[OTS] Add support for the MATH table.

src/math.cc

+// Copyright (c) 2014 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// We use an underscore to avoid confusion with the standard math.h library.
+#include "math_.h"
+
+#include <limits>
+#include <vector>
+
+#include "layout.h"
+#include "maxp.h"
+
+// MATH - The MATH Table
+// The specification is not yet public but has been submitted to the MPEG group
+// in response to the 'Call for Proposals for ISO/IEC 14496-22 "Open Font
+// Format" Color Font Technology and MATH layout support'. Meanwhile, you can
+// contact Microsoft's engineer Murray Sargent to obtain a copy.
+
+namespace {
+
+// The size of MATH header.
+// Version
+// MathConstants
+// MathGlyphInfo
+// MathVariants
+const unsigned kMathHeaderSize = 4 + 3 * 2;
+
+// The size of the MathGlyphInfo header.
+// MathItalicsCorrectionInfo
+// MathTopAccentAttachment
+// ExtendedShapeCoverage
+// MathKernInfo
+const unsigned kMathGlyphInfoHeaderSize = 4 * 2;
+
+// The size of the MathValueRecord.
+// Value
+// DeviceTable
+const unsigned kMathValueRecordSize = 2 * 2;
+
+// The size of the GlyphPartRecord.
+// glyph
+// StartConnectorLength
+// EndConnectorLength
+// FullAdvance
+// PartFlags
+const unsigned kGlyphPartRecordSize = 5 * 2;
+
+// Shared Table: MathValueRecord
+
+bool ParseMathValueRecord(ots::Buffer* subtable, const uint8_t *data,
+                          const size_t length) {
+  // Check the Value field.
+  if (!subtable->Skip(2)) {
+    return OTS_FAILURE();
+  }
+
+  // Check the offset to device table.
+  uint16_t offset = 0;
+  if (!subtable->ReadU16(&offset)) {
+    return OTS_FAILURE();
+  }
+  if (offset) {
+    if (offset >= length) {
+      return OTS_FAILURE();
+    }
+    if (!ots::ParseDeviceTable(data + offset, length - offset)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  return true;
+}
+
+bool ParseMathConstantsTable(const uint8_t *data, size_t length) {
+  ots::Buffer subtable(data, length);
+
+  // Part 1: int16 or uint16 constants.
+  //  ScriptPercentScaleDown
+  //  ScriptScriptPercentScaleDown
+  //  DelimitedSubFormulaMinHeight
+  //  DisplayOperatorMinHeight
+  if (!subtable.Skip(4 * 2)) {
+    return OTS_FAILURE();
+  }
+
+  // Part 2: MathValueRecord constants.
+  // MathLeading
+  // AxisHeight
+  // AccentBaseHeight
+  // FlattenedAccentBaseHeight
+  // SubscriptShiftDown
+  // SubscriptTopMax
+  // SubscriptBaselineDropMin
+  // SuperscriptShiftUp
+  // SuperscriptShiftUpCramped
+  // SuperscriptBottomMin
+  //
+  // SuperscriptBaselineDropMax
+  // SubSuperscriptGapMin
+  // SuperscriptBottomMaxWithSubscript
+  // SpaceAfterScript
+  // UpperLimitGapMin
+  // UpperLimitBaselineRiseMin
+  // LowerLimitGapMin
+  // LowerLimitBaselineDropMin
+  // StackTopShiftUp
+  // StackTopDisplayStyleShiftUp
+  //
+  // StackBottomShiftDown
+  // StackBottomDisplayStyleShiftDown
+  // StackGapMin
+  // StackDisplayStyleGapMin
+  // StretchStackTopShiftUp
+  // StretchStackBottomShiftDown
+  // StretchStackGapAboveMin
+  // StretchStackGapBelowMin
+  // FractionNumeratorShiftUp
+  // FractionNumeratorDisplayStyleShiftUp
+  //
+  // FractionDenominatorShiftDown
+  // FractionDenominatorDisplayStyleShiftDown
+  // FractionNumeratorGapMin
+  // FractionNumDisplayStyleGapMin
+  // FractionRuleThickness
+  // FractionDenominatorGapMin
+  // FractionDenomDisplayStyleGapMin
+  // SkewedFractionHorizontalGap
+  // SkewedFractionVerticalGap
+  // OverbarVerticalGap
+  //
+  // OverbarRuleThickness
+  // OverbarExtraAscender
+  // UnderbarVerticalGap
+  // UnderbarRuleThickness
+  // UnderbarExtraDescender
+  // RadicalVerticalGap
+  // RadicalDisplayStyleVerticalGap
+  // RadicalRuleThickness
+  // RadicalExtraAscender
+  // RadicalKernBeforeDegree
+  //
+  // RadicalKernAfterDegree
+  for (unsigned i = 0; i < static_cast<unsigned>(51); ++i) {
+    if (!ParseMathValueRecord(&subtable, data, length)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  // Part 3: uint16 constant
+  // RadicalDegreeBottomRaisePercent
+  if (!subtable.Skip(2)) {
+    return OTS_FAILURE();
+  }
+
+  return true;
+}
+
+bool ParseMathValueRecordSequenceForGlyphs(ots::Buffer* subtable,
+                                           const uint8_t *data,
+                                           const size_t length,
+                                           const uint16_t num_glyphs) {
+  // Check the header.
+  uint16_t offset_coverage = 0;
+  uint16_t sequence_count = 0;
+  if (!subtable->ReadU16(&offset_coverage) ||
+      !subtable->ReadU16(&sequence_count)) {
+    return OTS_FAILURE();
+  }
+
+  const unsigned sequence_end = static_cast<unsigned>(2 * 2) +
+      sequence_count * kMathValueRecordSize;
