text: """
  Implementation details for :mod:`.mathtext`.
  """
  
  from collections import namedtuple
  import enum
  import functools
  from io import StringIO
  import logging
  import os
  import types
  import unicodedata
  
  import numpy as np
  from pyparsing import (
      Combine, Empty, Forward, Group, Literal, oneOf, OneOrMore,
      Optional, ParseBaseException, ParseFatalException, ParserElement,
      ParseResults, QuotedString, Regex, StringEnd, Suppress, White, ZeroOrMore)
  
  import matplotlib as mpl
  from . import _api, cbook
  from ._mathtext_data import (
      latex_to_bakoma, latex_to_standard, stix_glyph_fixes, stix_virtual_fonts,
      tex2uni)
  from .afm import AFM
  from .font_manager import FontProperties, findfont, get_font
  from .ft2font import KERNING_DEFAULT
  
  
  ParserElement.enablePackrat()
  _log = logging.getLogger("matplotlib.mathtext")
  
  
  ##############################################################################
  # FONTS
  
  
  def get_unicode_index(symbol, math=True):
      r"""
      Return the integer index (from the Unicode table) of *symbol*.
  
      Parameters
      ----------
      symbol : str
          A single unicode character, a TeX command (e.g. r'\pi') or a Type1
          symbol name (e.g. 'phi').
      math : bool, default: True
          If False, always treat as a single unicode character.
      """
      # for a non-math symbol, simply return its unicode index
      if not math:
          return ord(symbol)
      # From UTF #25: U+2212 minus sign is the preferred
      # representation of the unary and binary minus sign rather than
      # the ASCII-derived U+002D hyphen-minus, because minus sign is
      # unambiguous and because it is rendered with a more desirable
      # length, usually longer than a hyphen.
      if symbol == '-':
          return 0x2212
      try:  # This will succeed if symbol is a single unicode char
          return ord(symbol)
      except TypeError:
          pass
      try:  # Is symbol a TeX symbol (i.e. \alpha)
          return tex2uni[symbol.strip("\\")]
      except KeyError as err:
          raise ValueError(
              "'{}' is not a valid Unicode character or TeX/Type1 symbol"
              .format(symbol)) from err
  
  
  class Fonts:
      """
      An abstract base class for a system of fonts to use for mathtext.
  
      The class must be able to take symbol keys and font file names and
      return the character metrics.  It also delegates to a backend class
      to do the actual drawing.
      """
  
      def __init__(self, default_font_prop, mathtext_backend):
          """
          Parameters
          ----------
          default_font_prop : `~.font_manager.FontProperties`
              The default non-math font, or the base font for Unicode (generic)
              font rendering.
          mathtext_backend : `MathtextBackend` subclass
              Backend to which rendering is actually delegated.
          """
          self.default_font_prop = default_font_prop
          self.mathtext_backend = mathtext_backend
          self.used_characters = {}
  
      @_api.deprecated("3.4")
      def destroy(self):
          """
          Fix any cyclical references before the object is about
          to be destroyed.
          """
          self.used_characters = None
  
      def get_kern(self, font1, fontclass1, sym1, fontsize1,
                   font2, fontclass2, sym2, fontsize2, dpi):
          """
          Get the kerning distance for font between *sym1* and *sym2*.
  
          See `~.Fonts.get_metrics` for a detailed description of the parameters.
          """
          return 0.
  
      def get_metrics(self, font, font_class, sym, fontsize, dpi, math=True):
          r"""
          Parameters
          ----------
          font : str
              One of the TeX font names: "tt", "it", "rm", "cal", "sf", "bf",
              "default", "regular", "bb", "frak", "scr".  "default" and "regular"
              are synonyms and use the non-math font.
          font_class : str
              One of the TeX font names (as for *font*), but **not** "bb",
              "frak", or "scr".  This is used to combine two font classes.  The
              only supported combination currently is ``get_metrics("frak", "bf",
              ...)``.
          sym : str
              A symbol in raw TeX form, e.g., "1", "x", or "\sigma".
          fontsize : float
              Font size in points.
          dpi : float
              Rendering dots-per-inch.
          math : bool
              Whether we are currently in math mode or not.
  
          Returns
          -------
          object
  
              The returned object has the following attributes (all floats,
              except *slanted*):
  
              - *advance*: The advance distance (in points) of the glyph.
              - *height*: The height of the glyph in points.
              - *width*: The width of the glyph in points.
              - *xmin*, *xmax*, *ymin*, *ymax*: The ink rectangle of the glyph
              - *iceberg*: The distance from the baseline to the top of the
                glyph.  (This corresponds to TeX's definition of "height".)
              - *slanted*: Whether the glyph should be considered as "slanted"
                (currently used for kerning sub/superscripts).
          """
          info = self._get_info(font, font_class, sym, fontsize, dpi, math)
          return info.metrics
  
      def set_canvas_size(self, w, h, d):
          """
          Set the size of the buffer used to render the math expression.
          Only really necessary for the bitmap backends.
          """
          self.width, self.height, self.depth = np.ceil([w, h, d])
          self.mathtext_backend.set_canvas_size(
              self.width, self.height, self.depth)
  
      @_api.rename_parameter("3.4", "facename", "font")
      def render_glyph(self, ox, oy, font, font_class, sym, fontsize, dpi):
          """
          At position (*ox*, *oy*), draw the glyph specified by the remaining
          parameters (see `get_metrics` for their detailed description).
          """
          info = self._get_info(font, font_class, sym, fontsize, dpi)
          self.used_characters.setdefault(info.font.fname, set()).add(info.num)
          self.mathtext_backend.render_glyph(ox, oy, info)
  
      def render_rect_filled(self, x1, y1, x2, y2):
          """
          Draw a filled rectangle from (*x1*, *y1*) to (*x2*, *y2*).
          """
          self.mathtext_backend.render_rect_filled(x1, y1, x2, y2)
  
      def get_xheight(self, font, fontsize, dpi):
          """
          Get the xheight for the given *font* and *fontsize*.
          """
          raise NotImplementedError()
  
      def get_underline_thickness(self, font, fontsize, dpi):
          """
          Get the line thickness that matches the given font.  Used as a
          base unit for drawing lines such as in a fraction or radical.
          """
          raise NotImplementedError()
  
      def get_used_characters(self):
          """
          Get the set of characters that were used in the math
          expression.  Used by backends that need to subset fonts so
          they know which glyphs to include.
          """
          return self.used_characters
  
      def get_results(self, box):
          """
          Get the data needed by the backend to render the math
          expression.  The return value is backend-specific.
          """
          result = self.mathtext_backend.get_results(
              box, self.get_used_characters())
          if self.destroy != TruetypeFonts.destroy.__get__(self):
              destroy = _api.deprecate_method_override(
                  __class__.destroy, self, since="3.4")
              if destroy:
                  destroy()
          return result
  
      def get_sized_alternatives_for_symbol(self, fontname, sym):
          """
          Override if your font provides multiple sizes of the same
          symbol.  Should return a list of symbols matching *sym* in
          various sizes.  The expression renderer will select the most
          appropriate size for a given situation from this list.
          """
          return [(fontname, sym)]
  
  
  class TruetypeFonts(Fonts):
      """
      A generic base class for all font setups that use Truetype fonts
      (through FT2Font).
      """
      def __init__(self, default_font_prop, mathtext_backend):
          super().__init__(default_font_prop, mathtext_backend)
          self.glyphd = {}
          self._fonts = {}
  
          filename = findfont(default_font_prop)
          default_font = get_font(filename)
          self._fonts['default'] = default_font
          self._fonts['regular'] = default_font
  
      @_api.deprecated("3.4")
      def destroy(self):
          self.glyphd = None
          super().destroy()
  
      def _get_font(self, font):
          if font in self.fontmap:
              basename = self.fontmap[font]
          else:
              basename = font
          cached_font = self._fonts.get(basename)
          if cached_font is None and os.path.exists(basename):
              cached_font = get_font(basename)
              self._fonts[basename] = cached_font
              self._fonts[cached_font.postscript_name] = cached_font
              self._fonts[cached_font.postscript_name.lower()] = cached_font
          return cached_font
  
      def _get_offset(self, font, glyph, fontsize, dpi):
          if font.postscript_name == 'Cmex10':
              return (glyph.height / 64 / 2) + (fontsize/3 * dpi/72)
          return 0.
  
      def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
          key = fontname, font_class, sym, fontsize, dpi
          bunch = self.glyphd.get(key)
          if bunch is not None:
              return bunch
  
          font, num, symbol_name, fontsize, slanted = \
              self._get_glyph(fontname, font_class, sym, fontsize, math)
  
          font.set_size(fontsize, dpi)
          glyph = font.load_char(
              num,
              flags=self.mathtext_backend.get_hinting_type())
  
          xmin, ymin, xmax, ymax = [val/64.0 for val in glyph.bbox]
          offset = self._get_offset(font, glyph, fontsize, dpi)
          metrics = types.SimpleNamespace(
              advance = glyph.linearHoriAdvance/65536.0,
              height  = glyph.height/64.0,
              width   = glyph.width/64.0,
              xmin    = xmin,
              xmax    = xmax,
              ymin    = ymin+offset,
              ymax    = ymax+offset,
              # iceberg is the equivalent of TeX's "height"
              iceberg = glyph.horiBearingY/64.0 + offset,
              slanted = slanted
              )
  
          result = self.glyphd[key] = types.SimpleNamespace(
              font            = font,
              fontsize        = fontsize,
              postscript_name = font.postscript_name,
              metrics         = metrics,
              symbol_name     = symbol_name,
              num             = num,
              glyph           = glyph,
              offset          = offset
              )
          return result
  
      def get_xheight(self, fontname, fontsize, dpi):
          font = self._get_font(fontname)
          font.set_size(fontsize, dpi)
          pclt = font.get_sfnt_table('pclt')
          if pclt is None:
              # Some fonts don't store the xHeight, so we do a poor man's xHeight
              metrics = self.get_metrics(
                  fontname, mpl.rcParams['mathtext.default'], 'x', fontsize, dpi)
              return metrics.iceberg
          xHeight = (pclt['xHeight'] / 64.0) * (fontsize / 12.0) * (dpi / 100.0)
          return xHeight
  
      def get_underline_thickness(self, font, fontsize, dpi):
          # This function used to grab underline thickness from the font
          # metrics, but that information is just too un-reliable, so it
          # is now hardcoded.
          return ((0.75 / 12.0) * fontsize * dpi) / 72.0
  
      def get_kern(self, font1, fontclass1, sym1, fontsize1,
                   font2, fontclass2, sym2, fontsize2, dpi):
          if font1 == font2 and fontsize1 == fontsize2:
              info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
              info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
              font = info1.font
              return font.get_kerning(info1.num, info2.num, KERNING_DEFAULT) / 64
          return super().get_kern(font1, fontclass1, sym1, fontsize1,
                                  font2, fontclass2, sym2, fontsize2, dpi)
  
  
  class BakomaFonts(TruetypeFonts):
      """
      Use the Bakoma TrueType fonts for rendering.
  
