/*
  This file is part of LilyPond, the GNU music typesetter.

  Copyright (C) 2009--2012 Joe Neeman <joeneeman@gmail.com>

  LilyPond 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 of the License, or
  (at your option) any later version.

  LilyPond 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 LilyPond.  If not, see <http://www.gnu.org/licenses/>.
*/

#include "page-layout-problem.hh"

#include "align-interface.hh"
#include "axis-group-interface.hh"
#include "hara-kiri-group-spanner.hh"
#include "international.hh"
#include "item.hh"
#include "output-def.hh"
#include "paper-book.hh"
#include "paper-column.hh"
#include "paper-score.hh"
#include "pointer-group-interface.hh"
#include "prob.hh"
#include "skyline-pair.hh"
#include "system.hh"
#include "text-interface.hh"

/*
 Returns the number of footntoes associated with a given line.
*/

vector<Grob *>
Page_layout_problem::get_footnote_grobs (SCM lines)
{
  vector<Grob *> footnotes;
  for (SCM s = lines; scm_is_pair (s); s = scm_cdr (s))
    {
      if (Grob *g = unsmob_grob (scm_car (s)))
        {
          System *sys = dynamic_cast<System *> (g);
          if (!sys)
            {
              programming_error ("got a grob for footnotes that wasn't a System");
              continue;
            }
          extract_grob_set (sys, "footnotes-after-line-breaking", footnote_grobs);
          footnotes.insert (footnotes.end (), footnote_grobs.begin (), footnote_grobs.end ());
        }
      else if (Prob *p = unsmob_prob (scm_car (s)))
        {
          SCM stencils = p->get_property ("footnotes");
          if (stencils == SCM_EOL)
            continue;
          for (SCM st = stencils; scm_is_pair (st); st = scm_cdr (st))
            footnotes.push_back (0);
        }
    }

  return footnotes;
}

vsize
Page_layout_problem::get_footnote_count (SCM lines)
{
  vector<Grob *> notes = get_footnote_grobs (lines);
  return notes.size ();
}

SCM
Page_layout_problem::get_footnotes_from_lines (SCM lines)
{
  if (!scm_is_pair (lines))
    return SCM_EOL;

  bool footnotes_added;
  if (Grob *g = unsmob_grob (scm_car (lines)))
    footnotes_added = !scm_is_null (g->get_property ("footnote-stencil"));
  else if (Prob *p = unsmob_prob (scm_car (lines)))
    footnotes_added = !scm_is_null (p->get_property ("footnote-stencil"));
  else
    {
      programming_error ("Systems on a page must be a prob or grob.");
      return SCM_EOL;
    }
  if (!footnotes_added)
    {
      programming_error ("Footnotes must be added to lines before they are retrieved.");
      return SCM_EOL;
    }

  SCM out = SCM_EOL;
  for (SCM s = lines; scm_is_pair (s); s = scm_cdr (s))
    {
      if (Grob *g = unsmob_grob (scm_car (s)))
        out = scm_cons (g->get_property ("footnote-stencil"), out);
      else if (Prob *p = unsmob_prob (scm_car (s)))
        out = scm_cons (p->get_property ("footnote-stencil"), out);
      else
        programming_error ("Systems on a page must be a prob or grob.");
    }

  return scm_reverse_x (out, SCM_EOL);
}

/*
   Adds a footnote stencil to each system.  This stencil may
   itself be comprised of several footnotes.

   This is a long function, but it seems better to keep it intact rather than
   splitting it into parts.
*/

void
Page_layout_problem::add_footnotes_to_lines (SCM lines, int counter, Paper_book *pb)
{
  /*
    first, we have to see how many footnotes are on this page.
    we need to do this first so that we can line them up
  */

  Output_def *paper = pb->paper_;

  if (!paper)
    {
      programming_error ("Cannot get footnotes because there is no valid paper block.");
      return;
    }

  SCM number_footnote_table = pb->top_paper ()->c_variable ("number-footnote-table");
  if (!scm_is_pair (number_footnote_table))
    number_footnote_table = SCM_EOL;
  SCM numbering_function = paper->c_variable ("footnote-numbering-function");
  SCM layout = paper->self_scm ();
  SCM props = scm_call_1 (ly_lily_module_constant ("layout-extract-page-properties"),
                          paper->self_scm ());
  Real padding = robust_scm2double (paper->c_variable ("footnote-padding"), 0.0);
  Real number_raise = robust_scm2double (paper->c_variable ("footnote-number-raise"), 0.0);

  vector<Grob *> fn_grobs = get_footnote_grobs (lines);
  vsize fn_count = fn_grobs.size ();

  // now, make the footnote stencils with the numbering function
  SCM numbers = SCM_EOL;
  SCM in_text_numbers = SCM_EOL;
  /*
    TODO: This recalculates numbering every time this function is called, including once
    after the balloon prints are called.  Although it is not a huge computational drain,
    it'd be more elegant to turn this calculation off when it is no longer needed.

