tor-browser

hb-ot-var-common.hh (72816B)

---

/*
* 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-alloc-pool.hh"
#include "hb-priority-queue.hh"
#include "hb-subset-instancer-iup.hh"


namespace OT {

using rebase_tent_result_scratch_t = hb_pair_t<rebase_tent_result_t, rebase_tent_result_t>;

/* https://docs.microsoft.com/en-us/typography/opentype/spec/otvarcommonformats#tuplevariationheader */
struct TupleVariationHeader
{
 friend struct tuple_delta_t;
 unsigned get_size (unsigned axis_count_times_2) const
 {
   // This function is super hot in mega-var-fonts with hundreds of masters.
   unsigned ti = tupleIndex;
   if (unlikely ((ti & (TupleIndex::EmbeddedPeakTuple | TupleIndex::IntermediateRegion))))
   {
     unsigned count = ((ti & TupleIndex::EmbeddedPeakTuple) != 0) + ((ti & TupleIndex::IntermediateRegion) != 0) * 2;
     return min_size + count * axis_count_times_2;
   }
   return min_size;
 }

 unsigned get_data_size () const { return varDataSize; }

 const TupleVariationHeader &get_next (unsigned axis_count_times_2) const
 { return StructAtOffset<TupleVariationHeader> (this, get_size (axis_count_times_2)); }

 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);
   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);
     end_tuple = get_end_tuple (axis_count);
   }

   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;
 }

 HB_ALWAYS_INLINE
 double calculate_scalar (hb_array_t<const int> coords, unsigned int coord_count,
		   const hb_array_t<const F2DOT14> shared_tuples,
		   hb_scalar_cache_t *shared_tuple_scalar_cache = nullptr) const
 {
   unsigned tuple_index = tupleIndex;

   const F2DOT14 *peak_tuple;

   bool has_interm = tuple_index & TupleIndex::IntermediateRegion; // Inlined for performance

   if (unlikely (tuple_index & TupleIndex::EmbeddedPeakTuple)) // Inlined for performance
   {
     peak_tuple = get_peak_tuple (coord_count);
     shared_tuple_scalar_cache = nullptr;
   }
   else
   {
     unsigned int index = tuple_index & TupleIndex::TupleIndexMask; // Inlined for performance

     float scalar;
     if (shared_tuple_scalar_cache &&
  shared_tuple_scalar_cache->get (index, &scalar))
     {
       if (has_interm && (scalar != 0 && scalar != 1.f))
  shared_tuple_scalar_cache = nullptr;
else
  return (double) scalar;
     }

     if (unlikely ((index + 1) * coord_count > shared_tuples.length))
       return 0.0;
     peak_tuple = shared_tuples.arrayZ + (coord_count * index);

   }

   const F2DOT14 *start_tuple = nullptr;
   const F2DOT14 *end_tuple = nullptr;

   if (has_interm)
   {
     start_tuple = get_start_tuple (coord_count);
     end_tuple = get_end_tuple (coord_count);
   }

   double scalar = 1.0;
#ifndef HB_OPTIMIZE_SIZE
#if HB_FAST_NUM_ACCESS
   bool skip = coord_count >= 16;
#endif
#endif
   for (unsigned int i = 0; i < coord_count; i++)
   {
#ifndef HB_OPTIMIZE_SIZE
#if HB_FAST_NUM_ACCESS
     if (skip)
     {
while (i + 4 <= coord_count && * (HBUINT64LE *) &peak_tuple[i] == 0)
  i += 4;
while (i < coord_count && peak_tuple[i].to_int () == 0)
  i += 1;
if (i >= coord_count)
  break;
     }
#endif
#endif

