Update metrics using TeX metrics instead of TTF metrics

Summary:
Instead of using the metrics from our generated TTF files, use the fonts that
TeX ships with. Pull the mapping out of the MathJax-dev repo from makeFF to get
the correct mapping of metrics to font characters, and use our own tfm reader to
extract metrics out of the tfm files into a useable format. Add a README and
Makefile rule to make this process easier in the future.

Also remove the silly 0.05em we put on supsubs because our italic correction
works now.

Test Plan:
- Run huxley tests, see that changes are because of font metric changes.
- See that the extension piece of `\bigl |` now extends above the top, as it is
  supposed to.

Reviewers: alpert

Reviewed By: alpert

Differential Revision: http://phabricator.khanacademy.org/D12867

Makefile

@@ -1,6 +1,6 @@
 UNAME=$(shell uname)
 
-.PHONY: build setup copy serve clean
+.PHONY: build setup copy serve clean metrics
 build: setup build/katex.js build/katex.less.css
 ifeq ($(UNAME),Darwin)
 build: pdiff
@@ -36,5 +36,8 @@ pdiff:
 	@printf "Comparing to reference pdiff image...\n"
 	@node test/pdiff.js
 
+metrics:
+	cd metrics && ./mapping.pl | ./extract_tfms.py | ./replace_line.py
+
 clean:
 	rm -rf build/*

metric_parse.rb

@@ -1,47 +0,0 @@
-require 'json'
-
-require 'rubygems'
-
-require 'ttfunk'
-
-def metrics_for_file(filename)
-  file = TTFunk::File.open(filename)
-  per_em = 1.0 * file.header.units_per_em
-
-  chars = {}
-
-  file.cmap.unicode[0].code_map.sort.each do |u, g|
-    horiz = file.horizontal_metrics.for(g)
-
-    # width = (horiz.advance_width / per_em).round(3)
-    height = 0
-    depth = 0
-    italic = 0
-
-    glyph = file.glyph_outlines.for(g)
-    if glyph
-      height = (glyph.y_max / per_em).round(3)
-      depth = (-glyph.y_min / per_em).round(3)
-      italic = [0, (glyph.x_max - horiz.advance_width) / per_em].max.round(3)
-    end
-
-    chars[u] = {
-      # :width => width,
-      :height => height,
-      :depth => depth,
-      :italic => italic,
-    }
-  end
-
-  chars
-end
-
-font_dir = File.join(File.dirname(__FILE__), 'static/fonts/')
-metrics = {}
-
-%w[Main-Regular Math-Italic AMS-Regular
-   Size1-Regular Size2-Regular Size3-Regular Size4-Regular].each do |face|
-  metrics[face] = metrics_for_file(File.join(font_dir, 'KaTeX_%s.ttf' % face))
-end
-
-puts "var metricMap = %s;" % metrics.to_json

metrics/README.md

@@ -0,0 +1,18 @@
+### How to generate new metrics
+-------------------------------
+
+There are several requirements for generating the metrics used by KaTeX.
+
+- You need to have an installation of TeX which supports kpathsea (you can check
+this by running `tex --version`, and seeing if it has a line that looks like >
+kpathsea version 6.2.0
+
+- You need the JSON module for perl. You can install this either from CPAN or with
+your package manager.
+
+Once you have these things, run
+
+    make metrics
+
+which should generate new metrics and place them into `fontMetrics.js`. You're
+done!

