hb-ot-var-common.hh

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/*

 * Copyright © 2021  Google, Inc.

 *  This is part of HarfBuzz, a text shaping library.

 * Permission is hereby granted, without written agreement and without

 * license or royalty fees, to use, copy, modify, and distribute this

 * software and its documentation for any purpose, provided that the

 * above copyright notice and the following two paragraphs appear in

 * all copies of this software.

 * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR

 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES

 * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN

 * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH

 * DAMAGE.

 * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,

 * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND

 * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS

 * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO

 * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.

*/

#ifndef HB_OT_VAR_COMMON_HH

#define HB_OT_VAR_COMMON_HH

#include "hb-ot-layout-common.hh"

#include "hb-priority-queue.hh"

#include "hb-subset-instancer-iup.hh"

namespace OT {

/* https://docs.microsoft.com/en-us/typography/opentype/spec/otvarcommonformats#tuplevariationheader */

struct TupleVariationHeader

  friend struct tuple_delta_t;

  unsigned get_size (unsigned axis_count) const

  { return min_size + get_all_tuples (axis_count).get_size (); }

  unsigned get_data_size () const { return varDataSize; }

  const TupleVariationHeader &get_next (unsigned axis_count) const

  { return StructAtOffset<TupleVariationHeader> (this, get_size (axis_count)); }

  bool unpack_axis_tuples (unsigned axis_count,

                           const hb_array_t<const F2DOT14> shared_tuples,

                           const hb_map_t *axes_old_index_tag_map,

                           hb_hashmap_t<hb_tag_t, Triple>& axis_tuples /* OUT */) const

    const F2DOT14 *peak_tuple = nullptr;

    if (has_peak ())

      peak_tuple = get_peak_tuple (axis_count).arrayZ;

    else

      unsigned int index = get_index ();

      if (unlikely ((index + 1) * axis_count > shared_tuples.length))

        return false;

      peak_tuple = shared_tuples.sub_array (axis_count * index, axis_count).arrayZ;

    const F2DOT14 *start_tuple = nullptr;

    const F2DOT14 *end_tuple = nullptr;

    bool has_interm = has_intermediate ();

    if (has_interm)

      start_tuple = get_start_tuple (axis_count).arrayZ;

      end_tuple = get_end_tuple (axis_count).arrayZ;

    for (unsigned i = 0; i < axis_count; i++)

      float peak = peak_tuple[i].to_float ();

      if (peak == 0.f) continue;

      hb_tag_t *axis_tag;

      if (!axes_old_index_tag_map->has (i, &axis_tag))

        return false;

      float start, end;

      if (has_interm)

        start = start_tuple[i].to_float ();

        end = end_tuple[i].to_float ();

      else

        start = hb_min (peak, 0.f);

        end = hb_max (peak, 0.f);

      axis_tuples.set (*axis_tag, Triple ((double) start, (double) peak, (double) end));

    return true;

  double calculate_scalar (hb_array_t<const int> coords, unsigned int coord_count,

			   const hb_array_t<const F2DOT14> shared_tuples,

			   const hb_vector_t<hb_pair_t<int,int>> *shared_tuple_active_idx = nullptr) const

    const F2DOT14 *peak_tuple;

    unsigned start_idx = 0;

    unsigned end_idx = coord_count;

    unsigned step = 1;

    if (has_peak ())

      peak_tuple = get_peak_tuple (coord_count).arrayZ;

    else

      unsigned int index = get_index ();

      if (unlikely ((index + 1) * coord_count > shared_tuples.length))

        return 0.0;

      peak_tuple = shared_tuples.sub_array (coord_count * index, coord_count).arrayZ;

      if (shared_tuple_active_idx)

	if (unlikely (index >= shared_tuple_active_idx->length))

	  return 0.0;

	auto _ = (*shared_tuple_active_idx).arrayZ[index];

	if (_.second != -1)

	  start_idx = _.first;

	  end_idx = _.second + 1;

	  step = _.second - _.first;

	else if (_.first != -1)

	  start_idx = _.first;

	  end_idx = start_idx + 1;

    const F2DOT14 *start_tuple = nullptr;

    const F2DOT14 *end_tuple = nullptr;

    bool has_interm = has_intermediate ();

    if (has_interm)

      start_tuple = get_start_tuple (coord_count).arrayZ;

      end_tuple = get_end_tuple (coord_count).arrayZ;

    double scalar = 1.0;

    for (unsigned int i = start_idx; i < end_idx; i += step)

      int peak = peak_tuple[i].to_int ();

      if (!peak) continue;

      int v = coords[i];

      if (v == peak) continue;

      if (has_interm)

        int start = start_tuple[i].to_int ();

        int end = end_tuple[i].to_int ();

        if (unlikely (start > peak || peak > end ||

                      (start < 0 && end > 0 && peak))) continue;

        if (v < start || v > end) return 0.0;

        if (v < peak)

        { if (peak != start) scalar *= (double) (v - start) / (peak - start); }

        else

        { if (peak != end) scalar *= (double) (end - v) / (end - peak); }

      else if (!v || v < hb_min (0, peak) || v > hb_max (0, peak)) return 0.0;

      else

        scalar *= (double) v / peak;

    return scalar;

  bool           has_peak () const { return tupleIndex & TuppleIndex::EmbeddedPeakTuple; }

  bool   has_intermediate () const { return tupleIndex & TuppleIndex::IntermediateRegion; }

  bool has_private_points () const { return tupleIndex & TuppleIndex::PrivatePointNumbers; }

  unsigned      get_index () const { return tupleIndex & TuppleIndex::TupleIndexMask; }

  protected:

  struct TuppleIndex : HBUINT16

    enum Flags {

      EmbeddedPeakTuple   = 0x8000u,

      IntermediateRegion  = 0x4000u,

      PrivatePointNumbers = 0x2000u,

      TupleIndexMask      = 0x0FFFu

};

    TuppleIndex& operator = (uint16_t i) { HBUINT16::operator= (i); return *this; }

    DEFINE_SIZE_STATIC (2);

};

  hb_array_t<const F2DOT14> get_all_tuples (unsigned axis_count) const

  { return StructAfter<UnsizedArrayOf<F2DOT14>> (tupleIndex).as_array ((has_peak () + has_intermediate () * 2) * axis_count); }

  hb_array_t<const F2DOT14> get_peak_tuple (unsigned axis_count) const

  { return get_all_tuples (axis_count).sub_array (0, axis_count); }

  hb_array_t<const F2DOT14> get_start_tuple (unsigned axis_count) const

  { return get_all_tuples (axis_count).sub_array (has_peak () * axis_count, axis_count); }

  hb_array_t<const F2DOT14> get_end_tuple (unsigned axis_count) const

  { return get_all_tuples (axis_count).sub_array (has_peak () * axis_count + axis_count, axis_count); }

  HBUINT16      varDataSize;    /* The size in bytes of the serialized

                                 * data for this tuple variation table. */

  TuppleIndex   tupleIndex;     /* A packed field. The high 4 bits are flags (see below).

                                   The low 12 bits are an index into a shared tuple

                                   records array. */

  /* UnsizedArrayOf<F2DOT14> peakTuple - optional */

                                /* Peak tuple record for this tuple variation table — optional,

                                 * determined by flags in the tupleIndex value.

