mathtext.py

r"""
:mod:`~matplotlib.mathtext` is a module for parsing a subset of the
TeX math syntax and drawing them to a matplotlib backend.

For a tutorial of its usage see :ref:`mathtext-tutorial`.  This
document is primarily concerned with implementation details.

The module uses pyparsing_ to parse the TeX expression.

.. _pyparsing: http://pyparsing.wikispaces.com/

The Bakoma distribution of the TeX Computer Modern fonts, and STIX
fonts are supported.  There is experimental support for using
arbitrary fonts, but results may vary without proper tweaking and
metrics for those fonts.

If you find TeX expressions that don't parse or render properly,
please email mdroe@stsci.edu, but please check KNOWN ISSUES below first.
"""
from __future__ import division
import os
from cStringIO import StringIO
from math import ceil
try:
    set
except NameError:
    from sets import Set as set
import unicodedata
from warnings import warn

from numpy import inf, isinf
import numpy as np
from matplotlib.pyparsing import Combine, Group, Optional, Forward, \
    Literal, OneOrMore, ZeroOrMore, ParseException, Empty, \
    ParseResults, Suppress, oneOf, StringEnd, ParseFatalException, \
    FollowedBy, Regex, ParserElement
# Enable packrat parsing
ParserElement.enablePackrat()

from matplotlib.afm import AFM
from matplotlib.cbook import Bunch, get_realpath_and_stat, \
    is_string_like, maxdict
from matplotlib.ft2font import FT2Font, FT2Image, KERNING_DEFAULT, LOAD_FORCE_AUTOHINT, LOAD_NO_HINTING
from matplotlib.font_manager import findfont, FontProperties
from matplotlib._mathtext_data import latex_to_bakoma, \
        latex_to_standard, tex2uni, latex_to_cmex, stix_virtual_fonts
from matplotlib import get_data_path, rcParams



import matplotlib.colors as mcolors
import matplotlib._png as _png
####################



##############################################################################
# FONTS

def get_unicode_index(symbol):
    """get_unicode_index(symbol) -> integer

Return the integer index (from the Unicode table) of symbol.  *symbol*
can be a single unicode character, a TeX command (i.e. r'\pi'), or a
Type1 symbol name (i.e. 'phi').
"""
    # 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:
        message = """'%(symbol)s' is not a valid Unicode character or
TeX/Type1 symbol"""%locals()
        raise ValueError, message


class MathtextBackend(object):
    """
    The base class for the mathtext backend-specific code.  The
    purpose of :class:`MathtextBackend` subclasses is to interface
    between mathtext and a specific matplotlib graphics backend.

    Subclasses need to override the following:

      - :meth:`render_glyph`
      - :meth:`render_filled_rect`
      - :meth:`get_results`

    And optionally, if you need to use a Freetype hinting style:

      - :meth:`get_hinting_type`
    """
    def __init__(self):
        self.fonts_object = None

    def set_canvas_size(self, w, h, d):
        'Dimension the drawing canvas'
        self.width  = w
        self.height = h
        self.depth  = d

    def render_glyph(self, ox, oy, info):
        """
        Draw a glyph described by *info* to the reference point (*ox*,
        *oy*).
        """
        raise NotImplementedError()

    def render_filled_rect(self, x1, y1, x2, y2):
        """
        Draw a filled black rectangle from (*x1*, *y1*) to (*x2*, *y2*).
        """
        raise NotImplementedError()

    def get_results(self, box):
        """
        Return a backend-specific tuple to return to the backend after
        all processing is done.
        """
        raise NotImplementedError()

    def get_hinting_type(self):
        """
        Get the Freetype hinting type to use with this particular
        backend.
        """
        return LOAD_NO_HINTING

class MathtextBackendBbox(MathtextBackend):
    """
    A backend whose only purpose is to get a precise bounding box.
    Only required for the Agg backend.
    """

    def __init__(self, real_backend):
        MathtextBackend.__init__(self)
        self.bbox = [0, 0, 0, 0]
        self.real_backend = real_backend

    def _update_bbox(self, x1, y1, x2, y2):
        self.bbox = [min(self.bbox[0], x1),
                     min(self.bbox[1], y1),
                     max(self.bbox[2], x2),
                     max(self.bbox[3], y2)]

    def render_glyph(self, ox, oy, info):
        self._update_bbox(ox + info.metrics.xmin,
                          oy - info.metrics.ymax,
                          ox + info.metrics.xmax,
                          oy - info.metrics.ymin)

    def render_rect_filled(self, x1, y1, x2, y2):
        self._update_bbox(x1, y1, x2, y2)

    def get_results(self, box):
        orig_height = box.height
        orig_depth  = box.depth
        ship(0, 0, box)
        bbox = self.bbox
        bbox = [bbox[0] - 1, bbox[1] - 1, bbox[2] + 1, bbox[3] + 1]
        self._switch_to_real_backend()
        self.fonts_object.set_canvas_size(
            bbox[2] - bbox[0],
            (bbox[3] - bbox[1]) - orig_depth,
            (bbox[3] - bbox[1]) - orig_height)
        ship(-bbox[0], -bbox[1], box)
        return self.fonts_object.get_results(box)

    def get_hinting_type(self):
        return self.real_backend.get_hinting_type()

    def _switch_to_real_backend(self):
        self.fonts_object.mathtext_backend = self.real_backend
        self.real_backend.fonts_object = self.fonts_object
        self.real_backend.ox = self.bbox[0]
        self.real_backend.oy = self.bbox[1]

class MathtextBackendAggRender(MathtextBackend):
    """
    Render glyphs and rectangles to an FTImage buffer, which is later
    transferred to the Agg image by the Agg backend.
    """
    def __init__(self):
        self.ox = 0
        self.oy = 0
        self.image = None
        MathtextBackend.__init__(self)

    def set_canvas_size(self, w, h, d):
        MathtextBackend.set_canvas_size(self, w, h, d)
        self.image = FT2Image(ceil(w), ceil(h + d))

    def render_glyph(self, ox, oy, info):
        info.font.draw_glyph_to_bitmap(
            self.image, ox, oy - info.metrics.ymax, info.glyph)

    def render_rect_filled(self, x1, y1, x2, y2):
        height = max(int(y2 - y1) - 1, 0)
        if height == 0:
            center = (y2 + y1) / 2.0
            y = int(center - (height + 1) / 2.0)
        else:
            y = int(y1)
        self.image.draw_rect_filled(int(x1), y, ceil(x2), y + height)

    def get_results(self, box):
        return (self.ox,
                self.oy,
                self.width,
                self.height + self.depth,
                self.depth,
                self.image,
                self.fonts_object.get_used_characters())