    In a separate commit, it'd be nice to streamline the way that page layout property
    is handled so that the process of building `config's in page-breaking does result
    in duplicated work, either by making this process less complicated or (preferably)
    by passing its results downstream.
  */

  // find the maximum X_AXIS length
  Real max_length = -infinity_f;

  for (vsize i = 0; i < fn_count; i++)
    {
      if (fn_grobs[i])
        {
          SCM assertion_function = fn_grobs[i]->get_property ("numbering-assertion-function");
          if (ly_is_procedure (assertion_function))
            (void) scm_call_1 (assertion_function, scm_from_int (counter));
        }
      SCM markup = scm_call_1 (numbering_function, scm_from_int (counter));
      SCM stencil = Text_interface::interpret_markup (layout, props, markup);
      Stencil *st = unsmob_stencil (stencil);
      if (!st)
        {
          programming_error ("Your numbering function needs to return a stencil.");
          markup = SCM_EOL;
          stencil = Stencil (Box (Interval (0, 0), Interval (0, 0)), SCM_EOL).smobbed_copy ();
          st = unsmob_stencil (stencil);
        }
      in_text_numbers = scm_cons (markup, in_text_numbers);
      numbers = scm_cons (stencil, numbers);

      if (!st->extent (X_AXIS).is_empty ())
        max_length = max (max_length, st->extent (X_AXIS)[RIGHT]);

      counter++;
    }

  in_text_numbers = scm_reverse_x (in_text_numbers, SCM_EOL);
  numbers = scm_reverse_x (numbers, SCM_EOL);

  /*
    translate each stencil such that it attains the correct maximum length and bundle the
    footnotes into a scheme object.
  */

  for (SCM p = numbers; scm_is_pair (p); p = scm_cdr (p))
    {
      Stencil *st = unsmob_stencil (scm_car (p));
      if (!st->extent (X_AXIS).is_empty ())
        st->translate_axis ((max_length - st->extent (X_AXIS)[RIGHT]),
                            X_AXIS);
    }

  // build the footnotes

  for (SCM s = lines; scm_is_pair (s); s = scm_cdr (s))
    {
      // Take care of musical systems.
      if (Grob *g = unsmob_grob (scm_car (s)))
        {
          System *sys = dynamic_cast<System *> (g);
          if (!sys)
            {
              programming_error ("got a grob for footnotes that wasn't a System");
              continue;
            }
          Stencil mol;
          Stencil in_note_mol;
          extract_grob_set (sys, "footnotes-after-line-breaking", footnote_grobs);
          for (vsize i = 0; i < footnote_grobs.size (); i++)
            {
              Grob *footnote = footnote_grobs[i];
              SCM footnote_markup = footnote->get_property ("footnote-text");
              if (Spanner *orig = dynamic_cast<Spanner *>(footnote))
                if (orig->is_broken ())
                  footnote_markup = orig->broken_intos_[0]->get_property ("footnote-text");

              SCM props = scm_call_1 (ly_lily_module_constant ("layout-extract-page-properties"),
                                      paper->self_scm ());

              SCM footnote_stl = Text_interface::interpret_markup (paper->self_scm (),
                                                                   props, footnote_markup);

              Stencil footnote_stencil = *unsmob_stencil (footnote_stl);
              bool do_numbering = to_boolean (footnote->get_property ("automatically-numbered"));
              if (Spanner *orig = dynamic_cast<Spanner *>(footnote))
                {
                  if (orig->is_broken ())
                    for (vsize i = 0; i < orig->broken_intos_.size (); i++)
                      do_numbering = do_numbering
                                     || to_boolean (orig->broken_intos_[i]->get_property ("automatically-numbered"));
                }
              if (do_numbering)
                {
                  SCM annotation_scm = scm_car (in_text_numbers);
                  footnote->set_property ("text", annotation_scm);
                  if (Spanner *orig = dynamic_cast<Spanner *>(footnote))
                    {
                      orig->set_property ("text", annotation_scm);
                      if (orig->is_broken ())
                        for (vsize i = 0; i < orig->broken_intos_.size (); i++)
                          orig->broken_intos_[i]->set_property ("text", annotation_scm);
                    }

                  Stencil annotation = *unsmob_stencil (scm_car (numbers));
                  annotation.translate_axis ((footnote_stencil.extent (Y_AXIS)[UP]
                                              + number_raise
                                              - annotation.extent (Y_AXIS)[UP]),
                                             Y_AXIS);
                  footnote_stencil.add_at_edge (X_AXIS, LEFT, annotation, 0.0);
                  numbers = scm_cdr (numbers);
                  in_text_numbers = scm_cdr (in_text_numbers);
                }
              if (!footnote_stencil.is_empty ())
                {
                  if (to_boolean (footnote->get_property ("footnote")))
                    mol.add_at_edge (Y_AXIS, DOWN, footnote_stencil, padding);
                  else
                    in_note_mol.add_at_edge (Y_AXIS, DOWN, footnote_stencil, padding);
                }
            }
          sys->set_property ("in-note-stencil", in_note_mol.smobbed_copy ());
          sys->set_property ("footnote-stencil", mol.smobbed_copy ());
        }
      // Take care of top-level markups
      else if (Prob *p = unsmob_prob (scm_car (s)))
        {
          SCM stencils = p->get_property ("footnotes");
          Stencil mol;

          for (SCM st = stencils; scm_is_pair (st); st = scm_cdr (st))
            {
              Stencil footnote_stencil = *unsmob_stencil (scm_caddar (st));
              bool do_numbering = to_boolean (scm_cadar (st));
              SCM in_text_stencil = Stencil ().smobbed_copy ();
              if (do_numbering)
                {
                  Stencil annotation = *unsmob_stencil (scm_car (numbers));
                  SCM in_text_annotation = scm_car (in_text_numbers);
                  in_text_stencil = Text_interface::interpret_markup (layout,
                                                                      props,
                                                                      in_text_annotation);
                  if (!unsmob_stencil (in_text_stencil))
                    in_text_stencil = SCM_EOL;
                  annotation.translate_axis ((footnote_stencil.extent (Y_AXIS)[UP]
                                              + number_raise
                                              - annotation.extent (Y_AXIS)[UP]),
                                             Y_AXIS);
                  footnote_stencil.add_at_edge (X_AXIS, LEFT, annotation, 0.0);
                  numbers = scm_cdr (numbers);
                  in_text_numbers = scm_cdr (in_text_numbers);
                }
              number_footnote_table = scm_cons (scm_cons (scm_caar (st),
                                                          in_text_stencil),
                                                number_footnote_table);
              if (!footnote_stencil.is_empty ())
                mol.add_at_edge (Y_AXIS, DOWN, footnote_stencil, padding);
            }
          p->set_property ("footnote-stencil", mol.smobbed_copy ());
        }
    }