metrics/extract_tfms.py

@@ -0,0 +1,70 @@
+#!/usr/bin/env python
+
+import collections
+import json
+import parse_tfm
+import subprocess
+import sys
+
+
+def find_font_path(font_name):
+    try:
+        font_path = subprocess.check_output(['kpsewhich', font_name])
+    except OSError:
+        raise RuntimeError("Couldn't find kpsewhich program, make sure you" +
+                           " have TeX installed")
+    except subprocess.CalledProcessError:
+        raise RuntimeError("Couldn't find font metrics: '%s'" % font_name)
+    return font_path.strip()
+
+
+def main():
+    mapping = json.load(sys.stdin)
+
+    fonts = [
+        'cmbsy10.tfm',
+        'cmbx10.tfm',
+        'cmex10.tfm',
+        'cmmi10.tfm',
+        'cmmib10.tfm',
+        'cmr10.tfm',
+        'cmsy10.tfm',
+        'cmti10.tfm',
+        'msam10.tfm',
+        'msbm10.tfm'
+    ]
+
+    font_name_to_tfm = {}
+
+    for font_name in fonts:
+        font_basename = font_name.split('.')[0]
+        font_path = find_font_path(font_name)
+        font_name_to_tfm[font_basename] = parse_tfm.read_tfm_file(font_path)
+
+    families = collections.defaultdict(dict)
+
+    for family, chars in mapping.iteritems():
+        for char, char_data in chars.iteritems():
+            char_num = int(char)
+
+            font = char_data['font']
+            tex_char_num = int(char_data['char'])
+            yshift = float(char_data['yshift'])
+
+            tfm_char = font_name_to_tfm[font].get_char_metrics(tex_char_num)
+
+            height = round(tfm_char.height + yshift / 1000.0, 3)
+            depth = round(tfm_char.depth - yshift / 1000.0, 3)
+            italic = round(tfm_char.italic_correction, 3)
+
+            families[family][char_num] = {
+                'height': height,
+                'depth': depth,
+                'italic': italic
+            }
+
+    sys.stdout.write(
+        json.dumps(families, separators=(',', ':'), sort_keys=True))
+
+if __name__ == '__main__':
+    main()