+  if (sequence_end > std::numeric_limits<uint16_t>::max()) {
+    return OTS_FAILURE();
+  }
+
+  // Check coverage table.
+  if (offset_coverage < sequence_end || offset_coverage >= length) {
+    return OTS_FAILURE();
+  }
+  if (!ots::ParseCoverageTable(data + offset_coverage,
+                               length - offset_coverage,
+                               num_glyphs, sequence_count)) {
+    return OTS_FAILURE();
+  }
+
+  // Check sequence.
+  for (unsigned i = 0; i < sequence_count; ++i) {
+    if (!ParseMathValueRecord(subtable, data, length)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  return true;
+}
+
+bool ParseMathItalicsCorrectionInfoTable(const uint8_t *data,
+                                         size_t length,
+                                         const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+  return ParseMathValueRecordSequenceForGlyphs(&subtable, data, length,
+                                               num_glyphs);
+}
+
+bool ParseMathTopAccentAttachmentTable(const uint8_t *data,
+                                       size_t length,
+                                       const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+  return ParseMathValueRecordSequenceForGlyphs(&subtable, data, length,
+                                               num_glyphs);
+}
+
+bool ParseMathKernTable(const uint8_t *data, size_t length) {
+  ots::Buffer subtable(data, length);
+
+  // Check the Height count.
+  uint16_t height_count = 0;
+  if (!subtable.ReadU16(&height_count)) {
+    return OTS_FAILURE();
+  }
+
+  // Check the Correction Heights.
+  for (unsigned i = 0; i < height_count; ++i) {
+    if (!ParseMathValueRecord(&subtable, data, length)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  // Check the Kern Values.
+  for (unsigned i = 0; i <= height_count; ++i) {
+    if (!ParseMathValueRecord(&subtable, data, length)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  return true;
+}
+
+bool ParseMathKernInfoTable(const uint8_t *data, size_t length,
+                            const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+
+  // Check the header.
+  uint16_t offset_coverage = 0;
+  uint16_t sequence_count = 0;
+  if (!subtable.ReadU16(&offset_coverage) ||
+      !subtable.ReadU16(&sequence_count)) {
+    return OTS_FAILURE();
+  }
+
+  const unsigned sequence_end = static_cast<unsigned>(2 * 2) +
+    sequence_count * 4 * 2;
+  if (sequence_end > std::numeric_limits<uint16_t>::max()) {
+    return OTS_FAILURE();
+  }
+
+  // Check coverage table.
+  if (offset_coverage < sequence_end || offset_coverage >= length) {
+    return OTS_FAILURE();
+  }
+  if (!ots::ParseCoverageTable(data + offset_coverage, length - offset_coverage,
+                               num_glyphs, sequence_count)) {
+    return OTS_FAILURE();
+  }
+
+  // Check sequence of MathKernInfoRecord
+  for (unsigned i = 0; i < sequence_count; ++i) {
+    // Check TopRight, TopLeft, BottomRight and BottomLeft Math Kern.
+    for (unsigned j = 0; j < 4; ++j) {
+      uint16_t offset_math_kern = 0;
+      if (!subtable.ReadU16(&offset_math_kern)) {
+        return OTS_FAILURE();
+      }
+      if (offset_math_kern) {
+        if (offset_math_kern < sequence_end || offset_math_kern >= length ||
+            !ParseMathKernTable(data + offset_math_kern,
+                                length - offset_math_kern)) {
+          return OTS_FAILURE();
+        }
+      }
+    }
+  }
+
+  return true;
+}
+
+bool ParseMathGlyphInfoTable(const uint8_t *data, size_t length,
+                             const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+
+  // Check Header.
+  uint16_t offset_math_italics_correction_info = 0;
+  uint16_t offset_math_top_accent_attachment = 0;
+  uint16_t offset_extended_shaped_coverage = 0;
+  uint16_t offset_math_kern_info = 0;
+  if (!subtable.ReadU16(&offset_math_italics_correction_info) ||
+      !subtable.ReadU16(&offset_math_top_accent_attachment) ||
+      !subtable.ReadU16(&offset_extended_shaped_coverage) ||
+      !subtable.ReadU16(&offset_math_kern_info)) {
+    return OTS_FAILURE();
+  }
+
+  // Check subtables.
+  // The specification does not say whether the offsets for
+  // MathItalicsCorrectionInfo, MathTopAccentAttachment and MathKernInfo may
+  // be NULL, but that's the case in some fonts (e.g STIX) so we accept that.
+  if (offset_math_italics_correction_info) {
+    if (offset_math_italics_correction_info >= length ||
+        offset_math_italics_correction_info < kMathGlyphInfoHeaderSize ||
+        !ParseMathItalicsCorrectionInfoTable(
+    data + offset_math_italics_correction_info,

