kc3-lang/harfbuzz/src/hb-ot-math-table.hh

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• Hash : e80b6d11
  Author :
  Date : 2025-08-21T19:24:35
  

  [ot-math] Fix constant scaling when checking if the font is Cambria Math (#5490)
  
  Co-authored-by: Khaled Hosny <khaled@aliftype.com>

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• src/hb-ot-math-table.hh

• /*
   * Copyright © 2016  Igalia S.L.
   *
   *  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.
   *
   * Igalia Author(s): Frédéric Wang
   */
  
  #ifndef HB_OT_MATH_TABLE_HH
  #define HB_OT_MATH_TABLE_HH
  
  #include "hb-open-type.hh"
  #include "hb-ot-layout-common.hh"
  #include "hb-ot-math.h"
  
  namespace OT {
  
  
  struct MathValueRecord
  {
    hb_position_t get_x_value (hb_font_t *font, const void *base) const
    { return font->em_scale_x (value) + (base+deviceTable).get_x_delta (font); }
    hb_position_t get_y_value (hb_font_t *font, const void *base) const
    { return font->em_scale_y (value) + (base+deviceTable).get_y_delta (font); }
  
    MathValueRecord* copy (hb_serialize_context_t *c, const void *base) const
    {
      TRACE_SERIALIZE (this);
      auto *out = c->embed (this);
      if (unlikely (!out)) return_trace (nullptr);
      out->deviceTable.serialize_copy (c, deviceTable, base, 0, hb_serialize_context_t::Head);
  
      return_trace (out);
    }
  
    bool sanitize (hb_sanitize_context_t *c, const void *base) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) && deviceTable.sanitize (c, base));
    }
  
    protected:
    HBINT16		value;		/* The X or Y value in design units */
    Offset16To<Device>	deviceTable;	/* Offset to the device table - from the
  					 * beginning of parent table.  May be NULL.
  					 * Suggested format for device table is 1. */
  
    public:
    DEFINE_SIZE_STATIC (4);
  };
  
  struct MathConstants
  {
    friend struct MATH;
  
    MathConstants* copy (hb_serialize_context_t *c) const
    {
      TRACE_SERIALIZE (this);
      auto *out = c->start_embed (this);
  
      HBINT16 *p = c->allocate_size<HBINT16> (HBINT16::static_size * 2);
      if (unlikely (!p)) return_trace (nullptr);
      hb_memcpy (p, percentScaleDown, HBINT16::static_size * 2);
  
      HBUINT16 *m = c->allocate_size<HBUINT16> (HBUINT16::static_size * 2);
      if (unlikely (!m)) return_trace (nullptr);
      hb_memcpy (m, minHeight, HBUINT16::static_size * 2);
  
      unsigned count = ARRAY_LENGTH (mathValueRecords);
      for (unsigned i = 0; i < count; i++)
        if (!c->copy (mathValueRecords[i], this))
          return_trace (nullptr);
  
      if (!c->embed (radicalDegreeBottomRaisePercent)) return_trace (nullptr);
      return_trace (out);
    }
  
    bool sanitize_math_value_records (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
  
      unsigned int count = ARRAY_LENGTH (mathValueRecords);
      for (unsigned int i = 0; i < count; i++)
        if (!mathValueRecords[i].sanitize (c, this))
  	return_trace (false);
  
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) && sanitize_math_value_records (c));
    }
  
    hb_position_t get_value (hb_ot_math_constant_t constant,
  			   hb_font_t *font) const
    {
      switch (constant) {
  
      case HB_OT_MATH_CONSTANT_SCRIPT_PERCENT_SCALE_DOWN:
      case HB_OT_MATH_CONSTANT_SCRIPT_SCRIPT_PERCENT_SCALE_DOWN:
        return percentScaleDown[constant - HB_OT_MATH_CONSTANT_SCRIPT_PERCENT_SCALE_DOWN];
  
      case HB_OT_MATH_CONSTANT_DELIMITED_SUB_FORMULA_MIN_HEIGHT:
      case HB_OT_MATH_CONSTANT_DISPLAY_OPERATOR_MIN_HEIGHT:
        return font->em_scale_y (minHeight[constant - HB_OT_MATH_CONSTANT_DELIMITED_SUB_FORMULA_MIN_HEIGHT]);
  
      case HB_OT_MATH_CONSTANT_RADICAL_KERN_AFTER_DEGREE:
      case HB_OT_MATH_CONSTANT_RADICAL_KERN_BEFORE_DEGREE:
      case HB_OT_MATH_CONSTANT_SKEWED_FRACTION_HORIZONTAL_GAP:
      case HB_OT_MATH_CONSTANT_SPACE_AFTER_SCRIPT:
        return mathValueRecords[constant - HB_OT_MATH_CONSTANT_MATH_LEADING].get_x_value (font, this);
  