    def get_hinting_type(self):
        return LOAD_FORCE_AUTOHINT

def MathtextBackendAgg():
    return MathtextBackendBbox(MathtextBackendAggRender())

class MathtextBackendBitmapRender(MathtextBackendAggRender):
    def get_results(self, box):
        return self.image, self.depth

def MathtextBackendBitmap():
    """
    A backend to generate standalone mathtext images.  No additional
    matplotlib backend is required.
    """
    return MathtextBackendBbox(MathtextBackendBitmapRender())

class MathtextBackendPs(MathtextBackend):
    """
    Store information to write a mathtext rendering to the PostScript
    backend.
    """
    def __init__(self):
        self.pswriter = StringIO()
        self.lastfont = None

    def render_glyph(self, ox, oy, info):
        oy = self.height - oy + info.offset
        postscript_name = info.postscript_name
        fontsize        = info.fontsize
        symbol_name     = info.symbol_name

        if (postscript_name, fontsize) != self.lastfont:
            ps = """/%(postscript_name)s findfont
%(fontsize)s scalefont
setfont
""" % locals()
            self.lastfont = postscript_name, fontsize
            self.pswriter.write(ps)

        ps = """%(ox)f %(oy)f moveto
/%(symbol_name)s glyphshow\n
""" % locals()
        self.pswriter.write(ps)

    def render_rect_filled(self, x1, y1, x2, y2):
        ps = "%f %f %f %f rectfill\n" % (x1, self.height - y2, x2 - x1, y2 - y1)
        self.pswriter.write(ps)

    def get_results(self, box):
        ship(0, -self.depth, box)
        #print self.depth
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.pswriter,
                self.fonts_object.get_used_characters())

class MathtextBackendPdf(MathtextBackend):
    """
    Store information to write a mathtext rendering to the PDF
    backend.
    """
    def __init__(self):
        self.glyphs = []
        self.rects = []

    def render_glyph(self, ox, oy, info):
        filename = info.font.fname
        oy = self.height - oy + info.offset
        self.glyphs.append(
            (ox, oy, filename, info.fontsize,
             info.num, info.symbol_name))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.rects.append((x1, self.height - y2, x2 - x1, y2 - y1))

    def get_results(self, box):
        ship(0, -self.depth, box)
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.glyphs,
                self.rects,
                self.fonts_object.get_used_characters())

class MathtextBackendSvg(MathtextBackend):
    """
    Store information to write a mathtext rendering to the SVG
    backend.
    """
    def __init__(self):
        self.svg_glyphs = []
        self.svg_rects = []

    def render_glyph(self, ox, oy, info):
        oy = self.height - oy + info.offset
        thetext = unichr(info.num)
        self.svg_glyphs.append(
            (info.font, info.fontsize, thetext, ox, oy, info.metrics))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.svg_rects.append(
            (x1, self.height - y1 + 1, x2 - x1, y2 - y1))

    def get_results(self, box):
        ship(0, -self.depth, box)
        svg_elements = Bunch(svg_glyphs = self.svg_glyphs,
                             svg_rects = self.svg_rects)
        return (self.width,
                self.height + self.depth,
                self.depth,
                svg_elements,
                self.fonts_object.get_used_characters())

class MathtextBackendCairo(MathtextBackend):
    """
    Store information to write a mathtext rendering to the Cairo
    backend.
    """

    def __init__(self):
        self.glyphs = []
        self.rects = []

    def render_glyph(self, ox, oy, info):
        oy = oy - info.offset - self.height
        thetext = unichr(info.num)
        self.glyphs.append(
            (info.font, info.fontsize, thetext, ox, oy))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.rects.append(
            (x1, y1 - self.height, x2 - x1, y2 - y1))

    def get_results(self, box):
        ship(0, -self.depth, box)
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.glyphs,
                self.rects)

class Fonts(object):
    """
    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):
        """
        *default_font_prop*: A
        :class:`~matplotlib.font_manager.FontProperties` object to use
        for the default non-math font, or the base font for Unicode
        (generic) font rendering.

        *mathtext_backend*: A subclass of :class:`MathTextBackend`
        used to delegate the actual rendering.
        """
        self.default_font_prop = default_font_prop
        self.mathtext_backend = mathtext_backend
        # Make these classes doubly-linked
        self.mathtext_backend.fonts_object = self
        self.used_characters = {}

    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*.

        *fontX*: one of the TeX font names::

          tt, it, rm, cal, sf, bf or default (non-math)

        *fontclassX*: TODO

        *symX*: a symbol in raw TeX form. e.g. '1', 'x' or '\sigma'

        *fontsizeX*: the fontsize in points

        *dpi*: the current dots-per-inch
        """
        return 0.

    def get_metrics(self, font, font_class, sym, fontsize, dpi):
        """
        *font*: one of the TeX font names::

          tt, it, rm, cal, sf, bf or default (non-math)

        *font_class*: TODO

        *sym*:  a symbol in raw TeX form. e.g. '1', 'x' or '\sigma'

        *fontsize*: font size in points

        *dpi*: current dots-per-inch

        Returns an object with the following attributes:

          - *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".
        """
        info = self._get_info(font, font_class, sym, fontsize, dpi)
        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 = ceil(w), ceil(h), ceil(d)
        self.mathtext_backend.set_canvas_size(self.width, self.height, self.depth)

    def render_glyph(self, ox, oy, facename, font_class, sym, fontsize, dpi):
        """
        Draw a glyph at

          - *ox*, *oy*: position

          - *facename*: One of the TeX face names

          - *font_class*:

          - *sym*: TeX symbol name or single character

          - *fontsize*: fontsize in points

          - *dpi*: The dpi to draw at.
        """
        info = self._get_info(facename, font_class, sym, fontsize, dpi)
        realpath, stat_key = get_realpath_and_stat(info.font.fname)
        used_characters = self.used_characters.setdefault(
            stat_key, (realpath, set()))
        used_characters[1].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.
        """
        return self.mathtext_backend.get_results(box)

    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).
    """
    class CachedFont:
        def __init__(self, font):
            self.font     = font
            self.charmap  = font.get_charmap()
            self.glyphmap = dict(
                [(glyphind, ccode) for ccode, glyphind in self.charmap.iteritems()])

        def __repr__(self):
            return repr(self.font)

    def __init__(self, default_font_prop, mathtext_backend):
        Fonts.__init__(self, default_font_prop, mathtext_backend)
        self.glyphd = {}
        self._fonts = {}

        filename = findfont(default_font_prop)
        default_font = self.CachedFont(FT2Font(str(filename)))
        self._fonts['default'] = default_font

    def destroy(self):
        self.glyphd = None
        Fonts.destroy(self)