  // note that this line of code doesn't do anything if numbering isn't turned on
  pb->top_paper ()->set_variable (ly_symbol2scm ("number-footnote-table"), number_footnote_table);
}

Stencil
Page_layout_problem::get_footnote_separator_stencil (Output_def *paper)
{
  SCM props = scm_call_1 (ly_lily_module_constant ("layout-extract-page-properties"),
                          paper->self_scm ());

  SCM markup = paper->c_variable ("footnote-separator-markup");

  if (!Text_interface::is_markup (markup))
    return Stencil ();

  SCM footnote_stencil = Text_interface::interpret_markup (paper->self_scm (),
                                                           props, markup);

  Stencil *footnote_separator = unsmob_stencil (footnote_stencil);

  return footnote_separator ? *footnote_separator : Stencil ();
}

Stencil
Page_layout_problem::add_footnotes_to_footer (SCM footnotes, Stencil foot, Paper_book *pb)
{

  bool footnotes_found = false;
  Real footnote_padding = robust_scm2double (pb->paper_->c_variable ("footnote-padding"), 0.0);
  Real footnote_footer_padding = robust_scm2double (pb->paper_->c_variable ("footnote-footer-padding"), 0.0);

  footnotes = scm_reverse (footnotes);

  for (SCM s = footnotes; scm_is_pair (s); s = scm_cdr (s))
    {
      Stencil *stencil = unsmob_stencil (scm_car (s));

      if (!stencil)
        continue;

      if (!stencil->is_empty ())
        {
          foot.add_at_edge (Y_AXIS, UP, *stencil, (!footnotes_found ? footnote_footer_padding : footnote_padding));
          footnotes_found = true;
        }
    }

  if (footnotes_found)
    {
      Stencil separator = get_footnote_separator_stencil (pb->paper_);
      if (!separator.is_empty ())
        foot.add_at_edge (Y_AXIS, UP, separator, footnote_padding);
    }

  return foot;
}

Page_layout_problem::Page_layout_problem (Paper_book *pb, SCM page_scm, SCM systems)
  : bottom_skyline_ (DOWN)
{
  Prob *page = unsmob_prob (page_scm);
  bottom_loose_baseline_ = 0;
  header_height_ = 0;
  footer_height_ = 0;
  header_padding_ = 0;
  footer_padding_ = 0;
  page_height_ = 100;
  force_ = 0;

  if (page)
    {
      Stencil *head = unsmob_stencil (page->get_property ("head-stencil"));
      Stencil *foot = unsmob_stencil (page->get_property ("foot-stencil"));

      Stencil foot_stencil = foot ? *foot : Stencil ();

      if (pb && pb->paper_)
        {
          SCM footnotes = get_footnotes_from_lines (systems);
          foot_stencil = add_footnotes_to_footer (footnotes, foot_stencil, pb);
        }
      else
        warning (_ ("A page layout problem has been initiated that cannot accommodate footnotes."));

      header_height_ = head ? head->extent (Y_AXIS).length () : 0;
      footer_height_ = foot_stencil.extent (Y_AXIS).length ();
      page_height_ = robust_scm2double (page->get_property ("paper-height"), 100);
    }

  // Initially, bottom_skyline_ represents the top of the page. Make
  // it solid, so that the top of the first system will be forced
  // below the top of the printable area.
  bottom_skyline_.set_minimum_height (-header_height_);

  SCM system_system_spacing = SCM_EOL;
  SCM score_system_spacing = SCM_EOL;
  SCM markup_system_spacing = SCM_EOL;
  SCM score_markup_spacing = SCM_EOL;
  SCM markup_markup_spacing = SCM_EOL;

  // top_system_spacing controls the spring from the top of the printable
  // area to the first staff. It allows the user to control the offset of
  // the first staff (as opposed to the top of the first system) from the
  // top of the page. Similarly for last_bottom_spacing.
  SCM top_system_spacing = SCM_EOL;
  SCM last_bottom_spacing = SCM_EOL;
  if (pb && pb->paper_)
    {
      Output_def *paper = pb->paper_;
      system_system_spacing = paper->c_variable ("system-system-spacing");
      score_system_spacing = paper->c_variable ("score-system-spacing");
      markup_system_spacing = paper->c_variable ("markup-system-spacing");
      score_markup_spacing = paper->c_variable ("score-markup-spacing");
      markup_markup_spacing = paper->c_variable ("markup-markup-spacing");
      last_bottom_spacing = paper->c_variable ("last-bottom-spacing");
      top_system_spacing = paper->c_variable ("top-system-spacing");
      if (scm_is_pair (systems) && unsmob_prob (scm_car (systems)))
        top_system_spacing = paper->c_variable ("top-markup-spacing");

      // Note: the page height here does _not_ reserve space for headers and
      // footers. This is because we want to anchor the top-system-spacing
      // spring at the _top_ of the header.
      page_height_ -= robust_scm2double (paper->c_variable ("top-margin"), 0)
                      + robust_scm2double (paper->c_variable ("bottom-margin"), 0);

      read_spacing_spec (top_system_spacing, &header_padding_, ly_symbol2scm ("padding"));
      read_spacing_spec (last_bottom_spacing, &footer_padding_, ly_symbol2scm ("padding"));
      in_note_padding_ = robust_scm2double (paper->c_variable ("in-note-padding"), 0.5);
      in_note_direction_ = robust_scm2dir (paper->c_variable ("in-note-direction"), UP);
    }
  bool last_system_was_title = false;

  for (SCM s = systems; scm_is_pair (s); s = scm_cdr (s))
    {
      bool first = (s == systems);

      if (Grob *g = unsmob_grob (scm_car (s)))
        {
          System *sys = dynamic_cast<System *> (g);
          if (!sys)
            {
              programming_error ("got a grob for vertical spacing that wasn't a System");
              continue;
            }