      case HB_OT_MATH_CONSTANT_ACCENT_BASE_HEIGHT:
      case HB_OT_MATH_CONSTANT_AXIS_HEIGHT:
      case HB_OT_MATH_CONSTANT_FLATTENED_ACCENT_BASE_HEIGHT:
      case HB_OT_MATH_CONSTANT_FRACTION_DENOMINATOR_DISPLAY_STYLE_SHIFT_DOWN:
      case HB_OT_MATH_CONSTANT_FRACTION_DENOMINATOR_GAP_MIN:
      case HB_OT_MATH_CONSTANT_FRACTION_DENOMINATOR_SHIFT_DOWN:
      case HB_OT_MATH_CONSTANT_FRACTION_DENOM_DISPLAY_STYLE_GAP_MIN:
      case HB_OT_MATH_CONSTANT_FRACTION_NUMERATOR_DISPLAY_STYLE_SHIFT_UP:
      case HB_OT_MATH_CONSTANT_FRACTION_NUMERATOR_GAP_MIN:
      case HB_OT_MATH_CONSTANT_FRACTION_NUMERATOR_SHIFT_UP:
      case HB_OT_MATH_CONSTANT_FRACTION_NUM_DISPLAY_STYLE_GAP_MIN:
      case HB_OT_MATH_CONSTANT_FRACTION_RULE_THICKNESS:
      case HB_OT_MATH_CONSTANT_LOWER_LIMIT_BASELINE_DROP_MIN:
      case HB_OT_MATH_CONSTANT_LOWER_LIMIT_GAP_MIN:
      case HB_OT_MATH_CONSTANT_MATH_LEADING:
      case HB_OT_MATH_CONSTANT_OVERBAR_EXTRA_ASCENDER:
      case HB_OT_MATH_CONSTANT_OVERBAR_RULE_THICKNESS:
      case HB_OT_MATH_CONSTANT_OVERBAR_VERTICAL_GAP:
      case HB_OT_MATH_CONSTANT_RADICAL_DISPLAY_STYLE_VERTICAL_GAP:
      case HB_OT_MATH_CONSTANT_RADICAL_EXTRA_ASCENDER:
      case HB_OT_MATH_CONSTANT_RADICAL_RULE_THICKNESS:
      case HB_OT_MATH_CONSTANT_RADICAL_VERTICAL_GAP:
      case HB_OT_MATH_CONSTANT_SKEWED_FRACTION_VERTICAL_GAP:
      case HB_OT_MATH_CONSTANT_STACK_BOTTOM_DISPLAY_STYLE_SHIFT_DOWN:
      case HB_OT_MATH_CONSTANT_STACK_BOTTOM_SHIFT_DOWN:
      case HB_OT_MATH_CONSTANT_STACK_DISPLAY_STYLE_GAP_MIN:
      case HB_OT_MATH_CONSTANT_STACK_GAP_MIN:
      case HB_OT_MATH_CONSTANT_STACK_TOP_DISPLAY_STYLE_SHIFT_UP:
      case HB_OT_MATH_CONSTANT_STACK_TOP_SHIFT_UP:
      case HB_OT_MATH_CONSTANT_STRETCH_STACK_BOTTOM_SHIFT_DOWN:
      case HB_OT_MATH_CONSTANT_STRETCH_STACK_GAP_ABOVE_MIN:
      case HB_OT_MATH_CONSTANT_STRETCH_STACK_GAP_BELOW_MIN:
      case HB_OT_MATH_CONSTANT_STRETCH_STACK_TOP_SHIFT_UP:
      case HB_OT_MATH_CONSTANT_SUBSCRIPT_BASELINE_DROP_MIN:
      case HB_OT_MATH_CONSTANT_SUBSCRIPT_SHIFT_DOWN:
      case HB_OT_MATH_CONSTANT_SUBSCRIPT_TOP_MAX:
      case HB_OT_MATH_CONSTANT_SUB_SUPERSCRIPT_GAP_MIN:
      case HB_OT_MATH_CONSTANT_SUPERSCRIPT_BASELINE_DROP_MAX:
      case HB_OT_MATH_CONSTANT_SUPERSCRIPT_BOTTOM_MAX_WITH_SUBSCRIPT:
      case HB_OT_MATH_CONSTANT_SUPERSCRIPT_BOTTOM_MIN:
      case HB_OT_MATH_CONSTANT_SUPERSCRIPT_SHIFT_UP:
      case HB_OT_MATH_CONSTANT_SUPERSCRIPT_SHIFT_UP_CRAMPED:
      case HB_OT_MATH_CONSTANT_UNDERBAR_EXTRA_DESCENDER:
      case HB_OT_MATH_CONSTANT_UNDERBAR_RULE_THICKNESS:
      case HB_OT_MATH_CONSTANT_UNDERBAR_VERTICAL_GAP:
      case HB_OT_MATH_CONSTANT_UPPER_LIMIT_BASELINE_RISE_MIN:
      case HB_OT_MATH_CONSTANT_UPPER_LIMIT_GAP_MIN:
        return mathValueRecords[constant - HB_OT_MATH_CONSTANT_MATH_LEADING].get_y_value (font, this);
  
      case HB_OT_MATH_CONSTANT_RADICAL_DEGREE_BOTTOM_RAISE_PERCENT:
        return radicalDegreeBottomRaisePercent;
  
      default:
        return 0;
      }
    }
  
    protected:
    HBINT16 percentScaleDown[2];
    HBUINT16 minHeight[2];
    MathValueRecord mathValueRecords[51];
    HBINT16 radicalDegreeBottomRaisePercent;
  
    public:
    DEFINE_SIZE_STATIC (214);
  };
  
  struct MathItalicsCorrectionInfo
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      const hb_set_t &glyphset = c->plan->_glyphset_mathed;
      const hb_map_t &glyph_map = *c->plan->glyph_map;
  
      auto *out = c->serializer->start_embed (*this);
      if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
  
      hb_sorted_vector_t<hb_codepoint_t> new_coverage;
      + hb_zip (this+coverage, italicsCorrection)
      | hb_filter (glyphset, hb_first)
      | hb_filter (serialize_math_record_array (c->serializer, out->italicsCorrection, this), hb_second)
      | hb_map (hb_first)
      | hb_map (glyph_map)
      | hb_sink (new_coverage)
      ;
  