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

     int v = coords[i];
     if (!v) { scalar = 0.0; break; }
     if (v == peak) continue;

     if (has_interm)
     {
shared_tuple_scalar_cache = nullptr;
       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) { scalar = 0.0; break; }
       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 < hb_min (0, peak) || v > hb_max (0, peak)) { scalar = 0.0; break; }
     else
       scalar *= (double) v / peak;
   }
   if (shared_tuple_scalar_cache)
     shared_tuple_scalar_cache->set (get_index (), scalar);
   return scalar;
 }

 bool           has_peak () const { return tupleIndex & TupleIndex::EmbeddedPeakTuple; }
 bool   has_intermediate () const { return tupleIndex & TupleIndex::IntermediateRegion; }
 bool has_private_points () const { return tupleIndex & TupleIndex::PrivatePointNumbers; }
 unsigned      get_index () const { return tupleIndex & TupleIndex::TupleIndexMask; }

 protected:
 struct TupleIndex : HBUINT16
 {
   enum Flags {
     EmbeddedPeakTuple   = 0x8000u,
     IntermediateRegion  = 0x4000u,
     PrivatePointNumbers = 0x2000u,
     TupleIndexMask      = 0x0FFFu
   };

   TupleIndex& 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); }
 const F2DOT14* get_all_tuples_base (unsigned axis_count) const
 { return StructAfter<UnsizedArrayOf<F2DOT14>> (tupleIndex).arrayZ; }
 const F2DOT14* get_peak_tuple (unsigned axis_count) const
 { return get_all_tuples_base (axis_count); }
 const F2DOT14* get_start_tuple (unsigned axis_count) const
 { return get_all_tuples_base (axis_count) + has_peak () * axis_count; }
 const F2DOT14* get_end_tuple (unsigned axis_count) const
 { return get_all_tuples_base (axis_count) + has_peak () * axis_count + axis_count; }

 HBUINT16      varDataSize;    /* The size in bytes of the serialized
                                * data for this tuple variation table. */
 TupleIndex    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 optimize_scratch_t
{
 iup_scratch_t iup;
 hb_vector_t<bool> opt_indices;
 hb_vector_t<int> rounded_x_deltas;
 hb_vector_t<int> rounded_y_deltas;
 hb_vector_t<float> opt_deltas_x;
 hb_vector_t<float> opt_deltas_y;
 hb_vector_t<unsigned char> opt_point_data;
 hb_vector_t<unsigned char> opt_deltas_data;
 hb_vector_t<unsigned char> point_data;
 hb_vector_t<unsigned char> deltas_data;
 hb_vector_t<int> rounded_deltas;
};

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<float> deltas_x;
 /* empty for cvar tuples */
 hb_vector_t<float> 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;

 hb_vector_t<F2DOT14> compiled_peak_coords;
 hb_vector_t<F2DOT14> compiled_interm_coords;

 tuple_delta_t (hb_alloc_pool_t *pool = nullptr) {}
 tuple_delta_t (const tuple_delta_t& o) = default;
 tuple_delta_t& operator = (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 copy_from (const tuple_delta_t& o, hb_alloc_pool_t *pool = nullptr)
 {
   axis_tuples = o.axis_tuples;
   indices.allocate_from_pool (pool, o.indices);
   deltas_x.allocate_from_pool (pool, o.deltas_x);
   deltas_y.allocate_from_pool (pool, o.deltas_y);
   compiled_tuple_header.allocate_from_pool (pool, o.compiled_tuple_header);
   compiled_deltas.allocate_from_pool (pool, o.compiled_deltas);
   compiled_peak_coords.allocate_from_pool (pool, o.compiled_peak_coords);
   compiled_interm_coords.allocate_from_pool (pool, o.compiled_interm_coords);
 }

 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 *= (float scalar)
 {
   if (scalar == 1.0f)
     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;
 }

 void change_tuple_var_axis_limit (hb_tag_t axis_tag, Triple axis_limit,
			    TripleDistances axis_triple_distances,
			    hb_vector_t<tuple_delta_t>& out,
			    rebase_tent_result_scratch_t &scratch,
			    hb_alloc_pool_t *pool = nullptr)
 {
   // May move *this out.