metrics/mapping.pl

@@ -0,0 +1,997 @@
+#! /usr/bin/perl
+
+# Adapted from the MathJax-dev repository file /fonts/OTF/TeX/makeFF under the
+# Apache 2 license
+
+# We use this file to recover the mapping from TeX fonts to KaTeX fonts, to
+# accurately extract the metrics from the corresponding .tfm (TeX font metric)
+# files
+
+use JSON;
+
+$map{cmr10} = {
+  "Main-Regular" => [
+    [0,1] => 0x393,         # \Gamma, \Delta
+    2 => 0x398,             # \Theta
+    3 => 0x39B,             # \Lambda
+    4 => 0x39E,             # \Xi
+    5 => 0x3A0,             # \Pi
+    6 => 0x3A3,             # \Sigma
+    [7,8] => 0x3A5,         # \Upsilon, \Phi
+    [9,0xA] => 0x3A8,       # \Psi, \Omega
+
+    0x10 => 0x131,          # \imath (roman)
+    0x11 => 0x237,          # \jmath (roman)
+    0x12 => 0x60,           # \grave
+    0x12 => 0x2CB,          # \grave
+    0x12 => [0x300,-500,0], # \grave (combining)
+    0x13 => 0xB4,           # \acute
+    0x13 => 0x2CA,          # \acute
+    0x13 => [0x301,-500,0], # \acute (combining)
+    0x14 => 0x2C7,          # \check
+    0x14 => [0x30C,-500,0], # \check (combining)
+    0x15 => 0x2D8,          # \breve
+    0x15 => [0x306,-500,0], # \breve (combining)
+    0x16 => 0xAF,           # \bar
+    0x16 => 0x2C9,          # \bar
+    0x16 => [0x304,-500,0], # \bar (combining)
+    0x17 => [0xB0,-125,0],  # ring above
+    0x17 => [0x2DA,-125,0], # ring above
+    0x17 => [0x30A,-625,0], # ring above (combining)
+
+    [0x21,0x2F] => 0x21,    # !, ", #, $, %, &, ', (, ), *, +, comma, -, ., /
+    0x22 => 0x201D,         # "
+    0x27 => 0x2019,         # '
+    [0x30,0x39] => 0x30,    # 0-9
+    [0x3A,0x3B] => 0x3A,    # :, ;
+    0x3D => 0x3D,           # =
+    [0x3F,0x40] => 0x3F,    # ?, @
+    [0x41,0x5A] => 0x41,    # A-Z
+    0x5B => 0x5B,           # [
+    0x5C => 0x201C,         # ``
+    [0x5D,0x5E] => 0x5D,    # ], ^
+    0x5E => 0x2C6,          # \hat
+    0x5E => [0x302,-500,0], # \hat (combining)
+    0x5F => [0x2D9,111,0],  # \dot
+    0x5F => [0x307,-389,0], # \dot (combining)
+    0x60 => 0x2018,         # `
+    [0x61,0x7A] => 0x61,    # a-z
+    [0x7B,0x7C] => 0x2013,  # \endash, \emdash
+    0x7B => [0x5F,0,-310],  # underline
+    0x7D => [0x30B,-500,0], # double acute (combining)
+    0x7E => [0x7E,0,-350],  # ~
+    0x7E => 0x2DC,          # \tilde
+    0x7E => [0x303,-500,0], # \tilde (combining)
+    0x7F => 0xA8,           # \ddot
+    0x7F => [0x308,-500,0], # \ddot (combining)
+  ],
+};
+
+$map{cmmi10} = {
+  "Math-Regular" => [
+    [0,1] => 0x393,         # \Gamma, \Delta
+    2 => 0x398,             # \Theta
+    3 => 0x39B,             # \Lambda
+    4 => 0x39E,             # \Xi
+    5 => 0x3A0,             # \Pi
+    6 => 0x3A3,             # \Sigma
+    [7,8] => 0x3A5,         # \Upsilon, \Phi
+    [9,0xA] => 0x3A8,       # \Psi, \Omega
+
+    [0xB,0xE] => 0x3B1,     # \alpha, \beta, \gamma, \delta
+    0xF => 0x3F5,           # \elpsilon
+    [0x10,0x18] => 0x3B6,   # \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu, \nu, \xi
+    [0x19,0x1A] => 0x3C0,   # \pi, \rho
+    [0x1B,0x1D] => 0x3C3,   # \sigma, \tau, \upsilon
+    0x1E => 0x3D5,          # \phi
+    [0x1F,0x21] => 0x3C7,   # \chi, \psi, \omega
+    0x22 => 0x3B5,          # \varepsilon
+    0x23 => 0x3D1,          # \vartheta
+    0x24 => 0x3D6,          # \varpi
+    0x25 => 0x3F1,          # \varrho
+    0x26 => 0x3C2,          # \varsigma