      out->coverage.serialize_serialize (c->serializer, new_coverage.iter ());
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  coverage.sanitize (c, this) &&
  		  italicsCorrection.sanitize (c, this));
    }
  
    hb_position_t get_value (hb_codepoint_t glyph,
  			   hb_font_t *font) const
    {
      unsigned int index = (this+coverage).get_coverage (glyph);
      return italicsCorrection[index].get_x_value (font, this);
    }
  
    protected:
    Offset16To<Coverage>       coverage;		/* Offset to Coverage table -
  						 * from the beginning of
  						 * MathItalicsCorrectionInfo
  						 * table. */
    Array16Of<MathValueRecord> italicsCorrection;	/* Array of MathValueRecords
  						 * defining italics correction
  						 * values for each
  						 * covered glyph. */
  
    public:
    DEFINE_SIZE_ARRAY (4, italicsCorrection);
  };
  
  struct MathTopAccentAttachment
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      const hb_set_t &glyphset = c->plan->_glyphset_mathed;
      const hb_map_t &glyph_map = *c->plan->glyph_map;
  
      auto *out = c->serializer->start_embed (*this);
      if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
  
      hb_sorted_vector_t<hb_codepoint_t> new_coverage;
      + hb_zip (this+topAccentCoverage, topAccentAttachment)
      | hb_filter (glyphset, hb_first)
      | hb_filter (serialize_math_record_array (c->serializer, out->topAccentAttachment, this), hb_second)
      | hb_map (hb_first)
      | hb_map (glyph_map)
      | hb_sink (new_coverage)
      ;
  
      out->topAccentCoverage.serialize_serialize (c->serializer, new_coverage.iter ());
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  topAccentCoverage.sanitize (c, this) &&
  		  topAccentAttachment.sanitize (c, this));
    }
  
    hb_position_t get_value (hb_codepoint_t glyph,
  			   hb_font_t *font) const
    {
      unsigned int index = (this+topAccentCoverage).get_coverage (glyph);
      if (index == NOT_COVERED)
        return font->get_glyph_h_advance (glyph) / 2;
      return topAccentAttachment[index].get_x_value (font, this);
    }
  
    protected:
    Offset16To<Coverage>       topAccentCoverage;   /* Offset to Coverage table -
  						 * from the beginning of
  						 * MathTopAccentAttachment
  						 * table. */
    Array16Of<MathValueRecord> topAccentAttachment; /* Array of MathValueRecords
  						 * defining top accent
  						 * attachment points for each
  						 * covered glyph. */
  
    public:
    DEFINE_SIZE_ARRAY (2 + 2, topAccentAttachment);
  };
  
  struct MathKern
  {
    MathKern* copy (hb_serialize_context_t *c) const
    {
      TRACE_SERIALIZE (this);
      auto *out = c->start_embed (this);
  
      if (unlikely (!c->embed (heightCount))) return_trace (nullptr);
  
      unsigned count = 2 * heightCount + 1;
      for (unsigned i = 0; i < count; i++)
        if (!c->copy (mathValueRecordsZ.arrayZ[i], this))
          return_trace (nullptr);
  
      return_trace (out);
    }
  
    bool sanitize_math_value_records (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      unsigned int count = 2 * heightCount + 1;
      for (unsigned int i = 0; i < count; i++)
        if (!mathValueRecordsZ.arrayZ[i].sanitize (c, this)) return_trace (false);
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  hb_barrier () &&
  		  c->check_array (mathValueRecordsZ.arrayZ, 2 * heightCount + 1) &&
  		  sanitize_math_value_records (c));
    }
  
    hb_position_t get_value (hb_position_t correction_height, hb_font_t *font) const
    {
      const MathValueRecord* correctionHeight = mathValueRecordsZ.arrayZ;
      const MathValueRecord* kernValue = mathValueRecordsZ.arrayZ + heightCount;
      int sign = font->y_scale < 0 ? -1 : +1;
  
      /* According to OpenType spec (v1.9), except for the boundary cases, the index
       * chosen for kern value should be i such that
       *    correctionHeight[i-1] <= correction_height < correctionHeight[i]
       * We can use the binary search algorithm of std::upper_bound(). Or, we can
       * use the internal hb_bsearch_impl.
       */
      unsigned int pos;
      auto cmp = +[](const void* key, const void* p,
                     int sign, hb_font_t* font, const MathKern* mathKern) -> int {
        return sign * *(hb_position_t*)key - sign * ((MathValueRecord*)p)->get_y_value(font, mathKern);
      };
      unsigned int i = hb_bsearch_impl(&pos, correction_height, correctionHeight,
                                       heightCount, MathValueRecord::static_size,
                                       cmp, sign, font, this) ? pos + 1 : pos;
      return kernValue[i].get_x_value (font, this);
    }
  
    unsigned int get_entries (unsigned int start_offset,
  			    unsigned int *entries_count, /* IN/OUT */
  			    hb_ot_math_kern_entry_t *kern_entries, /* OUT */
  			    hb_font_t *font) const
    {
      const MathValueRecord* correctionHeight = mathValueRecordsZ.arrayZ;
      const MathValueRecord* kernValue = mathValueRecordsZ.arrayZ + heightCount;
      const unsigned int entriesCount = heightCount + 1;
  