    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:
            font = FT2Font(basename)
            cached_font = self.CachedFont(font)
            self._fonts[basename] = cached_font
            self._fonts[font.postscript_name] = cached_font
            self._fonts[font.postscript_name.lower()] = cached_font
        return cached_font

    def _get_offset(self, cached_font, glyph, fontsize, dpi):
        if cached_font.font.postscript_name == 'Cmex10':
            return glyph.height/64.0/2.0 + 256.0/64.0 * dpi/72.0
        return 0.

    def _get_info(self, fontname, font_class, sym, fontsize, dpi):
        key = fontname, font_class, sym, fontsize, dpi
        bunch = self.glyphd.get(key)
        if bunch is not None:
            return bunch

        cached_font, num, symbol_name, fontsize, slanted = \
            self._get_glyph(fontname, font_class, sym, fontsize)

        font = cached_font.font
        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(cached_font, glyph, fontsize, dpi)
        metrics = Bunch(
            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] = Bunch(
            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, font, fontsize, dpi):
        cached_font = self._get_font(font)
        cached_font.font.set_size(fontsize, dpi)
        pclt = cached_font.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(font, 'it', '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) / 64.0
        return Fonts.get_kern(self, 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'
                 }
    fontmap = {}

    def __init__(self, *args, **kwargs):
        self._stix_fallback = StixFonts(*args, **kwargs)

        TruetypeFonts.__init__(self, *args, **kwargs)
        if not len(self.fontmap):
            for key, val in self._fontmap.iteritems():
                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):
        symbol_name = 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
            try:
                cached_font = self._get_font(basename)
            except RuntimeError:
                pass
            else:
                symbol_name = cached_font.font.get_glyph_name(num)
                num = cached_font.glyphmap[num]
        elif len(sym) == 1:
            slanted = (fontname == "it")
            try:
                cached_font = self._get_font(fontname)
            except RuntimeError:
                pass
            else:
                num = ord(sym)
                gid = cached_font.charmap.get(num)
                if gid is not None:
                    symbol_name = cached_font.font.get_glyph_name(
                        cached_font.charmap[num])

        if symbol_name is None:
            return self._stix_fallback._get_glyph(
                fontname, font_class, sym, fontsize)

        return cached_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 ommitted 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 [('\leftparen', '('),
                          ('\rightparent', ')'),
                          ('\leftbrace', '{'),
                          ('\rightbrace', '}'),
                          ('\leftbracket', '['),
                          ('\rightbracket', ']')]:
        _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.
    """
    fontmap = {}
    use_cmex = True

    def __init__(self, *args, **kwargs):
        # This must come first so the backend's owner is set correctly
        if rcParams['mathtext.fallback_to_cm']:
            self.cm_fallback = BakomaFonts(*args, **kwargs)
        else:
            self.cm_fallback = None
        TruetypeFonts.__init__(self, *args, **kwargs)
        if not len(self.fontmap):
            for texfont in "cal rm tt it bf sf".split():
                prop = rcParams['mathtext.' + texfont]
                font = findfont(prop)
                self.fontmap[texfont] = font
            prop = FontProperties('cmex10')
            font = findfont(prop)
            self.fontmap['ex'] = font

    _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):
        found_symbol = False

        if self.use_cmex:
            uniindex = latex_to_cmex.get(sym)
            if uniindex is not None:
                fontname = 'ex'
                found_symbol = True

        if not found_symbol:
            try:
                uniindex = get_unicode_index(sym)
                found_symbol = True
            except ValueError:
                uniindex = ord('?')
                warn("No TeX to unicode mapping for '%s'" %
                     sym.encode('ascii', 'backslashreplace'),
                     MathTextWarning)

        fontname, uniindex = self._map_virtual_font(
            fontname, font_class, uniindex)

        # Only characters in the "Letter" class should be italicized in 'it'
        # mode.  Greek capital letters should be Roman.
        if found_symbol:
            new_fontname = fontname

            if fontname == 'it':
                if uniindex < 0x10000:
                    unistring = unichr(uniindex)
                    if (not unicodedata.category(unistring)[0] == "L"
                        or unicodedata.name(unistring).startswith("GREEK CAPITAL")):
                        new_fontname = 'rm'

            slanted = (new_fontname == 'it') or sym in self._slanted_symbols
            found_symbol = False
            try:
                cached_font = self._get_font(new_fontname)
            except RuntimeError:
                pass
            else:
                try:
                    glyphindex = cached_font.charmap[uniindex]
                    found_symbol = True
                except KeyError:
                    pass

        if not found_symbol:
            if self.cm_fallback:
                warn("Substituting with a symbol from Computer Modern.",
                     MathTextWarning)
                return self.cm_fallback._get_glyph(
                    fontname, 'it', sym, fontsize)
            else:
                if fontname == 'it' and isinstance(self, StixFonts):
                    return self._get_glyph('rm', font_class, sym, fontsize)
                warn("Font '%s' does not have a glyph for '%s'" %
                     (fontname, sym.encode('ascii', 'backslashreplace')),
                     MathTextWarning)
                warn("Substituting with a dummy symbol.", MathTextWarning)
                fontname = 'rm'
                new_fontname = fontname
                cached_font = self._get_font(fontname)
                uniindex = 0xA4 # currency character, for lack of anything better
                glyphindex = cached_font.charmap[uniindex]
                slanted = False

        symbol_name = cached_font.font.get_glyph_name(glyphindex)
        return cached_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 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 : 'STIXSize1',
                 2 : 'STIXSize2',
                 3 : 'STIXSize3',
                 4 : 'STIXSize4',
                 5 : 'STIXSize5'
                 }
    fontmap = {}
    use_cmex = False
    cm_fallback = False
    _sans = False

    def __init__(self, *args, **kwargs):
        TruetypeFonts.__init__(self, *args, **kwargs)
        if not len(self.fontmap):
            for key, name in self._fontmap.iteritems():
                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:
            mapping = stix_virtual_fonts['sf']
            doing_sans_conversion = True
        else:
            doing_sans_conversion = False

        if mapping is not None:
            if isinstance(mapping, dict):
                mapping = mapping[font_class]

            # 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 uniindex >= range[0] and 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 = 'it'