                                 * Note that this must always be included in the 'cvar' table. */

  /* UnsizedArrayOf<F2DOT14> intermediateStartTuple - optional */

                                /* Intermediate start tuple record for this tuple variation table — optional,

                                   determined by flags in the tupleIndex value. */

  /* UnsizedArrayOf<F2DOT14> intermediateEndTuple - optional */

                                /* Intermediate end tuple record for this tuple variation table — optional,

                                 * determined by flags in the tupleIndex value. */

  public:

  DEFINE_SIZE_MIN (4);

};

struct tuple_delta_t

  static constexpr bool realloc_move = true;  // Watch out when adding new members!

  public:

  hb_hashmap_t<hb_tag_t, Triple> axis_tuples;

  /* indices_length = point_count, indice[i] = 1 means point i is referenced */

  hb_vector_t<bool> indices;

  hb_vector_t<double> deltas_x;

  /* empty for cvar tuples */

  hb_vector_t<double> deltas_y;

  /* compiled data: header and deltas

   * compiled point data is saved in a hashmap within tuple_variations_t cause

   * some point sets might be reused by different tuple variations */

  hb_vector_t<unsigned char> compiled_tuple_header;

  hb_vector_t<unsigned char> compiled_deltas;

  /* compiled peak coords, empty for non-gvar tuples */

  hb_vector_t<char> compiled_peak_coords;

  tuple_delta_t () = default;

  tuple_delta_t (const tuple_delta_t& o) = default;

  friend void swap (tuple_delta_t& a, tuple_delta_t& b) noexcept

    hb_swap (a.axis_tuples, b.axis_tuples);

    hb_swap (a.indices, b.indices);

    hb_swap (a.deltas_x, b.deltas_x);

    hb_swap (a.deltas_y, b.deltas_y);

    hb_swap (a.compiled_tuple_header, b.compiled_tuple_header);

    hb_swap (a.compiled_deltas, b.compiled_deltas);

    hb_swap (a.compiled_peak_coords, b.compiled_peak_coords);

  tuple_delta_t (tuple_delta_t&& o)  noexcept : tuple_delta_t ()

  { hb_swap (*this, o); }

  tuple_delta_t& operator = (tuple_delta_t&& o) noexcept

    hb_swap (*this, o);

    return *this;

  void remove_axis (hb_tag_t axis_tag)

  { axis_tuples.del (axis_tag); }

  bool set_tent (hb_tag_t axis_tag, Triple tent)

  { return axis_tuples.set (axis_tag, tent); }

  tuple_delta_t& operator += (const tuple_delta_t& o)

    unsigned num = indices.length;

    for (unsigned i = 0; i < num; i++)

      if (indices.arrayZ[i])

        if (o.indices.arrayZ[i])

          deltas_x[i] += o.deltas_x[i];

          if (deltas_y && o.deltas_y)

            deltas_y[i] += o.deltas_y[i];

      else

        if (!o.indices.arrayZ[i]) continue;

        indices.arrayZ[i] = true;

        deltas_x[i] = o.deltas_x[i];

        if (deltas_y && o.deltas_y)

          deltas_y[i] = o.deltas_y[i];

    return *this;

  tuple_delta_t& operator *= (double scalar)

    if (scalar == 1.0)

      return *this;

    unsigned num = indices.length;

    if (deltas_y)

      for (unsigned i = 0; i < num; i++)

	if (!indices.arrayZ[i]) continue;

	deltas_x[i] *= scalar;

	deltas_y[i] *= scalar;

    else

      for (unsigned i = 0; i < num; i++)

	if (!indices.arrayZ[i]) continue;

	deltas_x[i] *= scalar;

    return *this;

  hb_vector_t<tuple_delta_t> change_tuple_var_axis_limit (hb_tag_t axis_tag, Triple axis_limit,

                                                          TripleDistances axis_triple_distances) const

    hb_vector_t<tuple_delta_t> out;

    Triple *tent;

    if (!axis_tuples.has (axis_tag, &tent))

      out.push (*this);

      return out;

    if ((tent->minimum < 0.0 && tent->maximum > 0.0) ||

        !(tent->minimum <= tent->middle && tent->middle <= tent->maximum))

      return out;

    if (tent->middle == 0.0)

      out.push (*this);

      return out;

    rebase_tent_result_t solutions = rebase_tent (*tent, axis_limit, axis_triple_distances);

    for (auto &t : solutions)

      tuple_delta_t new_var = *this;

      if (t.second == Triple ())

        new_var.remove_axis (axis_tag);

      else

        new_var.set_tent (axis_tag, t.second);

      new_var *= t.first;

      out.push (std::move (new_var));

    return out;

  bool compile_peak_coords (const hb_map_t& axes_index_map,

                            const hb_map_t& axes_old_index_tag_map)

    unsigned axis_count = axes_index_map.get_population ();

    if (unlikely (!compiled_peak_coords.alloc (axis_count * F2DOT14::static_size)))

      return false;

    unsigned orig_axis_count = axes_old_index_tag_map.get_population ();

    for (unsigned i = 0; i < orig_axis_count; i++)

      if (!axes_index_map.has (i))

        continue;

      hb_tag_t axis_tag = axes_old_index_tag_map.get (i);

      Triple *coords;

      F2DOT14 peak_coord;

      if (axis_tuples.has (axis_tag, &coords))

        peak_coord.set_float (coords->middle);

      else

        peak_coord.set_int (0);

      /* push F2DOT14 value into char vector */

      int16_t val = peak_coord.to_int ();

      compiled_peak_coords.push (static_cast<char> (val >> 8));

      compiled_peak_coords.push (static_cast<char> (val & 0xFF));

    return !compiled_peak_coords.in_error ();

  /* deltas should be compiled already before we compile tuple

   * variation header cause we need to fill in the size of the

   * serialized data for this tuple variation */

  bool compile_tuple_var_header (const hb_map_t& axes_index_map,

                                 unsigned points_data_length,

                                 const hb_map_t& axes_old_index_tag_map,

                                 const hb_hashmap_t<const hb_vector_t<char>*, unsigned>* shared_tuples_idx_map)

    /* compiled_deltas could be empty after iup delta optimization, we can skip

     * compiling this tuple and return true */

    if (!compiled_deltas) return true;

    unsigned cur_axis_count = axes_index_map.get_population ();

    /* allocate enough memory: 1 peak + 2 intermediate coords + fixed header size */

    unsigned alloc_len = 3 * cur_axis_count * (F2DOT14::static_size) + 4;

    if (unlikely (!compiled_tuple_header.resize (alloc_len))) return false;

    unsigned flag = 0;

    /* skip the first 4 header bytes: variationDataSize+tupleIndex */

    F2DOT14* p = reinterpret_cast<F2DOT14 *> (compiled_tuple_header.begin () + 4);

    F2DOT14* end = reinterpret_cast<F2DOT14 *> (compiled_tuple_header.end ());

    hb_array_t<F2DOT14> coords (p, end - p);

    /* encode peak coords */

    unsigned peak_count = 0;

    unsigned *shared_tuple_idx;

    if (shared_tuples_idx_map &&

        shared_tuples_idx_map->has (&compiled_peak_coords, &shared_tuple_idx))

      flag = *shared_tuple_idx;

    else

      peak_count = encode_peak_coords(coords, flag, axes_index_map, axes_old_index_tag_map);

      if (!peak_count) return false;

    /* encode interim coords, it's optional so returned num could be 0 */

    unsigned interim_count = encode_interm_coords (coords.sub_array (peak_count), flag, axes_index_map, axes_old_index_tag_map);

    /* pointdata length = 0 implies "use shared points" */

    if (points_data_length)

      flag |= TupleVariationHeader::TuppleIndex::PrivatePointNumbers;

    unsigned serialized_data_size = points_data_length + compiled_deltas.length;

    TupleVariationHeader *o = reinterpret_cast<TupleVariationHeader *> (compiled_tuple_header.begin ());

    o->varDataSize = serialized_data_size;

    o->tupleIndex = flag;

    unsigned total_header_len = 4 + (peak_count + interim_count) * (F2DOT14::static_size);

    return compiled_tuple_header.resize (total_header_len);

  unsigned encode_peak_coords (hb_array_t<F2DOT14> peak_coords,

                               unsigned& flag,

                               const hb_map_t& axes_index_map,

                               const hb_map_t& axes_old_index_tag_map) const

    unsigned orig_axis_count = axes_old_index_tag_map.get_population ();

    auto it = peak_coords.iter ();

    unsigned count = 0;

    for (unsigned i = 0; i < orig_axis_count; i++)

      if (!axes_index_map.has (i)) /* axis pinned */

        continue;

      hb_tag_t axis_tag = axes_old_index_tag_map.get (i);

      Triple *coords;

      if (!axis_tuples.has (axis_tag, &coords))

        (*it).set_int (0);

      else

        (*it).set_float (coords->middle);

      it++;

      count++;

    flag |= TupleVariationHeader::TuppleIndex::EmbeddedPeakTuple;

    return count;