      Symbols are strewn about a number of font files, each of which has
      its own proprietary 8-bit encoding.
      """
      _fontmap = {
          'cal': 'cmsy10',
          'rm':  'cmr10',
          'tt':  'cmtt10',
          'it':  'cmmi10',
          'bf':  'cmb10',
          'sf':  'cmss10',
          'ex':  'cmex10',
      }
  
      def __init__(self, *args, **kwargs):
          self._stix_fallback = StixFonts(*args, **kwargs)
  
          super().__init__(*args, **kwargs)
          self.fontmap = {}
          for key, val in self._fontmap.items():
              fullpath = findfont(val)
              self.fontmap[key] = fullpath
              self.fontmap[val] = fullpath
  
      _slanted_symbols = set(r"\int \oint".split())
  
      def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
          symbol_name = None
          font = None
          if fontname in self.fontmap and sym in latex_to_bakoma:
              basename, num = latex_to_bakoma[sym]
              slanted = (basename == "cmmi10") or sym in self._slanted_symbols
              font = self._get_font(basename)
          elif len(sym) == 1:
              slanted = (fontname == "it")
              font = self._get_font(fontname)
              if font is not None:
                  num = ord(sym)
  
          if font is not None:
              gid = font.get_char_index(num)
              if gid != 0:
                  symbol_name = font.get_glyph_name(gid)
  
          if symbol_name is None:
              return self._stix_fallback._get_glyph(
                  fontname, font_class, sym, fontsize, math)
  
          return font, num, symbol_name, fontsize, slanted
  
      # The Bakoma fonts contain many pre-sized alternatives for the
      # delimiters.  The AutoSizedChar class will use these alternatives
      # and select the best (closest sized) glyph.
      _size_alternatives = {
          '(':           [('rm', '('), ('ex', '\xa1'), ('ex', '\xb3'),
                          ('ex', '\xb5'), ('ex', '\xc3')],
          ')':           [('rm', ')'), ('ex', '\xa2'), ('ex', '\xb4'),
                          ('ex', '\xb6'), ('ex', '\x21')],
          '{':           [('cal', '{'), ('ex', '\xa9'), ('ex', '\x6e'),
                          ('ex', '\xbd'), ('ex', '\x28')],
          '}':           [('cal', '}'), ('ex', '\xaa'), ('ex', '\x6f'),
                          ('ex', '\xbe'), ('ex', '\x29')],
          # The fourth size of '[' is mysteriously missing from the BaKoMa
          # font, so I've omitted it for both '[' and ']'
          '[':           [('rm', '['), ('ex', '\xa3'), ('ex', '\x68'),
                          ('ex', '\x22')],
          ']':           [('rm', ']'), ('ex', '\xa4'), ('ex', '\x69'),
                          ('ex', '\x23')],
          r'\lfloor':    [('ex', '\xa5'), ('ex', '\x6a'),
                          ('ex', '\xb9'), ('ex', '\x24')],
          r'\rfloor':    [('ex', '\xa6'), ('ex', '\x6b'),
                          ('ex', '\xba'), ('ex', '\x25')],
          r'\lceil':     [('ex', '\xa7'), ('ex', '\x6c'),
                          ('ex', '\xbb'), ('ex', '\x26')],
          r'\rceil':     [('ex', '\xa8'), ('ex', '\x6d'),
                          ('ex', '\xbc'), ('ex', '\x27')],
          r'\langle':    [('ex', '\xad'), ('ex', '\x44'),
                          ('ex', '\xbf'), ('ex', '\x2a')],
          r'\rangle':    [('ex', '\xae'), ('ex', '\x45'),
                          ('ex', '\xc0'), ('ex', '\x2b')],
          r'\__sqrt__':  [('ex', '\x70'), ('ex', '\x71'),
                          ('ex', '\x72'), ('ex', '\x73')],
          r'\backslash': [('ex', '\xb2'), ('ex', '\x2f'),
                          ('ex', '\xc2'), ('ex', '\x2d')],
          r'/':          [('rm', '/'), ('ex', '\xb1'), ('ex', '\x2e'),
                          ('ex', '\xcb'), ('ex', '\x2c')],
          r'\widehat':   [('rm', '\x5e'), ('ex', '\x62'), ('ex', '\x63'),
                          ('ex', '\x64')],
          r'\widetilde': [('rm', '\x7e'), ('ex', '\x65'), ('ex', '\x66'),
                          ('ex', '\x67')],
          r'<':          [('cal', 'h'), ('ex', 'D')],
          r'>':          [('cal', 'i'), ('ex', 'E')]
          }
  
      for alias, target in [(r'\leftparen', '('),
                            (r'\rightparent', ')'),
                            (r'\leftbrace', '{'),
                            (r'\rightbrace', '}'),
                            (r'\leftbracket', '['),
                            (r'\rightbracket', ']'),
                            (r'\{', '{'),
                            (r'\}', '}'),
                            (r'\[', '['),
                            (r'\]', ']')]:
          _size_alternatives[alias] = _size_alternatives[target]
  
      def get_sized_alternatives_for_symbol(self, fontname, sym):
          return self._size_alternatives.get(sym, [(fontname, sym)])
  
  
  class UnicodeFonts(TruetypeFonts):
      """
      An abstract base class for handling Unicode fonts.
  
      While some reasonably complete Unicode fonts (such as DejaVu) may
      work in some situations, the only Unicode font I'm aware of with a
      complete set of math symbols is STIX.
  
      This class will "fallback" on the Bakoma fonts when a required
      symbol can not be found in the font.
      """
      use_cmex = True  # Unused; delete once mathtext becomes private.
  
      def __init__(self, *args, **kwargs):
          # This must come first so the backend's owner is set correctly
          fallback_rc = mpl.rcParams['mathtext.fallback']
          font_cls = {'stix': StixFonts,
                      'stixsans': StixSansFonts,
                      'cm': BakomaFonts
                      }.get(fallback_rc)
          self.cm_fallback = font_cls(*args, **kwargs) if font_cls else None
  
          super().__init__(*args, **kwargs)
          self.fontmap = {}
          for texfont in "cal rm tt it bf sf".split():
              prop = mpl.rcParams['mathtext.' + texfont]
              font = findfont(prop)
              self.fontmap[texfont] = font
          prop = FontProperties('cmex10')
          font = findfont(prop)
          self.fontmap['ex'] = font
  
          # include STIX sized alternatives for glyphs if fallback is STIX
          if isinstance(self.cm_fallback, StixFonts):
              stixsizedaltfonts = {
                   0: 'STIXGeneral',
                   1: 'STIXSizeOneSym',
                   2: 'STIXSizeTwoSym',
                   3: 'STIXSizeThreeSym',
                   4: 'STIXSizeFourSym',
                   5: 'STIXSizeFiveSym'}
  
              for size, name in stixsizedaltfonts.items():
                  fullpath = findfont(name)
                  self.fontmap[size] = fullpath
                  self.fontmap[name] = fullpath
  
      _slanted_symbols = set(r"\int \oint".split())
  
      def _map_virtual_font(self, fontname, font_class, uniindex):
          return fontname, uniindex
  
      def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
          try:
              uniindex = get_unicode_index(sym, math)
              found_symbol = True
          except ValueError:
              uniindex = ord('?')
              found_symbol = False
              _log.warning("No TeX to unicode mapping for {!a}.".format(sym))
  
          fontname, uniindex = self._map_virtual_font(
              fontname, font_class, uniindex)
  
          new_fontname = fontname
  
          # Only characters in the "Letter" class should be italicized in 'it'
          # mode.  Greek capital letters should be Roman.
          if found_symbol:
              if fontname == 'it' and uniindex < 0x10000:
                  char = chr(uniindex)
                  if (unicodedata.category(char)[0] != "L"
                          or unicodedata.name(char).startswith("GREEK CAPITAL")):
                      new_fontname = 'rm'
  
              slanted = (new_fontname == 'it') or sym in self._slanted_symbols
              found_symbol = False
              font = self._get_font(new_fontname)
              if font is not None:
                  if font.family_name == "cmr10" and uniindex == 0x2212:
                      # minus sign exists in cmsy10 (not cmr10)
                      font = get_font(
                          cbook._get_data_path("fonts/ttf/cmsy10.ttf"))
                      uniindex = 0xa1
                  glyphindex = font.get_char_index(uniindex)
                  if glyphindex != 0:
                      found_symbol = True
  
          if not found_symbol:
              if self.cm_fallback:
                  if (fontname in ('it', 'regular')
                          and isinstance(self.cm_fallback, StixFonts)):
                      fontname = 'rm'
  
                  g = self.cm_fallback._get_glyph(fontname, font_class,
                                                  sym, fontsize)
                  fname = g[0].family_name
                  if fname in list(BakomaFonts._fontmap.values()):
                      fname = "Computer Modern"
                  _log.info("Substituting symbol %s from %s", sym, fname)
                  return g
  
              else:
                  if (fontname in ('it', 'regular')
                          and isinstance(self, StixFonts)):
                      return self._get_glyph('rm', font_class, sym, fontsize)
                  _log.warning("Font {!r} does not have a glyph for {!a} "
                               "[U+{:x}], substituting with a dummy "
                               "symbol.".format(new_fontname, sym, uniindex))
                  fontname = 'rm'
                  font = self._get_font(fontname)
                  uniindex = 0xA4  # currency char, for lack of anything better
                  glyphindex = font.get_char_index(uniindex)
                  slanted = False
  
          symbol_name = font.get_glyph_name(glyphindex)
          return font, uniindex, symbol_name, fontsize, slanted
  
      def get_sized_alternatives_for_symbol(self, fontname, sym):
          if self.cm_fallback:
              return self.cm_fallback.get_sized_alternatives_for_symbol(
                  fontname, sym)
          return [(fontname, sym)]
  
  
  class DejaVuFonts(UnicodeFonts):
      use_cmex = False  # Unused; delete once mathtext becomes private.
  
      def __init__(self, *args, **kwargs):
          # This must come first so the backend's owner is set correctly
          if isinstance(self, DejaVuSerifFonts):
              self.cm_fallback = StixFonts(*args, **kwargs)
          else:
              self.cm_fallback = StixSansFonts(*args, **kwargs)
          self.bakoma = BakomaFonts(*args, **kwargs)
          TruetypeFonts.__init__(self, *args, **kwargs)
          self.fontmap = {}
          # Include Stix sized alternatives for glyphs
          self._fontmap.update({
              1: 'STIXSizeOneSym',
              2: 'STIXSizeTwoSym',
              3: 'STIXSizeThreeSym',
              4: 'STIXSizeFourSym',
              5: 'STIXSizeFiveSym',
          })
          for key, name in self._fontmap.items():
              fullpath = findfont(name)
              self.fontmap[key] = fullpath
              self.fontmap[name] = fullpath
  
      def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
          # Override prime symbol to use Bakoma.
          if sym == r'\prime':
              return self.bakoma._get_glyph(
                  fontname, font_class, sym, fontsize, math)
          else:
              # check whether the glyph is available in the display font
              uniindex = get_unicode_index(sym)
              font = self._get_font('ex')
              if font is not None:
                  glyphindex = font.get_char_index(uniindex)
                  if glyphindex != 0:
                      return super()._get_glyph(
                          'ex', font_class, sym, fontsize, math)
              # otherwise return regular glyph
              return super()._get_glyph(
                  fontname, font_class, sym, fontsize, math)
  
  
  class DejaVuSerifFonts(DejaVuFonts):
      """
      A font handling class for the DejaVu Serif fonts
  
      If a glyph is not found it will fallback to Stix Serif
      """
      _fontmap = {
          'rm': 'DejaVu Serif',
          'it': 'DejaVu Serif:italic',
          'bf': 'DejaVu Serif:weight=bold',
          'sf': 'DejaVu Sans',
          'tt': 'DejaVu Sans Mono',
          'ex': 'DejaVu Serif Display',
          0:    'DejaVu Serif',
      }
  
  
  class DejaVuSansFonts(DejaVuFonts):
      """
      A font handling class for the DejaVu Sans fonts
  
      If a glyph is not found it will fallback to Stix Sans
      """
      _fontmap = {
          'rm': 'DejaVu Sans',
          'it': 'DejaVu Sans:italic',
          'bf': 'DejaVu Sans:weight=bold',
          'sf': 'DejaVu Sans',
          'tt': 'DejaVu Sans Mono',
          'ex': 'DejaVu Sans Display',
          0:    'DejaVu Sans',
      }
  
  
  class StixFonts(UnicodeFonts):
      """
      A font handling class for the STIX fonts.
  
      In addition to what UnicodeFonts provides, this class:
  
      - supports "virtual fonts" which are complete alpha numeric
        character sets with different font styles at special Unicode
        code points, such as "Blackboard".
  