+    0x27 => 0x3C6,          # \varphi
+
+    [0x41,0x5A] => 0x41,    # A-Z
+    [0x61,0x7A] => 0x61,    # a - z
+    0x6F => 0x3BF,          # omicron
+  ],
+
+  "Math-Italic" => [
+    [0,1] => 0x393,         # \Gamma, \Delta
+    2 => 0x398,             # \Theta
+    3 => 0x39B,             # \Lambda
+    4 => 0x39E,             # \Xi
+    5 => 0x3A0,             # \Pi
+    6 => 0x3A3,             # \Sigma
+    [7,8] => 0x3A5,         # \Upsilon, \Phi
+    [9,0xA] => 0x3A8,       # \Psi, \Omega
+
+    [0xB,0xE] => 0x3B1,     # \alpha, \beta, \gamma, \delta
+    0xF => 0x3F5,           # \elpsilon
+    [0x10,0x18] => 0x3B6,   # \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu, \nu, \xi
+    [0x19,0x1A] => 0x3C0,   # \pi, \rho
+    [0x1B,0x1D] => 0x3C3,   # \sigma, \tau, \upsilon
+    0x1E => 0x3D5,          # \phi
+    [0x1F,0x21] => 0x3C7,   # \chi, \psi, \omega
+    0x22 => 0x3B5,          # \varepsilon
+    0x23 => 0x3D1,          # \vartheta
+    0x24 => 0x3D6,          # \varpi
+    0x25 => 0x3F1,          # \varrho
+    0x26 => 0x3C2,          # \varsigma
+    0x27 => 0x3C6,          # \varphi
+
+    [0x41,0x5A] => 0x41,    # A-Z
+    [0x61,0x7A] => 0x61,    # a - z
+    0x6F => 0x3BF,          # omicron
+  ],
+
+  "Main-Regular" => [
+    0x28 => 0x21BC,         # \leftharpoonup
+    0x29 => 0x21BD,         # \leftharpoondown
+    0x2A => 0x21C0,         # \rightharpoonup
+    0x2B => 0x21C1,         # \rightharpoondown
+
+    0x2E => 0x25B9,         # \triangleright
+    0x2F => 0x25C3,         # \triangleleft
+
+    0x3A => 0x2E,           # .
+    0x3B => 0x2C,           # ,
+    0x3C => 0x3C,           # <
+    0x3D => 0x2215,         # /
+    0x3E => 0x3E,           # >
+    0x3F => 0x22C6,         # \star
+    0x40 => 0x2202,         # \partial
+
+    [0x5B,0x5D] => 0x266D,  # \flat, \natural, \sharp
+    0x5E => 0x2323,         # \smile
+    0x5F => 0x2322,         # \frown
+    0x60 => 0x2113,         # \ell
+
+    0x7B => 0x131,          # \imath
+    0x7C => 0x237,          # \jmath
+    0x7D => 0x2118,         # \wp
+    0x7E => [0x20D7,-653,0],# \vec
+  ]
+};
+
+$map{cmsy10} = {
+  "Main-Regular" => [
+    [0,1] => 0x2212,        # -
+    1 => 0x22C5,            # \cdot
+    2 => 0xD7,              # \times
+    3 => 0x2217,            # \ast
+    4 => 0xF7,              # \div
+    5 => 0x22C4,            # \diamond
+    6 => 0xB1,              # \pm
+    7 => 0x2213,            # \mp
+    [8,0xC] => 0x2295,      # \oplus, \ominus, \otimes, \oslash, \odot
+    0xD => 0x25EF,          # \bigcirc
+    [0xE,0xF] => 0x2218,    # \circ, \bullet
+
+    0x10 => 0x224D,         # \asymp
+    0x11 => 0x2261,         # \equiv
+    [0x12,0x13] => 0x2286,  # \subseteq, \supseteq
+    [0x14,0x15] => 0x2264,  # \leq, \geq
+    [0x16,0x17] => 0x2AAF,  # \preceq, \succeq
+    0x18 => 0x223C,         # \sim
+    0x19 => 0x2248,         # \approx
+    [0x1A,0x1B] => 0x2282,  # \subset, \supset
+    [0x1C,0x1D] => 0x226A,  # \ll, \gg
+    [0x1E,0x1F] => 0x227A,  # \prec, \succ
+
+    0x20 => 0x2190,         # \leftarrow
+    0x21 => 0x2192,         # \rightarrow
+    0x22 => 0x2191,         # \uparrow
+    0x23 => 0x2193,         # \downarrow
+    0x24 => 0x2194,         # \leftrightarrow
+    0x25 => 0x2197,         # \nearrow
+    0x26 => 0x2198,         # \searrow
+    0x27 => 0x2243,         # \simeq
+
+    0x28 => 0x21D0,         # \Leftarrow