[Kunihiko Sakamoto, 2014/01/17 13:01:55]

Oh, my comment wasn't very clear. I meant 4 spaces indent relative to the
previous line.

+    length - offset_math_italics_correction_info, num_glyphs)) {
+      return OTS_FAILURE();
+    }
+  }
+  if (offset_math_top_accent_attachment) {
+    if (offset_math_top_accent_attachment >= length ||
+        offset_math_top_accent_attachment < kMathGlyphInfoHeaderSize ||
+        !ParseMathTopAccentAttachmentTable(data +
+                                           offset_math_top_accent_attachment,
+                                           length -
+                                           offset_math_top_accent_attachment,
+                                           num_glyphs)) {
+      return OTS_FAILURE();
+    }
+  }
+  if (offset_extended_shaped_coverage) {
+    if (offset_extended_shaped_coverage >= length ||
+        offset_extended_shaped_coverage < kMathGlyphInfoHeaderSize ||
+        !ots::ParseCoverageTable(data + offset_extended_shaped_coverage,
+                                 length - offset_extended_shaped_coverage,
+                                 num_glyphs)) {
+      return OTS_FAILURE();
+    }
+  }
+  if (offset_math_kern_info) {
+    if (offset_math_kern_info >= length ||
+        offset_math_kern_info < kMathGlyphInfoHeaderSize ||
+        !ParseMathKernInfoTable(data + offset_math_kern_info,
+                                length - offset_math_kern_info, num_glyphs)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  return true;
+}
+
+bool ParseGlyphAssemblyTable(const uint8_t *data,
+                             size_t length, const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+
+  // Check the header.
+  uint16_t part_count = 0;
+  if (!ParseMathValueRecord(&subtable, data, length) ||
+      !subtable.ReadU16(&part_count)) {
+    return OTS_FAILURE();
+  }
+
+  const unsigned sequence_end = kMathValueRecordSize +
+    static_cast<unsigned>(2) + part_count * kGlyphPartRecordSize;
+  if (sequence_end > std::numeric_limits<uint16_t>::max()) {
+    return OTS_FAILURE();
+  }
+
+  // Check the sequence of GlyphPartRecord.
+  for (unsigned i = 0; i < part_count; ++i) {
+    uint16_t glyph = 0;
+    uint16_t part_flags = 0;
+    if (!subtable.ReadU16(&glyph) ||
+        !subtable.Skip(2 * 3) ||
+        !subtable.ReadU16(&part_flags)) {
+      return OTS_FAILURE();
+    }
+    if (glyph >= num_glyphs) {
+      OTS_WARNING("bad glyph ID: %u", glyph);
+      return OTS_FAILURE();
+    }
+    if (part_flags & ~0x00000001) {
+      OTS_WARNING("unknown part flag: %u", part_flags);
+      return OTS_FAILURE();
+    }
+  }
+
+  return true;
+}
+
+bool ParseMathGlyphConstructionTable(const uint8_t *data,
+                                     size_t length, const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+
+  // Check the header.
+  uint16_t offset_glyph_assembly = 0;
+  uint16_t variant_count = 0;
+  if (!subtable.ReadU16(&offset_glyph_assembly) ||
+      !subtable.ReadU16(&variant_count)) {
+    return OTS_FAILURE();
+  }
+
+  const unsigned sequence_end = static_cast<unsigned>(2 * 2) +
+    variant_count * 2 * 2;
+  if (sequence_end > std::numeric_limits<uint16_t>::max()) {
+    return OTS_FAILURE();
+  }
+
+  // Check the GlyphAssembly offset.
+  if (offset_glyph_assembly) {
+    if (offset_glyph_assembly >= length ||
+        offset_glyph_assembly < sequence_end) {
+      return OTS_FAILURE();
+    }
+    if (!ParseGlyphAssemblyTable(data + offset_glyph_assembly,
+                                 length - offset_glyph_assembly, num_glyphs)) {
+      return OTS_FAILURE();
+    }
+  }
+
+  // Check the sequence of MathGlyphVariantRecord.
+  for (unsigned i = 0; i < variant_count; ++i) {
+    uint16_t glyph = 0;
+    if (!subtable.ReadU16(&glyph) ||
+        !subtable.Skip(2)) {
+      return OTS_FAILURE();
+    }
+    if (glyph >= num_glyphs) {
+      OTS_WARNING("bad glyph ID: %u", glyph);
+      return OTS_FAILURE();
+    }
+  }
+
+  return true;
+}
+
+bool ParseMathGlyphConstructionSequence(ots::Buffer* subtable,