      - handles sized alternative characters for the STIXSizeX fonts.
      """
      _fontmap = {
          'rm': 'STIXGeneral',
          'it': 'STIXGeneral:italic',
          'bf': 'STIXGeneral:weight=bold',
          'nonunirm': 'STIXNonUnicode',
          'nonuniit': 'STIXNonUnicode:italic',
          'nonunibf': 'STIXNonUnicode:weight=bold',
          0: 'STIXGeneral',
          1: 'STIXSizeOneSym',
          2: 'STIXSizeTwoSym',
          3: 'STIXSizeThreeSym',
          4: 'STIXSizeFourSym',
          5: 'STIXSizeFiveSym',
      }
      use_cmex = False  # Unused; delete once mathtext becomes private.
      cm_fallback = False
      _sans = False
  
      def __init__(self, *args, **kwargs):
          TruetypeFonts.__init__(self, *args, **kwargs)
          self.fontmap = {}
          for key, name in self._fontmap.items():
              fullpath = findfont(name)
              self.fontmap[key] = fullpath
              self.fontmap[name] = fullpath
  
      def _map_virtual_font(self, fontname, font_class, uniindex):
          # Handle these "fonts" that are actually embedded in
          # other fonts.
          mapping = stix_virtual_fonts.get(fontname)
          if (self._sans and mapping is None
                  and fontname not in ('regular', 'default')):
              mapping = stix_virtual_fonts['sf']
              doing_sans_conversion = True
          else:
              doing_sans_conversion = False
  
          if mapping is not None:
              if isinstance(mapping, dict):
                  try:
                      mapping = mapping[font_class]
                  except KeyError:
                      mapping = mapping['rm']
  
              # Binary search for the source glyph
              lo = 0
              hi = len(mapping)
              while lo < hi:
                  mid = (lo+hi)//2
                  range = mapping[mid]
                  if uniindex < range[0]:
                      hi = mid
                  elif uniindex <= range[1]:
                      break
                  else:
                      lo = mid + 1
  
              if range[0] <= uniindex <= range[1]:
                  uniindex = uniindex - range[0] + range[3]
                  fontname = range[2]
              elif not doing_sans_conversion:
                  # This will generate a dummy character
                  uniindex = 0x1
                  fontname = mpl.rcParams['mathtext.default']
  
          # Fix some incorrect glyphs.
          if fontname in ('rm', 'it'):
              uniindex = stix_glyph_fixes.get(uniindex, uniindex)
  
          # Handle private use area glyphs
          if fontname in ('it', 'rm', 'bf') and 0xe000 <= uniindex <= 0xf8ff:
              fontname = 'nonuni' + fontname
  
          return fontname, uniindex
  
      @functools.lru_cache()
      def get_sized_alternatives_for_symbol(self, fontname, sym):
          fixes = {
              '\\{': '{', '\\}': '}', '\\[': '[', '\\]': ']',
              '<': '\N{MATHEMATICAL LEFT ANGLE BRACKET}',
              '>': '\N{MATHEMATICAL RIGHT ANGLE BRACKET}',
          }
          sym = fixes.get(sym, sym)
          try:
              uniindex = get_unicode_index(sym)
          except ValueError:
              return [(fontname, sym)]
          alternatives = [(i, chr(uniindex)) for i in range(6)
                          if self._get_font(i).get_char_index(uniindex) != 0]
          # The largest size of the radical symbol in STIX has incorrect
          # metrics that cause it to be disconnected from the stem.
          if sym == r'\__sqrt__':
              alternatives = alternatives[:-1]
          return alternatives
  
  
  class StixSansFonts(StixFonts):
      """
      A font handling class for the STIX fonts (that uses sans-serif
      characters by default).
      """
      _sans = True
  
  
  class StandardPsFonts(Fonts):
      """
      Use the standard postscript fonts for rendering to backend_ps
  
      Unlike the other font classes, BakomaFont and UnicodeFont, this
      one requires the Ps backend.
      """
      basepath = str(cbook._get_data_path('fonts/afm'))
  
      fontmap = {
          'cal': 'pzcmi8a',  # Zapf Chancery
          'rm':  'pncr8a',   # New Century Schoolbook
          'tt':  'pcrr8a',   # Courier
          'it':  'pncri8a',  # New Century Schoolbook Italic
          'sf':  'phvr8a',   # Helvetica
          'bf':  'pncb8a',   # New Century Schoolbook Bold
          None:  'psyr',     # Symbol
      }
  
      def __init__(self, default_font_prop, mathtext_backend=None):
          if mathtext_backend is None:
              # Circular import, can be dropped after public access to
              # StandardPsFonts is removed and mathtext_backend made a required
              # parameter.
              from . import mathtext
              mathtext_backend = mathtext.MathtextBackendPath()
          super().__init__(default_font_prop, mathtext_backend)
          self.glyphd = {}
          self.fonts = {}
  
          filename = findfont(default_font_prop, fontext='afm',
                              directory=self.basepath)
          if filename is None:
              filename = findfont('Helvetica', fontext='afm',
                                  directory=self.basepath)
          with open(filename, 'rb') as fd:
              default_font = AFM(fd)
          default_font.fname = filename
  
          self.fonts['default'] = default_font
          self.fonts['regular'] = default_font
  
      pswriter = _api.deprecated("3.4")(property(lambda self: StringIO()))
  
      def _get_font(self, font):
          if font in self.fontmap:
              basename = self.fontmap[font]
          else:
              basename = font
  
          cached_font = self.fonts.get(basename)
          if cached_font is None:
              fname = os.path.join(self.basepath, basename + ".afm")
              with open(fname, 'rb') as fd:
                  cached_font = AFM(fd)
              cached_font.fname = fname
              self.fonts[basename] = cached_font
              self.fonts[cached_font.get_fontname()] = cached_font
          return cached_font
  
      def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
          """Load the cmfont, metrics and glyph with caching."""
          key = fontname, sym, fontsize, dpi
          tup = self.glyphd.get(key)
  
          if tup is not None:
              return tup
  
          # Only characters in the "Letter" class should really be italicized.
          # This class includes greek letters, so we're ok
          if (fontname == 'it' and
                  (len(sym) > 1
                   or not unicodedata.category(sym).startswith("L"))):
              fontname = 'rm'
  
          found_symbol = False
  
          if sym in latex_to_standard:
              fontname, num = latex_to_standard[sym]
              glyph = chr(num)
              found_symbol = True
          elif len(sym) == 1:
              glyph = sym
              num = ord(glyph)
              found_symbol = True
          else:
              _log.warning(
                  "No TeX to built-in Postscript mapping for {!r}".format(sym))
  
          slanted = (fontname == 'it')
          font = self._get_font(fontname)
  
          if found_symbol:
              try:
                  symbol_name = font.get_name_char(glyph)
              except KeyError:
                  _log.warning(
                      "No glyph in standard Postscript font {!r} for {!r}"
                      .format(font.get_fontname(), sym))
                  found_symbol = False
  
          if not found_symbol:
              glyph = '?'
              num = ord(glyph)
              symbol_name = font.get_name_char(glyph)
  
          offset = 0
  
          scale = 0.001 * fontsize
  
          xmin, ymin, xmax, ymax = [val * scale
                                    for val in font.get_bbox_char(glyph)]
          metrics = types.SimpleNamespace(
              advance  = font.get_width_char(glyph) * scale,
              width    = font.get_width_char(glyph) * scale,
              height   = font.get_height_char(glyph) * scale,
              xmin = xmin,
              xmax = xmax,
              ymin = ymin+offset,
              ymax = ymax+offset,
              # iceberg is the equivalent of TeX's "height"
              iceberg = ymax + offset,
              slanted = slanted
              )
  
          self.glyphd[key] = types.SimpleNamespace(
              font            = font,
              fontsize        = fontsize,
              postscript_name = font.get_fontname(),
              metrics         = metrics,
              symbol_name     = symbol_name,
              num             = num,
              glyph           = glyph,
              offset          = offset
              )
  
          return self.glyphd[key]
  
      def get_kern(self, font1, fontclass1, sym1, fontsize1,
                   font2, fontclass2, sym2, fontsize2, dpi):
          if font1 == font2 and fontsize1 == fontsize2:
              info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
              info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
              font = info1.font
              return (font.get_kern_dist(info1.glyph, info2.glyph)
                      * 0.001 * fontsize1)
          return super().get_kern(font1, fontclass1, sym1, fontsize1,
                                  font2, fontclass2, sym2, fontsize2, dpi)
  
      def get_xheight(self, font, fontsize, dpi):
          font = self._get_font(font)
          return font.get_xheight() * 0.001 * fontsize
  
      def get_underline_thickness(self, font, fontsize, dpi):
          font = self._get_font(font)
          return font.get_underline_thickness() * 0.001 * fontsize
  
  
  ##############################################################################
  # TeX-LIKE BOX MODEL
  
  # The following is based directly on the document 'woven' from the
  # TeX82 source code.  This information is also available in printed
  # form:
  #
  #    Knuth, Donald E.. 1986.  Computers and Typesetting, Volume B:
  #    TeX: The Program.  Addison-Wesley Professional.
  #
  # The most relevant "chapters" are:
  #    Data structures for boxes and their friends
  #    Shipping pages out (Ship class)
  #    Packaging (hpack and vpack)
  #    Data structures for math mode
  #    Subroutines for math mode
  #    Typesetting math formulas
  #
  # Many of the docstrings below refer to a numbered "node" in that
  # book, e.g., node123
  #
  # Note that (as TeX) y increases downward, unlike many other parts of
  # matplotlib.
  
  # How much text shrinks when going to the next-smallest level.  GROW_FACTOR
  # must be the inverse of SHRINK_FACTOR.
  SHRINK_FACTOR   = 0.7
  GROW_FACTOR     = 1 / SHRINK_FACTOR
  # The number of different sizes of chars to use, beyond which they will not
  # get any smaller
  NUM_SIZE_LEVELS = 6
  
  
  class FontConstantsBase:
      """
      A set of constants that controls how certain things, such as sub-
      and superscripts are laid out.  These are all metrics that can't
      be reliably retrieved from the font metrics in the font itself.
      """
      # Percentage of x-height of additional horiz. space after sub/superscripts
      script_space = 0.05
  
      # Percentage of x-height that sub/superscripts drop below the baseline
      subdrop = 0.4
  
      # Percentage of x-height that superscripts are raised from the baseline
      sup1 = 0.7
  
      # Percentage of x-height that subscripts drop below the baseline
      sub1 = 0.3
  
      # Percentage of x-height that subscripts drop below the baseline when a
      # superscript is present
      sub2 = 0.5
  
      # Percentage of x-height that sub/supercripts are offset relative to the
      # nucleus edge for non-slanted nuclei
      delta = 0.025
  
      # Additional percentage of last character height above 2/3 of the
      # x-height that supercripts are offset relative to the subscript
      # for slanted nuclei
      delta_slanted = 0.2
  
      # Percentage of x-height that supercripts and subscripts are offset for
      # integrals
      delta_integral = 0.1
  
  
  class ComputerModernFontConstants(FontConstantsBase):
      script_space = 0.075
      subdrop = 0.2
      sup1 = 0.45
      sub1 = 0.2
      sub2 = 0.3
      delta = 0.075
      delta_slanted = 0.3
      delta_integral = 0.3
  
  
  class STIXFontConstants(FontConstantsBase):
      script_space = 0.1
      sup1 = 0.8
      sub2 = 0.6
      delta = 0.05
      delta_slanted = 0.3
      delta_integral = 0.3
  
  
  class STIXSansFontConstants(FontConstantsBase):
      script_space = 0.05
      sup1 = 0.8
      delta_slanted = 0.6
      delta_integral = 0.3
  
  
  class DejaVuSerifFontConstants(FontConstantsBase):
      pass
  
  
  class DejaVuSansFontConstants(FontConstantsBase):
      pass
  
  
  # Maps font family names to the FontConstantBase subclass to use
  _font_constant_mapping = {
      'DejaVu Sans': DejaVuSansFontConstants,
      'DejaVu Sans Mono': DejaVuSansFontConstants,
      'DejaVu Serif': DejaVuSerifFontConstants,
      'cmb10': ComputerModernFontConstants,
      'cmex10': ComputerModernFontConstants,
      'cmmi10': ComputerModernFontConstants,
      'cmr10': ComputerModernFontConstants,
      'cmss10': ComputerModernFontConstants,
      'cmsy10': ComputerModernFontConstants,
      'cmtt10': ComputerModernFontConstants,
      'STIXGeneral': STIXFontConstants,
      'STIXNonUnicode': STIXFontConstants,
      'STIXSizeFiveSym': STIXFontConstants,
      'STIXSizeFourSym': STIXFontConstants,
      'STIXSizeThreeSym': STIXFontConstants,
      'STIXSizeTwoSym': STIXFontConstants,
      'STIXSizeOneSym': STIXFontConstants,
      # Map the fonts we used to ship, just for good measure
      'Bitstream Vera Sans': DejaVuSansFontConstants,
      'Bitstream Vera': DejaVuSansFontConstants,
      }
  
  
  def _get_font_constant_set(state):
      constants = _font_constant_mapping.get(
          state.font_output._get_font(state.font).family_name,
          FontConstantsBase)
      # STIX sans isn't really its own fonts, just different code points
      # in the STIX fonts, so we have to detect this one separately.
      if (constants is STIXFontConstants and
              isinstance(state.font_output, StixSansFonts)):
          return STIXSansFontConstants
      return constants
  
  
  class Node:
      """A node in the TeX box model."""
  