+    0x29 => 0x21D2,         # \Rightarrow
+    0x2A => 0x21D1,         # \Uparrow
+    0x2B => 0x21D3,         # \Downarrow
+    0x2C => 0x21D4,         # \Leftrightarrow
+    0x2D => 0x2196,         # \nwarrow
+    0x2E => 0x2199,         # \swarrow
+    0x2F => 0x221D,         # \propto
+
+    0x30 => 0x2032,         # \prime
+    0x31 => 0x221E,         # \infty
+    0x32 => 0x2208,         # \in
+    0x33 => 0x220B,         # \ni
+    0x34 => 0x25B3,         # \bigtriangleup and \triangle
+    0x35 => 0x25BD,         # \bigtriangledown
+    0x36 => [0x338,-778,0], # \not (combining)
+
+    0x38 => 0x2200,         # \forall
+    0x39 => 0x2203,         # \exists
+    0x3A => 0xAC,           # \neg
+    0x3B => 0x2205,         # \emptyset
+    0x3C => 0x211C,         # \Re
+    0x3D => 0x2111,         # \Im
+    0x3E => 0x22A4,         # \top
+    0x3F => 0x22A5,         # \bot
+
+    0x40 => 0x2135,         # \aleph
+
+    0x5B => 0x222A,         # \cup
+    0x5C => 0x2229,         # \cap
+    0x5D => 0x228E,         # \uplus
+    [0x5E,0x5F] => 0x2227,  # \wedge, \vee
+
+    [0x60,0x61] => 0x22A2,  # \vdash, \dashv
+    [0x62,0x63] => 0x230A,  # \lfloor, \rfloor
+    [0x64,0x65] => 0x2308,  # \lceil, \rceil
+    0x66 => 0x7B,           # {
+    0x67 => 0x7D,           # }
+    [0x68,0x69] => 0x27E8,  # \langle, \rangle
+    0x6A => 0x7C,           # |
+    0x6A => 0x2223,         # \vert
+    0x6B => 0x2225,         # \Vert
+    0x6C => 0x2195,         # \updownarrow
+    0x6D => 0x21D5,         # \Updownarrow
+    0x6E => 0x5C,           # \backslash
+    0x6E => 0x2216,         # \setminus
+    0x6F => 0x2240,         # \wr
+
+    0x70 => [0x221A,0,760], # \surd    ### adjust position so font doesn't have a large depth
+    0x71 => 0x2A3F,         # \amalg
+    0x72 => 0x2207,         # \nabla
+    0x73 => 0x222B,         # \int
+    0x74 => 0x2294,         # \sqcup
+    0x75 => 0x2293,         # \sqcap
+    [0x76,0x77] => 0x2291,  # \sqsubseteq, \sqsupseteq
+
+    [0x79,0x7A] => 0x2020,  # \dagger, \ddagger
+
+    0x7C => 0x2663,         # \clubsuit
+    0x7D => 0x2662,         # \diamondsuit
+    0x7E => 0x2661,         # \heartsuit
+    0x7F => 0x2660,         # \spadesuit
+  ],
+
+  "Math-Italic" => [
+    0x36 => 0x2F            # \not
+  ],
+};
+
+$map{cmex10} = {
+  "Size1" => [
+    0 => [0x28,0,810],      # (
+    1 => [0x29,0,810],      # )
+    2 => [0x5B,0,810],      # [
+    3 => [0x5D,0,810],      # ]
+    4 => [0x230A,0,810],    # \lfloor
+    5 => [0x230B,0,810],    # \rfloor
+    6 => [0x2308,0,810],    # \lceil
+    7 => [0x2309,0,810],    # \rceil
+    8 => [0x7B,0,810],      # {
+    9 => [0x7D,0,810],      # }
+    0xA => [0x27E8,0,810],  # \langle
+    0xB => [0x27E9,0,810],  # \rangle
+    0xC => [0x2223,0,606],  # \vert
+    0xD => [0x2225,0,606],  # \Vert
+    0xE => [0x2F,0,810],    # /
+    0xF => [0x5C,0,810],    # \
+
+    0x46 => [0x2A06,0,750], # \bigsqcup
+    0x48 => [0x222E,0,805], # \oint
+    0x4A => [0x2A00,0,750], # \bigodot
+    0x4C => [0x2A01,0,750], # \bigoplus
+    0x4E => [0x2A02,0,750], # \bigotimes
+
+    0x50 => [0x2211,0,750], # \sum
+    0x51 => [0x220F,0,750], # \prod
+    0x52 => [0x222B,0,805], # \int
+    0x53 => [0x22C3,0,750], # \bigcup
+    0x54 => [0x22C2,0,750], # \bigcap
+    0x55 => [0x2A04,0,750], # \biguplus
+    0x56 => [0x22C0,0,750], # \bigwedge
+    0x57 => [0x22C1,0,750], # \bigvee
+