        # Handle private use area glyphs
        if (fontname in ('it', 'rm', 'bf') and
            uniindex >= 0xe000 and uniindex <= 0xf8ff):
            fontname = 'nonuni' + fontname

        return fontname, uniindex

    _size_alternatives = {}
    def get_sized_alternatives_for_symbol(self, fontname, sym):
        alternatives = self._size_alternatives.get(sym)
        if alternatives:
            return alternatives

        alternatives = []
        try:
            uniindex = get_unicode_index(sym)
        except ValueError:
            return [(fontname, sym)]

        fix_ups = {
            ord('<'): 0x27e8,
            ord('>'): 0x27e9 }

        uniindex = fix_ups.get(uniindex, uniindex)

        for i in range(6):
            cached_font = self._get_font(i)
            glyphindex = cached_font.charmap.get(uniindex)
            if glyphindex is not None:
                alternatives.append((i, unichr(uniindex)))

        self._size_alternatives[sym] = alternatives
        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 = os.path.join( 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):
        Fonts.__init__(self, default_font_prop, MathtextBackendPs())
        self.glyphd = {}
        self.fonts = {}

        filename = findfont(default_font_prop, fontext='afm')
        default_font = AFM(file(filename, 'r'))
        default_font.fname = filename

        self.fonts['default'] = default_font
        self.pswriter = 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")
            cached_font = AFM(file(fname, 'r'))
            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):
        '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(unicode(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:
            warn("No TeX to built-in Postscript mapping for '%s'" % sym,
                 MathTextWarning)

        slanted = (fontname == 'it')
        font = self._get_font(fontname)

        if found_symbol:
            try:
                symbol_name = font.get_name_char(glyph)
            except KeyError:
                warn("No glyph in standard Postscript font '%s' for '%s'" %
                     (font.postscript_name, sym),
                     MathTextWarning)
                found_symbol = False

        if not found_symbol:
            glyph = sym = '?'
            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 = Bunch(
            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] = Bunch(
            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 Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1,
                              font2, fontclass2, sym2, fontsize2, dpi)

    def get_xheight(self, font, fontsize, dpi):
        cached_font = self._get_font(font)
        return cached_font.get_xheight() * 0.001 * fontsize

    def get_underline_thickness(self, font, fontsize, dpi):
        cached_font = self._get_font(font)
        return cached_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     = 1.0 / SHRINK_FACTOR
# The number of different sizes of chars to use, beyond which they will not
# get any smaller
NUM_SIZE_LEVELS = 4
# Percentage of x-height of additional horiz. space after sub/superscripts
SCRIPT_SPACE    = 0.2
# Percentage of x-height that sub/superscripts drop below the baseline
SUBDROP         = 0.3
# Percentage of x-height that superscripts drop below the baseline
SUP1            = 0.5
# Percentage of x-height that subscripts drop below the baseline
SUB1            = 0.0
# Percentage of x-height that superscripts are offset relative to the subscript
DELTA           = 0.18

class MathTextWarning(Warning):
    pass

class Node(object):
    """
    A node in the TeX box model
    """
    def __init__(self):
        self.size = 0

    def __repr__(self):
        return self.__internal_repr__()

    def __internal_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):
    """
    Represents any node with a physical location.
    """
    def __init__(self, width, height, depth):
        Node.__init__(self)
        self.width  = width
        self.height = height
        self.depth  = depth

    def shrink(self):
        Node.shrink(self)
        if self.size < NUM_SIZE_LEVELS:
            self.width  *= SHRINK_FACTOR
            self.height *= SHRINK_FACTOR
            self.depth  *= SHRINK_FACTOR

    def grow(self):
        Node.grow(self)
        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):
        Box.__init__(self, 0., height, depth)

class Hbox(Box):
    """
    A box with only width (zero height and depth).
    """
    def __init__(self, width):
        Box.__init__(self, width, 0., 0.)

class Char(Node):
    """
    Represents a single character.  Unlike TeX, the font information
    and metrics are stored with each :class:`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 way, and the advance (if different
    from width) must be converted into a :class:`Kern` node when the
    :class:`Char` is added to its parent :class:`Hlist`.
    """
    def __init__(self, c, state):
        Node.__init__(self)
        self.c = c
        self.font_output = state.font_output
        assert isinstance(state.font, (str, unicode, int))
        self.font = state.font
        self.font_class = state.font_class
        self.fontsize = state.fontsize
        self.dpi = state.dpi
        # The real width, height and depth will be set during the
        # pack phase, after we know the real fontsize
        self._update_metrics()

    def __internal_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)
        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.  Called when characters are strung together into
        :class:`Hlist` to create :class:`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):
        Node.shrink(self)
        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):
        Node.grow(self)
        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):
        Char.shrink(self)
        self._update_metrics()

    def grow(self):
        Char.grow(self)
        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):
        Box.__init__(self, 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]' % (
            self.__internal_repr__(),
            self.width, self.height,
            self.depth, self.shift_amount,
            ' '.join([repr(x) for x in self.children]))

    def _determine_order(self, totals):
        """
        A helper function to determine the highest order of glue
        used by the members of this list.  Used by vpack and hpack.
        """
        o = 0
        for i in range(len(totals) - 1, 0, -1):
            if totals[i] != 0.0:
                o = i
                break
        return o

    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):
                warn("%s %s: %r" % (error_type, self.__class__.__name__, self),
                     MathTextWarning)

    def shrink(self):
        for child in self.children:
            child.shrink()
        Box.shrink(self)
        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()
        Box.grow(self)
        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):
        List.__init__(self, elements)
        if do_kern:
            self.kern()
        self.hpack()

    def kern(self):
        """
        Insert :class:`Kern` nodes between :class:`Char` nodes to set
        kerning.  The :class:`Char` nodes themselves determine the
        amount of kerning they need (in :meth:`~Char.get_kerning`),
        and this function just creates the linked list in the correct
        way.
        """
        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'):
        """
        The main duty of :meth:`hpack` is to compute the dimensions of
        the resulting boxes, and to 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.

          - *w*: specifies a width

          - *m*: is either 'exactly' or 'additional'.

        Thus, ``hpack(w, 'exactly')`` produces a box whose width is
        exactly *w*, while ``hpack(w, 'additional')`` yields a box
        whose width is the natural width plus *w*.  The default values
        produce a box with the natural width.
        """
        # 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 isinf(p.height) and not 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'):
        List.__init__(self, elements)
        self.vpack()

    def vpack(self, h=0., m='additional', l=float(inf)):
        """
        The main duty of :meth:`vpack` is to compute the dimensions of
        the resulting boxes, and to adjust the glue if one of those
        dimensions is pre-specified.