      def __init__(self):
          self.size = 0
  
      def __repr__(self):
          return self.__class__.__name__
  
      def get_kerning(self, next):
          return 0.0
  
      def shrink(self):
          """
          Shrinks one level smaller.  There are only three levels of
          sizes, after which things will no longer get smaller.
          """
          self.size += 1
  
      def grow(self):
          """
          Grows one level larger.  There is no limit to how big
          something can get.
          """
          self.size -= 1
  
      def render(self, x, y):
          pass
  
  
  class Box(Node):
      """A node with a physical location."""
  
      def __init__(self, width, height, depth):
          super().__init__()
          self.width  = width
          self.height = height
          self.depth  = depth
  
      def shrink(self):
          super().shrink()
          if self.size < NUM_SIZE_LEVELS:
              self.width  *= SHRINK_FACTOR
              self.height *= SHRINK_FACTOR
              self.depth  *= SHRINK_FACTOR
  
      def grow(self):
          super().grow()
          self.width  *= GROW_FACTOR
          self.height *= GROW_FACTOR
          self.depth  *= GROW_FACTOR
  
      def render(self, x1, y1, x2, y2):
          pass
  
  
  class Vbox(Box):
      """A box with only height (zero width)."""
  
      def __init__(self, height, depth):
          super().__init__(0., height, depth)
  
  
  class Hbox(Box):
      """A box with only width (zero height and depth)."""
  
      def __init__(self, width):
          super().__init__(width, 0., 0.)
  
  
  class Char(Node):
      """
      A single character.
  
      Unlike TeX, the font information and metrics are stored with each `Char`
      to make it easier to lookup the font metrics when needed.  Note that TeX
      boxes have a width, height, and depth, unlike Type1 and TrueType which use
      a full bounding box and an advance in the x-direction.  The metrics must
      be converted to the TeX model, and the advance (if different from width)
      must be converted into a `Kern` node when the `Char` is added to its parent
      `Hlist`.
      """
  
      def __init__(self, c, state, math=True):
          super().__init__()
          self.c = c
          self.font_output = state.font_output
          self.font = state.font
          self.font_class = state.font_class
          self.fontsize = state.fontsize
          self.dpi = state.dpi
          self.math = math
          # The real width, height and depth will be set during the
          # pack phase, after we know the real fontsize
          self._update_metrics()
  
      def __repr__(self):
          return '`%s`' % self.c
  
      def _update_metrics(self):
          metrics = self._metrics = self.font_output.get_metrics(
              self.font, self.font_class, self.c, self.fontsize, self.dpi,
              self.math)
          if self.c == ' ':
              self.width = metrics.advance
          else:
              self.width = metrics.width
          self.height = metrics.iceberg
          self.depth = -(metrics.iceberg - metrics.height)
  
      def is_slanted(self):
          return self._metrics.slanted
  
      def get_kerning(self, next):
          """
          Return the amount of kerning between this and the given character.
  
          This method is called when characters are strung together into `Hlist`
          to create `Kern` nodes.
          """
          advance = self._metrics.advance - self.width
          kern = 0.
          if isinstance(next, Char):
              kern = self.font_output.get_kern(
                  self.font, self.font_class, self.c, self.fontsize,
                  next.font, next.font_class, next.c, next.fontsize,
                  self.dpi)
          return advance + kern
  
      def render(self, x, y):
          """
          Render the character to the canvas
          """
          self.font_output.render_glyph(
              x, y,
              self.font, self.font_class, self.c, self.fontsize, self.dpi)
  
      def shrink(self):
          super().shrink()
          if self.size < NUM_SIZE_LEVELS:
              self.fontsize *= SHRINK_FACTOR
              self.width    *= SHRINK_FACTOR
              self.height   *= SHRINK_FACTOR
              self.depth    *= SHRINK_FACTOR
  
      def grow(self):
          super().grow()
          self.fontsize *= GROW_FACTOR
          self.width    *= GROW_FACTOR
          self.height   *= GROW_FACTOR
          self.depth    *= GROW_FACTOR
  
  
  class Accent(Char):
      """
      The font metrics need to be dealt with differently for accents,
      since they are already offset correctly from the baseline in
      TrueType fonts.
      """
      def _update_metrics(self):
          metrics = self._metrics = self.font_output.get_metrics(
              self.font, self.font_class, self.c, self.fontsize, self.dpi)
          self.width = metrics.xmax - metrics.xmin
          self.height = metrics.ymax - metrics.ymin
          self.depth = 0
  
      def shrink(self):
          super().shrink()
          self._update_metrics()
  
      def grow(self):
          super().grow()
          self._update_metrics()
  
      def render(self, x, y):
          """
          Render the character to the canvas.
          """
          self.font_output.render_glyph(
              x - self._metrics.xmin, y + self._metrics.ymin,
              self.font, self.font_class, self.c, self.fontsize, self.dpi)
  
  
  class List(Box):
      """A list of nodes (either horizontal or vertical)."""
  
      def __init__(self, elements):
          super().__init__(0., 0., 0.)
          self.shift_amount = 0.   # An arbitrary offset
          self.children     = elements  # The child nodes of this list
          # The following parameters are set in the vpack and hpack functions
          self.glue_set     = 0.   # The glue setting of this list
          self.glue_sign    = 0    # 0: normal, -1: shrinking, 1: stretching
          self.glue_order   = 0    # The order of infinity (0 - 3) for the glue
  
      def __repr__(self):
          return '[%s <%.02f %.02f %.02f %.02f> %s]' % (
              super().__repr__(),
              self.width, self.height,
              self.depth, self.shift_amount,
              ' '.join([repr(x) for x in self.children]))
  
      @staticmethod
      def _determine_order(totals):
          """
          Determine the highest order of glue used by the members of this list.
  
          Helper function used by vpack and hpack.
          """
          for i in range(len(totals))[::-1]:
              if totals[i] != 0:
                  return i
          return 0
  
      def _set_glue(self, x, sign, totals, error_type):
          o = self._determine_order(totals)
          self.glue_order = o
          self.glue_sign = sign
          if totals[o] != 0.:
              self.glue_set = x / totals[o]
          else:
              self.glue_sign = 0
              self.glue_ratio = 0.
          if o == 0:
              if len(self.children):
                  _log.warning("%s %s: %r",
                               error_type, self.__class__.__name__, self)
  
      def shrink(self):
          for child in self.children:
              child.shrink()
          super().shrink()
          if self.size < NUM_SIZE_LEVELS:
              self.shift_amount *= SHRINK_FACTOR
              self.glue_set     *= SHRINK_FACTOR
  
      def grow(self):
          for child in self.children:
              child.grow()
          super().grow()
          self.shift_amount *= GROW_FACTOR
          self.glue_set     *= GROW_FACTOR
  
  
  class Hlist(List):
      """A horizontal list of boxes."""
  
      def __init__(self, elements, w=0., m='additional', do_kern=True):
          super().__init__(elements)
          if do_kern:
              self.kern()
          self.hpack()
  
      def kern(self):
          """
          Insert `Kern` nodes between `Char` nodes to set kerning.
  
          The `Char` nodes themselves determine the amount of kerning they need
          (in `~Char.get_kerning`), and this function just creates the correct
          linked list.
          """
          new_children = []
          num_children = len(self.children)
          if num_children:
              for i in range(num_children):
                  elem = self.children[i]
                  if i < num_children - 1:
                      next = self.children[i + 1]
                  else:
                      next = None
  
                  new_children.append(elem)
                  kerning_distance = elem.get_kerning(next)
                  if kerning_distance != 0.:
                      kern = Kern(kerning_distance)
                      new_children.append(kern)
              self.children = new_children
  
      # This is a failed experiment to fake cross-font kerning.
  #     def get_kerning(self, next):
  #         if len(self.children) >= 2 and isinstance(self.children[-2], Char):
  #             if isinstance(next, Char):
  #                 print "CASE A"
  #                 return self.children[-2].get_kerning(next)
  #             elif (isinstance(next, Hlist) and len(next.children)
  #                   and isinstance(next.children[0], Char)):
  #                 print "CASE B"
  #                 result = self.children[-2].get_kerning(next.children[0])
  #                 print result
  #                 return result
  #         return 0.0
  
      def hpack(self, w=0., m='additional'):
          r"""
          Compute the dimensions of the resulting boxes, and adjust the glue if
          one of those dimensions is pre-specified.  The computed sizes normally
          enclose all of the material inside the new box; but some items may
          stick out if negative glue is used, if the box is overfull, or if a
          ``\vbox`` includes other boxes that have been shifted left.
  
          Parameters
          ----------
          w : float, default: 0
              A width.
          m : {'exactly', 'additional'}, default: 'additional'
              Whether to produce a box whose width is 'exactly' *w*; or a box
              with the natural width of the contents, plus *w* ('additional').
  
          Notes
          -----
          The defaults produce a box with the natural width of the contents.
          """
          # I don't know why these get reset in TeX.  Shift_amount is pretty
          # much useless if we do.
          # self.shift_amount = 0.
          h = 0.
          d = 0.
          x = 0.
          total_stretch = [0.] * 4
          total_shrink = [0.] * 4
          for p in self.children:
              if isinstance(p, Char):
                  x += p.width
                  h = max(h, p.height)
                  d = max(d, p.depth)
              elif isinstance(p, Box):
                  x += p.width
                  if not np.isinf(p.height) and not np.isinf(p.depth):
                      s = getattr(p, 'shift_amount', 0.)
                      h = max(h, p.height - s)
                      d = max(d, p.depth + s)
              elif isinstance(p, Glue):
                  glue_spec = p.glue_spec
                  x += glue_spec.width
                  total_stretch[glue_spec.stretch_order] += glue_spec.stretch
                  total_shrink[glue_spec.shrink_order] += glue_spec.shrink
              elif isinstance(p, Kern):
                  x += p.width
          self.height = h
          self.depth = d
  
          if m == 'additional':
              w += x
          self.width = w
          x = w - x
  
          if x == 0.:
              self.glue_sign = 0
              self.glue_order = 0
              self.glue_ratio = 0.
              return
          if x > 0.:
              self._set_glue(x, 1, total_stretch, "Overfull")
          else:
              self._set_glue(x, -1, total_shrink, "Underfull")
  
  
  class Vlist(List):
      """A vertical list of boxes."""
  
      def __init__(self, elements, h=0., m='additional'):
          super().__init__(elements)
          self.vpack()
  
      def vpack(self, h=0., m='additional', l=np.inf):
          """
          Compute the dimensions of the resulting boxes, and to adjust the glue
          if one of those dimensions is pre-specified.
  
          Parameters
          ----------
          h : float, default: 0
              A height.
          m : {'exactly', 'additional'}, default: 'additional'
              Whether to produce a box whose height is 'exactly' *w*; or a box
              with the natural height of the contents, plus *w* ('additional').
          l : float, default: np.inf
              The maximum height.
  