+    0x60 => [0x2210,0,750], # \coprod
+    0x62 => 0x2C6,          # \widehat
+    0x62 => [0x302,-556,0], # \widehat (combining)
+    0x65 => 0x2DC,          # \widetilde
+    0x65 => [0x303,-556,0], # \widetilde (combining)
+
+    0x70 => [0x221A,0,810], # surd
+    0x3F => [0x23D0,0,601], # arrow extension
+    0x77 => [0x2016,0,601], # Arrow extension (non-standard)
+    0x78 => [0x2191,0,600], # uparrow top
+    0x79 => [0x2193,0,600], # downarrow bottom
+    0x7E => [0x21D1,0,600], # Uparrow top
+    0x7F => [0x21D3,0,600], # Downarrow bottom
+  ],
+
+  "Size2" => [
+    0x10 => [0x28,0,1110],  # (
+    0x11 => [0x29,0,1110],  # )
+    0x2E => [0x2F,0,1110],  # /
+    0x2F => [0x5C,0,1110],  # \
+    0x44 => [0x27E8,0,1110],# \langle
+    0x45 => [0x27E9,0,1110],# \rangle
+
+    0x47 => [0x2A06,0,950], # \bigsqcup
+    0x49 => [0x222E,0,1360],# \oint
+    0x4B => [0x2A00,0,950], # \bigodot
+    0x4D => [0x2A01,0,950], # \bigoplus
+    0x4F => [0x2A02,0,950], # \bigotimes
+
+    0x58 => [0x2211,0,950], # \sum
+    0x59 => [0x220F,0,950], # \prod
+    0x5A => [0x222B,0,1360],# \int
+    0x5B => [0x22C3,0,950], # \bigcup
+    0x5C => [0x22C2,0,950], # \bigcap
+    0x5D => [0x2A04,0,950], # \biguplus
+    0x5E => [0x22C0,0,950], # \bigwedge
+    0x5F => [0x22C1,0,950], # \bigvee
+    0x61 => [0x2210,0,950], # \coprod
+
+    0x63 => 0x2C6,          # \widehat
+    0x63 => [0x302,-1000,0],# \widehat (combining)
+    0x66 => 0x2DC,          # \widetilde
+    0x66 => [0x303,-1000,0],# \widetilde (combining)
+
+    0x68 => [0x5B,0,1110],  # [
+    0x69 => [0x5D,0,1110],  # ]
+    0x6A => [0x230A,0,1110],# \lfloor
+    0x6B => [0x230B,0,1110],# \rfloor
+    0x6C => [0x2308,0,1110],# \lceil
+    0x6D => [0x2309,0,1110],# \rceil
+    0x6E => [0x7B,0,1110],  # {
+    0x6F => [0x7D,0,1110],  # }
+    0x71 => [0x221A,0,1110],# surd
+  ],
+
+  "Size3" => [
+    0x12 => [0x28,0,1410],  # (
+    0x13 => [0x29,0,1410],  # )
+    0x14 => [0x5B,0,1410],  # [
+    0x15 => [0x5D,0,1410],  # ]
+    0x16 => [0x230A,0,1410],# \lfloor
+    0x17 => [0x230B,0,1410],# \rfloor
+    0x18 => [0x2308,0,1410],# \lceil
+    0x19 => [0x2309,0,1410],# \rceil
+    0x1A => [0x7B,0,1410],  # {
+    0x1B => [0x7D,0,1410],  # }
+    0x1C => [0x27E8,0,1410],# \langle
+    0x1D => [0x27E9,0,1410],# \rangle
+    0x1E => [0x2F,0,1410],  # /
+    0x1F => [0x5C,0,1410],  # \
+    0x64 => 0x2C6,          # \widehat
+    0x64 => [0x302,-1444,0],# \widehat (combining)
+    0x67 => 0x2DC,          # \widetilde
+    0x67 => [0x303,-1444,0],# \widetilde (combining)
+    0x72 => [0x221A,0,1410],# surd
+  ],
+
+  "Size4" => [
+    0x20 => [0x28,0,1710],  # (
+    0x21 => [0x29,0,1710],  # )
+    0x22 => [0x5B,0,1710],  # [
+    0x23 => [0x5D,0,1710],  # ]
+    0x24 => [0x230A,0,1710],# \lfloor
+    0x25 => [0x230B,0,1710],# \rfloor
+    0x26 => [0x2308,0,1710],# \lceil
+    0x27 => [0x2309,0,1710],# \rceil
+    0x28 => [0x7B,0,1710],  # {
+    0x29 => [0x7D,0,1710],  # }
+    0x2A => [0x27E8,0,1710],# \langle
+    0x2B => [0x27E9,0,1710],# \rangle
+    0x2C => [0x2F,0,1710],  # /
+    0x2D => [0x5C,0,1710],  # \
+    0x73 => [0x221A,0,1710],# surd
+
+    0x30 => [0x239B,0,1115],# left paren upper hook
+    0x31 => [0x239E,0,1115],# right paren upper hook
+    0x32 => [0x23A1,0,1115],# left square bracket upper corner
+    0x33 => [0x23A4,0,1115],# right square bracket upper corner
+    0x34 => [0x23A3,0,1115],# left square bracket lower corner