      if (entries_count)
      {
        unsigned int start = hb_min (start_offset, entriesCount);
        unsigned int end = hb_min (start + *entries_count, entriesCount);
        *entries_count = end - start;
  
        for (unsigned int i = 0; i < *entries_count; i++) {
  	unsigned int j = start + i;
  
  	hb_position_t max_height;
  	if (j == heightCount) {
  	  max_height = INT32_MAX;
  	} else {
  	  max_height = correctionHeight[j].get_y_value (font, this);
  	}
  
  	kern_entries[i] = {max_height, kernValue[j].get_x_value (font, this)};
        }
      }
      return entriesCount;
    }
  
    protected:
    HBUINT16	heightCount;
    UnsizedArrayOf<MathValueRecord>
  		mathValueRecordsZ;
  				/* Array of correction heights at
  				 * which the kern value changes.
  				 * Sorted by the height value in
  				 * design units (heightCount entries),
  				 * Followed by:
  				 * Array of kern values corresponding
  				 * to heights. (heightCount+1 entries).
  				 */
  
    public:
    DEFINE_SIZE_ARRAY (2, mathValueRecordsZ);
  };
  
  struct MathKernInfoRecord
  {
    MathKernInfoRecord* copy (hb_serialize_context_t *c, const void *base) const
    {
      TRACE_SERIALIZE (this);
      auto *out = c->embed (this);
      if (unlikely (!out)) return_trace (nullptr);
  
      unsigned count = ARRAY_LENGTH (mathKern);
      for (unsigned i = 0; i < count; i++)
        out->mathKern[i].serialize_copy (c, mathKern[i], base, 0, hb_serialize_context_t::Head);
  
      return_trace (out);
    }
  
    bool sanitize (hb_sanitize_context_t *c, const void *base) const
    {
      TRACE_SANITIZE (this);
  
      unsigned int count = ARRAY_LENGTH (mathKern);
      for (unsigned int i = 0; i < count; i++)
        if (unlikely (!mathKern[i].sanitize (c, base)))
  	return_trace (false);
  
      return_trace (true);
    }
  
    hb_position_t get_kerning (hb_ot_math_kern_t kern,
  			     hb_position_t correction_height,
  			     hb_font_t *font,
  			     const void *base) const
    {
      unsigned int idx = kern;
      if (unlikely (idx >= ARRAY_LENGTH (mathKern))) return 0;
      return (base+mathKern[idx]).get_value (correction_height, font);
    }
  
    unsigned int get_kernings (hb_ot_math_kern_t kern,
  			     unsigned int start_offset,
  			     unsigned int *entries_count, /* IN/OUT */
  			     hb_ot_math_kern_entry_t *kern_entries, /* OUT */
  			     hb_font_t *font,
  			     const void *base) const
    {
      unsigned int idx = kern;
      if (unlikely (idx >= ARRAY_LENGTH (mathKern)) || !mathKern[idx]) {
        if (entries_count) *entries_count = 0;
        return 0;
      }
      return (base+mathKern[idx]).get_entries (start_offset,
  					     entries_count,
  					     kern_entries,
  					     font);
    }
  
    protected:
    /* Offset to MathKern table for each corner -
     * from the beginning of MathKernInfo table.  May be NULL. */
    Offset16To<MathKern> mathKern[4];
  
    public:
    DEFINE_SIZE_STATIC (8);
  };
  
  struct MathKernInfo
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      const hb_set_t &glyphset = c->plan->_glyphset_mathed;
      const hb_map_t &glyph_map = *c->plan->glyph_map;
  
      auto *out = c->serializer->start_embed (*this);
      if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
  
      hb_sorted_vector_t<hb_codepoint_t> new_coverage;
      + hb_zip (this+mathKernCoverage, mathKernInfoRecords)
      | hb_filter (glyphset, hb_first)
      | hb_filter (serialize_math_record_array (c->serializer, out->mathKernInfoRecords, this), hb_second)
      | hb_map (hb_first)
      | hb_map (glyph_map)
      | hb_sink (new_coverage)
      ;
  
      out->mathKernCoverage.serialize_serialize (c->serializer, new_coverage.iter ());
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  mathKernCoverage.sanitize (c, this) &&
  		  mathKernInfoRecords.sanitize (c, this));
    }
  
    hb_position_t get_kerning (hb_codepoint_t glyph,
  			     hb_ot_math_kern_t kern,
  			     hb_position_t correction_height,
  			     hb_font_t *font) const
    {
      unsigned int index = (this+mathKernCoverage).get_coverage (glyph);
      return mathKernInfoRecords[index].get_kerning (kern, correction_height, font, this);
    }
  
    unsigned int get_kernings (hb_codepoint_t glyph,
  			     hb_ot_math_kern_t kern,
  			     unsigned int start_offset,
  			     unsigned int *entries_count, /* IN/OUT */
  			     hb_ot_math_kern_entry_t *kern_entries, /* OUT */
  			     hb_font_t *font) const
    {
      unsigned int index = (this+mathKernCoverage).get_coverage (glyph);
      return mathKernInfoRecords[index].get_kernings (kern,
  						    start_offset,
  						    entries_count,
  						    kern_entries,
  						    font,
  						    this);
    }
  
    protected:
    Offset16To<Coverage>
  		mathKernCoverage;
  				/* Offset to Coverage table -
  				 * from the beginning of the
  				 * MathKernInfo table. */
    Array16Of<MathKernInfoRecord>
  		mathKernInfoRecords;
  				/* Array of MathKernInfoRecords,
  				 * per-glyph information for
  				 * mathematical positioning
  				 * of subscripts and
  				 * superscripts. */
  