          SCM spec = system_system_spacing;
          if (first)
            spec = top_system_spacing;
          else if (last_system_was_title)
            spec = markup_system_spacing;
          else if (0 == Paper_column::get_rank (sys->get_bound (LEFT)))
            spec = score_system_spacing;

          Spring spring (0, 0);
          Real padding = 0.0;
          Real indent = line_dimensions_int (sys->paper_score ()->layout (), sys->get_rank ())[LEFT];
          alter_spring_from_spacing_spec (spec, &spring);
          read_spacing_spec (spec, &padding, ly_symbol2scm ("padding"));

          append_system (sys, spring, indent, padding);
          last_system_was_title = false;
        }
      else if (Prob *p = unsmob_prob (scm_car (s)))
        {
          SCM spec = first ? top_system_spacing
                     : (last_system_was_title ? markup_markup_spacing : score_markup_spacing);
          Spring spring (0, 0);
          Real padding = 0.0;
          alter_spring_from_spacing_spec (spec, &spring);
          read_spacing_spec (spec, &padding, ly_symbol2scm ("padding"));

          append_prob (p, spring, padding);
          last_system_was_title = true;
        }
      else
        programming_error ("got a system that was neither a Grob nor a Prob");
    }

  Spring last_spring (0, 0);
  Real last_padding = 0;
  alter_spring_from_spacing_spec (last_bottom_spacing, &last_spring);
  read_spacing_spec (last_bottom_spacing, &last_padding, ly_symbol2scm ("padding"));
  last_spring.ensure_min_distance (last_padding - bottom_skyline_.max_height () + footer_height_);
  springs_.push_back (last_spring);

  if (elements_.size ())
    {
      Real bottom_padding = 0;

      // TODO: junk bottom-space now that we have last-bottom-spacing?
      // bottom-space has the flexibility that one can do it per-system.
      // NOTE: bottom-space is misnamed since it is not stretchable space.
      if (Prob *p = elements_.back ().prob)
        bottom_padding = robust_scm2double (p->get_property ("bottom-space"), 0);
      else if (elements_.back ().staves.size ())
        {
          SCM details = get_details (elements_.back ());
          bottom_padding = robust_scm2double (ly_assoc_get (ly_symbol2scm ("bottom-space"),
                                                            details,
                                                            SCM_BOOL_F),
                                              0.0);
        }
      page_height_ -= bottom_padding;
    }
}

void
Page_layout_problem::set_header_height (Real height)
{
  header_height_ = height;
}

void
Page_layout_problem::set_footer_height (Real height)
{
  footer_height_ = height;
}

void
Page_layout_problem::append_system (System *sys, Spring const &spring, Real indent, Real padding)
{
  Grob *align = unsmob_grob (sys->get_object ("vertical-alignment"));
  if (!align)
    return;

  align->set_property ("positioning-done", SCM_BOOL_T);

  extract_grob_set (align, "elements", all_elts);
  vector<Grob *> elts = filter_dead_elements (all_elts);
  vector<Real> minimum_offsets = Align_interface::get_minimum_translations_without_min_dist (align, elts, Y_AXIS);
  vector<Real> minimum_offsets_with_min_dist = Align_interface::get_minimum_translations (align, elts, Y_AXIS);

  Skyline up_skyline (UP);
  Skyline down_skyline (DOWN);
  build_system_skyline (elts, minimum_offsets_with_min_dist, &up_skyline, &down_skyline);
  up_skyline.shift (indent);
  down_skyline.shift (indent);
  Stencil *in_note_stencil = unsmob_stencil (sys->get_property ("in-note-stencil"));

  if (in_note_stencil && in_note_stencil->extent (Y_AXIS).length () > 0)
    {
      sys->set_property ("in-note-padding", scm_from_double (in_note_padding_));
      sys->set_property ("in-note-direction", scm_from_int (in_note_direction_));
      Skyline *sky = in_note_direction_ == UP ? &up_skyline : &down_skyline;
      sky->set_minimum_height (sky->max_height ()
                               + in_note_direction_
                               * (in_note_padding_
                                  + in_note_stencil->extent (Y_AXIS).length ()));
    }

  /*
    We need to call distance with skyline-horizontal-padding because
    the system skyline-horizontal-padding is not added during the creation
    of an individual staff.  So we add the padding for the distance check
    at the time of adding in the system.
  */
  Real minimum_distance = up_skyline.distance (bottom_skyline_,
                                               robust_scm2double (sys->get_property ("skyline-horizontal-padding"),
                                                   0))
                          + padding;

  Spring spring_copy = spring;
  spring_copy.ensure_min_distance (minimum_distance);
  springs_.push_back (spring_copy);

  if (elts.size () && !is_spaceable (elts[0]))
    {
      // store the minimum distance, considering relative indents,
      // for a loose line
      Skyline first_skyline (UP);
      Skyline_pair *sky = Skyline_pair::unsmob (elts[0]->get_property ("vertical-skylines"));
      if (sky)
        first_skyline.merge ((*sky)[UP]);
      first_skyline.shift (indent);
      minimum_distance = first_skyline.distance (bottom_skyline_) - bottom_loose_baseline_;
    }
  bottom_skyline_ = down_skyline;
  elements_.push_back (Element (elts, minimum_offsets, minimum_distance, padding));

  // Add the springs for the VerticalAxisGroups in this system.