+    0x35 => [0x23A6,0,1115],# right square bracket lower hook
+    0x36 => [0x23A2,0,601], # left square bracket extension
+    0x37 => [0x23A5,0,601], # right square bracket extension
+    0x38 => [0x23A7,0,900], # left curly brace upper hook
+    0x39 => [0x23AB,0,900], # right curly brace upper hook
+    0x3A => 0x23A9,         # left curly brace lower hook
+    0x3B => 0x23AD,         # right curly brace lower hook
+    0x3C => [0x23A8,0,1150],# left curly brace middle
+    0x3D => [0x23AC,0,1150],# right curly brace middle
+    0x3E => [0x23AA,0,300], # curly brace extension
+
+    0x40 => [0x239D,0,1115],# left paren lower hook
+    0x41 => [0x23A0,0,1115],# right paren lower hook
+    0x42 => [0x239C,0,600], # left paren extension
+    0x43 => [0x239F,0,600], # right paren extension
+
+    0x74 => [0x23B7,0,915], # radical bottom
+    0x75 => [0xE000,0,605], # radical extension (PUA)
+    0x76 => [0xE001,0,565], # radical top (PUA)
+    [0x7A,0x7D] => 0xE150,  # \braceld, \bracerd, \bracelu, \braceru (PUA)
+  ],
+};
+
+$map{cmti10} = {
+  "Main-Italic" => [
+    [0,1] => 0x393,         # \Gamma, \Delta
+    2 => 0x398,             # \Theta
+    3 => 0x39B,             # \Lambda
+    4 => 0x39E,             # \Xi
+    5 => 0x3A0,             # \Pi
+    6 => 0x3A3,             # \Sigma
+    [7,8] => 0x3A5,         # \Upsilon, \Phi
+    [9,0xA] => 0x3A8,       # \Psi, \Omega
+
+    0x10 => 0x131,          # \imath (roman)
+    0x11 => 0x237,          # \jmath (roman)
+    0x12 => [0x300,-511,0], # \grave (combining)
+    0x13 => [0x301,-511,0], # \acute (combining)
+    0x14 => [0x30C,-511,0], # \check (combining)
+    0x15 => [0x306,-511,0], # \breve (combining)
+    0x16 => [0x304,-511,0], # \bar (combining)
+    0x17 => [0x30A,-671,0], # ring above (combining)
+
+    [0x21,0x23] => 0x21,    # !, ", #,
+    0x22 => 0x201D,         # "
+    0x24 => 0xA3,           # pound sign
+    [0x25,0x2F] => 0x25,    # %, &, ', (, ), *, +, comma, -, ., /
+    0x27 => 0x2019,         # '
+    [0x30,0x39] => 0x30,    # 0-9
+    [0x3A,0x3B] => 0x3A,    # :, ;
+    0x3D => 0x3D,           # =
+    [0x3F,0x40] => 0x3F,    # ?, @
+    [0x41,0x5A] => 0x41,    # A-Z
+    0x5B => 0x5B,           # [
+    0x5C => 0x201C,         # ``
+    [0x5D,0x5E] => 0x5D,    # ], ^
+    0x5E => [0x302,-511,0], # \hat (combining)
+    0x5F => [0x307,-409,0], # \dot (combining)
+    0x60 => 0x2018,         # `
+    [0x61,0x7A] => 0x61,    # a-z
+    [0x7B,0x7C] => 0x2013,  # \endash, \emdash
+    0x7B => [0x5F,0,-310],  # underline
+    0x7D => [0x30B,-511,0], # double acute (combining)
+    0x7E => [0x7E,0,-350],  # ~
+    0x7E => [0x303,-511,0], # \tilde (combining)
+    0x7F => [0x308,-511,0], # \ddot (combining)
+  ],
+};
+
+$map{cmbx10} = {
+  "Main-Bold" => [
+    [0,1] => 0x393,         # \Gamma, \Delta
+    2 => 0x398,             # \Theta
+    3 => 0x39B,             # \Lambda
+    4 => 0x39E,             # \Xi
+    5 => 0x3A0,             # \Pi
+    6 => 0x3A3,             # \Sigma
+    [7,8] => 0x3A5,         # \Upsilon, \Phi
+    [9,0xA] => 0x3A8,       # \Psi, \Omega
+
+    0x10 => 0x131,          # \imath (roman bold)
+    0x11 => 0x237,          # \jmath (roman bold)
+    0x12 => 0x60,           # \grave
+    0x12 => 0x2CB,          # \grave
+    0x12 => [0x300,-575,0], # \grave (combining)
+    0x13 => 0xB4,           # \acute
+    0x13 => 0x2CA,          # \acute