   out.reset ();
   Triple *tent;
   if (!axis_tuples.has (axis_tag, &tent))
   {
     out.push (std::move (*this));
     return;
   }

   if ((tent->minimum < 0.0 && tent->maximum > 0.0) ||
       !(tent->minimum <= tent->middle && tent->middle <= tent->maximum))
     return;

   if (tent->middle == 0.0)
   {
     out.push (std::move (*this));
     return;
   }

   rebase_tent_result_t &solutions = scratch.first;
   rebase_tent (*tent, axis_limit, axis_triple_distances, solutions, scratch.second);
   for (unsigned i = 0; i < solutions.length; i++)
   {
     auto &t = solutions.arrayZ[i];

     tuple_delta_t new_var;
     if (i < solutions.length - 1)
new_var.copy_from (*this, pool);
     else
new_var = std::move (*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));
   }
 }

 bool compile_coords (const hb_map_t& axes_index_map,
	       const hb_map_t& axes_old_index_tag_map,
	       hb_alloc_pool_t *pool= nullptr)
 {
   unsigned cur_axis_count = axes_index_map.get_population ();
   if (pool)
   {
     if (unlikely (!compiled_peak_coords.allocate_from_pool (pool, cur_axis_count)))
return false;
   }
   else if (unlikely (!compiled_peak_coords.resize (cur_axis_count)))
     return false;

   hb_array_t<F2DOT14> start_coords, end_coords;

   unsigned orig_axis_count = axes_old_index_tag_map.get_population ();
   unsigned j = 0;
   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 = nullptr;
     if (axis_tuples.has (axis_tag, &coords))
     {
float min_val = coords->minimum;
float val = coords->middle;
float max_val = coords->maximum;

compiled_peak_coords.arrayZ[j].set_float (val);

if (min_val != hb_min (val, 0.f) || max_val != hb_max (val, 0.f))
{
  if (!compiled_interm_coords)
  {
    if (pool)
    {
      if (unlikely (!compiled_interm_coords.allocate_from_pool (pool, 2 * cur_axis_count)))
	return false;
    }
    else if (unlikely (!compiled_interm_coords.resize (2 * cur_axis_count)))
      return false;
    start_coords = compiled_interm_coords.as_array ().sub_array (0, cur_axis_count);
    end_coords = compiled_interm_coords.as_array ().sub_array (cur_axis_count);

    for (unsigned k = 0; k < j; k++)
    {
      signed peak = compiled_peak_coords.arrayZ[k].to_int ();
      if (!peak) continue;
      start_coords.arrayZ[k].set_int (hb_min (peak, 0));
      end_coords.arrayZ[k].set_int (hb_max (peak, 0));
    }
  }

}

if (compiled_interm_coords)
{
  start_coords.arrayZ[j].set_float (min_val);
  end_coords.arrayZ[j].set_float (max_val);
}
     }

     j++;
   }

   return !compiled_peak_coords.in_error () && !compiled_interm_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<F2DOT14>*, unsigned>* shared_tuples_idx_map,
			 hb_alloc_pool_t *pool = nullptr)
 {
   /* 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.allocate_from_pool (pool, alloc_len, false))) 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);

   if (!shared_tuples_idx_map)
     compile_coords (axes_index_map, axes_old_index_tag_map); // non-gvar tuples do not have compiled coords yet

   /* 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);
     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);

   /* pointdata length = 0 implies "use shared points" */
   if (points_data_length)
     flag |= TupleVariationHeader::TupleIndex::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);
   compiled_tuple_header.shrink_back_to_pool (pool, total_header_len);
   return true;
 }

 unsigned encode_peak_coords (hb_array_t<F2DOT14> peak_coords,
                              unsigned& flag) const
 {
   hb_memcpy (&peak_coords[0], &compiled_peak_coords[0], compiled_peak_coords.length * sizeof (compiled_peak_coords[0]));
   flag |= TupleVariationHeader::TupleIndex::EmbeddedPeakTuple;
   return compiled_peak_coords.length;
 }