    public:
    DEFINE_SIZE_ARRAY (4, mathKernInfoRecords);
  };
  
  struct MathGlyphInfo
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      auto *out = c->serializer->embed (*this);
      if (unlikely (!out)) return_trace (false);
  
      out->mathItalicsCorrectionInfo.serialize_subset (c, mathItalicsCorrectionInfo, this);
      out->mathTopAccentAttachment.serialize_subset (c, mathTopAccentAttachment, this);
  
      const hb_set_t &glyphset = c->plan->_glyphset_mathed;
      const hb_map_t &glyph_map = *c->plan->glyph_map;
  
      auto it =
      + hb_iter (this+extendedShapeCoverage)
      | hb_take (c->plan->source->get_num_glyphs ())
      | hb_filter (glyphset)
      | hb_map_retains_sorting (glyph_map)
      ;
  
      if (it) out->extendedShapeCoverage.serialize_serialize (c->serializer, it);
      else out->extendedShapeCoverage = 0;
  
      out->mathKernInfo.serialize_subset (c, mathKernInfo, this);
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  mathItalicsCorrectionInfo.sanitize (c, this) &&
  		  mathTopAccentAttachment.sanitize (c, this) &&
  		  extendedShapeCoverage.sanitize (c, this) &&
  		  mathKernInfo.sanitize (c, this));
    }
  
    hb_position_t
    get_italics_correction (hb_codepoint_t  glyph, hb_font_t *font) const
    { return (this+mathItalicsCorrectionInfo).get_value (glyph, font); }
  
    hb_position_t
    get_top_accent_attachment (hb_codepoint_t  glyph, hb_font_t *font) const
    { return (this+mathTopAccentAttachment).get_value (glyph, font); }
  
    bool is_extended_shape (hb_codepoint_t glyph) const
    { return (this+extendedShapeCoverage).get_coverage (glyph) != NOT_COVERED; }
  
    hb_position_t get_kerning (hb_codepoint_t glyph,
  			     hb_ot_math_kern_t kern,
  			     hb_position_t correction_height,
  			     hb_font_t *font) const
    { return (this+mathKernInfo).get_kerning (glyph, kern, correction_height, font); }
  
    hb_position_t get_kernings (hb_codepoint_t glyph,
  			      hb_ot_math_kern_t kern,
  			      unsigned int start_offset,
  			      unsigned int *entries_count, /* IN/OUT */
  			      hb_ot_math_kern_entry_t *kern_entries, /* OUT */
  			      hb_font_t *font) const
    { return (this+mathKernInfo).get_kernings (glyph,
  					     kern,
  					     start_offset,
  					     entries_count,
  					     kern_entries,
  					     font); }
  
    protected:
    /* Offset to MathItalicsCorrectionInfo table -
     * from the beginning of MathGlyphInfo table. */
    Offset16To<MathItalicsCorrectionInfo> mathItalicsCorrectionInfo;
  
    /* Offset to MathTopAccentAttachment table -
     * from the beginning of MathGlyphInfo table. */
    Offset16To<MathTopAccentAttachment> mathTopAccentAttachment;
  
    /* Offset to coverage table for Extended Shape glyphs -
     * from the beginning of MathGlyphInfo table. When the left or right glyph of
     * a box is an extended shape variant, the (ink) box (and not the default
     * position defined by values in MathConstants table) should be used for
     * vertical positioning purposes.  May be NULL.. */
    Offset16To<Coverage> extendedShapeCoverage;
  
     /* Offset to MathKernInfo table -
      * from the beginning of MathGlyphInfo table. */
    Offset16To<MathKernInfo> mathKernInfo;
  
    public:
    DEFINE_SIZE_STATIC (8);
  };
  
  struct MathGlyphVariantRecord
  {
    friend struct MathGlyphConstruction;
  
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      auto *out = c->serializer->embed (this);
      if (unlikely (!out)) return_trace (false);
  
      const hb_map_t& glyph_map = *c->plan->glyph_map;
      return_trace (c->serializer->check_assign (out->variantGlyph, glyph_map.get (variantGlyph), HB_SERIALIZE_ERROR_INT_OVERFLOW));
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this));
    }
  
    void closure_glyphs (hb_set_t *variant_glyphs) const
    { variant_glyphs->add (variantGlyph); }
  
    protected:
    HBGlyphID16 variantGlyph;       /* Glyph ID for the variant. */
    HBUINT16  advanceMeasurement; /* Advance width/height, in design units, of the
  				 * variant, in the direction of requested
  				 * glyph extension. */
  
    public:
    DEFINE_SIZE_STATIC (4);
  };
  
  struct PartFlags : HBUINT16
  {
    enum Flags {
      Extender	= 0x0001u, /* If set, the part can be skipped or repeated. */
  