+                                        const uint8_t *data,
+                                        size_t length,
+                                        const uint16_t num_glyphs,
+                                        uint16_t offset_coverage,
+                                        uint16_t glyph_count,
+                                        const unsigned sequence_end) {
+  // Check coverage table.
+  if (offset_coverage < sequence_end || offset_coverage >= length) {
+    return OTS_FAILURE();
+  }
+  if (!ots::ParseCoverageTable(data + offset_coverage,
+                               length - offset_coverage,
+                               num_glyphs, glyph_count)) {
+    return OTS_FAILURE();
+  }
+
+  // Check sequence of MathGlyphConstruction.
+  for (unsigned i = 0; i < glyph_count; ++i) {
+      uint16_t offset_glyph_construction = 0;
+      if (!subtable->ReadU16(&offset_glyph_construction)) {
+        return OTS_FAILURE();
+      }
+      if (offset_glyph_construction < sequence_end ||
+          offset_glyph_construction >= length ||
+          !ParseMathGlyphConstructionTable(data + offset_glyph_construction,
+                                           length - offset_glyph_construction,
+                                           num_glyphs)) {
+        return OTS_FAILURE();
+      }
+  }
+
+  return true;
+}
+
+bool ParseMathVariantsTable(const uint8_t *data,
+                            size_t length, const uint16_t num_glyphs) {
+  ots::Buffer subtable(data, length);
+
+  // Check the header.
+  uint16_t offset_vert_glyph_coverage = 0;
+  uint16_t offset_horiz_glyph_coverage = 0;
+  uint16_t vert_glyph_count = 0;
+  uint16_t horiz_glyph_count = 0;
+  if (!subtable.Skip(2) ||  // MinConnectorOverlap
+      !subtable.ReadU16(&offset_vert_glyph_coverage) ||
+      !subtable.ReadU16(&offset_horiz_glyph_coverage) ||
+      !subtable.ReadU16(&vert_glyph_count) ||
+      !subtable.ReadU16(&horiz_glyph_count)) {
+    return OTS_FAILURE();
+  }
+
+  const unsigned sequence_end = 5 * 2 + vert_glyph_count * 2 +
+    horiz_glyph_count * 2;
+  if (sequence_end > std::numeric_limits<uint16_t>::max()) {
+    return OTS_FAILURE();
+  }
+
+  if (!ParseMathGlyphConstructionSequence(&subtable, data, length, num_glyphs,
+                                          offset_vert_glyph_coverage,
+                                          vert_glyph_count,
+                                          sequence_end) ||
+      !ParseMathGlyphConstructionSequence(&subtable, data, length, num_glyphs,
+                                          offset_horiz_glyph_coverage,
+                                          horiz_glyph_count,
+                                          sequence_end)) {
+    return OTS_FAILURE();
+  }
+
+  return true;
+}
+
+}  // namespace
+
+#define DROP_THIS_TABLE \
+  do { file->math->data = 0; file->math->length = 0; } while (0)
+
+namespace ots {
+
+bool ots_math_parse(OpenTypeFile *file, const uint8_t *data, size_t length) {
+  // Grab the number of glyphs in the file from the maxp table to check
+  // GlyphIDs in MATH table.
+  if (!file->maxp) {
+    return OTS_FAILURE();
+  }
+  const uint16_t num_glyphs = file->maxp->num_glyphs;
+
+  Buffer table(data, length);
+
+  OpenTypeMATH* math = new OpenTypeMATH;
+  file->math = math;
+
+  uint32_t version = 0;
+  if (!table.ReadU32(&version)) {
+    return OTS_FAILURE();
+  }
+  if (version != 0x00010000) {
+    OTS_WARNING("bad MATH version");
+    DROP_THIS_TABLE;
+    return true;
+  }
+
+  uint16_t offset_math_constants = 0;
+  uint16_t offset_math_glyph_info = 0;
+  uint16_t offset_math_variants = 0;
+  if (!table.ReadU16(&offset_math_constants) ||
+      !table.ReadU16(&offset_math_glyph_info) ||
+      !table.ReadU16(&offset_math_variants)) {
+    return OTS_FAILURE();
+  }
+
+  if (offset_math_constants >= length ||
+      offset_math_constants < kMathHeaderSize ||
+      offset_math_glyph_info >= length ||
+      offset_math_glyph_info < kMathHeaderSize ||
+      offset_math_variants >= length ||
+      offset_math_variants < kMathHeaderSize) {
+    DROP_THIS_TABLE;