  // If the user has specified the offsets of the individual staves, fix the
  // springs at the given distances. Otherwise, use stretchable springs.
  SCM details = get_details (elements_.back ());
  SCM manual_dists = ly_assoc_get (ly_symbol2scm ("alignment-distances"), details, SCM_EOL);
  vsize last_spaceable_staff = 0;
  bool found_spaceable_staff = false;
  for (vsize i = 0; i < elts.size (); ++i)
    {
      if (is_spaceable (elts[i]))
        {
          if (!found_spaceable_staff)
            {
              // Ensure space for any loose lines above this system
              if (i > 0)
                springs_.back ().ensure_min_distance (bottom_loose_baseline_
                                                      - minimum_offsets_with_min_dist[i]
                                                      + padding);
              found_spaceable_staff = true;
              last_spaceable_staff = i;
              // We don't add a spring for the first staff, since
              // we are only adding springs _between_ staves here.
              continue;
            }

          Spring spring (0.5, 0.0);
          SCM spec = elts[last_spaceable_staff]->get_property ("staff-staff-spacing");
          alter_spring_from_spacing_spec (spec, &spring);

          springs_.push_back (spring);
          Real min_distance = (found_spaceable_staff ? minimum_offsets_with_min_dist[last_spaceable_staff] : 0) - minimum_offsets_with_min_dist[i];
          springs_.back ().ensure_min_distance (min_distance);

          if (scm_is_pair (manual_dists))
            {
              if (scm_is_number (scm_car (manual_dists)))
                {
                  Real dy = scm_to_double (scm_car (manual_dists));

                  springs_.back ().set_distance (dy);
                  springs_.back ().set_min_distance (dy);
                  springs_.back ().set_inverse_stretch_strength (0);
                }
              manual_dists = scm_cdr (manual_dists);
            }
          last_spaceable_staff = i;
        }
    }

  bottom_loose_baseline_ = found_spaceable_staff
                           ? ( minimum_offsets_with_min_dist[last_spaceable_staff]
                               - minimum_offsets_with_min_dist.back ())
                           : 0;

  // Corner case: there was only one staff, and it wasn't spaceable.
  if (!found_spaceable_staff && elts.size ())
    mark_as_spaceable (elts[0]);
}

void
Page_layout_problem::append_prob (Prob *prob, Spring const &spring, Real padding)
{
  Skyline_pair *sky = Skyline_pair::unsmob (prob->get_property ("vertical-skylines"));
  Real minimum_distance = 0;
  bool tight_spacing = to_boolean (prob->get_property ("tight-spacing"));

  if (sky)
    {
      minimum_distance = max ((*sky)[UP].distance (bottom_skyline_),
                              bottom_loose_baseline_);
      bottom_skyline_ = (*sky)[DOWN];
    }
  else if (Stencil *sten = unsmob_stencil (prob->get_property ("stencil")))
    {
      Interval iv = sten->extent (Y_AXIS);
      minimum_distance = iv[UP] - bottom_skyline_.max_height ();

      bottom_skyline_.clear ();
      bottom_skyline_.set_minimum_height (iv[DOWN]);
    }
  bottom_loose_baseline_ = 0.0;

  Spring spring_copy = spring;
  if (tight_spacing)
    {
      spring_copy.set_min_distance (minimum_distance);
      spring_copy.set_inverse_stretch_strength (0.0);
      spring_copy.set_distance (0.0);
    }
  else
    spring_copy.ensure_min_distance (minimum_distance + padding);

  springs_.push_back (spring_copy);
  elements_.push_back (Element (prob, padding));
}

/**
   For ragged-last pages, we usually want to stretch the page so that it
   is not much more compressed than the previous page.  Here, if ragged is
   true and you pass a value of fixed_force that !isinf, then I will try
   to space this page using the given force.  If it does not fit, I will
   resort to just filling the page (non-raggedly).
*/
void
Page_layout_problem::solve_rod_spring_problem (bool ragged, Real fixed_force)
{
  Simple_spacer spacer;

  for (vsize i = 0; i < springs_.size (); ++i)
    spacer.add_spring (springs_[i]);

  if (ragged && !isinf (fixed_force))
    {
      // We need to tell the spacer it isn't ragged.  Otherwise, it will
      // refuse to stretch.
      spacer.solve (page_height_, false);

      if (spacer.configuration_length (fixed_force) <= page_height_)
        spacer.set_force (fixed_force);
    }
  else
    spacer.solve (page_height_, ragged);

  solution_ = spacer.spring_positions ();
  force_ = spacer.force ();

  if (!spacer.fits ())
    {
      Real overflow = spacer.configuration_length (spacer.force ())
                      - page_height_;
      if (ragged && overflow < 1e-6)
        warning (_ ("ragged-bottom was specified, but page must be compressed"));
      else
        {
          warning (_f ("compressing over-full page by %.1f staff-spaces",
                       overflow));
          force_ = -infinity_f;
          vsize space_count = solution_.size ();
          Real spacing_increment = overflow / (space_count - 2);
          for (vsize i = 2; i < space_count; i++)
            solution_[i] -= (i - 1) * spacing_increment;
        }
    }
}

Real
Page_layout_problem::force () const
{
  return force_;
}

// The solution_ vector stores the position of every live VerticalAxisGroup
// and every title. From that information,
// 1) within each system, stretch the staves so they land at the right position
// 2) find the offset of each system (relative to the printable area of the page).
// TODO: this function is getting too long, maybe split it up?
SCM
Page_layout_problem::find_system_offsets ()
{
  SCM system_offsets = SCM_EOL;
  SCM *tail = &system_offsets;