      Defined	= 0x0001u, /* All defined flags. */
    };
  
    public:
    DEFINE_SIZE_STATIC (2);
  };
  
  struct MathGlyphPartRecord
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      auto *out = c->serializer->embed (this);
      if (unlikely (!out)) return_trace (false);
  
      const hb_map_t& glyph_map = *c->plan->glyph_map;
      return_trace (c->serializer->check_assign (out->glyph, glyph_map.get (glyph), HB_SERIALIZE_ERROR_INT_OVERFLOW));
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this));
    }
  
    void extract (hb_ot_math_glyph_part_t &out,
  		int64_t mult,
  		hb_font_t *font) const
    {
      out.glyph			= glyph;
  
      out.start_connector_length	= font->em_mult (startConnectorLength, mult);
      out.end_connector_length	= font->em_mult (endConnectorLength, mult);
      out.full_advance		= font->em_mult (fullAdvance, mult);
  
      static_assert ((unsigned int) HB_OT_MATH_GLYPH_PART_FLAG_EXTENDER ==
  		   (unsigned int) PartFlags::Extender, "");
  
      out.flags = (hb_ot_math_glyph_part_flags_t)
  		(unsigned int)
  		(partFlags & PartFlags::Defined);
    }
  
    void closure_glyphs (hb_set_t *variant_glyphs) const
    { variant_glyphs->add (glyph); }
  
    protected:
    HBGlyphID16	glyph;		/* Glyph ID for the part. */
    HBUINT16	startConnectorLength;
  				/* Advance width/ height of the straight bar
  				 * connector material, in design units, is at
  				 * the beginning of the glyph, in the
  				 * direction of the extension. */
    HBUINT16	endConnectorLength;
  				/* Advance width/ height of the straight bar
  				 * connector material, in design units, is at
  				 * the end of the glyph, in the direction of
  				 * the extension. */
    HBUINT16	fullAdvance;	/* Full advance width/height for this part,
  				 * in the direction of the extension.
  				 * In design units. */
    PartFlags	partFlags;	/* Part qualifiers. */
  
    public:
    DEFINE_SIZE_STATIC (10);
  };
  
  struct MathGlyphAssembly
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
  
      if (!c->serializer->copy (italicsCorrection, this)) return_trace (false);
      if (!c->serializer->copy<HBUINT16> (partRecords.len)) return_trace (false);
  
      for (const auto& record : partRecords.iter ())
        if (!record.subset (c)) return_trace (false);
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  italicsCorrection.sanitize (c, this) &&
  		  partRecords.sanitize (c));
    }
  
    unsigned int get_parts (hb_direction_t direction,
  			  hb_font_t *font,
  			  unsigned int start_offset,
  			  unsigned int *parts_count, /* IN/OUT */
  			  hb_ot_math_glyph_part_t *parts /* OUT */,
  			  hb_position_t *italics_correction /* OUT */) const
    {
      if (parts_count)
      {
        int64_t mult = font->dir_mult (direction);
        for (auto _ : hb_zip (partRecords.as_array ().sub_array (start_offset, parts_count),
  			    hb_array (parts, *parts_count)))
  	_.first.extract (_.second, mult, font);
      }
  
      if (italics_correction)
        *italics_correction = italicsCorrection.get_x_value (font, this);
  
      return partRecords.len;
    }
  
    void closure_glyphs (hb_set_t *variant_glyphs) const
    {
      for (const auto& _ : partRecords.iter ())
        _.closure_glyphs (variant_glyphs);
    }
  
    protected:
    MathValueRecord
  		italicsCorrection;
  				/* Italics correction of this
  				 * MathGlyphAssembly. Should not
  				 * depend on the assembly size. */
    Array16Of<MathGlyphPartRecord>
  		partRecords;	/* Array of part records, from
  				 * left to right and bottom to
  				 * top. */
  
    public:
    DEFINE_SIZE_ARRAY (6, partRecords);
  };
  
  struct MathGlyphConstruction
  {
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      auto *out = c->serializer->start_embed (*this);
      if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
  
      out->glyphAssembly.serialize_subset (c, glyphAssembly, this);
  
      if (!c->serializer->check_assign (out->mathGlyphVariantRecord.len, mathGlyphVariantRecord.len, HB_SERIALIZE_ERROR_INT_OVERFLOW))
        return_trace (false);
      for (const auto& record : mathGlyphVariantRecord.iter ())
        if (!record.subset (c)) return_trace (false);
  
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  glyphAssembly.sanitize (c, this) &&
  		  mathGlyphVariantRecord.sanitize (c));
    }
  
    const MathGlyphAssembly &get_assembly () const { return this+glyphAssembly; }
  
    unsigned int get_variants (hb_direction_t direction,
  			     hb_font_t *font,
  			     unsigned int start_offset,
  			     unsigned int *variants_count, /* IN/OUT */
  			     hb_ot_math_glyph_variant_t *variants /* OUT */) const
    {
      if (variants_count)
      {
        int64_t mult = font->dir_mult (direction);
        for (auto _ : hb_zip (mathGlyphVariantRecord.as_array ().sub_array (start_offset, variants_count),
  			    hb_array (variants, *variants_count)))
  	_.second = {_.first.variantGlyph, font->em_mult (_.first.advanceMeasurement, mult)};
      }
      return mathGlyphVariantRecord.len;
    }
  
    void closure_glyphs (hb_set_t *variant_glyphs) const
    {
      (this+glyphAssembly).closure_glyphs (variant_glyphs);
  
      for (const auto& _ : mathGlyphVariantRecord.iter ())
        _.closure_glyphs (variant_glyphs);
    }
  
    protected:
    /* Offset to MathGlyphAssembly table for this shape - from the beginning of
       MathGlyphConstruction table.  May be NULL. */
    Offset16To<MathGlyphAssembly>	  glyphAssembly;
  