          Notes
          -----
          The defaults produce a box with the natural height of the contents.
          """
          # I don't know why these get reset in TeX.  Shift_amount is pretty
          # much useless if we do.
          # self.shift_amount = 0.
          w = 0.
          d = 0.
          x = 0.
          total_stretch = [0.] * 4
          total_shrink = [0.] * 4
          for p in self.children:
              if isinstance(p, Box):
                  x += d + p.height
                  d = p.depth
                  if not np.isinf(p.width):
                      s = getattr(p, 'shift_amount', 0.)
                      w = max(w, p.width + s)
              elif isinstance(p, Glue):
                  x += d
                  d = 0.
                  glue_spec = p.glue_spec
                  x += glue_spec.width
                  total_stretch[glue_spec.stretch_order] += glue_spec.stretch
                  total_shrink[glue_spec.shrink_order] += glue_spec.shrink
              elif isinstance(p, Kern):
                  x += d + p.width
                  d = 0.
              elif isinstance(p, Char):
                  raise RuntimeError(
                      "Internal mathtext error: Char node found in Vlist")
  
          self.width = w
          if d > l:
              x += d - l
              self.depth = l
          else:
              self.depth = d
  
          if m == 'additional':
              h += x
          self.height = h
          x = h - x
  
          if x == 0:
              self.glue_sign = 0
              self.glue_order = 0
              self.glue_ratio = 0.
              return
  
          if x > 0.:
              self._set_glue(x, 1, total_stretch, "Overfull")
          else:
              self._set_glue(x, -1, total_shrink, "Underfull")
  
  
  class Rule(Box):
      """
      A solid black rectangle.
  
      It has *width*, *depth*, and *height* fields just as in an `Hlist`.
      However, if any of these dimensions is inf, the actual value will be
      determined by running the rule up to the boundary of the innermost
      enclosing box.  This is called a "running dimension".  The width is never
      running in an `Hlist`; the height and depth are never running in a `Vlist`.
      """
  
      def __init__(self, width, height, depth, state):
          super().__init__(width, height, depth)
          self.font_output = state.font_output
  
      def render(self, x, y, w, h):
          self.font_output.render_rect_filled(x, y, x + w, y + h)
  
  
  class Hrule(Rule):
      """Convenience class to create a horizontal rule."""
  
      def __init__(self, state, thickness=None):
          if thickness is None:
              thickness = state.font_output.get_underline_thickness(
                  state.font, state.fontsize, state.dpi)
          height = depth = thickness * 0.5
          super().__init__(np.inf, height, depth, state)
  
  
  class Vrule(Rule):
      """Convenience class to create a vertical rule."""
  
      def __init__(self, state):
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
          super().__init__(thickness, np.inf, np.inf, state)
  
  
  _GlueSpec = namedtuple(
      "_GlueSpec", "width stretch stretch_order shrink shrink_order")
  _GlueSpec._named = {
      'fil':         _GlueSpec(0., 1., 1, 0., 0),
      'fill':        _GlueSpec(0., 1., 2, 0., 0),
      'filll':       _GlueSpec(0., 1., 3, 0., 0),
      'neg_fil':     _GlueSpec(0., 0., 0, 1., 1),
      'neg_fill':    _GlueSpec(0., 0., 0, 1., 2),
      'neg_filll':   _GlueSpec(0., 0., 0, 1., 3),
      'empty':       _GlueSpec(0., 0., 0, 0., 0),
      'ss':          _GlueSpec(0., 1., 1, -1., 1),
  }
  
  
  class Glue(Node):
      """
      Most of the information in this object is stored in the underlying
      ``_GlueSpec`` class, which is shared between multiple glue objects.
      (This is a memory optimization which probably doesn't matter anymore, but
      it's easier to stick to what TeX does.)
      """
  
      def __init__(self, glue_type):
          super().__init__()
          if isinstance(glue_type, str):
              glue_spec = _GlueSpec._named[glue_type]
          elif isinstance(glue_type, _GlueSpec):
              glue_spec = glue_type
          else:
              raise ValueError("glue_type must be a glue spec name or instance")
          self.glue_spec = glue_spec
  
      def shrink(self):
          super().shrink()
          if self.size < NUM_SIZE_LEVELS:
              g = self.glue_spec
              self.glue_spec = g._replace(width=g.width * SHRINK_FACTOR)
  
      def grow(self):
          super().grow()
          g = self.glue_spec
          self.glue_spec = g._replace(width=g.width * GROW_FACTOR)
  
  
  class HCentered(Hlist):
      """
      A convenience class to create an `Hlist` whose contents are
      centered within its enclosing box.
      """
  
      def __init__(self, elements):
          super().__init__([Glue('ss'), *elements, Glue('ss')], do_kern=False)
  
  
  class VCentered(Vlist):
      """
      A convenience class to create a `Vlist` whose contents are
      centered within its enclosing box.
      """
  
      def __init__(self, elements):
          super().__init__([Glue('ss'), *elements, Glue('ss')])
  
  
  class Kern(Node):
      """
      A `Kern` node has a width field to specify a (normally
      negative) amount of spacing. This spacing correction appears in
      horizontal lists between letters like A and V when the font
      designer said that it looks better to move them closer together or
      further apart. A kern node can also appear in a vertical list,
      when its *width* denotes additional spacing in the vertical
      direction.
      """
  
      height = 0
      depth = 0
  
      def __init__(self, width):
          super().__init__()
          self.width = width
  
      def __repr__(self):
          return "k%.02f" % self.width
  
      def shrink(self):
          super().shrink()
          if self.size < NUM_SIZE_LEVELS:
              self.width *= SHRINK_FACTOR
  
      def grow(self):
          super().grow()
          self.width *= GROW_FACTOR
  
  
  class SubSuperCluster(Hlist):
      """
      A hack to get around that fact that this code does a two-pass parse like
      TeX.  This lets us store enough information in the hlist itself, namely the
      nucleus, sub- and super-script, such that if another script follows that
      needs to be attached, it can be reconfigured on the fly.
      """
  
      def __init__(self):
          self.nucleus = None
          self.sub = None
          self.super = None
          super().__init__([])
  
  
  class AutoHeightChar(Hlist):
      """
      A character as close to the given height and depth as possible.
  
      When using a font with multiple height versions of some characters (such as
      the BaKoMa fonts), the correct glyph will be selected, otherwise this will
      always just return a scaled version of the glyph.
      """
  
      def __init__(self, c, height, depth, state, always=False, factor=None):
          alternatives = state.font_output.get_sized_alternatives_for_symbol(
              state.font, c)
  
          xHeight = state.font_output.get_xheight(
              state.font, state.fontsize, state.dpi)
  
          state = state.copy()
          target_total = height + depth
          for fontname, sym in alternatives:
              state.font = fontname
              char = Char(sym, state)
              # Ensure that size 0 is chosen when the text is regular sized but
              # with descender glyphs by subtracting 0.2 * xHeight
              if char.height + char.depth >= target_total - 0.2 * xHeight:
                  break
  
          shift = 0
          if state.font != 0:
              if factor is None:
                  factor = target_total / (char.height + char.depth)
              state.fontsize *= factor
              char = Char(sym, state)
  
              shift = (depth - char.depth)
  
          super().__init__([char])
          self.shift_amount = shift
  
  
  class AutoWidthChar(Hlist):
      """
      A character as close to the given width as possible.
  
      When using a font with multiple width versions of some characters (such as
      the BaKoMa fonts), the correct glyph will be selected, otherwise this will
      always just return a scaled version of the glyph.
      """
  
      def __init__(self, c, width, state, always=False, char_class=Char):
          alternatives = state.font_output.get_sized_alternatives_for_symbol(
              state.font, c)
  
          state = state.copy()
          for fontname, sym in alternatives:
              state.font = fontname
              char = char_class(sym, state)
              if char.width >= width:
                  break
  
          factor = width / char.width
          state.fontsize *= factor
          char = char_class(sym, state)
  
          super().__init__([char])
          self.width = char.width
  
  
  class Ship:
      """
      Ship boxes to output once they have been set up, this sends them to output.
  
      Since boxes can be inside of boxes inside of boxes, the main work of `Ship`
      is done by two mutually recursive routines, `hlist_out` and `vlist_out`,
      which traverse the `Hlist` nodes and `Vlist` nodes inside of horizontal
      and vertical boxes.  The global variables used in TeX to store state as it
      processes have become member variables here.
      """
  
      def __call__(self, ox, oy, box):
          self.max_push    = 0  # Deepest nesting of push commands so far
          self.cur_s       = 0
          self.cur_v       = 0.
          self.cur_h       = 0.
          self.off_h       = ox
          self.off_v       = oy + box.height
          self.hlist_out(box)
  
      @staticmethod
      def clamp(value):
          if value < -1000000000.:
              return -1000000000.
          if value > 1000000000.:
              return 1000000000.
          return value
  
      def hlist_out(self, box):
          cur_g         = 0
          cur_glue      = 0.
          glue_order    = box.glue_order
          glue_sign     = box.glue_sign
          base_line     = self.cur_v
          left_edge     = self.cur_h
          self.cur_s    += 1
          self.max_push = max(self.cur_s, self.max_push)
          clamp         = self.clamp
  
          for p in box.children:
              if isinstance(p, Char):
                  p.render(self.cur_h + self.off_h, self.cur_v + self.off_v)
                  self.cur_h += p.width
              elif isinstance(p, Kern):
                  self.cur_h += p.width
              elif isinstance(p, List):
                  # node623
                  if len(p.children) == 0:
                      self.cur_h += p.width
                  else:
                      edge = self.cur_h
                      self.cur_v = base_line + p.shift_amount
                      if isinstance(p, Hlist):
                          self.hlist_out(p)
                      else:
                          # p.vpack(box.height + box.depth, 'exactly')
                          self.vlist_out(p)
                      self.cur_h = edge + p.width
                      self.cur_v = base_line
              elif isinstance(p, Box):
                  # node624
                  rule_height = p.height
                  rule_depth  = p.depth
                  rule_width  = p.width
                  if np.isinf(rule_height):
                      rule_height = box.height
                  if np.isinf(rule_depth):
                      rule_depth = box.depth
                  if rule_height > 0 and rule_width > 0:
                      self.cur_v = base_line + rule_depth
                      p.render(self.cur_h + self.off_h,
                               self.cur_v + self.off_v,
                               rule_width, rule_height)
                      self.cur_v = base_line
                  self.cur_h += rule_width
              elif isinstance(p, Glue):
                  # node625
                  glue_spec = p.glue_spec
                  rule_width = glue_spec.width - cur_g
                  if glue_sign != 0:  # normal
                      if glue_sign == 1:  # stretching
                          if glue_spec.stretch_order == glue_order:
                              cur_glue += glue_spec.stretch
                              cur_g = round(clamp(box.glue_set * cur_glue))
                      elif glue_spec.shrink_order == glue_order:
                          cur_glue += glue_spec.shrink
                          cur_g = round(clamp(box.glue_set * cur_glue))
                  rule_width += cur_g
                  self.cur_h += rule_width
          self.cur_s -= 1
  
      def vlist_out(self, box):
          cur_g         = 0
          cur_glue      = 0.
          glue_order    = box.glue_order
          glue_sign     = box.glue_sign
          self.cur_s    += 1
          self.max_push = max(self.max_push, self.cur_s)
          left_edge     = self.cur_h
          self.cur_v    -= box.height
          top_edge      = self.cur_v
          clamp         = self.clamp
  
          for p in box.children:
              if isinstance(p, Kern):
                  self.cur_v += p.width
              elif isinstance(p, List):
                  if len(p.children) == 0:
                      self.cur_v += p.height + p.depth
                  else:
                      self.cur_v += p.height
                      self.cur_h = left_edge + p.shift_amount
                      save_v = self.cur_v
                      p.width = box.width
                      if isinstance(p, Hlist):
                          self.hlist_out(p)
                      else:
                          self.vlist_out(p)
                      self.cur_v = save_v + p.depth
                      self.cur_h = left_edge
              elif isinstance(p, Box):
                  rule_height = p.height
                  rule_depth = p.depth
                  rule_width = p.width
                  if np.isinf(rule_width):
                      rule_width = box.width
                  rule_height += rule_depth
                  if rule_height > 0 and rule_depth > 0:
                      self.cur_v += rule_height
                      p.render(self.cur_h + self.off_h,
                               self.cur_v + self.off_v,
                               rule_width, rule_height)
              elif isinstance(p, Glue):
                  glue_spec = p.glue_spec
                  rule_height = glue_spec.width - cur_g
                  if glue_sign != 0:  # normal
                      if glue_sign == 1:  # stretching
                          if glue_spec.stretch_order == glue_order:
                              cur_glue += glue_spec.stretch
                              cur_g = round(clamp(box.glue_set * cur_glue))
                      elif glue_spec.shrink_order == glue_order:  # shrinking
                          cur_glue += glue_spec.shrink
                          cur_g = round(clamp(box.glue_set * cur_glue))
                  rule_height += cur_g
                  self.cur_v += rule_height
              elif isinstance(p, Char):
                  raise RuntimeError(
                      "Internal mathtext error: Char node found in vlist")
          self.cur_s -= 1
  
  
  ship = Ship()
  
  
  ##############################################################################
  # PARSER
  
  
  def Error(msg):
      """Helper class to raise parser errors."""
      def raise_error(s, loc, toks):
          raise ParseFatalException(s, loc, msg)
  
      empty = Empty()
      empty.setParseAction(raise_error)
      return empty
  
  
  class Parser:
      """
      A pyparsing-based parser for strings containing math expressions.
  