[Kunihiko Sakamoto, 2014/01/17 13:01:55]

Can you add

 OTS_WARNING("bad offset in MATH header");

before this line?

+    return true;
+  }
+
+  if (!ParseMathConstantsTable(data + offset_math_constants,
+                               length - offset_math_constants)) {
+    DROP_THIS_TABLE;
+    return true;
+  }
+  if (!ParseMathGlyphInfoTable(data + offset_math_glyph_info,
+                               length - offset_math_glyph_info, num_glyphs)) {
+    DROP_THIS_TABLE;
+    return true;
+  }
+  if (!ParseMathVariantsTable(data + offset_math_variants,
+                              length - offset_math_variants, num_glyphs)) {
+    DROP_THIS_TABLE;
+    return true;
+  }
+
+  math->data = data;
+  math->length = length;
+  return true;
+}
+
+bool ots_math_should_serialise(OpenTypeFile *file) {
+  return file->math != NULL && file->math->data != NULL;
+}
+
+bool ots_math_serialise(OTSStream *out, OpenTypeFile *file) {
+  if (!out->Write(file->math->data, file->math->length)) {
+    return OTS_FAILURE();
+  }
+
+  return true;
+}
+
+void ots_math_free(OpenTypeFile *file) {
+  delete file->math;
+}
+
+}  // namespace ots
+