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

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  • Author : Garret Rieger
    Date : 2023-06-12 23:38:26
    Hash : db700b56
    Message : [subset] fix fuzzer timeout. Fixes: https://oss-fuzz.com/testcase-detail/6681253479579648. Limits iteration of coverage table during MATH subset to valid glyphs.

  • 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
    {
      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) &&
    		  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;
    
        /* The description of the MathKern table is a ambiguous, but interpreting
         * "between the two heights found at those indexes" for 0 < i < len as
         *
         *   correctionHeight[i-1] < correction_height <= correctionHeight[i]
         *
         * makes the result consistent with the limit cases and we can just use the
         * binary search algorithm of std::upper_bound:
         */
        unsigned int i = 0;
        unsigned int count = heightCount;
        while (count > 0)
        {
          unsigned int half = count / 2;
          hb_position_t height = correctionHeight[i + half].get_y_value (font, this);
          if (sign * height < sign * correction_height)
          {
    	i += half + 1;
    	count -= half + 1;
          } else
    	count = half;
        }
        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) &&
    		  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) &&
    		  mathConstants.sanitize (c, this) &&
    		  mathGlyphInfo.sanitize (c, this) &&
    		  mathVariants.sanitize (c, this));
      }
    
      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 */