      Raw text may also appear outside of pairs of ``$``.
  
      The grammar is based directly on that in TeX, though it cuts a few corners.
      """
  
      class _MathStyle(enum.Enum):
          DISPLAYSTYLE = enum.auto()
          TEXTSTYLE = enum.auto()
          SCRIPTSTYLE = enum.auto()
          SCRIPTSCRIPTSTYLE = enum.auto()
  
      _binary_operators = set('''
        + * -
        \\pm             \\sqcap                   \\rhd
        \\mp             \\sqcup                   \\unlhd
        \\times          \\vee                     \\unrhd
        \\div            \\wedge                   \\oplus
        \\ast            \\setminus                \\ominus
        \\star           \\wr                      \\otimes
        \\circ           \\diamond                 \\oslash
        \\bullet         \\bigtriangleup           \\odot
        \\cdot           \\bigtriangledown         \\bigcirc
        \\cap            \\triangleleft            \\dagger
        \\cup            \\triangleright           \\ddagger
        \\uplus          \\lhd                     \\amalg'''.split())
  
      _relation_symbols = set('''
        = < > :
        \\leq        \\geq        \\equiv   \\models
        \\prec       \\succ       \\sim     \\perp
        \\preceq     \\succeq     \\simeq   \\mid
        \\ll         \\gg         \\asymp   \\parallel
        \\subset     \\supset     \\approx  \\bowtie
        \\subseteq   \\supseteq   \\cong    \\Join
        \\sqsubset   \\sqsupset   \\neq     \\smile
        \\sqsubseteq \\sqsupseteq \\doteq   \\frown
        \\in         \\ni         \\propto  \\vdash
        \\dashv      \\dots       \\dotplus \\doteqdot'''.split())
  
      _arrow_symbols = set('''
        \\leftarrow              \\longleftarrow           \\uparrow
        \\Leftarrow              \\Longleftarrow           \\Uparrow
        \\rightarrow             \\longrightarrow          \\downarrow
        \\Rightarrow             \\Longrightarrow          \\Downarrow
        \\leftrightarrow         \\longleftrightarrow      \\updownarrow
        \\Leftrightarrow         \\Longleftrightarrow      \\Updownarrow
        \\mapsto                 \\longmapsto              \\nearrow
        \\hookleftarrow          \\hookrightarrow          \\searrow
        \\leftharpoonup          \\rightharpoonup          \\swarrow
        \\leftharpoondown        \\rightharpoondown        \\nwarrow
        \\rightleftharpoons      \\leadsto'''.split())
  
      _spaced_symbols = _binary_operators | _relation_symbols | _arrow_symbols
  
      _punctuation_symbols = set(r', ; . ! \ldotp \cdotp'.split())
  
      _overunder_symbols = set(r'''
         \sum \prod \coprod \bigcap \bigcup \bigsqcup \bigvee
         \bigwedge \bigodot \bigotimes \bigoplus \biguplus
         '''.split())
  
      _overunder_functions = set(
          "lim liminf limsup sup max min".split())
  
      _dropsub_symbols = set(r'''\int \oint'''.split())
  
      _fontnames = set("rm cal it tt sf bf default bb frak scr regular".split())
  
      _function_names = set("""
        arccos csc ker min arcsin deg lg Pr arctan det lim sec arg dim
        liminf sin cos exp limsup sinh cosh gcd ln sup cot hom log tan
        coth inf max tanh""".split())
  
      _ambi_delim = set("""
        | \\| / \\backslash \\uparrow \\downarrow \\updownarrow \\Uparrow
        \\Downarrow \\Updownarrow . \\vert \\Vert \\\\|""".split())
  
      _left_delim = set(r"( [ \{ < \lfloor \langle \lceil".split())
  
      _right_delim = set(r") ] \} > \rfloor \rangle \rceil".split())
  
      def __init__(self):
          p = types.SimpleNamespace()
          # All forward declarations are here
          p.accent           = Forward()
          p.ambi_delim       = Forward()
          p.apostrophe       = Forward()
          p.auto_delim       = Forward()
          p.binom            = Forward()
          p.bslash           = Forward()
          p.c_over_c         = Forward()
          p.customspace      = Forward()
          p.end_group        = Forward()
          p.float_literal    = Forward()
          p.font             = Forward()
          p.frac             = Forward()
          p.dfrac            = Forward()
          p.function         = Forward()
          p.genfrac          = Forward()
          p.group            = Forward()
          p.int_literal      = Forward()
          p.latexfont        = Forward()
          p.lbracket         = Forward()
          p.left_delim       = Forward()
          p.lbrace           = Forward()
          p.main             = Forward()
          p.math             = Forward()
          p.math_string      = Forward()
          p.non_math         = Forward()
          p.operatorname     = Forward()
          p.overline         = Forward()
          p.overset          = Forward()
          p.placeable        = Forward()
          p.rbrace           = Forward()
          p.rbracket         = Forward()
          p.required_group   = Forward()
          p.right_delim      = Forward()
          p.right_delim_safe = Forward()
          p.simple           = Forward()
          p.simple_group     = Forward()
          p.single_symbol    = Forward()
          p.accentprefixed   = Forward()
          p.space            = Forward()
          p.sqrt             = Forward()
          p.start_group      = Forward()
          p.subsuper         = Forward()
          p.subsuperop       = Forward()
          p.symbol           = Forward()
          p.symbol_name      = Forward()
          p.token            = Forward()
          p.underset         = Forward()
          p.unknown_symbol   = Forward()
  
          # Set names on everything -- very useful for debugging
          for key, val in vars(p).items():
              if not key.startswith('_'):
                  val.setName(key)
  
          p.float_literal <<= Regex(r"[-+]?([0-9]+\.?[0-9]*|\.[0-9]+)")
          p.int_literal   <<= Regex("[-+]?[0-9]+")
  
          p.lbrace        <<= Literal('{').suppress()
          p.rbrace        <<= Literal('}').suppress()
          p.lbracket      <<= Literal('[').suppress()
          p.rbracket      <<= Literal(']').suppress()
          p.bslash        <<= Literal('\\')
  
          p.space         <<= oneOf(list(self._space_widths))
          p.customspace   <<= (
              Suppress(Literal(r'\hspace'))
              - ((p.lbrace + p.float_literal + p.rbrace)
                 | Error(r"Expected \hspace{n}"))
          )
  
          unicode_range = "\U00000080-\U0001ffff"
          p.single_symbol <<= Regex(
              r"([a-zA-Z0-9 +\-*/<>=:,.;!\?&'@()\[\]|%s])|(\\[%%${}\[\]_|])" %
              unicode_range)
          p.accentprefixed <<= Suppress(p.bslash) + oneOf(self._accentprefixed)
          p.symbol_name   <<= (
              Combine(p.bslash + oneOf(list(tex2uni)))
              + Suppress(Regex("(?=[^A-Za-z]|$)").leaveWhitespace())
          )
          p.symbol        <<= (p.single_symbol | p.symbol_name).leaveWhitespace()
  
          p.apostrophe    <<= Regex("'+")
  
          p.c_over_c      <<= (
              Suppress(p.bslash)
              + oneOf(list(self._char_over_chars))
          )
  
          p.accent        <<= Group(
              Suppress(p.bslash)
              + oneOf([*self._accent_map, *self._wide_accents])
              + Suppress(Optional(White()))
              - p.placeable
          )
  
          p.function      <<= (
              Suppress(p.bslash)
              + oneOf(list(self._function_names))
          )
  
          p.start_group    <<= Optional(p.latexfont) + p.lbrace
          p.end_group      <<= p.rbrace.copy()
          p.simple_group   <<= Group(p.lbrace + ZeroOrMore(p.token) + p.rbrace)
          p.required_group <<= Group(p.lbrace + OneOrMore(p.token) + p.rbrace)
          p.group          <<= Group(
              p.start_group + ZeroOrMore(p.token) + p.end_group
          )
  
          p.font          <<= Suppress(p.bslash) + oneOf(list(self._fontnames))
          p.latexfont     <<= (
              Suppress(p.bslash)
              + oneOf(['math' + x for x in self._fontnames])
          )
  
          p.frac          <<= Group(
              Suppress(Literal(r"\frac"))
              - ((p.required_group + p.required_group)
                 | Error(r"Expected \frac{num}{den}"))
          )
  
          p.dfrac         <<= Group(
              Suppress(Literal(r"\dfrac"))
              - ((p.required_group + p.required_group)
                 | Error(r"Expected \dfrac{num}{den}"))
          )
  
          p.binom         <<= Group(
              Suppress(Literal(r"\binom"))
              - ((p.required_group + p.required_group)
                 | Error(r"Expected \binom{num}{den}"))
          )
  
          p.ambi_delim    <<= oneOf(list(self._ambi_delim))
          p.left_delim    <<= oneOf(list(self._left_delim))
          p.right_delim   <<= oneOf(list(self._right_delim))
          p.right_delim_safe <<= oneOf([*(self._right_delim - {'}'}), r'\}'])
  
          p.genfrac <<= Group(
              Suppress(Literal(r"\genfrac"))
              - (((p.lbrace
                   + Optional(p.ambi_delim | p.left_delim, default='')
                   + p.rbrace)
                  + (p.lbrace
                     + Optional(p.ambi_delim | p.right_delim_safe, default='')
                     + p.rbrace)
                  + (p.lbrace + p.float_literal + p.rbrace)
                  + p.simple_group + p.required_group + p.required_group)
                 | Error("Expected "
                         r"\genfrac{ldelim}{rdelim}{rulesize}{style}{num}{den}"))
          )
  
          p.sqrt <<= Group(
              Suppress(Literal(r"\sqrt"))
              - ((Group(Optional(
                  p.lbracket + OneOrMore(~p.rbracket + p.token) + p.rbracket))
                  + p.required_group)
                 | Error("Expected \\sqrt{value}"))
          )
  
          p.overline <<= Group(
              Suppress(Literal(r"\overline"))
              - (p.required_group | Error("Expected \\overline{value}"))
          )
  
          p.overset <<= Group(
              Suppress(Literal(r"\overset"))
              - ((p.simple_group + p.simple_group)
                 | Error("Expected \\overset{body}{annotation}"))
          )
  
          p.underset <<= Group(
              Suppress(Literal(r"\underset"))
              - ((p.simple_group + p.simple_group)
                 | Error("Expected \\underset{body}{annotation}"))
          )
  
          p.unknown_symbol <<= Combine(p.bslash + Regex("[A-Za-z]*"))
  
          p.operatorname <<= Group(
              Suppress(Literal(r"\operatorname"))
              - ((p.lbrace + ZeroOrMore(p.simple | p.unknown_symbol) + p.rbrace)
                 | Error("Expected \\operatorname{value}"))
          )
  
          p.placeable     <<= (
              p.accentprefixed  # Must be before accent so named symbols that are
                                # prefixed with an accent name work
              | p.accent   # Must be before symbol as all accents are symbols
              | p.symbol   # Must be third to catch all named symbols and single
                           # chars not in a group
              | p.c_over_c
              | p.function
              | p.group
              | p.frac
              | p.dfrac
              | p.binom
              | p.genfrac
              | p.overset
              | p.underset
              | p.sqrt
              | p.overline
              | p.operatorname
          )
  
          p.simple        <<= (
              p.space
              | p.customspace
              | p.font
              | p.subsuper
          )
  
          p.subsuperop    <<= oneOf(["_", "^"])
  
          p.subsuper      <<= Group(
              (Optional(p.placeable)
               + OneOrMore(p.subsuperop - p.placeable)
               + Optional(p.apostrophe))
              | (p.placeable + Optional(p.apostrophe))
              | p.apostrophe
          )
  
          p.token         <<= (
              p.simple
              | p.auto_delim
              | p.unknown_symbol  # Must be last
          )
  
          p.auto_delim    <<= (
              Suppress(Literal(r"\left"))
              - ((p.left_delim | p.ambi_delim)
                 | Error("Expected a delimiter"))
              + Group(ZeroOrMore(p.simple | p.auto_delim))
              + Suppress(Literal(r"\right"))
              - ((p.right_delim | p.ambi_delim)
                 | Error("Expected a delimiter"))
          )
  
          p.math          <<= OneOrMore(p.token)
  
          p.math_string   <<= QuotedString('$', '\\', unquoteResults=False)
  
          p.non_math      <<= Regex(r"(?:(?:\\[$])|[^$])*").leaveWhitespace()
  
          p.main          <<= (
              p.non_math + ZeroOrMore(p.math_string + p.non_math) + StringEnd()
          )
  
          # Set actions
          for key, val in vars(p).items():
              if not key.startswith('_'):
                  if hasattr(self, key):
                      val.setParseAction(getattr(self, key))
  
          self._expression = p.main
          self._math_expression = p.math
  
      def parse(self, s, fonts_object, fontsize, dpi):
          """
          Parse expression *s* using the given *fonts_object* for
          output, at the given *fontsize* and *dpi*.
  