    /* MathGlyphVariantRecords for alternative variants of the glyphs. */
    Array16Of<MathGlyphVariantRecord> mathGlyphVariantRecord;
  
    public:
    DEFINE_SIZE_ARRAY (4, mathGlyphVariantRecord);
  };
  
  struct MathVariants
  {
    void closure_glyphs (const hb_set_t *glyph_set,
                         hb_set_t *variant_glyphs) const
    {
      const hb_array_t<const Offset16To<MathGlyphConstruction>> glyph_construction_offsets = glyphConstruction.as_array (vertGlyphCount + horizGlyphCount);
  
      if (vertGlyphCoverage)
      {
        const auto vert_offsets = glyph_construction_offsets.sub_array (0, vertGlyphCount);
        + hb_zip (this+vertGlyphCoverage, vert_offsets)
        | hb_filter (glyph_set, hb_first)
        | hb_map (hb_second)
        | hb_map (hb_add (this))
        | hb_apply ([=] (const MathGlyphConstruction &_) { _.closure_glyphs (variant_glyphs); })
        ;
      }
  
      if (horizGlyphCoverage)
      {
        const auto hori_offsets = glyph_construction_offsets.sub_array (vertGlyphCount, horizGlyphCount);
        + hb_zip (this+horizGlyphCoverage, hori_offsets)
        | hb_filter (glyph_set, hb_first)
        | hb_map (hb_second)
        | hb_map (hb_add (this))
        | hb_apply ([=] (const MathGlyphConstruction &_) { _.closure_glyphs (variant_glyphs); })
        ;
      }
    }
  
    void collect_coverage_and_indices (hb_sorted_vector_t<hb_codepoint_t>& new_coverage,
                                       const Offset16To<Coverage>& coverage,
                                       unsigned i,
                                       unsigned end_index,
                                       hb_set_t& indices,
                                       const hb_set_t& glyphset,
                                       const hb_map_t& glyph_map) const
    {
      if (!coverage) return;
  
      for (const auto _ : (this+coverage).iter ())
      {
        if (i >= end_index) return;
        if (glyphset.has (_))
        {
          unsigned new_gid = glyph_map.get (_);
          new_coverage.push (new_gid);
          indices.add (i);
        }
        i++;
      }
    }
  
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      const hb_set_t &glyphset = c->plan->_glyphset_mathed;
      const hb_map_t &glyph_map = *c->plan->glyph_map;
  
      auto *out = c->serializer->start_embed (*this);
      if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
      if (!c->serializer->check_assign (out->minConnectorOverlap, minConnectorOverlap, HB_SERIALIZE_ERROR_INT_OVERFLOW))
        return_trace (false);
  
      hb_sorted_vector_t<hb_codepoint_t> new_vert_coverage;
      hb_sorted_vector_t<hb_codepoint_t> new_hori_coverage;
      hb_set_t indices;
      collect_coverage_and_indices (new_vert_coverage, vertGlyphCoverage, 0, vertGlyphCount, indices, glyphset, glyph_map);
      collect_coverage_and_indices (new_hori_coverage, horizGlyphCoverage, vertGlyphCount, vertGlyphCount + horizGlyphCount, indices, glyphset, glyph_map);
  
      if (!c->serializer->check_assign (out->vertGlyphCount, new_vert_coverage.length, HB_SERIALIZE_ERROR_INT_OVERFLOW))
        return_trace (false);
      if (!c->serializer->check_assign (out->horizGlyphCount, new_hori_coverage.length, HB_SERIALIZE_ERROR_INT_OVERFLOW))
        return_trace (false);
  
      for (unsigned i : indices.iter ())
      {
        auto *o = c->serializer->embed (glyphConstruction[i]);
        if (!o) return_trace (false);
        o->serialize_subset (c, glyphConstruction[i], this);
      }
  
      if (new_vert_coverage)
        out->vertGlyphCoverage.serialize_serialize (c->serializer, new_vert_coverage.iter ());
  
      if (new_hori_coverage)
      out->horizGlyphCoverage.serialize_serialize (c->serializer, new_hori_coverage.iter ());
      return_trace (true);
    }
  
    bool sanitize_offsets (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      unsigned int count = vertGlyphCount + horizGlyphCount;
      for (unsigned int i = 0; i < count; i++)
        if (!glyphConstruction.arrayZ[i].sanitize (c, this)) return_trace (false);
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (c->check_struct (this) &&
  		  vertGlyphCoverage.sanitize (c, this) &&
  		  horizGlyphCoverage.sanitize (c, this) &&
  		  hb_barrier () &&
  		  c->check_array (glyphConstruction.arrayZ, vertGlyphCount + horizGlyphCount) &&
  		  sanitize_offsets (c));
    }
  
    hb_position_t get_min_connector_overlap (hb_direction_t direction,
  						  hb_font_t *font) const
    { return font->em_scale_dir (minConnectorOverlap, direction); }
  
    unsigned int get_glyph_variants (hb_codepoint_t glyph,
  				   hb_direction_t direction,
  				   hb_font_t *font,
  				   unsigned int start_offset,
  				   unsigned int *variants_count, /* IN/OUT */
  				   hb_ot_math_glyph_variant_t *variants /* OUT */) const
    { return get_glyph_construction (glyph, direction, font)
  	   .get_variants (direction, font, start_offset, variants_count, variants); }
  
    unsigned int get_glyph_parts (hb_codepoint_t glyph,
  				hb_direction_t direction,
  				hb_font_t *font,
  				unsigned int start_offset,
  				unsigned int *parts_count, /* IN/OUT */
  				hb_ot_math_glyph_part_t *parts /* OUT */,
  				hb_position_t *italics_correction /* OUT */) const
    { return get_glyph_construction (glyph, direction, font)
  	   .get_assembly ()
  	   .get_parts (direction, font,
  		       start_offset, parts_count, parts,
  		       italics_correction); }
  