          - *h*: specifies a height
          - *m*: is either 'exactly' or 'additional'.
          - *l*: a maximum height

        Thus, ``vpack(h, 'exactly')`` produces a box whose height is
        exactly *h*, while ``vpack(h, 'additional')`` yields a box
        whose height is the natural height plus *h*.  The default
        values produce a box with the natural width.
        """
        # 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 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 :class:`Rule` node stands for a solid black rectangle; it has
    *width*, *depth*, and *height* fields just as in an
    :class:`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 :class:`Hlist`; the
    height and depth are never running in a :class:`Vlist`.
    """
    def __init__(self, width, height, depth, state):
        Box.__init__(self, 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 = state.font_output.get_underline_thickness(
            state.font, state.fontsize, state.dpi)
        height = depth = thickness * 0.5
        Rule.__init__(self, 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)
        Rule.__init__(self, thickness, inf, inf, state)

class Glue(Node):
    """
    Most of the information in this object is stored in the underlying
    :class:`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, copy=False):
        Node.__init__(self)
        self.glue_subtype   = 'normal'
        if is_string_like(glue_type):
            glue_spec = GlueSpec.factory(glue_type)
        elif isinstance(glue_type, GlueSpec):
            glue_spec = glue_type
        else:
            raise ArgumentError("glue_type must be a glue spec name or instance.")
        if copy:
            glue_spec = glue_spec.copy()
        self.glue_spec      = glue_spec

    def shrink(self):
        Node.shrink(self)
        if self.size < NUM_SIZE_LEVELS:
            if self.glue_spec.width != 0.:
                self.glue_spec = self.glue_spec.copy()
                self.glue_spec.width *= SHRINK_FACTOR

    def grow(self):
        Node.grow(self)
        if self.glue_spec.width != 0.:
            self.glue_spec = self.glue_spec.copy()
            self.glue_spec.width *= GROW_FACTOR

class GlueSpec(object):
    """
    See :class:`Glue`.
    """
    def __init__(self, width=0., stretch=0., stretch_order=0, shrink=0., shrink_order=0):
        self.width         = width
        self.stretch       = stretch
        self.stretch_order = stretch_order
        self.shrink        = shrink
        self.shrink_order  = shrink_order

    def copy(self):
        return GlueSpec(
            self.width,
            self.stretch,
            self.stretch_order,
            self.shrink,
            self.shrink_order)

    def factory(cls, glue_type):
        return cls._types[glue_type]
    factory = classmethod(factory)

GlueSpec._types = {
    '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)
}

# Some convenient ways to get common kinds of glue

class Fil(Glue):
    def __init__(self):
        Glue.__init__(self, 'fil')

class Fill(Glue):
    def __init__(self):
        Glue.__init__(self, 'fill')

class Filll(Glue):
    def __init__(self):
        Glue.__init__(self, 'filll')

class NegFil(Glue):
    def __init__(self):
        Glue.__init__(self, 'neg_fil')

class NegFill(Glue):
    def __init__(self):
        Glue.__init__(self, 'neg_fill')

class NegFilll(Glue):
    def __init__(self):
        Glue.__init__(self, 'neg_filll')

class SsGlue(Glue):
    def __init__(self):
        Glue.__init__(self, 'ss')

class HCentered(Hlist):
    """
    A convenience class to create an :class:`Hlist` whose contents are
    centered within its enclosing box.
    """
    def __init__(self, elements):
        Hlist.__init__(self, [SsGlue()] + elements + [SsGlue()],
                       do_kern=False)

class VCentered(Hlist):
    """
    A convenience class to create a :class:`Vlist` whose contents are
    centered within its enclosing box.
    """
    def __init__(self, elements):
        Vlist.__init__(self, [SsGlue()] + elements + [SsGlue()])

class Kern(Node):
    """
    A :class:`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.
    """
    def __init__(self, width):
        Node.__init__(self)
        self.width = width

    def __repr__(self):
        return "k%.02f" % self.width

    def shrink(self):
        Node.shrink(self)
        if self.size < NUM_SIZE_LEVELS:
            self.width *= SHRINK_FACTOR

    def grow(self):
        Node.grow(self)
        self.width *= GROW_FACTOR

class SubSuperCluster(Hlist):
    """
    :class:`SubSuperCluster` is a sort of hack to get around that fact
    that this code do 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
        Hlist.__init__(self, [])

class AutoHeightChar(Hlist):
    """
    :class:`AutoHeightChar` will create 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):
        alternatives = state.font_output.get_sized_alternatives_for_symbol(
            state.font, c)

        state = state.copy()
        target_total = height + depth
        for fontname, sym in alternatives:
            state.font = fontname
            char = Char(sym, state)
            if char.height + char.depth >= target_total:
                break

        factor = target_total / (char.height + char.depth)
        state.fontsize *= factor
        char = Char(sym, state)

        shift = (depth - char.depth)
        Hlist.__init__(self, [char])
        self.shift_amount = shift

class AutoWidthChar(Hlist):
    """
    :class:`AutoWidthChar` will create 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)

        Hlist.__init__(self, [char])
        self.width = char.width

class Ship(object):
    """
    Once the boxes have been set up, this sends them to output.  Since
    boxes can be inside of boxes inside of boxes, the main work of
    :class:`Ship` is done by two mutually recursive routines,
    :meth:`hlist_out` and :meth:`vlist_out`, which traverse the
    :class:`Hlist` nodes and :class:`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)

    def clamp(value):
        if value < -1000000000.:
            return -1000000000.
        if value > 1000000000.:
            return 1000000000.
        return value
    clamp = staticmethod(clamp)

    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 isinf(rule_height):
                    rule_height = box.height
                if isinf(rule_depth):
                    rule_depth = box.depth
                if rule_height > 0 and rule_width > 0:
                    self.cur_v = baseline + rule_depth
                    p.render(self.cur_h + self.off_h,
                             self.cur_v + self.off_v,
                             rule_width, rule_height)
                    self.cur_v = baseline
                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(float(box.glue_set) * cur_glue))
                    elif glue_spec.shrink_order == glue_order:
                        cur_glue += glue_spec.shrink
                        cur_g = round(clamp(float(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 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(float(box.glue_set) * cur_glue))
                    elif glue_spec.shrink_order == glue_order: # shrinking
                        cur_glue += glue_spec.shrink
                        cur_g = round(clamp(float(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(msg + "\n" + s)

    empty = Empty()
    empty.setParseAction(raise_error)
    return empty

class Parser(object):
    """
    This is the pyparsing-based parser for math expressions.  It
    actually parses full strings *containing* math expressions, in
    that raw text may also appear outside of pairs of ``$``.