  // spring_idx 0 is the top of the page. Interesting values start from 1.
  vsize spring_idx = 1;
  vector<Grob *> loose_lines;
  vector<Real> loose_line_min_distances;
  Grob *last_spaceable_line = 0;
  Real last_spaceable_line_translation = 0;
  Interval last_title_extent;
  for (vsize i = 0; i < elements_.size (); ++i)
    {
      if (elements_[i].prob)
        {
          *tail = scm_cons (scm_from_double (solution_[spring_idx]), SCM_EOL);
          tail = SCM_CDRLOC (*tail);
          Interval prob_extent = unsmob_stencil (elements_[i].prob->get_property ("stencil"))->extent (Y_AXIS);

          // Lay out any non-spaceable lines between this line and
          // the last one.
          if (loose_lines.size ())
            {
              Interval loose_extent = loose_lines.back ()->extent (loose_lines.back (), Y_AXIS);
              Real min_distance = (-loose_extent[DOWN] + prob_extent[UP]
                                   + elements_[i].padding);

              loose_line_min_distances.push_back (min_distance);
              loose_lines.push_back (0);

              distribute_loose_lines (loose_lines, loose_line_min_distances,
                                      last_spaceable_line_translation, -solution_[spring_idx]);
              loose_lines.clear ();
              loose_line_min_distances.clear ();
            }

          last_spaceable_line = 0;
          last_spaceable_line_translation = -solution_[spring_idx];
          last_title_extent = prob_extent;
          spring_idx++;
        }
      else
        {
          // Getting this signs right here is a little tricky. The configuration
          // we return has zero at the top of the page and positive numbers further
          // down, as does the solution_ vector.  Within a staff, however, positive
          // numbers are up.
          // TODO: perhaps change the way the page 'configuration variable works so
          // that it is consistent with the usual up/down sign conventions in
          // Lilypond. Then this would be less confusing.

          // These two positions are relative to the page (with positive numbers being
          // down).
          Real first_staff_position = solution_[spring_idx];
          Real first_staff_min_translation = elements_[i].min_offsets.size () ? elements_[i].min_offsets[0] : 0;
          Real system_position = first_staff_position + first_staff_min_translation;

          // Position the staves within this system.
          vector<Real> const &min_offsets = elements_[i].min_offsets;
          bool found_spaceable_staff = false;
          for (vsize staff_idx = 0; staff_idx < elements_[i].staves.size (); ++staff_idx)
            {
              Grob *staff = elements_[i].staves[staff_idx];
              staff->set_property ("system-Y-offset", scm_from_double (-system_position));

              if (is_spaceable (staff))
                {
                  // this is relative to the system: negative numbers are down.
                  staff->translate_axis (system_position - solution_[spring_idx], Y_AXIS);

                  // Lay out any non-spaceable lines between this line and
                  // the last one.
                  if (loose_lines.size ())
                    {
                      if (staff_idx)
                        loose_line_min_distances.push_back (min_offsets[staff_idx - 1] - min_offsets[staff_idx]);
                      else
                        {
                          // A null line to break any staff-affinity from the previous system
                          loose_line_min_distances.push_back (0.0);
                          loose_lines.push_back (0);
                          loose_line_min_distances.push_back (elements_[i].padding - min_offsets[0]);
                        }
                      loose_lines.push_back (staff);

                      distribute_loose_lines (loose_lines, loose_line_min_distances,
                                              last_spaceable_line_translation, -solution_[spring_idx]);
                      loose_lines.clear ();
                      loose_line_min_distances.clear ();
                    }
                  last_spaceable_line = staff;
                  last_spaceable_line_translation = -solution_[spring_idx];
                  found_spaceable_staff = true;
                  spring_idx++;
                }
              else // ! is_spaceable
                {
                  if (staff->extent (staff, Y_AXIS).is_empty ())
                    continue;

                  if (loose_lines.empty ())
                    loose_lines.push_back (last_spaceable_line);

                  if (staff_idx)
                    // NOTE: the way we do distances between loose lines (and other lines too, actually)
                    // is not the most accurate way possible: we only insert rods between adjacent
                    // lines.  To be more accurate, we could insert rods between non-adjacent lines
                    // using a scheme similar to the one in set_column_rods.
                    loose_line_min_distances.push_back (min_offsets[staff_idx - 1] - min_offsets[staff_idx]);
                  else
                    {
                      // this is the first line in a system
                      Real min_dist = 0;
                      if (loose_lines.back ())
                        {
                          // distance to the final line in the preceding system,
                          // including 'system-system-spacing 'padding
                          min_dist = elements_[i].min_distance + elements_[i].padding;
                          // A null line to break any staff-affinity for the previous system
                          loose_line_min_distances.push_back (0.0);
                          loose_lines.push_back (0);
                        }
                      else if (!last_title_extent.is_empty ())
                        // distance to the preceding title,
                        //  including 'markup-system-wg 'padding
                        min_dist = (staff->extent (staff, Y_AXIS)[UP] - last_title_extent[DOWN]
                                    + elements_[i].padding);
                      else // distance to the top margin
                        min_dist = header_padding_ + header_height_ + staff->extent (staff, Y_AXIS)[UP];

                      loose_line_min_distances.push_back (min_dist);
                    }
                  loose_lines.push_back (staff);
                }
            }

          // Corner case: even if a system has no live staves, it still takes up
          // one spring (a system with one live staff also takes up one spring),
          // which we need to increment past.
          if (!found_spaceable_staff)
            spring_idx++;

          *tail = scm_cons (scm_from_double (system_position), SCM_EOL);
          tail = SCM_CDRLOC (*tail);
        }
    }

  if (loose_lines.size ())
    {
      Grob *last = loose_lines.back ();
      Interval last_ext = last->extent (last, Y_AXIS);
      loose_line_min_distances.push_back (-last_ext[DOWN] + footer_height_ + footer_padding_);
      loose_lines.push_back (0);

      distribute_loose_lines (loose_lines, loose_line_min_distances,
                              last_spaceable_line_translation, -page_height_);