 /* if no need to encode intermediate coords, then just return p */
 unsigned encode_interm_coords (hb_array_t<F2DOT14> coords,
                                unsigned& flag) const
 {
   if (compiled_interm_coords)
   {
     hb_memcpy (&coords[0], &compiled_interm_coords[0], compiled_interm_coords.length * sizeof (compiled_interm_coords[0]));
     flag |= TupleVariationHeader::TupleIndex::IntermediateRegion;
   }
   return compiled_interm_coords.length;
 }

 bool compile_deltas (hb_vector_t<int> &rounded_deltas_scratch,
	       hb_alloc_pool_t *pool = nullptr)
 { return compile_deltas (indices, deltas_x, deltas_y, compiled_deltas, rounded_deltas_scratch, pool); }

 static bool compile_deltas (hb_array_t<const bool> point_indices,
		      hb_array_t<const float> x_deltas,
		      hb_array_t<const float> y_deltas,
		      hb_vector_t<unsigned char> &compiled_deltas, /* OUT */
		      hb_vector_t<int> &rounded_deltas, /* scratch */
		      hb_alloc_pool_t *pool = nullptr)
 {
   if (unlikely (!rounded_deltas.resize_dirty  (point_indices.length)))
     return false;

   unsigned j = 0;
   for (unsigned i = 0; i < point_indices.length; i++)
   {
     if (!point_indices[i]) continue;
     rounded_deltas.arrayZ[j++] = (int) roundf (x_deltas.arrayZ[i]);
   }
   rounded_deltas.resize (j);

   if (!rounded_deltas) return true;
   /* Allocate enough memory: this is the correct bound:
    * Worst case scenario is that each delta has to be encoded in 4 bytes, and there
    * are runs of 64 items each. Any delta encoded in less than 4 bytes (2, 1, or 0)
    * is still smaller than the 4-byte encoding even with their control byte.
    * The initial 2 is to handle length==0, for both x and y deltas. */
   unsigned alloc_len = 2 + 4 * rounded_deltas.length + (rounded_deltas.length + 63) / 64;
   if (y_deltas)
     alloc_len *= 2;

   if (unlikely (!compiled_deltas.allocate_from_pool (pool, alloc_len, false))) 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);
   }
   compiled_deltas.shrink_back_to_pool (pool, encoded_len);
   return true;
 }

 static unsigned compile_deltas (hb_array_t<unsigned char> encoded_bytes,
			  hb_array_t<const int> deltas)
 {
   return TupleValues::compile_unsafe (deltas, encoded_bytes);
 }

 bool calc_inferred_deltas (const contour_point_vector_t& orig_points,
		     hb_vector_t<unsigned> &scratch)
 {
   unsigned point_count = orig_points.length;
   if (point_count != indices.length)
     return false;

   unsigned ref_count = 0;

   hb_vector_t<unsigned> &end_points = scratch.reset ();

   for (unsigned i = 0; i < point_count; i++)
   {
     ref_count += indices.arrayZ[i];
     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_bit_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,
                                           (double) deltas_x.arrayZ[prev], (double) 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,
                                           (double) deltas_y.arrayZ[prev], (double) 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,
	 optimize_scratch_t &scratch,
                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 = scratch.opt_indices.reset ();
   hb_vector_t<int> &rounded_x_deltas = scratch.rounded_x_deltas;
   hb_vector_t<int> &rounded_y_deltas = scratch.rounded_y_deltas;

   if (unlikely (!rounded_x_deltas.resize_dirty  (count) ||
                 !rounded_y_deltas.resize_dirty  (count)))
     return false;

   for (unsigned i = 0; i < count; i++)
   {
     rounded_x_deltas.arrayZ[i] = (int) roundf (deltas_x.arrayZ[i]);
     rounded_y_deltas.arrayZ[i] = (int) roundf (deltas_y.arrayZ[i]);
   }