  /* if no need to encode intermediate coords, then just return p */

  unsigned encode_interm_coords (hb_array_t<F2DOT14> coords,

                                 unsigned& flag,

                                 const hb_map_t& axes_index_map,

                                 const hb_map_t& axes_old_index_tag_map) const

    unsigned orig_axis_count = axes_old_index_tag_map.get_population ();

    unsigned cur_axis_count = axes_index_map.get_population ();

    auto start_coords_iter = coords.sub_array (0, cur_axis_count).iter ();

    auto end_coords_iter = coords.sub_array (cur_axis_count).iter ();

    bool encode_needed = false;

    unsigned count = 0;

    for (unsigned i = 0; i < orig_axis_count; i++)

      if (!axes_index_map.has (i)) /* axis pinned */

        continue;

      hb_tag_t axis_tag = axes_old_index_tag_map.get (i);

      Triple *coords;

      float min_val = 0.f, val = 0.f, max_val = 0.f;

      if (axis_tuples.has (axis_tag, &coords))

        min_val = coords->minimum;

        val = coords->middle;

        max_val = coords->maximum;

      (*start_coords_iter).set_float (min_val);

      (*end_coords_iter).set_float (max_val);

      start_coords_iter++;

      end_coords_iter++;

      count += 2;

      if (min_val != hb_min (val, 0.f) || max_val != hb_max (val, 0.f))

        encode_needed = true;

    if (encode_needed)

      flag |= TupleVariationHeader::TuppleIndex::IntermediateRegion;

      return count;

    return 0;

  bool compile_deltas ()

  { return compile_deltas (indices, deltas_x, deltas_y, compiled_deltas); }

  static bool compile_deltas (const hb_vector_t<bool> &point_indices,

			      const hb_vector_t<double> &x_deltas,

			      const hb_vector_t<double> &y_deltas,

			      hb_vector_t<unsigned char> &compiled_deltas /* OUT */)

    hb_vector_t<int> rounded_deltas;

    if (unlikely (!rounded_deltas.alloc (point_indices.length)))

      return false;

    for (unsigned i = 0; i < point_indices.length; i++)

      if (!point_indices[i]) continue;

      int rounded_delta = (int) roundf (x_deltas.arrayZ[i]);

      rounded_deltas.push (rounded_delta);

    if (!rounded_deltas) return true;

    /* allocate enough memories 5 * num_deltas */

    unsigned alloc_len = 5 * rounded_deltas.length;

    if (y_deltas)

      alloc_len *= 2;

    if (unlikely (!compiled_deltas.resize (alloc_len))) return false;

    unsigned encoded_len = compile_deltas (compiled_deltas, rounded_deltas);

    if (y_deltas)

      /* reuse the rounded_deltas vector, check that y_deltas have the same num of deltas as x_deltas */

      unsigned j = 0;

      for (unsigned idx = 0; idx < point_indices.length; idx++)

        if (!point_indices[idx]) continue;

        int rounded_delta = (int) roundf (y_deltas.arrayZ[idx]);

        if (j >= rounded_deltas.length) return false;

        rounded_deltas[j++] = rounded_delta;

      if (j != rounded_deltas.length) return false;

      encoded_len += compile_deltas (compiled_deltas.as_array ().sub_array (encoded_len), rounded_deltas);

    return compiled_deltas.resize (encoded_len);

  static unsigned compile_deltas (hb_array_t<unsigned char> encoded_bytes,

				  hb_array_t<const int> deltas)

    return TupleValues::compile (deltas, encoded_bytes);

  bool calc_inferred_deltas (const contour_point_vector_t& orig_points)

    unsigned point_count = orig_points.length;

    if (point_count != indices.length)

      return false;

    unsigned ref_count = 0;

    hb_vector_t<unsigned> end_points;

    for (unsigned i = 0; i < point_count; i++)

      if (indices.arrayZ[i])

        ref_count++;

      if (orig_points.arrayZ[i].is_end_point)

        end_points.push (i);

    /* all points are referenced, nothing to do */

    if (ref_count == point_count)

      return true;

    if (unlikely (end_points.in_error ())) return false;

    hb_set_t inferred_idxes;

    unsigned start_point = 0;

    for (unsigned end_point : end_points)

      /* Check the number of unreferenced points in a contour. If no unref points or no ref points, nothing to do. */

      unsigned unref_count = 0;

      for (unsigned i = start_point; i < end_point + 1; i++)

        unref_count += indices.arrayZ[i];

      unref_count = (end_point - start_point + 1) - unref_count;

      unsigned j = start_point;

      if (unref_count == 0 || unref_count > end_point - start_point)

        goto no_more_gaps;

      for (;;)

        /* Locate the next gap of unreferenced points between two referenced points prev and next.

         * Note that a gap may wrap around at left (start_point) and/or at right (end_point).

*/

        unsigned int prev, next, i;

        for (;;)

          i = j;

          j = next_index (i, start_point, end_point);

          if (indices.arrayZ[i] && !indices.arrayZ[j]) break;

        prev = j = i;

        for (;;)

          i = j;

          j = next_index (i, start_point, end_point);

          if (!indices.arrayZ[i] && indices.arrayZ[j]) break;

        next = j;

       /* Infer deltas for all unref points in the gap between prev and next */

        i = prev;

        for (;;)

          i = next_index (i, start_point, end_point);

          if (i == next) break;

          deltas_x.arrayZ[i] = infer_delta ((double) orig_points.arrayZ[i].x,

                                            (double) orig_points.arrayZ[prev].x,

                                            (double) orig_points.arrayZ[next].x,

                                            deltas_x.arrayZ[prev], deltas_x.arrayZ[next]);

          deltas_y.arrayZ[i] = infer_delta ((double) orig_points.arrayZ[i].y,

                                            (double) orig_points.arrayZ[prev].y,

                                            (double) orig_points.arrayZ[next].y,

                                            deltas_y.arrayZ[prev], deltas_y.arrayZ[next]);

          inferred_idxes.add (i);

          if (--unref_count == 0) goto no_more_gaps;

    no_more_gaps:

      start_point = end_point + 1;

    for (unsigned i = 0; i < point_count; i++)

      /* if points are not referenced and deltas are not inferred, set to 0.

       * reference all points for gvar */

      if ( !indices[i])

        if (!inferred_idxes.has (i))

          deltas_x.arrayZ[i] = 0.0;

          deltas_y.arrayZ[i] = 0.0;

        indices[i] = true;

    return true;

  bool optimize (const contour_point_vector_t& contour_points,

                 bool is_composite,

                 double tolerance = 0.5 + 1e-10)

    unsigned count = contour_points.length;

    if (deltas_x.length != count ||

        deltas_y.length != count)

      return false;

    hb_vector_t<bool> opt_indices;

    hb_vector_t<int> rounded_x_deltas, rounded_y_deltas;

    if (unlikely (!rounded_x_deltas.alloc (count) ||

                  !rounded_y_deltas.alloc (count)))

      return false;

    for (unsigned i = 0; i < count; i++)

      int rounded_x_delta = (int) roundf (deltas_x.arrayZ[i]);

      int rounded_y_delta = (int) roundf (deltas_y.arrayZ[i]);

      rounded_x_deltas.push (rounded_x_delta);

      rounded_y_deltas.push (rounded_y_delta);

    if (!iup_delta_optimize (contour_points, rounded_x_deltas, rounded_y_deltas, opt_indices, tolerance))

      return false;

    unsigned ref_count = 0;

    for (bool ref_flag : opt_indices)

       ref_count += ref_flag;

    if (ref_count == count) return true;

    hb_vector_t<double> opt_deltas_x, opt_deltas_y;

    bool is_comp_glyph_wo_deltas = (is_composite && ref_count == 0);

    if (is_comp_glyph_wo_deltas)

      if (unlikely (!opt_deltas_x.resize (count) ||

                    !opt_deltas_y.resize (count)))

        return false;

      opt_indices.arrayZ[0] = true;

      for (unsigned i = 1; i < count; i++)

        opt_indices.arrayZ[i] = false;

    hb_vector_t<unsigned char> opt_point_data;

    if (!compile_point_set (opt_indices, opt_point_data))

      return false;

    hb_vector_t<unsigned char> opt_deltas_data;

    if (!compile_deltas (opt_indices,

                         is_comp_glyph_wo_deltas ? opt_deltas_x : deltas_x,

                         is_comp_glyph_wo_deltas ? opt_deltas_y : deltas_y,

                         opt_deltas_data))

      return false;

    hb_vector_t<unsigned char> point_data;

    if (!compile_point_set (indices, point_data))

      return false;

    hb_vector_t<unsigned char> deltas_data;

    if (!compile_deltas (indices, deltas_x, deltas_y, deltas_data))

      return false;

    if (opt_point_data.length + opt_deltas_data.length < point_data.length + deltas_data.length)

      indices.fini ();

      indices = std::move (opt_indices);

      if (is_comp_glyph_wo_deltas)

        deltas_x.fini ();

        deltas_x = std::move (opt_deltas_x);

        deltas_y.fini ();

        deltas_y = std::move (opt_deltas_y);

    return !indices.in_error () && !deltas_x.in_error () && !deltas_y.in_error ();

  static bool compile_point_set (const hb_vector_t<bool> &point_indices,

                                 hb_vector_t<unsigned char>& compiled_points /* OUT */)

    unsigned num_points = 0;

    for (bool i : point_indices)

      if (i) num_points++;