    }

  assert (spring_idx == solution_.size () - 1);
  return system_offsets;
}

// Given two lines that are already spaced (the first and last
// elements of loose_lines), distribute some unspaced lines between
// them.
// first_translation and last_translation are relative to the page.
void
Page_layout_problem::distribute_loose_lines (vector<Grob *> const &loose_lines,
                                             vector<Real> const &min_distances,
                                             Real first_translation, Real last_translation)
{
  Simple_spacer spacer;
  for (vsize i = 0; i + 1 < loose_lines.size (); ++i)
    {
      SCM spec = get_spacing_spec (loose_lines[i], loose_lines[i + 1], false, 0, INT_MAX);
      Spring spring (1.0, 0.0);
      alter_spring_from_spacing_spec (spec, &spring);
      spring.ensure_min_distance (min_distances[i]);
      spacer.add_spring (spring);
    }

  // Remember: offsets are decreasing, since we're going from UP to DOWN!
  spacer.solve (first_translation - last_translation, false);

  vector<Real> solution = spacer.spring_positions ();
  for (vsize i = 1; i + 1 < solution.size (); ++i)
    if (loose_lines[i])
      {
        Real system_offset = scm_to_double (loose_lines[i]->get_property ("system-Y-offset"));
        loose_lines[i]->translate_axis (first_translation - solution[i] - system_offset, Y_AXIS);
      }
}

SCM
Page_layout_problem::fixed_force_solution (Real force)
{
  solve_rod_spring_problem (true, force);
  return find_system_offsets ();
}

SCM
Page_layout_problem::solution (bool ragged)
{
  solve_rod_spring_problem (ragged, -infinity_f);
  return find_system_offsets ();
}

// Build upper and lower skylines for a system. We don't yet know the positions
// of the staves within the system, so we make the skyline as conservative as
// possible. That is, for the upper skyline, we pretend that all of the staves
// in the system are packed together close to the top system; for the lower
// skyline, we pretend that all of the staves are packed together close to
// the bottom system.
//
// The upper skyline is relative to the top staff; the lower skyline is relative to
// the bottom staff.
void
Page_layout_problem::build_system_skyline (vector<Grob *> const &staves,
                                           vector<Real> const &minimum_translations,
                                           Skyline *up,
                                           Skyline *down)
{
  if (minimum_translations.empty ())
    return;

  assert (staves.size () == minimum_translations.size ());
  Real first_translation = minimum_translations[0];
  Real last_spaceable_dy = 0;
  Real first_spaceable_dy = 0;
  bool found_spaceable_staff = false;

  for (vsize i = 0; i < staves.size (); ++i)
    {
      Real dy = minimum_translations[i] - first_translation;
      Grob *g = staves[i];
      Skyline_pair *sky = Skyline_pair::unsmob (g->get_property ("vertical-skylines"));
      if (sky)
        {
          up->raise (-dy);
          up->merge ((*sky)[UP]);
          up->raise (dy);

          down->raise (-dy);
          down->merge ((*sky)[DOWN]);
          down->raise (dy);
        }
      if (is_spaceable (staves[i]))
        {
          if (!found_spaceable_staff)
            {
              found_spaceable_staff = true;
              first_spaceable_dy = dy;
            }
          last_spaceable_dy = dy;
        }
    }

  // Leave the up skyline at a position relative
  // to the top spaceable staff.
  up->raise (-first_spaceable_dy);

  // Leave the down skyline at a position
  // relative to the bottom spaceable staff.
  down->raise (-last_spaceable_dy);
}

Interval
Page_layout_problem::prob_extent (Prob *p)
{
  Stencil *sten = unsmob_stencil (p->get_property ("stencil"));
  return sten ? sten->extent (Y_AXIS) : Interval (0, 0);
}

Interval
Page_layout_problem::first_staff_extent (Element const &e)
{
  if (e.prob)
    return prob_extent (e.prob);
  else if (e.staves.size ())
    return e.staves[0]->extent (e.staves[0], Y_AXIS);

  return Interval (0, 0);
}

Interval
Page_layout_problem::last_staff_extent (Element const &e)
{
  if (e.prob)
    return prob_extent (e.prob);
  else if (e.staves.size ())
    return e.staves.back ()->extent (e.staves.back (), Y_AXIS);

  return Interval (0, 0);
}

SCM
Page_layout_problem::get_details (Element const &elt)
{
  if (elt.staves.empty ())
    return SCM_EOL;

  return get_details (elt.staves.back ()->get_system ());
}

SCM
Page_layout_problem::get_details (Grob *g)
{
  Grob *left_bound = dynamic_cast<Spanner *> (g)->get_bound (LEFT);
  return left_bound->get_property ("line-break-system-details");
}

bool
Page_layout_problem::is_spaceable (Grob *g)
{
  return !scm_is_number (g->get_property ("staff-affinity"));
}

void
Page_layout_problem::mark_as_spaceable (Grob *g)
{
  g->set_property ("staff-affinity", SCM_BOOL_F);
}

bool
Page_layout_problem::read_spacing_spec (SCM spec, Real *dest, SCM sym)
{
  SCM pair = scm_sloppy_assq (sym, spec);
  if (scm_is_pair (pair) && scm_is_number (scm_cdr (pair)))
    {
      *dest = scm_to_double (scm_cdr (pair));
      return true;
    }
  return false;
}