   if (!iup_delta_optimize (contour_points, rounded_x_deltas, rounded_y_deltas, opt_indices, scratch.iup, 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<float> &opt_deltas_x = scratch.opt_deltas_x.reset ();
   hb_vector_t<float> &opt_deltas_y = scratch.opt_deltas_y.reset ();
   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 = scratch.opt_point_data.reset ();
   if (!compile_point_set (opt_indices, opt_point_data))
     return false;
   hb_vector_t<unsigned char> &opt_deltas_data = scratch.opt_deltas_data.reset ();
   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,
		 scratch.rounded_deltas))
     return false;

   hb_vector_t<unsigned char> &point_data = scratch.point_data.reset ();
   if (!compile_point_set (indices, point_data))
     return false;
   hb_vector_t<unsigned char> &deltas_data = scratch.deltas_data.reset ();
   if (!compile_deltas (indices, deltas_x, deltas_y, deltas_data, scratch.rounded_deltas))
     return false;

   if (opt_point_data.length + opt_deltas_data.length < point_data.length + deltas_data.length)
   {
     indices = std::move (opt_indices);

     if (is_comp_glyph_wo_deltas)
     {
       deltas_x = std::move (opt_deltas_x);
       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_dirty  (num_bytes)))
     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_dirty  (pos);
 }

 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); }
};

template <typename OffType = HBUINT16>
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_times_2) 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_times_2) + tuple_var_header->get_data_size ();
     tuple_var_header = &tuple_var_header->get_next (axis_count_times_2);
   }

   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<unsigned 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<unsigned char> *shared_points_bytes = nullptr;

   /* total compiled byte size as TupleVariationData format, initialized to 0 */
   unsigned compiled_byte_size = 0;
   bool needs_padding = false;

   /* 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,
			     hb_alloc_pool_t *pool = nullptr,
                                    bool is_composite_glyph = false)
   {
     hb_vector_t<unsigned> private_indices;
     hb_vector_t<int> deltas_x;
     hb_vector_t<int> deltas_y;
     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;

private_indices.reset ();
       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;

       if (unlikely (!deltas_x.resize_dirty  (num_deltas) ||
                     !TupleVariationData::decompile_deltas (p, deltas_x, end)))
         return false;

       if (is_gvar)
       {
         if (unlikely (!deltas_y.resize_dirty  (num_deltas) ||
                       !TupleVariationData::decompile_deltas (p, deltas_y, end)))
           return false;
       }

       tuple_delta_t var;
       var.axis_tuples = std::move (axis_tuples);
       if (unlikely (!var.indices.allocate_from_pool (pool, point_count) ||
                     !var.deltas_x.allocate_from_pool (pool, point_count, false)))
         return false;

       if (is_gvar && unlikely (!var.deltas_y.allocate_from_pool (pool, 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_dirty  (item_count) ||
           !tuple.indices.resize_dirty  (item_count))
         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,
				      hb_alloc_pool_t *pool = nullptr)
   {
     /* 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);

     // Reused vectors for reduced malloc pressure.
     rebase_tent_result_scratch_t scratch;
     hb_vector_t<tuple_delta_t> out;

     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 (tuple_delta_t& var : tuple_vars)
       {
  // This may move var out.
  var.change_tuple_var_axis_limit (axis_tag, *axis_limit, axis_triple_distances, out, scratch, pool);
         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 = 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;
     // The pre-allocation is essential for address stability of pointers
     // we store in the hashmap.
     if (unlikely (!new_vars.alloc (tuple_vars.length)))
return false;
     hb_hashmap_t<const hb_hashmap_t<hb_tag_t, Triple>*, unsigned> m;
     for (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
       {
  auto *new_var = new_vars.push ();
  if (unlikely (new_vars.in_error ()))
    return false;
         hb_swap (*new_var, var);
         if (unlikely (!m.set (&(new_var->axis_tuples), new_vars.length - 1)))
           return false;
       }
     }
     m.fini (); // Just in case, since it points into new_vars data.
	 // Shouldn't be necessary though, since we only move new_vars, not its
	 // contents.
     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,
		       hb_vector_t<unsigned> &scratch)
   {
     for (tuple_delta_t& var : tuple_vars)
       if (!var.calc_inferred_deltas (contour_points, scratch))
         return false;