    /* when iup optimization is enabled, num of referenced points could be 0 */

    if (!num_points) return true;

    unsigned indices_length = point_indices.length;

    /* If the points set consists of all points in the glyph, it's encoded with a

     * single zero byte */

    if (num_points == indices_length)

      return compiled_points.resize (1);

    /* allocate enough memories: 2 bytes for count + 3 bytes for each point */

    unsigned num_bytes = 2 + 3 *num_points;

    if (unlikely (!compiled_points.resize (num_bytes, false)))

      return false;

    unsigned pos = 0;

    /* binary data starts with the total number of reference points */

    if (num_points < 0x80)

      compiled_points.arrayZ[pos++] = num_points;

    else

      compiled_points.arrayZ[pos++] = ((num_points >> 8) | 0x80);

      compiled_points.arrayZ[pos++] = num_points & 0xFF;

    const unsigned max_run_length = 0x7F;

    unsigned i = 0;

    unsigned last_value = 0;

    unsigned num_encoded = 0;

    while (i < indices_length && num_encoded < num_points)

      unsigned run_length = 0;

      unsigned header_pos = pos;

      compiled_points.arrayZ[pos++] = 0;

      bool use_byte_encoding = false;

      bool new_run = true;

      while (i < indices_length && num_encoded < num_points &&

             run_length <= max_run_length)

        // find out next referenced point index

        while (i < indices_length && !point_indices[i])

          i++;

        if (i >= indices_length) break;

        unsigned cur_value = i;

        unsigned delta = cur_value - last_value;

        if (new_run)

          use_byte_encoding = (delta <= 0xFF);

          new_run = false;

        if (use_byte_encoding && delta > 0xFF)

          break;

        if (use_byte_encoding)

          compiled_points.arrayZ[pos++] = delta;

        else

          compiled_points.arrayZ[pos++] = delta >> 8;

          compiled_points.arrayZ[pos++] = delta & 0xFF;

        i++;

        last_value = cur_value;

        run_length++;

        num_encoded++;

      if (use_byte_encoding)

        compiled_points.arrayZ[header_pos] = run_length - 1;

      else

        compiled_points.arrayZ[header_pos] = (run_length - 1) | 0x80;

    return compiled_points.resize (pos, false);

  static double infer_delta (double target_val, double prev_val, double next_val, double prev_delta, double next_delta)

    if (prev_val == next_val)

      return (prev_delta == next_delta) ? prev_delta : 0.0;

    else if (target_val <= hb_min (prev_val, next_val))

      return (prev_val < next_val) ? prev_delta : next_delta;

    else if (target_val >= hb_max (prev_val, next_val))

      return (prev_val > next_val) ? prev_delta : next_delta;

    double r = (target_val - prev_val) / (next_val - prev_val);

    return prev_delta + r * (next_delta - prev_delta);

  static unsigned int next_index (unsigned int i, unsigned int start, unsigned int end)

  { return (i >= end) ? start : (i + 1); }

};

struct TupleVariationData

  bool sanitize (hb_sanitize_context_t *c) const

    TRACE_SANITIZE (this);

    // here check on min_size only, TupleVariationHeader and var data will be

    // checked while accessing through iterator.

    return_trace (c->check_struct (this));

  unsigned get_size (unsigned axis_count) const

    unsigned total_size = min_size;

    unsigned count = tupleVarCount.get_count ();

    const TupleVariationHeader *tuple_var_header = &(get_tuple_var_header());

    for (unsigned i = 0; i < count; i++)

      total_size += tuple_var_header->get_size (axis_count) + tuple_var_header->get_data_size ();

      tuple_var_header = &tuple_var_header->get_next (axis_count);

    return total_size;

  const TupleVariationHeader &get_tuple_var_header (void) const

  { return StructAfter<TupleVariationHeader> (data); }

  struct tuple_iterator_t;

  struct tuple_variations_t

    hb_vector_t<tuple_delta_t> tuple_vars;

    private:

    /* referenced point set->compiled point data map */

    hb_hashmap_t<const hb_vector_t<bool>*, hb_vector_t<char>> point_data_map;

    /* referenced point set-> count map, used in finding shared points */

    hb_hashmap_t<const hb_vector_t<bool>*, unsigned> point_set_count_map;

    /* empty for non-gvar tuples.

     * shared_points_bytes is a pointer to some value in the point_data_map,

     * which will be freed during map destruction. Save it for serialization, so

     * no need to do find_shared_points () again */

    hb_vector_t<char> *shared_points_bytes = nullptr;

    /* total compiled byte size as TupleVariationData format, initialized to its

     * min_size: 4 */

    unsigned compiled_byte_size = 4;

    /* for gvar iup delta optimization: whether this is a composite glyph */

    bool is_composite = false;

    public:

    tuple_variations_t () = default;

    tuple_variations_t (const tuple_variations_t&) = delete;

    tuple_variations_t& operator=(const tuple_variations_t&) = delete;

    tuple_variations_t (tuple_variations_t&&) = default;

    tuple_variations_t& operator=(tuple_variations_t&&) = default;

    ~tuple_variations_t () = default;

    explicit operator bool () const { return bool (tuple_vars); }

    unsigned get_var_count () const

      unsigned count = 0;

      /* when iup delta opt is enabled, compiled_deltas could be empty and we

       * should skip this tuple */

      for (auto& tuple: tuple_vars)

        if (tuple.compiled_deltas) count++;

      if (shared_points_bytes && shared_points_bytes->length)

        count |= TupleVarCount::SharedPointNumbers;

      return count;

    unsigned get_compiled_byte_size () const

    { return compiled_byte_size; }

    bool create_from_tuple_var_data (tuple_iterator_t iterator,

                                     unsigned tuple_var_count,

                                     unsigned point_count,

                                     bool is_gvar,

                                     const hb_map_t *axes_old_index_tag_map,

                                     const hb_vector_t<unsigned> &shared_indices,

                                     const hb_array_t<const F2DOT14> shared_tuples,

                                     bool is_composite_glyph)

do

        const HBUINT8 *p = iterator.get_serialized_data ();

        unsigned int length = iterator.current_tuple->get_data_size ();

        if (unlikely (!iterator.var_data_bytes.check_range (p, length)))

          return false;

        hb_hashmap_t<hb_tag_t, Triple> axis_tuples;

        if (!iterator.current_tuple->unpack_axis_tuples (iterator.get_axis_count (), shared_tuples, axes_old_index_tag_map, axis_tuples)

            || axis_tuples.is_empty ())

          return false;

        hb_vector_t<unsigned> private_indices;

        bool has_private_points = iterator.current_tuple->has_private_points ();

        const HBUINT8 *end = p + length;

        if (has_private_points &&

            !TupleVariationData::decompile_points (p, private_indices, end))

          return false;

        const hb_vector_t<unsigned> &indices = has_private_points ? private_indices : shared_indices;

        bool apply_to_all = (indices.length == 0);

        unsigned num_deltas = apply_to_all ? point_count : indices.length;

        hb_vector_t<int> deltas_x;

        if (unlikely (!deltas_x.resize (num_deltas, false) ||

                      !TupleVariationData::decompile_deltas (p, deltas_x, end)))

          return false;

        hb_vector_t<int> deltas_y;

        if (is_gvar)

          if (unlikely (!deltas_y.resize (num_deltas, false) ||

                        !TupleVariationData::decompile_deltas (p, deltas_y, end)))

            return false;

        tuple_delta_t var;

        var.axis_tuples = std::move (axis_tuples);

        if (unlikely (!var.indices.resize (point_count) ||

                      !var.deltas_x.resize (point_count, false)))

          return false;

        if (is_gvar && unlikely (!var.deltas_y.resize (point_count, false)))

          return false;

        for (unsigned i = 0; i < num_deltas; i++)

          unsigned idx = apply_to_all ? i : indices[i];

          if (idx >= point_count) continue;

          var.indices[idx] = true;

          var.deltas_x[idx] = deltas_x[i];

          if (is_gvar)

            var.deltas_y[idx] = deltas_y[i];

        tuple_vars.push (std::move (var));