    The grammar is based directly on that in TeX, though it cuts a few
    corners.
    """
    _binary_operators = set(r'''
      + *
      \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(r'''
      = < > :
      \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'''.split())

    _arrow_symbols = set(r'''
      \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(
        r"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 circled scr".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())

    _ambiDelim = set(r"""
      | \| / \backslash \uparrow \downarrow \updownarrow \Uparrow
      \Downarrow \Updownarrow .""".split())

    _leftDelim = set(r"( [ { < \lfloor \langle \lceil".split())

    _rightDelim = set(r") ] } > \rfloor \rangle \rceil".split())

    def __init__(self):
        # All forward declarations are here
        font = Forward().setParseAction(self.font).setName("font")
        latexfont = Forward()
        subsuper = Forward().setParseAction(self.subsuperscript).setName("subsuper")
        placeable = Forward().setName("placeable")
        simple = Forward().setName("simple")
        autoDelim = Forward().setParseAction(self.auto_sized_delimiter)
        self._expression = Forward().setParseAction(self.finish).setName("finish")

        float        = Regex(r"[-+]?([0-9]+\.?[0-9]*|\.[0-9]+)")

        lbrace       = Literal('{').suppress()
        rbrace       = Literal('}').suppress()
        start_group  = (Optional(latexfont) - lbrace)
        start_group.setParseAction(self.start_group)
        end_group    = rbrace.copy()
        end_group.setParseAction(self.end_group)

        bslash       = Literal('\\')

        accent       = oneOf(self._accent_map.keys() +
                             list(self._wide_accents))

        function     = oneOf(list(self._function_names))

        fontname     = oneOf(list(self._fontnames))
        latex2efont  = oneOf(['math' + x for x in self._fontnames])

        space        =(FollowedBy(bslash)
                     + oneOf([r'\ ',
                              r'\/',
                              r'\,',
                              r'\;',
                              r'\quad',
                              r'\qquad',
                              r'\!'])
                      ).setParseAction(self.space).setName('space')

        customspace  =(Literal(r'\hspace')
                     - (( lbrace
                        - float
                        - rbrace
                       ) | Error(r"Expected \hspace{n}"))
                     ).setParseAction(self.customspace).setName('customspace')

        unicode_range = u"\U00000080-\U0001ffff"
        symbol       =(Regex(UR"([a-zA-Z0-9 +\-*/<>=:,.;!'@()\[\]|%s])|(\\[%%${}\[\]_|])" % unicode_range)
                     | (Combine(
                         bslash
                       + oneOf(tex2uni.keys())
                       ) + FollowedBy(Regex("[^a-zA-Z]")))
                     ).setParseAction(self.symbol).leaveWhitespace()

        c_over_c     =(Suppress(bslash)
                     + oneOf(self._char_over_chars.keys())
                     ).setParseAction(self.char_over_chars)

        accent       = Group(
                         Suppress(bslash)
                       + accent
                       - placeable
                     ).setParseAction(self.accent).setName("accent")

        function     =(Suppress(bslash)
                     + function
                     ).setParseAction(self.function).setName("function")

        group        = Group(
                         start_group
                       + ZeroOrMore(
                           autoDelim
                         ^ simple)
                       - end_group
                     ).setParseAction(self.group).setName("group")

        font        <<(Suppress(bslash)
                     + fontname)

        latexfont   <<(Suppress(bslash)
                     + latex2efont)

        frac         = Group(
                       Suppress(Literal(r"\frac"))
                     + ((group + group)
                        | Error(r"Expected \frac{num}{den}"))
                     ).setParseAction(self.frac).setName("frac")

        sqrt         = Group(
                       Suppress(Literal(r"\sqrt"))
                     + Optional(
                         Suppress(Literal("["))
                       - Regex("[0-9]+")
                       - Suppress(Literal("]")),
                         default = None
                       )
                     + (group | Error("Expected \sqrt{value}"))
                     ).setParseAction(self.sqrt).setName("sqrt")

        placeable   <<(accent
                     ^ function
                     ^ (c_over_c | symbol)
                     ^ group
                     ^ frac
                     ^ sqrt
                     )

        simple      <<(space
                     | customspace
                     | font
                     | subsuper
                     )

        subsuperop   = oneOf(["_", "^"])

        subsuper    << Group(
                         ( Optional(placeable)
                         + OneOrMore(
                             subsuperop
                           - placeable
                           )
                         )
                       | placeable
                     )

        ambiDelim    = oneOf(list(self._ambiDelim))
        leftDelim    = oneOf(list(self._leftDelim))
        rightDelim   = oneOf(list(self._rightDelim))
        autoDelim   <<(Suppress(Literal(r"\left"))
                     + ((leftDelim | ambiDelim) | Error("Expected a delimiter"))
                     + Group(
                         autoDelim
                       ^ OneOrMore(simple))
                     + Suppress(Literal(r"\right"))
                     + ((rightDelim | ambiDelim) | Error("Expected a delimiter"))
                     )

        math         = OneOrMore(
                       autoDelim
                     ^ simple
                     ).setParseAction(self.math).setName("math")

        math_delim   = ~bslash + Literal('$')

        non_math     = Regex(r"(?:(?:\\[$])|[^$])*"
                     ).setParseAction(self.non_math).setName("non_math").leaveWhitespace()

        self._expression << (
            non_math
          + ZeroOrMore(
                Suppress(math_delim)
              + Optional(math)
              + (Suppress(math_delim)
                 | Error("Expected end of math '$'"))
              + non_math
            )
          ) + StringEnd()

        self.clear()

    def clear(self):
        """
        Clear any state before parsing.
        """
        self._expr = None
        self._state_stack = None
        self._em_width_cache = {}

    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 :class:`Node` instances.
        """
        self._state_stack = [self.State(fonts_object, 'default', 'rm', fontsize, dpi)]
        try:
            self._expression.parseString(s)
        except ParseException, err:
            raise ValueError("\n".join([
                        "",
                        err.line,
                        " " * (err.column - 1) + "^",
                        str(err)]))
        return self._expr

    # 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(object):
        """
        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)

        def _get_font(self):
            return self._font
        def _set_font(self, name):
            if name in ('it', 'rm', 'bf'):
                self.font_class = name
            self._font = name
        font = property(_get_font, _set_font)

    def get_state(self):
        """
        Get the current :class:`State` of the parser.
        """
        return self._state_stack[-1]

    def pop_state(self):
        """
        Pop a :class:`State` off of the stack.
        """
        self._state_stack.pop()

    def push_state(self):
        """
        Push a new :class:`State` onto the stack which is just a copy
        of the current state.
        """
        self._state_stack.append(self.get_state().copy())

    def finish(self, s, loc, toks):
        #~ print "finish", toks
        self._expr = Hlist(toks)
        return [self._expr]

    def math(self, s, loc, toks):
        #~ print "math", toks
        hlist = Hlist(toks)
        self.pop_state()
        return [hlist]

    def non_math(self, s, loc, toks):
        #~ print "non_math", toks
        s = toks[0].replace(r'\$', '$')
        symbols = [Char(c, self.get_state()) 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 = 'it'
        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, 'it', 'm', state.fontsize, state.dpi)
            width = metrics.advance
            self._em_width_cache[key] = width
        return Kern(width * percentage)

