i].keep_inside_line_.is_empty ())
+		{
+		  spacer.add_rod (i - st, end - st, cols[i].keep_inside_line_[RIGHT]);
+		  spacer.add_rod (0, i - st, cols[i].keep_inside_line_[LEFT]);
+		}
+	    }
+	  spacer.solve ((b == 0) ? line_len - indent : line_len, ragged);
+	  force[b * breaks.size () + c] = spacer.force ();
+	  if (!spacer.fits ())
+	    {
+	      force[b * breaks.size () + c] = infinity_f;
+	      break;
 	    }
 	}
     }
+  return force;
 }
 
-Simple_spacer_wrapper::Simple_spacer_wrapper ()
+Column_x_positions
+get_line_configuration (vector<Grob*>const &columns,
+			Real line_len,
+			Real indent,
+			bool ragged)
 {
-  spacer_ = new Simple_spacer ();
-}
+  vector<Column_desc> cols;
+  Simple_spacer spacer;
+  Column_x_positions ret;
 
-Simple_spacer_wrapper::~Simple_spacer_wrapper ()
-{
-  delete spacer_;
+  ret.cols_.push_back (dynamic_cast<Item*> (columns[0])->find_prebroken_piece (RIGHT));
+  for (vsize i = 1; i < columns.size () - 1; i++)
+    {
+      if (is_loose (columns[i]))
+	ret.loose_cols_.push_back (columns[i]);
+      else
+	ret.cols_.push_back (columns[i]);
+    }
+  ret.cols_.push_back (dynamic_cast<Item*> (columns.back ())->find_prebroken_piece (LEFT));
+
+  cols.resize (ret.cols_.size () - 1);
+
+  /* since we've already put our line-ending column in the column list, we can ignore
+     the end_XXX_ fields of our column_desc */
+  for (vsize i = 0; i < cols.size (); i++)
+    {
+      cols[i] = get_column_desc (ret.cols_, i, i == 0);
+      spacer.add_spring (cols[i].ideal_, cols[i].inverse_hooke_);
+    }
+  for (vsize i = 0; i < cols.size (); i++)
+    for (vsize r = 0; r < cols[i].rods_.size (); r++)
+      spacer.add_rod (i, cols[i].rods_[r].r_, cols[i].rods_[r].dist_);
+
+  spacer.solve (line_len, ragged);
+  ret.force_ = spacer.force ();
+
+  /*
+    We used to have a penalty for compression, no matter what, but that
+    fucked up wtk1-fugue2 (taking 3 full pages.)
+  */
+  ret.config_ = spacer.spring_positions ();
+  for (vsize i = 0; i < ret.config_.size (); i++)
+    ret.config_[i] += indent;
+
+  ret.satisfies_constraints_ = spacer.fits ();
+
+  /*
+    Check if breaking constraints are met.
+  */
+  int sz = ret.cols_.size ();
+  for (int i = sz; i--;)
+    {
+      SCM p = ret.cols_[i]->get_property ("penalty");
+      if (scm_is_number (p))
+	{
+	  if (scm_to_double (p) < -9999)
+	    ret.satisfies_constraints_ = ret.satisfies_constraints_ && (i == 0 || i == sz -1);
+	  if (scm_to_double (p) > 9999)
+	    ret.satisfies_constraints_ = ret.satisfies_constraints_ && ! (i == 0 || i == sz -1);
+	}
+    }
+
+  return ret;
 }
 
-Simple_spacer_wrapper::Simple_spacer_wrapper (Simple_spacer_wrapper const &)
+static int
+compare_paper_column_rank (Grob *const &a,
+			   Grob *const &b)
 {
+  return Paper_column::get_rank (a) - Paper_column::get_rank (b);
 }
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