     return true;
   }

   bool iup_optimize (const contour_point_vector_t& contour_points,
	       optimize_scratch_t &scratch)
   {
     for (tuple_delta_t& var : tuple_vars)
     {
       if (!var.optimize (contour_points, is_composite, scratch))
         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,
	      optimize_scratch_t &scratch,
	      hb_alloc_pool_t *pool = nullptr,
                     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, pool))
       return false;
     /* compute inferred deltas only for gvar */
     if (contour_points)
     {
hb_vector_t<unsigned> scratch;
if (!calc_inferred_deltas (*contour_points, scratch))
  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, scratch)) 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,
                       bool is_gvar = false,
                       const hb_hashmap_t<const hb_vector_t<F2DOT14>*, unsigned>* shared_tuples_idx_map = nullptr,
		hb_alloc_pool_t *pool = nullptr)
   {
     // return true for empty glyph
     if (!tuple_vars)
       return true;

     // compile points set and store data in hashmap
     if (!compile_all_point_sets ())
       return false;

     /* total compiled byte size as TupleVariationData format, initialized to its
      * min_size: 4 */
     compiled_byte_size += 4;

     if (use_shared_points)
     {
       find_shared_points ();
       if (shared_points_bytes)
         compiled_byte_size += shared_points_bytes->length;
     }
     hb_vector_t<int> rounded_deltas_scratch;
     // 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<unsigned 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 (rounded_deltas_scratch, pool))
         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,
				     pool))
         return false;
       compiled_byte_size += tuple.compiled_tuple_header.length + points_data_length + tuple.compiled_deltas.length;
     }

     if (is_gvar && (compiled_byte_size % 2))
     {
       needs_padding = true;
       compiled_byte_size += 1;
     }

     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_ubytes_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<unsigned char> *point_data;
       if (!point_data_map.has (points_set, &point_data))
         return_trace (false);

       if (!is_gvar || point_data != shared_points_bytes)
       {
         hb_ubytes_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 && needs_padding)
     {
       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> ();
     tuples_left = var_data->tupleVarCount.get_count ();
     axis_count = axis_count_;
     axis_count_times_2 = axis_count_ * 2;
     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 ()
   {
     if (unlikely (tuples_left <= 0))
return false;

     current_tuple_size = TupleVariationHeader::min_size;
     if (unlikely (!var_data_bytes.check_end ((const char *) current_tuple + current_tuple_size)))
return false;

     current_tuple_size = current_tuple->get_size (axis_count_times_2);
     if (unlikely (!var_data_bytes.check_end ((const char *) current_tuple + current_tuple_size)))
return false;

     return true;
   }

   HB_ALWAYS_INLINE
   bool move_to_next ()
   {
     data_offset += current_tuple->get_data_size ();
     current_tuple = &StructAtOffset<TupleVariationHeader> (current_tuple, current_tuple_size);
     tuples_left--;
     return is_valid ();
   }

   // TODO: Make it return (sanitized) hb_bytes_t
   const HBUINT8 *get_serialized_data () const
   { return &(table_base+var_data->data) + data_offset; }

   private:
   signed tuples_left;
   const TupleVariationData *var_data;
   unsigned int axis_count;
   unsigned int axis_count_times_2;
   unsigned int data_offset;
   unsigned int current_tuple_size;
   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_dirty  (count))) 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>
 HB_ALWAYS_INLINE
 static bool decompile_deltas (const HBUINT8 *&p /* IN/OUT */,
			hb_vector_t<T> &deltas /* IN/OUT */,
			const HBUINT8 *end,
			bool consume_all = false,
			unsigned start = 0)
 {
   return TupleValues::decompile (p, deltas, end, consume_all, start);
 }