      } while (iterator.move_to_next ());

      is_composite = is_composite_glyph;

      return true;

    bool create_from_item_var_data (const VarData &var_data,

                                    const hb_vector_t<hb_hashmap_t<hb_tag_t, Triple>>& regions,

                                    const hb_map_t& axes_old_index_tag_map,

                                    unsigned& item_count,

                                    const hb_inc_bimap_t* inner_map = nullptr)

      /* NULL offset, to keep original varidx valid, just return */

      if (&var_data == &Null (VarData))

        return true;

      unsigned num_regions = var_data.get_region_index_count ();

      if (!tuple_vars.alloc (num_regions)) return false;

      item_count = inner_map ? inner_map->get_population () : var_data.get_item_count ();

      if (!item_count) return true;

      unsigned row_size = var_data.get_row_size ();

      const HBUINT8 *delta_bytes = var_data.get_delta_bytes ();

      for (unsigned r = 0; r < num_regions; r++)

        /* In VarData, deltas are organized in rows, convert them into

         * column(region) based tuples, resize deltas_x first */

        tuple_delta_t tuple;

        if (!tuple.deltas_x.resize (item_count, false) ||

            !tuple.indices.resize (item_count, false))

          return false;

        for (unsigned i = 0; i < item_count; i++)

          tuple.indices.arrayZ[i] = true;

          tuple.deltas_x.arrayZ[i] = var_data.get_item_delta_fast (inner_map ? inner_map->backward (i) : i,

                                                                   r, delta_bytes, row_size);

        unsigned region_index = var_data.get_region_index (r);

        if (region_index >= regions.length) return false;

        tuple.axis_tuples = regions.arrayZ[region_index];

        tuple_vars.push (std::move (tuple));

      return !tuple_vars.in_error ();

    private:

    static int _cmp_axis_tag (const void *pa, const void *pb)

      const hb_tag_t *a = (const hb_tag_t*) pa;

      const hb_tag_t *b = (const hb_tag_t*) pb;

      return (int)(*a) - (int)(*b);

    bool change_tuple_variations_axis_limits (const hb_hashmap_t<hb_tag_t, Triple>& normalized_axes_location,

                                              const hb_hashmap_t<hb_tag_t, TripleDistances>& axes_triple_distances)

      /* sort axis_tag/axis_limits, make result deterministic */

      hb_vector_t<hb_tag_t> axis_tags;

      if (!axis_tags.alloc (normalized_axes_location.get_population ()))

        return false;

      for (auto t : normalized_axes_location.keys ())

        axis_tags.push (t);

      axis_tags.qsort (_cmp_axis_tag);

      for (auto axis_tag : axis_tags)

        Triple *axis_limit;

        if (!normalized_axes_location.has (axis_tag, &axis_limit))

          return false;

        TripleDistances axis_triple_distances{1.0, 1.0};

        if (axes_triple_distances.has (axis_tag))

          axis_triple_distances = axes_triple_distances.get (axis_tag);

        hb_vector_t<tuple_delta_t> new_vars;

        for (const tuple_delta_t& var : tuple_vars)

          hb_vector_t<tuple_delta_t> out = var.change_tuple_var_axis_limit (axis_tag, *axis_limit, axis_triple_distances);

          if (!out) continue;

          unsigned new_len = new_vars.length + out.length;

          if (unlikely (!new_vars.alloc (new_len, false)))

            return false;

          for (unsigned i = 0; i < out.length; i++)

            new_vars.push (std::move (out[i]));

        tuple_vars.fini ();

        tuple_vars = std::move (new_vars);

      return true;

    /* merge tuple variations with overlapping tents, if iup delta optimization

     * is enabled, add default deltas to contour_points */

    bool merge_tuple_variations (contour_point_vector_t* contour_points = nullptr)

      hb_vector_t<tuple_delta_t> new_vars;

      hb_hashmap_t<const hb_hashmap_t<hb_tag_t, Triple>*, unsigned> m;

      unsigned i = 0;

      for (const tuple_delta_t& var : tuple_vars)

        /* if all axes are pinned, drop the tuple variation */

        if (var.axis_tuples.is_empty ())

          /* if iup_delta_optimize is enabled, add deltas to contour coords */

          if (contour_points && !contour_points->add_deltas (var.deltas_x,

                                                             var.deltas_y,

                                                             var.indices))

            return false;

          continue;

        unsigned *idx;

        if (m.has (&(var.axis_tuples), &idx))

          new_vars[*idx] += var;

        else

          new_vars.push (var);

          if (!m.set (&(var.axis_tuples), i))

            return false;

          i++;

      tuple_vars.fini ();

      tuple_vars = std::move (new_vars);

      return true;

    /* compile all point set and store byte data in a point_set->hb_bytes_t hashmap,

     * also update point_set->count map, which will be used in finding shared

     * point set*/

    bool compile_all_point_sets ()

      for (const auto& tuple: tuple_vars)

        const hb_vector_t<bool>* points_set = &(tuple.indices);

        if (point_data_map.has (points_set))

          unsigned *count;

          if (unlikely (!point_set_count_map.has (points_set, &count) ||

                        !point_set_count_map.set (points_set, (*count) + 1)))

            return false;

          continue;

        hb_vector_t<unsigned char> compiled_point_data;

        if (!tuple_delta_t::compile_point_set (*points_set, compiled_point_data))

          return false;

        if (!point_data_map.set (points_set, std::move (compiled_point_data)) ||

            !point_set_count_map.set (points_set, 1))

          return false;

      return true;

    /* find shared points set which saves most bytes */

    void find_shared_points ()

      unsigned max_saved_bytes = 0;

      for (const auto& _ : point_data_map.iter_ref ())

        const hb_vector_t<bool>* points_set = _.first;

        unsigned data_length = _.second.length;

        if (!data_length) continue;

        unsigned *count;

        if (unlikely (!point_set_count_map.has (points_set, &count) ||

                      *count <= 1))

          shared_points_bytes = nullptr;

          return;

        unsigned saved_bytes = data_length * ((*count) -1);

        if (saved_bytes > max_saved_bytes)

          max_saved_bytes = saved_bytes;

          shared_points_bytes = &(_.second);

    bool calc_inferred_deltas (const contour_point_vector_t& contour_points)

      for (tuple_delta_t& var : tuple_vars)

        if (!var.calc_inferred_deltas (contour_points))

          return false;

      return true;

    bool iup_optimize (const contour_point_vector_t& contour_points)

      for (tuple_delta_t& var : tuple_vars)

        if (!var.optimize (contour_points, is_composite))

          return false;

      return true;

    public:

    bool instantiate (const hb_hashmap_t<hb_tag_t, Triple>& normalized_axes_location,

                      const hb_hashmap_t<hb_tag_t, TripleDistances>& axes_triple_distances,

                      contour_point_vector_t* contour_points = nullptr,

                      bool optimize = false)

      if (!tuple_vars) return true;

      if (!change_tuple_variations_axis_limits (normalized_axes_location, axes_triple_distances))

        return false;

      /* compute inferred deltas only for gvar */

      if (contour_points)

        if (!calc_inferred_deltas (*contour_points))

          return false;

      /* if iup delta opt is on, contour_points can't be null */

      if (optimize && !contour_points)

        return false;

      if (!merge_tuple_variations (optimize ? contour_points : nullptr))

        return false;

      if (optimize && !iup_optimize (*contour_points)) return false;

      return !tuple_vars.in_error ();

    bool compile_bytes (const hb_map_t& axes_index_map,

                        const hb_map_t& axes_old_index_tag_map,

                        bool use_shared_points,

                        const hb_hashmap_t<const hb_vector_t<char>*, unsigned>* shared_tuples_idx_map = nullptr)