    private:
    const MathGlyphConstruction &
    get_glyph_construction (hb_codepoint_t glyph,
  			  hb_direction_t direction,
  			  hb_font_t *font HB_UNUSED) const
    {
      bool vertical = HB_DIRECTION_IS_VERTICAL (direction);
      unsigned int count = vertical ? vertGlyphCount : horizGlyphCount;
      const Offset16To<Coverage> &coverage = vertical ? vertGlyphCoverage
  						  : horizGlyphCoverage;
  
      unsigned int index = (this+coverage).get_coverage (glyph);
      if (unlikely (index >= count)) return Null (MathGlyphConstruction);
  
      if (!vertical)
        index += vertGlyphCount;
  
      return this+glyphConstruction[index];
    }
  
    protected:
    HBUINT16	minConnectorOverlap;
  				/* Minimum overlap of connecting
  				 * glyphs during glyph construction,
  				 * in design units. */
    Offset16To<Coverage> vertGlyphCoverage;
  				/* Offset to Coverage table -
  				 * from the beginning of MathVariants
  				 * table. */
    Offset16To<Coverage> horizGlyphCoverage;
  				/* Offset to Coverage table -
  				 * from the beginning of MathVariants
  				 * table. */
    HBUINT16	vertGlyphCount;	/* Number of glyphs for which
  				 * information is provided for
  				 * vertically growing variants. */
    HBUINT16	horizGlyphCount;/* Number of glyphs for which
  				 * information is provided for
  				 * horizontally growing variants. */
  
    /* Array of offsets to MathGlyphConstruction tables - from the beginning of
       the MathVariants table, for shapes growing in vertical/horizontal
       direction. */
    UnsizedArrayOf<Offset16To<MathGlyphConstruction>>
  			glyphConstruction;
  
    public:
    DEFINE_SIZE_ARRAY (10, glyphConstruction);
  };
  
  
  /*
   * MATH -- Mathematical typesetting
   * https://docs.microsoft.com/en-us/typography/opentype/spec/math
   */
  
  struct MATH
  {
    static constexpr hb_tag_t tableTag = HB_OT_TAG_MATH;
  
    bool has_data () const { return version.to_int (); }
  
    void closure_glyphs (hb_set_t *glyph_set) const
    {
      if (mathVariants)
      {
        hb_set_t variant_glyphs;
        (this+mathVariants).closure_glyphs (glyph_set, &variant_glyphs);
        hb_set_union (glyph_set, &variant_glyphs);
      }
    }
  
    bool subset (hb_subset_context_t *c) const
    {
      TRACE_SUBSET (this);
      auto *out = c->serializer->embed (*this);
      if (unlikely (!out)) return_trace (false);
  
      out->mathConstants.serialize_copy (c->serializer, mathConstants, this, 0, hb_serialize_context_t::Head);
      out->mathGlyphInfo.serialize_subset (c, mathGlyphInfo, this);
      out->mathVariants.serialize_subset (c, mathVariants, this);
      return_trace (true);
    }
  
    bool sanitize (hb_sanitize_context_t *c) const
    {
      TRACE_SANITIZE (this);
      return_trace (version.sanitize (c) &&
  		  likely (version.major == 1) &&
  		  hb_barrier () &&
  		  mathConstants.sanitize (c, this) &&
  		  mathGlyphInfo.sanitize (c, this) &&
  		  mathVariants.sanitize (c, this));
    }
  
    // https://github.com/harfbuzz/harfbuzz/issues/4653
    HB_INTERNAL bool is_bad_cambria (hb_font_t *font) const
    {
  #ifndef HB_NO_MATH
      switch HB_CODEPOINT_ENCODE3 (font->face->table.MATH.get_blob ()->length,
                                   (this+mathConstants).minHeight[1], // displayOperatorMinHeight
                                   (this+mathConstants).minHeight[0]) // delimitedSubFormulaMinHeight
      {
        /* sha1sum:ab4a4fe054d23061f3c039493d6f665cfda2ecf5  cambria.ttc
         * sha1sum:086855301bff644f9d8827b88491fcf73a6d4cb9  cambria.ttc
         * sha1sum:b1e5a3feaca2ea3dfcf79ccb377de749ecf60343  cambria.ttc */
        case HB_CODEPOINT_ENCODE3 (25722, 2500, 3000):
          return true;
      }
  #endif
      return false;
    }
  
    hb_position_t get_constant (hb_ot_math_constant_t  constant,
  			      hb_font_t		   *font) const
    { return (this+mathConstants).get_value (constant, font); }
  
    const MathGlyphInfo &get_glyph_info () const { return this+mathGlyphInfo; }
  
    const MathVariants &get_variants () const    { return this+mathVariants; }
  
    protected:
    FixedVersion<>version;	/* Version of the MATH table
  				 * initially set to 0x00010000u */
    Offset16To<MathConstants>
  		mathConstants;	/* MathConstants table */
    Offset16To<MathGlyphInfo>
  		mathGlyphInfo;	/* MathGlyphInfo table */
    Offset16To<MathVariants>
  		mathVariants;	/* MathVariants table */
  
    public:
    DEFINE_SIZE_STATIC (10);
  };
  
  } /* namespace OT */
  
  
  #endif /* HB_OT_MATH_TABLE_HH */
  

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