 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 */
			   hb_alloc_pool_t *pool = nullptr,
                                  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,
						pool,
                                                       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. */
 OffsetTo<HBUINT8, OffType>
               data;           /* Offset from the start of the base table
                                * to the serialized data. */
 /* TupleVariationHeader tupleVariationHeaders[] *//* Array of tuple variation headers. */
 public:
 DEFINE_SIZE_MIN (2 + OffType::static_size);
};

// TODO: Move tuple_variations_t to outside of TupleVariationData
using tuple_variations_t = TupleVariationData<HBUINT16>::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)
 {
   optimize_scratch_t scratch;
   for (tuple_variations_t& tuple_vars : vars)
     if (!tuple_vars.instantiate (normalized_axes_location, axes_triple_distances, scratch))
       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
 {
   uint64_t encoded;

   combined_gain_idx_tuple_t () = default;
   combined_gain_idx_tuple_t (unsigned gain, unsigned i, unsigned j)
       : encoded ((uint64_t (0xFFFFFF - gain) << 40) | (uint64_t (i) << 20) | uint64_t (j))
   {
     assert (gain < 0xFFFFFF);
     assert (i < 0xFFFFFFF && j < 0xFFFFFFF);
   }

   bool operator < (const combined_gain_idx_tuple_t& o)
   {
     return encoded < o.encoded;
   }

   bool operator <= (const combined_gain_idx_tuple_t& o)
   {
     return encoded <= o.encoded;
   }

   unsigned idx_1 () const { return (encoded >> 20) & 0xFFFFF; };
   unsigned idx_2 () const { return encoded & 0xFFFFF; };
 };

 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;

   /* delta_rows map, used for filtering out duplicate rows */
   hb_vector_t<const hb_vector_t<int> *> major_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];

     if (!num_rows) continue;

     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;
         has_long |= rounded_delta < -65536 || rounded_delta > 65535;
       }
     }

     major_rows.reset ();
     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;

if (delta_rows_map.has (&row))
  continue;

delta_rows_map.set (&row, 1);

major_rows.push (&row);
     }

     if (major_rows)
encoding_objs.push (delta_row_encoding_t (std::move (major_rows), num_cols));

     start_row += num_rows;
   }

   /* return directly if no optimization, maintain original VariationIndex so
    * varidx_map would be empty */
   if (!optimize)
   {
     encodings = std::move (encoding_objs);
     return !encodings.in_error ();
   }

   /* NOTE: Fonttools instancer always optimizes VarStore from scratch. This
    * is too costly for large fonts. So, instead, we retain the encodings of
    * the original VarStore, and just try to combine them if possible. This
    * is a compromise between optimization and performance and practically
    * works very well. */

   // This produces slightly smaller results in some cases.
   encoding_objs.qsort ();

   /* main algorithm: repeatedly pick 2 best encodings to combine, and combine them */
   using item_t = hb_priority_queue_t<combined_gain_idx_tuple_t>::item_t;
   hb_vector_t<item_t> queue_items;
   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_items.push (item_t (combined_gain_idx_tuple_t (combining_gain, i, j), 0));
     }
   }

   hb_priority_queue_t<combined_gain_idx_tuple_t> queue (std::move (queue_items));

   hb_bit_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);

     encoding.merge (other_encoding);

     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];
// In the unlikely event that the same encoding exists already, combine it.
       if (obj.width == encoding.width && obj.chars == encoding.chars)
       {
  // This is straight port from fonttools algorithm. I added this branch there
  // because I thought it can happen. But looks like we never get in here in
  // practice. I'm not confident enough to remove it though; in theory it can
  // happen. I think it's just that our tests are not extensive enough to hit
  // this path.

         for (const auto& row : obj.items)
           encoding.add_row (row);

         removed_todo_idxes.add (idx);
         continue;
       }

       int combined_gain = encoding.gain_from_merging (obj);
       if (combined_gain > 0)
         queue.insert (combined_gain_idx_tuple_t (combined_gain, idx, encoding_objs.length), 0);
     }

     auto moved_encoding = std::move (encoding);
     encoding_objs.push (moved_encoding);
   }

   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]));
   }

   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 */