      // compile points set and store data in hashmap

      if (!compile_all_point_sets ())

        return false;

      if (use_shared_points)

        find_shared_points ();

        if (shared_points_bytes)

          compiled_byte_size += shared_points_bytes->length;

      // compile delta and tuple var header for each tuple variation

      for (auto& tuple: tuple_vars)

        const hb_vector_t<bool>* points_set = &(tuple.indices);

        hb_vector_t<char> *points_data;

        if (unlikely (!point_data_map.has (points_set, &points_data)))

          return false;

        /* when iup optimization is enabled, num of referenced points could be 0

         * and thus the compiled points bytes is empty, we should skip compiling

         * this tuple */

        if (!points_data->length)

          continue;

        if (!tuple.compile_deltas ())

          return false;

        unsigned points_data_length = (points_data != shared_points_bytes) ? points_data->length : 0;

        if (!tuple.compile_tuple_var_header (axes_index_map, points_data_length, axes_old_index_tag_map,

                                             shared_tuples_idx_map))

          return false;

        compiled_byte_size += tuple.compiled_tuple_header.length + points_data_length + tuple.compiled_deltas.length;

      return true;

    bool serialize_var_headers (hb_serialize_context_t *c, unsigned& total_header_len) const

      TRACE_SERIALIZE (this);

      for (const auto& tuple: tuple_vars)

        tuple.compiled_tuple_header.as_array ().copy (c);

        if (c->in_error ()) return_trace (false);

        total_header_len += tuple.compiled_tuple_header.length;

      return_trace (true);

    bool serialize_var_data (hb_serialize_context_t *c, bool is_gvar) const

      TRACE_SERIALIZE (this);

      if (is_gvar && shared_points_bytes)

        hb_bytes_t s (shared_points_bytes->arrayZ, shared_points_bytes->length);

        s.copy (c);

      for (const auto& tuple: tuple_vars)

        const hb_vector_t<bool>* points_set = &(tuple.indices);

        hb_vector_t<char> *point_data;

        if (!point_data_map.has (points_set, &point_data))

          return_trace (false);

        if (!is_gvar || point_data != shared_points_bytes)

          hb_bytes_t s (point_data->arrayZ, point_data->length);

          s.copy (c);

        tuple.compiled_deltas.as_array ().copy (c);

        if (c->in_error ()) return_trace (false);

      /* padding for gvar */

      if (is_gvar && (compiled_byte_size % 2))

        HBUINT8 pad;

        pad = 0;

        if (!c->embed (pad)) return_trace (false);

      return_trace (true);

};

  struct tuple_iterator_t

    unsigned get_axis_count () const { return axis_count; }

    void init (hb_bytes_t var_data_bytes_, unsigned int axis_count_, const void *table_base_)

      var_data_bytes = var_data_bytes_;

      var_data = var_data_bytes_.as<TupleVariationData> ();

      index = 0;

      axis_count = axis_count_;

      current_tuple = &var_data->get_tuple_var_header ();

      data_offset = 0;

      table_base = table_base_;

    bool get_shared_indices (hb_vector_t<unsigned int> &shared_indices /* OUT */)

      if (var_data->has_shared_point_numbers ())

        const HBUINT8 *base = &(table_base+var_data->data);

        const HBUINT8 *p = base;

        if (!decompile_points (p, shared_indices, (const HBUINT8 *) (var_data_bytes.arrayZ + var_data_bytes.length))) return false;

        data_offset = p - base;

      return true;

    bool is_valid () const

      return (index < var_data->tupleVarCount.get_count ()) &&

             var_data_bytes.check_range (current_tuple, TupleVariationHeader::min_size) &&

             var_data_bytes.check_range (current_tuple, hb_max (current_tuple->get_data_size (),

                                                                current_tuple->get_size (axis_count)));

    bool move_to_next ()

      data_offset += current_tuple->get_data_size ();

      current_tuple = &current_tuple->get_next (axis_count);

      index++;

      return is_valid ();

    const HBUINT8 *get_serialized_data () const

    { return &(table_base+var_data->data) + data_offset; }

    private:

    const TupleVariationData *var_data;

    unsigned int index;

    unsigned int axis_count;

    unsigned int data_offset;

    const void *table_base;

    public:

    hb_bytes_t var_data_bytes;

    const TupleVariationHeader *current_tuple;

};

  static bool get_tuple_iterator (hb_bytes_t var_data_bytes, unsigned axis_count,

                                  const void *table_base,

                                  hb_vector_t<unsigned int> &shared_indices /* OUT */,

                                  tuple_iterator_t *iterator /* OUT */)

    iterator->init (var_data_bytes, axis_count, table_base);

    if (!iterator->get_shared_indices (shared_indices))

      return false;

    return iterator->is_valid ();

  bool has_shared_point_numbers () const { return tupleVarCount.has_shared_point_numbers (); }

  static bool decompile_points (const HBUINT8 *&p /* IN/OUT */,

				hb_vector_t<unsigned int> &points /* OUT */,

				const HBUINT8 *end)

    enum packed_point_flag_t

      POINTS_ARE_WORDS     = 0x80,

      POINT_RUN_COUNT_MASK = 0x7F

};

    if (unlikely (p + 1 > end)) return false;

    unsigned count = *p++;

    if (count & POINTS_ARE_WORDS)

      if (unlikely (p + 1 > end)) return false;

      count = ((count & POINT_RUN_COUNT_MASK) << 8) | *p++;

    if (unlikely (!points.resize (count, false))) return false;

    unsigned n = 0;

    unsigned i = 0;

    while (i < count)

      if (unlikely (p + 1 > end)) return false;

      unsigned control = *p++;

      unsigned run_count = (control & POINT_RUN_COUNT_MASK) + 1;

      unsigned stop = i + run_count;

      if (unlikely (stop > count)) return false;

      if (control & POINTS_ARE_WORDS)

        if (unlikely (p + run_count * HBUINT16::static_size > end)) return false;

        for (; i < stop; i++)

          n += *(const HBUINT16 *)p;

          points.arrayZ[i] = n;

          p += HBUINT16::static_size;

      else

        if (unlikely (p + run_count > end)) return false;

        for (; i < stop; i++)

          n += *p++;

          points.arrayZ[i] = n;

    return true;

  template <typename T>

  static bool decompile_deltas (const HBUINT8 *&p /* IN/OUT */,

				hb_vector_t<T> &deltas /* IN/OUT */,

				const HBUINT8 *end,

				bool consume_all = false)

    return TupleValues::decompile (p, deltas, end, consume_all);

  bool has_data () const { return tupleVarCount; }

  bool decompile_tuple_variations (unsigned point_count,

                                   bool is_gvar,

                                   tuple_iterator_t iterator,

                                   const hb_map_t *axes_old_index_tag_map,

                                   const hb_vector_t<unsigned> &shared_indices,

                                   const hb_array_t<const F2DOT14> shared_tuples,

                                   tuple_variations_t& tuple_variations, /* OUT */

                                   bool is_composite_glyph = false) const

    return tuple_variations.create_from_tuple_var_data (iterator, tupleVarCount,

                                                        point_count, is_gvar,

                                                        axes_old_index_tag_map,

                                                        shared_indices,

                                                        shared_tuples,

                                                        is_composite_glyph);

  bool serialize (hb_serialize_context_t *c,

                  bool is_gvar,

                  const tuple_variations_t& tuple_variations) const

    TRACE_SERIALIZE (this);

    /* empty tuple variations, just return and skip serialization. */

    if (!tuple_variations) return_trace (true);

    auto *out = c->start_embed (this);

    if (unlikely (!c->extend_min (out))) return_trace (false);

    if (!c->check_assign (out->tupleVarCount, tuple_variations.get_var_count (),

                          HB_SERIALIZE_ERROR_INT_OVERFLOW)) return_trace (false);

    unsigned total_header_len = 0;

    if (!tuple_variations.serialize_var_headers (c, total_header_len))

      return_trace (false);

    unsigned data_offset = min_size + total_header_len;

    if (!is_gvar) data_offset += 4;

    if (!c->check_assign (out->data, data_offset, HB_SERIALIZE_ERROR_INT_OVERFLOW)) return_trace (false);

    return tuple_variations.serialize_var_data (c, is_gvar);

  protected:

  struct TupleVarCount : HBUINT16

    friend struct tuple_variations_t;

    bool has_shared_point_numbers () const { return ((*this) & SharedPointNumbers); }

    unsigned int get_count () const { return (*this) & CountMask; }

    TupleVarCount& operator = (uint16_t i) { HBUINT16::operator= (i); return *this; }

    explicit operator bool () const { return get_count (); }

    protected:

    enum Flags

      SharedPointNumbers= 0x8000u,

      CountMask         = 0x0FFFu

};

    public:

    DEFINE_SIZE_STATIC (2);

};

  TupleVarCount tupleVarCount;  /* A packed field. The high 4 bits are flags, and the

                                 * low 12 bits are the number of tuple variation tables

                                 * for this glyph. The number of tuple variation tables

                                 * can be any number between 1 and 4095. */

  Offset16To<HBUINT8>

                data;           /* Offset from the start of the base table

                                 * to the serialized data. */

  /* TupleVariationHeader tupleVariationHeaders[] *//* Array of tuple variation headers. */

  public:

  DEFINE_SIZE_MIN (4);

};

using tuple_variations_t = TupleVariationData::tuple_variations_t;

struct item_variations_t

  using region_t = const hb_hashmap_t<hb_tag_t, Triple>*;

  private:

  /* each subtable is decompiled into a tuple_variations_t, in which all tuples

   * have the same num of deltas (rows) */

  hb_vector_t<tuple_variations_t> vars;

  /* num of retained rows for each subtable, there're 2 cases when var_data is empty:

   * 1. retained item_count is zero

   * 2. regions is empty and item_count is non-zero.

   * when converting to tuples, both will be dropped because the tuple is empty,

   * however, we need to retain 2. as all-zero rows to keep original varidx

   * valid, so we need a way to remember the num of rows for each subtable */

  hb_vector_t<unsigned> var_data_num_rows;

  /* original region list, decompiled from item varstore, used when rebuilding

   * region list after instantiation */

  hb_vector_t<hb_hashmap_t<hb_tag_t, Triple>> orig_region_list;

  /* region list: vector of Regions, maintain the original order for the regions

   * that existed before instantiate (), append the new regions at the end.

   * Regions are stored in each tuple already, save pointers only.

   * When converting back to item varstore, unused regions will be pruned */

  hb_vector_t<region_t> region_list;

  /* region -> idx map after instantiation and pruning unused regions */

  hb_hashmap_t<region_t, unsigned> region_map;

  /* all delta rows after instantiation */

  hb_vector_t<hb_vector_t<int>> delta_rows;

  /* final optimized vector of encoding objects used to assemble the varstore */

  hb_vector_t<delta_row_encoding_t> encodings;

  /* old varidxes -> new var_idxes map */

  hb_map_t varidx_map;

  /* has long words */

  bool has_long = false;

  public:

  bool has_long_word () const

  { return has_long; }

  const hb_vector_t<region_t>& get_region_list () const

  { return region_list; }

  const hb_vector_t<delta_row_encoding_t>& get_vardata_encodings () const

  { return encodings; }

  const hb_map_t& get_varidx_map () const

  { return varidx_map; }

  bool instantiate (const ItemVariationStore& varStore,

                    const hb_subset_plan_t *plan,

                    bool optimize=true,

                    bool use_no_variation_idx=true,

                    const hb_array_t <const hb_inc_bimap_t> inner_maps = hb_array_t<const hb_inc_bimap_t> ())

    if (!create_from_item_varstore (varStore, plan->axes_old_index_tag_map, inner_maps))

      return false;

    if (!instantiate_tuple_vars (plan->axes_location, plan->axes_triple_distances))

      return false;

    return as_item_varstore (optimize, use_no_variation_idx);

  /* keep below APIs public only for unit test: test-item-varstore */

  bool create_from_item_varstore (const ItemVariationStore& varStore,

                                  const hb_map_t& axes_old_index_tag_map,

                                  const hb_array_t <const hb_inc_bimap_t> inner_maps = hb_array_t<const hb_inc_bimap_t> ())

    const VarRegionList& regionList = varStore.get_region_list ();

    if (!regionList.get_var_regions (axes_old_index_tag_map, orig_region_list))

      return false;

    unsigned num_var_data = varStore.get_sub_table_count ();

    if (inner_maps && inner_maps.length != num_var_data) return false;

    if (!vars.alloc (num_var_data) ||

        !var_data_num_rows.alloc (num_var_data)) return false;

    for (unsigned i = 0; i < num_var_data; i++)

      if (inner_maps && !inner_maps.arrayZ[i].get_population ())

          continue;

      tuple_variations_t var_data_tuples;

      unsigned item_count = 0;

      if (!var_data_tuples.create_from_item_var_data (varStore.get_sub_table (i),

                                                      orig_region_list,

                                                      axes_old_index_tag_map,

                                                      item_count,

                                                      inner_maps ? &(inner_maps.arrayZ[i]) : nullptr))

        return false;

      var_data_num_rows.push (item_count);

      vars.push (std::move (var_data_tuples));

    return !vars.in_error () && !var_data_num_rows.in_error () && vars.length == var_data_num_rows.length;

  bool instantiate_tuple_vars (const hb_hashmap_t<hb_tag_t, Triple>& normalized_axes_location,

                               const hb_hashmap_t<hb_tag_t, TripleDistances>& axes_triple_distances)

    for (tuple_variations_t& tuple_vars : vars)

      if (!tuple_vars.instantiate (normalized_axes_location, axes_triple_distances))

        return false;

    if (!build_region_list ()) return false;

    return true;

  bool build_region_list ()

    /* scan all tuples and collect all unique regions, prune unused regions */

    hb_hashmap_t<region_t, unsigned> all_regions;

    hb_hashmap_t<region_t, unsigned> used_regions;

    /* use a vector when inserting new regions, make result deterministic */

    hb_vector_t<region_t> all_unique_regions;

    for (const tuple_variations_t& sub_table : vars)

      for (const tuple_delta_t& tuple : sub_table.tuple_vars)

        region_t r = &(tuple.axis_tuples);

        if (!used_regions.has (r))

          bool all_zeros = true;

          for (float d : tuple.deltas_x)

            int delta = (int) roundf (d);

            if (delta != 0)

              all_zeros = false;

              break;

          if (!all_zeros)

            if (!used_regions.set (r, 1))

              return false;

        if (all_regions.has (r))

          continue;

        if (!all_regions.set (r, 1))

          return false;

        all_unique_regions.push (r);

    /* regions are empty means no variation data, return true */

    if (!all_regions || !all_unique_regions) return true;

    if (!region_list.alloc (all_regions.get_population ()))

      return false;

    unsigned idx = 0;

    /* append the original regions that pre-existed */

    for (const auto& r : orig_region_list)

      if (!all_regions.has (&r) || !used_regions.has (&r))

        continue;

      region_list.push (&r);

      if (!region_map.set (&r, idx))

        return false;

      all_regions.del (&r);

      idx++;

    /* append the new regions at the end */

    for (const auto& r: all_unique_regions)

      if (!all_regions.has (r) || !used_regions.has (r))

        continue;

      region_list.push (r);

      if (!region_map.set (r, idx))

        return false;

      all_regions.del (r);

      idx++;

    return (!region_list.in_error ()) && (!region_map.in_error ());

  /* main algorithm ported from fonttools VarStore_optimize() method, optimize

   * varstore by default */

  struct combined_gain_idx_tuple_t

    int gain;

    unsigned idx_1;

    unsigned idx_2;

    combined_gain_idx_tuple_t () = default;

    combined_gain_idx_tuple_t (int gain_, unsigned i, unsigned j)

        :gain (gain_), idx_1 (i), idx_2 (j) {}

    bool operator < (const combined_gain_idx_tuple_t& o)

      if (gain != o.gain)

        return gain < o.gain;

      if (idx_1 != o.idx_1)

        return idx_1 < o.idx_1;

      return idx_2 < o.idx_2;

    bool operator <= (const combined_gain_idx_tuple_t& o)

      if (*this < o) return true;

      return gain == o.gain && idx_1 == o.idx_1 && idx_2 == o.idx_2;

};

  bool as_item_varstore (bool optimize=true, bool use_no_variation_idx=true)

    /* return true if no variation data */

    if (!region_list) return true;

    unsigned num_cols = region_list.length;