          Returns the parse tree of `Node` instances.
          """
          self._state_stack = [
              self.State(fonts_object, 'default', 'rm', fontsize, dpi)]
          self._em_width_cache = {}
          try:
              result = self._expression.parseString(s)
          except ParseBaseException as err:
              raise ValueError("\n".join(["",
                                          err.line,
                                          " " * (err.column - 1) + "^",
                                          str(err)])) from err
          self._state_stack = None
          self._em_width_cache = {}
          self._expression.resetCache()
          return result[0]
  
      # The state of the parser is maintained in a stack.  Upon
      # entering and leaving a group { } or math/non-math, the stack
      # is pushed and popped accordingly.  The current state always
      # exists in the top element of the stack.
      class State:
          """
          Stores the state of the parser.
  
          States are pushed and popped from a stack as necessary, and
          the "current" state is always at the top of the stack.
          """
          def __init__(self, font_output, font, font_class, fontsize, dpi):
              self.font_output = font_output
              self._font = font
              self.font_class = font_class
              self.fontsize = fontsize
              self.dpi = dpi
  
          def copy(self):
              return Parser.State(
                  self.font_output,
                  self.font,
                  self.font_class,
                  self.fontsize,
                  self.dpi)
  
          @property
          def font(self):
              return self._font
  
          @font.setter
          def font(self, name):
              if name in ('rm', 'it', 'bf'):
                  self.font_class = name
              self._font = name
  
      def get_state(self):
          """Get the current `State` of the parser."""
          return self._state_stack[-1]
  
      def pop_state(self):
          """Pop a `State` off of the stack."""
          self._state_stack.pop()
  
      def push_state(self):
          """Push a new `State` onto the stack, copying the current state."""
          self._state_stack.append(self.get_state().copy())
  
      def main(self, s, loc, toks):
          return [Hlist(toks)]
  
      def math_string(self, s, loc, toks):
          return self._math_expression.parseString(toks[0][1:-1])
  
      def math(self, s, loc, toks):
          hlist = Hlist(toks)
          self.pop_state()
          return [hlist]
  
      def non_math(self, s, loc, toks):
          s = toks[0].replace(r'\$', '$')
          symbols = [Char(c, self.get_state(), math=False) for c in s]
          hlist = Hlist(symbols)
          # We're going into math now, so set font to 'it'
          self.push_state()
          self.get_state().font = mpl.rcParams['mathtext.default']
          return [hlist]
  
      def _make_space(self, percentage):
          # All spaces are relative to em width
          state = self.get_state()
          key = (state.font, state.fontsize, state.dpi)
          width = self._em_width_cache.get(key)
          if width is None:
              metrics = state.font_output.get_metrics(
                  state.font, mpl.rcParams['mathtext.default'], 'm',
                  state.fontsize, state.dpi)
              width = metrics.advance
              self._em_width_cache[key] = width
          return Kern(width * percentage)
  
      _space_widths = {
          r'\,':         0.16667,   # 3/18 em = 3 mu
          r'\thinspace': 0.16667,   # 3/18 em = 3 mu
          r'\/':         0.16667,   # 3/18 em = 3 mu
          r'\>':         0.22222,   # 4/18 em = 4 mu
          r'\:':         0.22222,   # 4/18 em = 4 mu
          r'\;':         0.27778,   # 5/18 em = 5 mu
          r'\ ':         0.33333,   # 6/18 em = 6 mu
          r'~':          0.33333,   # 6/18 em = 6 mu, nonbreakable
          r'\enspace':   0.5,       # 9/18 em = 9 mu
          r'\quad':      1,         # 1 em = 18 mu
          r'\qquad':     2,         # 2 em = 36 mu
          r'\!':         -0.16667,  # -3/18 em = -3 mu
      }
  
      def space(self, s, loc, toks):
          tok, = toks
          num = self._space_widths[tok]
          box = self._make_space(num)
          return [box]
  
      def customspace(self, s, loc, toks):
          return [self._make_space(float(toks[0]))]
  
      def symbol(self, s, loc, toks):
          c, = toks
          try:
              char = Char(c, self.get_state())
          except ValueError as err:
              raise ParseFatalException(s, loc,
                                        "Unknown symbol: %s" % c) from err
  
          if c in self._spaced_symbols:
              # iterate until we find previous character, needed for cases
              # such as ${ -2}$, $ -2$, or $   -2$.
              prev_char = next((c for c in s[:loc][::-1] if c != ' '), '')
              # Binary operators at start of string should not be spaced
              if (c in self._binary_operators and
                      (len(s[:loc].split()) == 0 or prev_char == '{' or
                       prev_char in self._left_delim)):
                  return [char]
              else:
                  return [Hlist([self._make_space(0.2),
                                 char,
                                 self._make_space(0.2)],
                                do_kern=True)]
          elif c in self._punctuation_symbols:
  
              # Do not space commas between brackets
              if c == ',':
                  prev_char = next((c for c in s[:loc][::-1] if c != ' '), '')
                  next_char = next((c for c in s[loc + 1:] if c != ' '), '')
                  if prev_char == '{' and next_char == '}':
                      return [char]
  
              # Do not space dots as decimal separators
              if c == '.' and s[loc - 1].isdigit() and s[loc + 1].isdigit():
                  return [char]
              else:
                  return [Hlist([char, self._make_space(0.2)], do_kern=True)]
          return [char]
  
      accentprefixed = symbol
  
      def unknown_symbol(self, s, loc, toks):
          c, = toks
          raise ParseFatalException(s, loc, "Unknown symbol: %s" % c)
  
      _char_over_chars = {
          # The first 2 entries in the tuple are (font, char, sizescale) for
          # the two symbols under and over.  The third element is the space
          # (in multiples of underline height)
          r'AA': (('it', 'A', 1.0), (None, '\\circ', 0.5), 0.0),
      }
  
      def c_over_c(self, s, loc, toks):
          sym, = toks
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
  
          under_desc, over_desc, space = \
              self._char_over_chars.get(sym, (None, None, 0.0))
          if under_desc is None:
              raise ParseFatalException("Error parsing symbol")
  
          over_state = state.copy()
          if over_desc[0] is not None:
              over_state.font = over_desc[0]
          over_state.fontsize *= over_desc[2]
          over = Accent(over_desc[1], over_state)
  
          under_state = state.copy()
          if under_desc[0] is not None:
              under_state.font = under_desc[0]
          under_state.fontsize *= under_desc[2]
          under = Char(under_desc[1], under_state)
  
          width = max(over.width, under.width)
  
          over_centered = HCentered([over])
          over_centered.hpack(width, 'exactly')
  
          under_centered = HCentered([under])
          under_centered.hpack(width, 'exactly')
  
          return Vlist([
                  over_centered,
                  Vbox(0., thickness * space),
                  under_centered
                  ])
  
      _accent_map = {
          r'hat':            r'\circumflexaccent',
          r'breve':          r'\combiningbreve',
          r'bar':            r'\combiningoverline',
          r'grave':          r'\combininggraveaccent',
          r'acute':          r'\combiningacuteaccent',
          r'tilde':          r'\combiningtilde',
          r'dot':            r'\combiningdotabove',
          r'ddot':           r'\combiningdiaeresis',
          r'dddot':          r'\combiningthreedotsabove',
          r'ddddot':         r'\combiningfourdotsabove',
          r'vec':            r'\combiningrightarrowabove',
          r'"':              r'\combiningdiaeresis',
          r"`":              r'\combininggraveaccent',
          r"'":              r'\combiningacuteaccent',
          r'~':              r'\combiningtilde',
          r'.':              r'\combiningdotabove',
          r'^':              r'\circumflexaccent',
          r'overrightarrow': r'\rightarrow',
          r'overleftarrow':  r'\leftarrow',
          r'mathring':       r'\circ',
      }
  
      _wide_accents = set(r"widehat widetilde widebar".split())
  
      # make a lambda and call it to get the namespace right
      _accentprefixed = (lambda am: [
          p for p in tex2uni
          if any(p.startswith(a) and a != p for a in am)
      ])(set(_accent_map))
  
      def accent(self, s, loc, toks):
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
          (accent, sym), = toks
          if accent in self._wide_accents:
              accent_box = AutoWidthChar(
                  '\\' + accent, sym.width, state, char_class=Accent)
          else:
              accent_box = Accent(self._accent_map[accent], state)
          if accent == 'mathring':
              accent_box.shrink()
              accent_box.shrink()
          centered = HCentered([Hbox(sym.width / 4.0), accent_box])
          centered.hpack(sym.width, 'exactly')
          return Vlist([
                  centered,
                  Vbox(0., thickness * 2.0),
                  Hlist([sym])
                  ])
  
      def function(self, s, loc, toks):
          hlist = self.operatorname(s, loc, toks)
          hlist.function_name, = toks
          return hlist
  
      def operatorname(self, s, loc, toks):
          self.push_state()
          state = self.get_state()
          state.font = 'rm'
          hlist_list = []
          # Change the font of Chars, but leave Kerns alone
          for c in toks[0]:
              if isinstance(c, Char):
                  c.font = 'rm'
                  c._update_metrics()
                  hlist_list.append(c)
              elif isinstance(c, str):
                  hlist_list.append(Char(c, state))
              else:
                  hlist_list.append(c)
          next_char_loc = loc + len(toks[0]) + 1
          if isinstance(toks[0], ParseResults):
              next_char_loc += len('operatorname{}')
          next_char = next((c for c in s[next_char_loc:] if c != ' '), '')
          delimiters = self._left_delim | self._ambi_delim | self._right_delim
          delimiters |= {'^', '_'}
          if (next_char not in delimiters and
                  toks[0] not in self._overunder_functions):
              # Add thin space except when followed by parenthesis, bracket, etc.
              hlist_list += [self._make_space(self._space_widths[r'\,'])]
          self.pop_state()
          return Hlist(hlist_list)
  
      def start_group(self, s, loc, toks):
          self.push_state()
          # Deal with LaTeX-style font tokens
          if len(toks):
              self.get_state().font = toks[0][4:]
          return []
  
      def group(self, s, loc, toks):
          grp = Hlist(toks[0])
          return [grp]
      required_group = simple_group = group
  
      def end_group(self, s, loc, toks):
          self.pop_state()
          return []
  
      def font(self, s, loc, toks):
          name, = toks
          self.get_state().font = name
          return []
  
      def is_overunder(self, nucleus):
          if isinstance(nucleus, Char):
              return nucleus.c in self._overunder_symbols
          elif isinstance(nucleus, Hlist) and hasattr(nucleus, 'function_name'):
              return nucleus.function_name in self._overunder_functions
          return False
  