    _space_widths = { r'\ '      : 0.3,
                      r'\,'      : 0.4,
                      r'\;'      : 0.8,
                      r'\quad'   : 1.6,
                      r'\qquad'  : 3.2,
                      r'\!'      : -0.4,
                      r'\/'      : 0.4 }
    def space(self, s, loc, toks):
        assert(len(toks)==1)
        num = self._space_widths[toks[0]]
        box = self._make_space(num)
        return [box]

    def customspace(self, s, loc, toks):
        return [self._make_space(float(toks[1]))]

    def symbol(self, s, loc, toks):
        # print "symbol", toks
        c = toks[0]
        try:
            char = Char(c, self.get_state())
        except ValueError:
            raise ParseFatalException("Unknown symbol: %s" % c)

        if c in self._spaced_symbols:
            return [Hlist( [self._make_space(0.2),
                            char,
                            self._make_space(0.2)] ,
                           do_kern = False)]
        elif c in self._punctuation_symbols:
            return [Hlist( [char,
                            self._make_space(0.2)] ,
                           do_kern = False)]
        return [char]

    _char_over_chars = {
        # The first 2 entires 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' : (  ('rm', 'A', 1.0), (None, '\circ', 0.5), 0.0),
    }

    def char_over_chars(self, s, loc, toks):
        sym = toks[0]
        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'ddot'  : r'\combiningdiaeresis',
        r'tilde' : r'\combiningtilde',
        r'dot'   : r'\combiningdotabove',
        r'vec'   : r'\combiningrightarrowabove',
        r'"'     : r'\combiningdiaeresis',
        r"`"     : r'\combininggraveaccent',
        r"'"     : r'\combiningacuteaccent',
        r'~'     : r'\combiningtilde',
        r'.'     : r'\combiningdotabove',
        r'^'     : r'\circumflexaccent'
        }

    _wide_accents = set(r"widehat widetilde".split())

    def accent(self, s, loc, toks):
        assert(len(toks)==1)
        state = self.get_state()
        thickness = state.font_output.get_underline_thickness(
            state.font, state.fontsize, state.dpi)
        if len(toks[0]) != 2:
            raise ParseFatalException("Error parsing accent")
        accent, sym = toks[0]
        if accent in self._wide_accents:
            accent = AutoWidthChar(
                '\\' + accent, sym.width, state, char_class=Accent)
        else:
            accent = Accent(self._accent_map[accent], state)
        centered = HCentered([accent])
        centered.hpack(sym.width, 'exactly')
        return Vlist([
                centered,
                Vbox(0., thickness * 2.0),
                Hlist([sym])
                ])

    def function(self, s, loc, toks):
        #~ print "function", toks
        self.push_state()
        state = self.get_state()
        state.font = 'rm'
        hlist = Hlist([Char(c, state) for c in toks[0]])
        self.pop_state()
        hlist.function_name = toks[0]
        return hlist

    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]

    def end_group(self, s, loc, toks):
        self.pop_state()
        return []

    def font(self, s, loc, toks):
        assert(len(toks)==1)
        name = toks[0]
        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 subsuperscript(self, s, loc, toks):
        assert(len(toks)==1)
        # print 'subsuperscript', toks

        nucleus = None
        sub = None
        super = None

        if len(toks[0]) == 1:
            return toks[0].asList()
        elif len(toks[0]) == 2:
            op, next = toks[0]
            nucleus = Hbox(0.0)
            if op == '_':
                sub = next
            else:
                super = next
        elif len(toks[0]) == 3:
            nucleus, op, next = toks[0]
            if op == '_':
                sub = next
            else:
                super = next
        elif len(toks[0]) == 5:
            nucleus, op1, next1, op2, next2 = toks[0]
            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)

        # Handle over/under symbols, such as sum or integral
        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)

            if super is not None:
                hlist = HCentered([super])
                hlist.hpack(width, 'exactly')
                vlist.extend([hlist, Kern(rule_thickness * 3.0)])
            hlist = HCentered([nucleus])
            hlist.hpack(width, 'exactly')
            vlist.append(hlist)
            if sub is not None:
                hlist = HCentered([sub])
                hlist.hpack(width, 'exactly')
                vlist.extend([Kern(rule_thickness * 3.0), hlist])
                shift = hlist.height + hlist.depth + rule_thickness * 2.0
            vlist = Vlist(vlist)
            vlist.shift_amount = shift + nucleus.depth * 0.5
            result = Hlist([vlist])
            return [result]

        # Handle regular sub/superscripts
        shift_up = nucleus.height - SUBDROP * xHeight
        if self.is_dropsub(nucleus):
            shift_down = nucleus.depth + SUBDROP * xHeight
        else:
            shift_down = SUBDROP * xHeight
        if super is None:
            # node757
            sub.shrink()
            x = Hlist([sub])
            # x.width += SCRIPT_SPACE * xHeight
            shift_down = max(shift_down, SUB1)
            clr = x.height - (abs(xHeight * 4.0) / 5.0)
            shift_down = max(shift_down, clr)
            x.shift_amount = shift_down
        else:
            super.shrink()
            x = Hlist([super, Kern(SCRIPT_SPACE * xHeight)])
            # x.width += SCRIPT_SPACE * xHeight
            clr = SUP1 * xHeight
            shift_up = max(shift_up, clr)
            clr = x.depth + (abs(xHeight) / 4.0)
            shift_up = max(shift_up, clr)
            if sub is None:
                x.shift_amount = -shift_up
            else: # Both sub and superscript
                sub.shrink()
                y = Hlist([sub])
                # y.width += SCRIPT_SPACE * xHeight
                shift_down = max(shift_down, SUB1 * xHeight)
                clr = (2.0 * rule_thickness -
                       ((shift_up - x.depth) - (y.height - shift_down)))
                if clr > 0.:
                    shift_up += clr
                    shift_down += clr
                if self.is_slanted(nucleus):
                    x.shift_amount = DELTA * (shift_up + shift_down)
                x = Vlist([x,
                           Kern((shift_up - x.depth) - (y.height - shift_down)),
                           y])
                x.shift_amount = shift_down

        result = Hlist([nucleus, x])
        return [result]

    def frac(self, s, loc, toks):
        assert(len(toks)==1)
        assert(len(toks[0])==2)
        state = self.get_state()
        thickness = state.font_output.get_underline_thickness(
            state.font, state.fontsize, state.dpi)

        num, den = toks[0]
        num.shrink()
        den.shrink()
        cnum = HCentered([num])
        cden = HCentered([den])
        width = max(num.width, den.width) + thickness * 10.
        cnum.hpack(width, 'exactly')
        cden.hpack(width, 'exactly')
        vlist = Vlist([cnum,                      # numerator
                       Vbox(0, thickness * 2.0),  # space
                       Hrule(state),              # rule
                       Vbox(0, thickness * 4.0),  # space
                       cden                       # denominator
                       ])