    /* pre-alloc a 2D vector for all sub_table's VarData rows */

    unsigned total_rows = 0;

    for (unsigned major = 0; major < var_data_num_rows.length; major++)

      total_rows += var_data_num_rows[major];

    if (!delta_rows.resize (total_rows)) return false;

    /* init all rows to [0]*num_cols */

    for (unsigned i = 0; i < total_rows; i++)

      if (!(delta_rows[i].resize (num_cols))) return false;

    /* old VarIdxes -> full encoding_row mapping */

    hb_hashmap_t<unsigned, const hb_vector_t<int>*> front_mapping;

    unsigned start_row = 0;

    hb_vector_t<delta_row_encoding_t> encoding_objs;

    hb_hashmap_t<hb_vector_t<uint8_t>, unsigned> chars_idx_map;

    /* delta_rows map, used for filtering out duplicate rows */

    hb_hashmap_t<const hb_vector_t<int>*, unsigned> delta_rows_map;

    for (unsigned major = 0; major < vars.length; major++)

      /* deltas are stored in tuples(column based), convert them back into items

       * (row based) delta */

      const tuple_variations_t& tuples = vars[major];

      unsigned num_rows = var_data_num_rows[major];

      for (const tuple_delta_t& tuple: tuples.tuple_vars)

        if (tuple.deltas_x.length != num_rows)

          return false;

        /* skip unused regions */

        unsigned *col_idx;

        if (!region_map.has (&(tuple.axis_tuples), &col_idx))

          continue;

        for (unsigned i = 0; i < num_rows; i++)

          int rounded_delta = roundf (tuple.deltas_x[i]);

          delta_rows[start_row + i][*col_idx] += rounded_delta;

          if ((!has_long) && (rounded_delta < -65536 || rounded_delta > 65535))

            has_long = true;

      if (!optimize)

        /* assemble a delta_row_encoding_t for this subtable, skip optimization so

         * chars is not initialized, we only need delta rows for serialization */

        delta_row_encoding_t obj;

        for (unsigned r = start_row; r < start_row + num_rows; r++)

          obj.add_row (&(delta_rows.arrayZ[r]));

        encodings.push (std::move (obj));

        start_row += num_rows;

        continue;

      for (unsigned minor = 0; minor < num_rows; minor++)

        const hb_vector_t<int>& row = delta_rows[start_row + minor];

        if (use_no_variation_idx)

          bool all_zeros = true;

          for (int delta : row)

            if (delta != 0)

              all_zeros = false;

              break;

          if (all_zeros)

            continue;

        if (!front_mapping.set ((major<<16) + minor, &row))

          return false;

        hb_vector_t<uint8_t> chars = delta_row_encoding_t::get_row_chars (row);

        if (!chars) return false;

        if (delta_rows_map.has (&row))

          continue;

        delta_rows_map.set (&row, 1);

        unsigned *obj_idx;

        if (chars_idx_map.has (chars, &obj_idx))

          delta_row_encoding_t& obj = encoding_objs[*obj_idx];

          if (!obj.add_row (&row))

            return false;

        else

          if (!chars_idx_map.set (chars, encoding_objs.length))

            return false;

          delta_row_encoding_t obj (std::move (chars), &row);

          encoding_objs.push (std::move (obj));

      start_row += num_rows;

    /* return directly if no optimization, maintain original VariationIndex so

     * varidx_map would be empty */

    if (!optimize) return !encodings.in_error ();

    /* sort encoding_objs */

    encoding_objs.qsort ();

    /* main algorithm: repeatedly pick 2 best encodings to combine, and combine

     * them */

    hb_priority_queue_t<combined_gain_idx_tuple_t> queue;

    unsigned num_todos = encoding_objs.length;

    for (unsigned i = 0; i < num_todos; i++)

      for (unsigned j = i + 1; j < num_todos; j++)

        int combining_gain = encoding_objs.arrayZ[i].gain_from_merging (encoding_objs.arrayZ[j]);

        if (combining_gain > 0)

          queue.insert (combined_gain_idx_tuple_t (-combining_gain, i, j), 0);

    hb_set_t removed_todo_idxes;

    while (queue)

      auto t = queue.pop_minimum ().first;

      unsigned i = t.idx_1;

      unsigned j = t.idx_2;

      if (removed_todo_idxes.has (i) || removed_todo_idxes.has (j))

        continue;

      delta_row_encoding_t& encoding = encoding_objs.arrayZ[i];

      delta_row_encoding_t& other_encoding = encoding_objs.arrayZ[j];

      removed_todo_idxes.add (i);

      removed_todo_idxes.add (j);

      hb_vector_t<uint8_t> combined_chars;

      if (!combined_chars.alloc (encoding.chars.length))

        return false;

      for (unsigned idx = 0; idx < encoding.chars.length; idx++)

        uint8_t v = hb_max (encoding.chars.arrayZ[idx], other_encoding.chars.arrayZ[idx]);

        combined_chars.push (v);

      delta_row_encoding_t combined_encoding_obj (std::move (combined_chars));

      for (const auto& row : hb_concat (encoding.items, other_encoding.items))

        combined_encoding_obj.add_row (row);

      for (unsigned idx = 0; idx < encoding_objs.length; idx++)

        if (removed_todo_idxes.has (idx)) continue;

        const delta_row_encoding_t& obj = encoding_objs.arrayZ[idx];

        if (obj.chars == combined_chars)

          for (const auto& row : obj.items)

            combined_encoding_obj.add_row (row);

          removed_todo_idxes.add (idx);

          continue;

        int combined_gain = combined_encoding_obj.gain_from_merging (obj);

        if (combined_gain > 0)

          queue.insert (combined_gain_idx_tuple_t (-combined_gain, idx, encoding_objs.length), 0);

      encoding_objs.push (std::move (combined_encoding_obj));

    int num_final_encodings = (int) encoding_objs.length - (int) removed_todo_idxes.get_population ();

    if (num_final_encodings <= 0) return false;

    if (!encodings.alloc (num_final_encodings)) return false;

    for (unsigned i = 0; i < encoding_objs.length; i++)

      if (removed_todo_idxes.has (i)) continue;

      encodings.push (std::move (encoding_objs.arrayZ[i]));

    /* sort again based on width, make result deterministic */

    encodings.qsort (delta_row_encoding_t::cmp_width);

    return compile_varidx_map (front_mapping);

  private:

  /* compile varidx_map for one VarData subtable (index specified by major) */

  bool compile_varidx_map (const hb_hashmap_t<unsigned, const hb_vector_t<int>*>& front_mapping)

    /* full encoding_row -> new VarIdxes mapping */

    hb_hashmap_t<const hb_vector_t<int>*, unsigned> back_mapping;

    for (unsigned major = 0; major < encodings.length; major++)

      delta_row_encoding_t& encoding = encodings[major];

      /* just sanity check, this shouldn't happen */

      if (encoding.is_empty ())

        return false;

      unsigned num_rows = encoding.items.length;

      /* sort rows, make result deterministic */

      encoding.items.qsort (_cmp_row);

      /* compile old to new var_idxes mapping */

      for (unsigned minor = 0; minor < num_rows; minor++)

        unsigned new_varidx = (major << 16) + minor;

        back_mapping.set (encoding.items.arrayZ[minor], new_varidx);

    for (auto _ : front_mapping.iter ())

      unsigned old_varidx = _.first;

      unsigned *new_varidx;

      if (back_mapping.has (_.second, &new_varidx))

        varidx_map.set (old_varidx, *new_varidx);

      else

        varidx_map.set (old_varidx, HB_OT_LAYOUT_NO_VARIATIONS_INDEX);

    return !varidx_map.in_error ();

  static int _cmp_row (const void *pa, const void *pb)

    /* compare pointers of vectors(const hb_vector_t<int>*) that represent a row */

    const hb_vector_t<int>** a = (const hb_vector_t<int>**) pa;

    const hb_vector_t<int>** b = (const hb_vector_t<int>**) pb;

    for (unsigned i = 0; i < (*b)->length; i++)

      int va = (*a)->arrayZ[i];

      int vb = (*b)->arrayZ[i];

      if (va != vb)

        return va < vb ? -1 : 1;

    return 0;

};

} /* namespace OT */

#endif /* HB_OT_VAR_COMMON_HH */