// If there is a forced, fixed spacing between BEFORE and AFTER, return it.
// Otherwise, return -infinity_f.
// If after is spaceable, it is the (spaceable_index + 1)th spaceable grob in
// its alignment.
Real
Page_layout_problem::get_fixed_spacing (Grob *before, Grob *after, int spaceable_index, bool pure, int start, int end)
{
  Spanner *after_sp = dynamic_cast<Spanner *> (after);
  SCM cache_symbol = (is_spaceable (before) && is_spaceable (after))
                     ? ly_symbol2scm ("spaceable-fixed-spacing")
                     : ly_symbol2scm ("loose-fixed-spacing");
  if (pure)
    {
      // The result of this function doesn't depend on "end," so we can reduce the
      // size of the cache by ignoring it.
      SCM cached = after_sp->get_cached_pure_property (cache_symbol, start, 0);
      if (scm_is_number (cached))
        return robust_scm2double (cached, 0.0);
    }

  Real ret = -infinity_f;

  // If we're pure, then paper-columns have not had their systems set,
  // and so elts[i]->get_system () is unreliable.
  System *sys = pure ? Grob::get_system (before) : before->get_system ();
  Grob *left_bound = sys ? sys->get_maybe_pure_bound (LEFT, pure, start, end) : 0;

  if (is_spaceable (before) && is_spaceable (after) && left_bound)
    {
      SCM details = left_bound->get_property ("line-break-system-details");
      SCM manual_dists = ly_assoc_get (ly_symbol2scm ("alignment-distances"), details, SCM_EOL);
      if (scm_is_pair (manual_dists))
        {
          SCM forced = robust_list_ref (spaceable_index - 1, manual_dists);
          if (scm_is_number (forced))
            ret = max (ret, scm_to_double (forced));
        }
    }

  // Cache the result.  As above, we ignore "end."
  if (pure)
    after_sp->cache_pure_property (cache_symbol, start, 0, scm_from_double (ret));

  return ret;
}

static SCM
add_stretchability (SCM alist, Real stretch)
{
  if (!scm_is_pair (scm_sloppy_assq (ly_symbol2scm ("stretchability"), alist)))
    return scm_acons (ly_symbol2scm ("stretchability"), scm_from_double (stretch), alist);

  return alist;
}

// We want to put a large stretch between a non-spaceable line and its
// non-affinity staff. We want to put an even larger stretch between
// a non-spaceable line and the top/bottom of the page. That way,
// a spacing-affinity UP line at the bottom of the page will still be
// placed close to its staff.
const double LARGE_STRETCH = 10e5;
const double HUGE_STRETCH = 10e7;

// Returns the spacing spec connecting BEFORE to AFTER.
SCM
Page_layout_problem::get_spacing_spec (Grob *before, Grob *after, bool pure, int start, int end)
{
  // If there are no spacing wishes, return a very flexible spring.
  // This will occur, for example, if there are lyrics at the bottom of
  // the page, in which case we don't want the spring from the lyrics to
  // the bottom of the page to have much effect.
  if (!before || !after)
    return add_stretchability (SCM_EOL, HUGE_STRETCH);

  if (is_spaceable (before))
    {
      if (is_spaceable (after))
        return before->get_maybe_pure_property ("staff-staff-spacing", pure, start, end);
      else
        {
          Direction affinity = to_dir (after->get_maybe_pure_property ("staff-affinity", pure, start, end));
          return (affinity == DOWN)
                 ? add_stretchability (after->get_maybe_pure_property ("nonstaff-unrelatedstaff-spacing", pure, start, end),
                                       LARGE_STRETCH)
                 : after->get_maybe_pure_property ("nonstaff-relatedstaff-spacing", pure, start, end);
        }
    }
  else
    {
      if (is_spaceable (after))
        {
          Direction affinity = to_dir (before->get_maybe_pure_property ("staff-affinity", pure, start, end));
          return (affinity == UP)
                 ? add_stretchability (before->get_maybe_pure_property ("nonstaff-unrelatedstaff-spacing", pure, start, end),
                                       LARGE_STRETCH)
                 : before->get_maybe_pure_property ("nonstaff-relatedstaff-spacing", pure, start, end);
        }
      else
        {
          Direction before_affinity = to_dir (before->get_maybe_pure_property ("staff-affinity", pure, start, end));
          Direction after_affinity = to_dir (after->get_maybe_pure_property ("staff-affinity", pure, start, end));
          static bool warned = false;
          if (after_affinity > before_affinity
              && !warned && !pure)
            {
              warning (_ ("staff-affinities should only decrease"));
              warned = true;
            }
          if (before_affinity != UP)
            return before->get_maybe_pure_property ("nonstaff-nonstaff-spacing", pure, start, end);
          else if (after_affinity != DOWN)
            return before->get_maybe_pure_property ("nonstaff-nonstaff-spacing", pure, start, end);
          return add_stretchability (before->get_maybe_pure_property ("nonstaff-unrelatedstaff-spacing", pure, start, end),
                                     LARGE_STRETCH);
        }
    }

  assert (0);
  return SCM_BOOL_F;
}

void
Page_layout_problem::alter_spring_from_spacing_spec (SCM spec, Spring *spring)
{
  Real space;
  Real stretch;
  Real min_dist;
  if (read_spacing_spec (spec, &space, ly_symbol2scm ("basic-distance")))
    spring->set_distance (space);
  if (read_spacing_spec (spec, &min_dist, ly_symbol2scm ("minimum-distance")))
    spring->set_min_distance (min_dist);
  spring->set_default_strength ();

  if (read_spacing_spec (spec, &stretch, ly_symbol2scm ("stretchability")))
    spring->set_inverse_stretch_strength (stretch);
}

vector<Grob *>
Page_layout_problem::filter_dead_elements (vector<Grob *> const &input)
{
  vector<Grob *> output;
  for (vsize i = 0; i < input.size (); ++i)
    {
      if (Hara_kiri_group_spanner::has_interface (input[i]))
        Hara_kiri_group_spanner::consider_suicide (input[i]);

      if (input[i]->is_live ())
        output.push_back (input[i]);
    }

  return output;
}