      def is_dropsub(self, nucleus):
          if isinstance(nucleus, Char):
              return nucleus.c in self._dropsub_symbols
          return False
  
      def is_slanted(self, nucleus):
          if isinstance(nucleus, Char):
              return nucleus.is_slanted()
          return False
  
      def is_between_brackets(self, s, loc):
          return False
  
      def subsuper(self, s, loc, toks):
          assert len(toks) == 1
  
          nucleus = None
          sub = None
          super = None
  
          # Pick all of the apostrophes out, including first apostrophes that
          # have been parsed as characters
          napostrophes = 0
          new_toks = []
          for tok in toks[0]:
              if isinstance(tok, str) and tok not in ('^', '_'):
                  napostrophes += len(tok)
              elif isinstance(tok, Char) and tok.c == "'":
                  napostrophes += 1
              else:
                  new_toks.append(tok)
          toks = new_toks
  
          if len(toks) == 0:
              assert napostrophes
              nucleus = Hbox(0.0)
          elif len(toks) == 1:
              if not napostrophes:
                  return toks[0]  # .asList()
              else:
                  nucleus = toks[0]
          elif len(toks) in (2, 3):
              # single subscript or superscript
              nucleus = toks[0] if len(toks) == 3 else Hbox(0.0)
              op, next = toks[-2:]
              if op == '_':
                  sub = next
              else:
                  super = next
          elif len(toks) in (4, 5):
              # subscript and superscript
              nucleus = toks[0] if len(toks) == 5 else Hbox(0.0)
              op1, next1, op2, next2 = toks[-4:]
              if op1 == op2:
                  if op1 == '_':
                      raise ParseFatalException("Double subscript")
                  else:
                      raise ParseFatalException("Double superscript")
              if op1 == '_':
                  sub = next1
                  super = next2
              else:
                  super = next1
                  sub = next2
          else:
              raise ParseFatalException(
                  "Subscript/superscript sequence is too long. "
                  "Use braces { } to remove ambiguity.")
  
          state = self.get_state()
          rule_thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
          xHeight = state.font_output.get_xheight(
              state.font, state.fontsize, state.dpi)
  
          if napostrophes:
              if super is None:
                  super = Hlist([])
              for i in range(napostrophes):
                  super.children.extend(self.symbol(s, loc, ['\\prime']))
              # kern() and hpack() needed to get the metrics right after
              # extending
              super.kern()
              super.hpack()
  
          # Handle over/under symbols, such as sum or prod
          if self.is_overunder(nucleus):
              vlist = []
              shift = 0.
              width = nucleus.width
              if super is not None:
                  super.shrink()
                  width = max(width, super.width)
              if sub is not None:
                  sub.shrink()
                  width = max(width, sub.width)
  
              vgap = rule_thickness * 3.0
              if super is not None:
                  hlist = HCentered([super])
                  hlist.hpack(width, 'exactly')
                  vlist.extend([hlist, Vbox(0, vgap)])
              hlist = HCentered([nucleus])
              hlist.hpack(width, 'exactly')
              vlist.append(hlist)
              if sub is not None:
                  hlist = HCentered([sub])
                  hlist.hpack(width, 'exactly')
                  vlist.extend([Vbox(0, vgap), hlist])
                  shift = hlist.height + vgap
              vlist = Vlist(vlist)
              vlist.shift_amount = shift + nucleus.depth
              result = Hlist([vlist])
              return [result]
  
          # We remove kerning on the last character for consistency (otherwise
          # it will compute kerning based on non-shrunk characters and may put
          # them too close together when superscripted)
          # We change the width of the last character to match the advance to
          # consider some fonts with weird metrics: e.g. stix's f has a width of
          # 7.75 and a kerning of -4.0 for an advance of 3.72, and we want to put
          # the superscript at the advance
          last_char = nucleus
          if isinstance(nucleus, Hlist):
              new_children = nucleus.children
              if len(new_children):
                  # remove last kern
                  if (isinstance(new_children[-1], Kern) and
                          hasattr(new_children[-2], '_metrics')):
                      new_children = new_children[:-1]
                  last_char = new_children[-1]
                  if hasattr(last_char, '_metrics'):
                      last_char.width = last_char._metrics.advance
              # create new Hlist without kerning
              nucleus = Hlist(new_children, do_kern=False)
          else:
              if isinstance(nucleus, Char):
                  last_char.width = last_char._metrics.advance
              nucleus = Hlist([nucleus])
  
          # Handle regular sub/superscripts
          constants = _get_font_constant_set(state)
          lc_height   = last_char.height
          lc_baseline = 0
          if self.is_dropsub(last_char):
              lc_baseline = last_char.depth
  
          # Compute kerning for sub and super
          superkern = constants.delta * xHeight
          subkern = constants.delta * xHeight
          if self.is_slanted(last_char):
              superkern += constants.delta * xHeight
              superkern += (constants.delta_slanted *
                            (lc_height - xHeight * 2. / 3.))
              if self.is_dropsub(last_char):
                  subkern = (3 * constants.delta -
                             constants.delta_integral) * lc_height
                  superkern = (3 * constants.delta +
                               constants.delta_integral) * lc_height
              else:
                  subkern = 0
  
          if super is None:
              # node757
              x = Hlist([Kern(subkern), sub])
              x.shrink()
              if self.is_dropsub(last_char):
                  shift_down = lc_baseline + constants.subdrop * xHeight
              else:
                  shift_down = constants.sub1 * xHeight
              x.shift_amount = shift_down
          else:
              x = Hlist([Kern(superkern), super])
              x.shrink()
              if self.is_dropsub(last_char):
                  shift_up = lc_height - constants.subdrop * xHeight
              else:
                  shift_up = constants.sup1 * xHeight
              if sub is None:
                  x.shift_amount = -shift_up
              else:  # Both sub and superscript
                  y = Hlist([Kern(subkern), sub])
                  y.shrink()
                  if self.is_dropsub(last_char):
                      shift_down = lc_baseline + constants.subdrop * xHeight
                  else:
                      shift_down = constants.sub2 * xHeight
                  # If sub and superscript collide, move super up
                  clr = (2.0 * rule_thickness -
                         ((shift_up - x.depth) - (y.height - shift_down)))
                  if clr > 0.:
                      shift_up += clr
                  x = Vlist([
                      x,
                      Kern((shift_up - x.depth) - (y.height - shift_down)),
                      y])
                  x.shift_amount = shift_down
  
          if not self.is_dropsub(last_char):
              x.width += constants.script_space * xHeight
          result = Hlist([nucleus, x])
  
          return [result]
  
      def _genfrac(self, ldelim, rdelim, rule, style, num, den):
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
  
          rule = float(rule)
  
          if style is not self._MathStyle.DISPLAYSTYLE:
              num.shrink()
              den.shrink()
          cnum = HCentered([num])
          cden = HCentered([den])
          width = max(num.width, den.width)
          cnum.hpack(width, 'exactly')
          cden.hpack(width, 'exactly')
          vlist = Vlist([cnum,                      # numerator
                         Vbox(0, thickness * 2.0),  # space
                         Hrule(state, rule),        # rule
                         Vbox(0, thickness * 2.0),  # space
                         cden                       # denominator
                         ])
  
          # Shift so the fraction line sits in the middle of the
          # equals sign
          metrics = state.font_output.get_metrics(
              state.font, mpl.rcParams['mathtext.default'],
              '=', state.fontsize, state.dpi)
          shift = (cden.height -
                   ((metrics.ymax + metrics.ymin) / 2 -
                    thickness * 3.0))
          vlist.shift_amount = shift
  
          result = [Hlist([vlist, Hbox(thickness * 2.)])]
          if ldelim or rdelim:
              if ldelim == '':
                  ldelim = '.'
              if rdelim == '':
                  rdelim = '.'
              return self._auto_sized_delimiter(ldelim, result, rdelim)
          return result
  
      def genfrac(self, s, loc, toks):
          args, = toks
          return self._genfrac(*args)
  
      def frac(self, s, loc, toks):
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
          (num, den), = toks
          return self._genfrac('', '', thickness, self._MathStyle.TEXTSTYLE,
                               num, den)
  
      def dfrac(self, s, loc, toks):
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
          (num, den), = toks
          return self._genfrac('', '', thickness, self._MathStyle.DISPLAYSTYLE,
                               num, den)
  
      def binom(self, s, loc, toks):
          (num, den), = toks
          return self._genfrac('(', ')', 0.0, self._MathStyle.TEXTSTYLE,
                               num, den)
  
      def _genset(self, s, loc, toks):
          (annotation, body), = toks
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
  
          annotation.shrink()
          cannotation = HCentered([annotation])
          cbody = HCentered([body])
          width = max(cannotation.width, cbody.width)
          cannotation.hpack(width, 'exactly')
          cbody.hpack(width, 'exactly')
  
          vgap = thickness * 3
          if s[loc + 1] == "u":  # \underset
              vlist = Vlist([cbody,                       # body
                             Vbox(0, vgap),               # space
                             cannotation                  # annotation
                             ])
              # Shift so the body sits in the same vertical position
              vlist.shift_amount = cbody.depth + cannotation.height + vgap
          else:  # \overset
              vlist = Vlist([cannotation,                 # annotation
                             Vbox(0, vgap),               # space
                             cbody                        # body
                             ])
  
          # To add horizontal gap between symbols: wrap the Vlist into
          # an Hlist and extend it with an Hbox(0, horizontal_gap)
          return vlist
  
      overset = underset = _genset
  
      def sqrt(self, s, loc, toks):
          (root, body), = toks
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
  
          # Determine the height of the body, and add a little extra to
          # the height so it doesn't seem cramped
          height = body.height - body.shift_amount + thickness * 5.0
          depth = body.depth + body.shift_amount
          check = AutoHeightChar(r'\__sqrt__', height, depth, state, always=True)
          height = check.height - check.shift_amount
          depth = check.depth + check.shift_amount
  
          # Put a little extra space to the left and right of the body
          padded_body = Hlist([Hbox(2 * thickness), body, Hbox(2 * thickness)])
          rightside = Vlist([Hrule(state), Glue('fill'), padded_body])
          # Stretch the glue between the hrule and the body
          rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
                          'exactly', depth)
  
          # Add the root and shift it upward so it is above the tick.
          # The value of 0.6 is a hard-coded hack ;)
          if not root:
              root = Box(check.width * 0.5, 0., 0.)
          else:
              root = Hlist(root)
              root.shrink()
              root.shrink()
  
          root_vlist = Vlist([Hlist([root])])
          root_vlist.shift_amount = -height * 0.6
  
          hlist = Hlist([root_vlist,               # Root
                         # Negative kerning to put root over tick
                         Kern(-check.width * 0.5),
                         check,                    # Check
                         rightside])               # Body
          return [hlist]
  
      def overline(self, s, loc, toks):
          (body,), = toks
  
          state = self.get_state()
          thickness = state.font_output.get_underline_thickness(
              state.font, state.fontsize, state.dpi)
  
          height = body.height - body.shift_amount + thickness * 3.0
          depth = body.depth + body.shift_amount
  
          # Place overline above body
          rightside = Vlist([Hrule(state), Glue('fill'), Hlist([body])])
  
          # Stretch the glue between the hrule and the body
          rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
                          'exactly', depth)
  
          hlist = Hlist([rightside])
          return [hlist]
  
      def _auto_sized_delimiter(self, front, middle, back):
          state = self.get_state()
          if len(middle):
              height = max(x.height for x in middle)
              depth = max(x.depth for x in middle)
              factor = None
          else:
              height = 0
              depth = 0
              factor = 1.0
          parts = []
          # \left. and \right. aren't supposed to produce any symbols
          if front != '.':
              parts.append(
                  AutoHeightChar(front, height, depth, state, factor=factor))
          parts.extend(middle)
          if back != '.':
              parts.append(
                  AutoHeightChar(back, height, depth, state, factor=factor))
          hlist = Hlist(parts)
          return hlist
  
      def auto_delim(self, s, loc, toks):
          front, middle, back = toks
  
          return self._auto_sized_delimiter(front, middle.asList(), back)
  