        # Shift so the fraction line sits in the middle of the
        # equals sign
        metrics = state.font_output.get_metrics(
            state.font, 'it', '=', state.fontsize, state.dpi)
        shift = (cden.height -
                 ((metrics.ymax + metrics.ymin) / 2 -
                  thickness * 3.0))
        vlist.shift_amount = shift

        hlist = Hlist([vlist, Hbox(thickness * 2.)])
        return [hlist]

    def sqrt(self, s, loc, toks):
        #~ print "sqrt", toks
        root, body = toks[0]
        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(thickness * 2.0),
                             body,
                             Hbox(thickness * 2.0)])
        rightside = Vlist([Hrule(state),
                           Fill(),
                           padded_body])
        # Stretch the glue between the hrule and the body
        rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
                        depth, 'exactly')

        # Add the root and shift it upward so it is above the tick.
        # The value of 0.6 is a hard-coded hack ;)
        if root is None:
            root = Box(check.width * 0.5, 0., 0.)
        else:
            root = Hlist([Char(x, state) for x in 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 auto_sized_delimiter(self, s, loc, toks):
        #~ print "auto_sized_delimiter", toks
        front, middle, back = toks
        state = self.get_state()
        height = max([x.height for x in middle])
        depth = max([x.depth for x in middle])
        parts = []
        # \left. and \right. aren't supposed to produce any symbols
        if front != '.':
            parts.append(AutoHeightChar(front, height, depth, state))
        parts.extend(middle.asList())
        if back != '.':
            parts.append(AutoHeightChar(back, height, depth, state))
        hlist = Hlist(parts)
        return hlist

###

##############################################################################
# MAIN

class MathTextParser(object):
    _parser = None

    _backend_mapping = {
        'bitmap': MathtextBackendBitmap,
        'agg'   : MathtextBackendAgg,
        'ps'    : MathtextBackendPs,
        'pdf'   : MathtextBackendPdf,
        'svg'   : MathtextBackendSvg,
        'cairo' : MathtextBackendCairo,
        'macosx': MathtextBackendAgg,
        }

    _font_type_mapping = {
        'cm'       : BakomaFonts,
        'stix'     : StixFonts,
        'stixsans' : StixSansFonts,
        'custom'   : UnicodeFonts
        }

    def __init__(self, output):
        """
        Create a MathTextParser for the given backend *output*.
        """
        self._output = output.lower()
        self._cache = maxdict(50)

    def parse(self, s, dpi = 72, prop = None):
        """
        Parse the given math expression *s* at the given *dpi*.  If
        *prop* is provided, it is a
        :class:`~matplotlib.font_manager.FontProperties` object
        specifying the "default" font to use in the math expression,
        used for all non-math text.

        The results are cached, so multiple calls to :meth:`parse`
        with the same expression should be fast.
        """
        if prop is None:
            prop = FontProperties()
        cacheKey = (s, dpi, hash(prop))
        result = self._cache.get(cacheKey)
        if result is not None:
            return result

        if self._output == 'ps' and rcParams['ps.useafm']:
            font_output = StandardPsFonts(prop)
        else:
            backend = self._backend_mapping[self._output]()
            fontset = rcParams['mathtext.fontset']
            fontset_class = self._font_type_mapping.get(fontset.lower())
            if fontset_class is not None:
                font_output = fontset_class(prop, backend)
            else:
                raise ValueError(
                    "mathtext.fontset must be either 'cm', 'stix', "
                    "'stixsans', or 'custom'")

        fontsize = prop.get_size_in_points()

        # This is a class variable so we don't rebuild the parser
        # with each request.
        if self._parser is None:
            self.__class__._parser = Parser()

        box = self._parser.parse(s, font_output, fontsize, dpi)
        font_output.set_canvas_size(box.width, box.height, box.depth)
        result = font_output.get_results(box)
        self._cache[cacheKey] = result
        # Free up the transient data structures
        self._parser.clear()

        # Fix cyclical references
        font_output.destroy()
        font_output.mathtext_backend.fonts_object = None
        font_output.mathtext_backend = None

        return result

    def to_mask(self, texstr, dpi=120, fontsize=14):
        """
        *texstr*
            A valid mathtext string, eg r'IQ: $\sigma_i=15$'

        *dpi*
            The dots-per-inch to render the text

        *fontsize*
            The font size in points

        Returns a tuple (*array*, *depth*)

          - *array* is an NxM uint8 alpha ubyte mask array of
            rasterized tex.

          - depth is the offset of the baseline from the bottom of the
            image in pixels.
        """
        assert(self._output=="bitmap")
        prop = FontProperties(size=fontsize)
        ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop)

        x = ftimage.as_array()
        return x, depth

    def to_rgba(self, texstr, color='black', dpi=120, fontsize=14):
        """
        *texstr*
            A valid mathtext string, eg r'IQ: $\sigma_i=15$'

        *color*
            Any matplotlib color argument

        *dpi*
            The dots-per-inch to render the text

        *fontsize*
            The font size in points

        Returns a tuple (*array*, *depth*)

          - *array* is an NxM uint8 alpha ubyte mask array of
            rasterized tex.

          - depth is the offset of the baseline from the bottom of the
            image in pixels.
        """
        x, depth = self.to_mask(texstr, dpi=dpi, fontsize=fontsize)

        r, g, b = mcolors.colorConverter.to_rgb(color)
        RGBA = np.zeros((x.shape[0], x.shape[1], 4), dtype=np.uint8)
        RGBA[:,:,0] = int(255*r)
        RGBA[:,:,1] = int(255*g)
        RGBA[:,:,2] = int(255*b)
        RGBA[:,:,3] = x
        return RGBA, depth

    def to_png(self, filename, texstr, color='black', dpi=120, fontsize=14):
        """
        Writes a tex expression to a PNG file.

        Returns the offset of the baseline from the bottom of the
        image in pixels.

        *filename*
            A writable filename or fileobject

        *texstr*
            A valid mathtext string, eg r'IQ: $\sigma_i=15$'

        *color*
            A valid matplotlib color argument

        *dpi*
            The dots-per-inch to render the text

        *fontsize*
            The font size in points

        Returns the offset of the baseline from the bottom of the
        image in pixels.
        """

        rgba, depth = self.to_rgba(texstr, color=color, dpi=dpi, fontsize=fontsize)
        numrows, numcols, tmp = rgba.shape
        _png.write_png(rgba.tostring(), numcols, numrows, filename)
        return depth

    def get_depth(self, texstr, dpi=120, fontsize=14):
        """
        Returns the offset of the baseline from the bottom of the
        image in pixels.

        *texstr*
            A valid mathtext string, eg r'IQ: $\sigma_i=15$'

        *dpi*
            The dots-per-inch to render the text

        *fontsize*
            The font size in points
        """
        assert(self._output=="bitmap")
        prop = FontProperties(size=fontsize)
        ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop)
        return depth