+    0x13 => [0x301,-575,0], # \acute (combining)
+    0x14 => 0x2C7,          # \check
+    0x14 => [0x30C,-575,0], # \check (combining)
+    0x15 => 0x2D8,          # \breve
+    0x15 => [0x306,-575,0], # \breve (combining)
+    0x16 => 0xAF,           # \bar
+    0x16 => 0x2C9,          # \bar
+    0x16 => [0x304,-575,0], # \bar (combining)
+    0x17 => [0xB0,-147,0],  # ring above
+    0x17 => [0x2DA,-147,0], # ring above
+    0x17 => [0x30A,-722,0], # ring above (combining)
+
+    [0x21,0x2F] => 0x21,    # !, ", #, $, %, &, ', (, ), *, +, comma, -, ., /
+    0x22 => 0x201D,         # "
+    0x27 => 0x2019,         # '
+    [0x30,0x39] => 0x30,    # 0-9
+    [0x3A,0x3B] => 0x3A,    # :, ;
+    0x3D => 0x3D,           # =
+    [0x3F,0x40] => 0x3F,    # ?, @
+    [0x41,0x5A] => 0x41,    # A-Z
+    0x5B => 0x5B,           # [
+    0x5C => 0x201C,         # ``
+    [0x5D,0x5E] => 0x5D,    # ], ^
+    0x5E => 0x2C6,          # \hat
+    0x5E => [0x302,-575,0], # \hat (combining)
+    0x5F => [0x2D9,128,0],  # \dot
+    0x5F => [0x307,-447,0], # \dot (combining)
+    0x60 => 0x2018,         # `
+    [0x61,0x7A] => 0x61,    # a-z
+    [0x7B,0x7C] => 0x2013,  # \endash, \emdash
+    0x7B => [0x5F,0,-310],  # underline
+    0x7D => [0x30B,-575,0], # double acute (combining)
+    0x7E => [0x7E,0,-350],  # ~
+    0x7E => 0x2DC,          # \tilde
+    0x7E => [0x303,-575,0], # \tilde (combining)
+    0x7F => 0xA8,           # \ddot
+    0x7F => [0x308,-575,0], # \ddot (combining)
+  ],
+};
+
+$map{cmmib10} = {
+  "Math-BoldItalic" => [
+    [0,1] => 0x393,         # \Gamma, \Delta
+    2 => 0x398,             # \Theta
+    3 => 0x39B,             # \Lambda
+    4 => 0x39E,             # \Xi
+    5 => 0x3A0,             # \Pi
+    6 => 0x3A3,             # \Sigma
+    [7,8] => 0x3A5,         # \Upsilon, \Phi
+    [9,0xA] => 0x3A8,       # \Psi, \Omega
+
+    [0xB,0xE] => 0x3B1,     # \alpha, \beta, \gamma, \delta
+    0xF => 0x3F5,           # \elpsilon
+    [0x10,0x18] => 0x3B6,   # \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu, \nu, \xi
+    [0x19,0x1A] => 0x3C0,   # \pi, \rho
+    [0x1B,0x1D] => 0x3C3,   # \sigma, \tau, \upsilon
+    0x1E => 0x3D5,          # \phi
+    [0x1F,0x21] => 0x3C7,   # \chi, \psi, \omega
+    0x22 => 0x3B5,          # \varepsilon
+    0x23 => 0x3D1,          # \vartheta
+    0x24 => 0x3D6,          # \varpi
+    0x25 => 0x3F1,          # \varrho
+    0x26 => 0x3C2,          # \varsigma
+    0x27 => 0x3C6,          # \varphi
+
+    [0x41,0x5A] => 0x41,    # A-Z
+    [0x61,0x7A] => 0x61,    # a - z
+    0x6F => 0x3BF,          # omicron
+  ],
+
+  "Main-Bold" => [
+    0x28 => 0x21BC,         # \leftharpoonup
+    0x29 => 0x21BD,         # \leftharpoondown
+    0x2A => 0x21C0,         # \rightharpoonup
+    0x2B => 0x21C1,         # \rightharpoondown
+
+    0x2E => 0x25B9,         # \triangleright
+    0x2F => 0x25C3,         # \triangleleft
+
+    0x3A => 0x2E,           # .
+    0x3B => 0x2C,           # ,
+    0x3C => 0x3C,           # <
+    0x3D => 0x2215,         # /
+    0x3E => 0x3E,           # >
+    0x3F => 0x22C6,         # \star
+    0x40 => 0x2202,         # \partial
+
+    [0x5B,0x5D] => 0x266D,  # \flat, \natural, \sharp
+    0x5E => 0x2323,         # \smile
+    0x5F => 0x2322,         # \frown
+    0x60 => 0x2113,         # \ell
+    0x68 => 0x210F,         # \hbar (bar added below)
+
+    0x7B => 0x131,          # \imath
+    0x7C => 0x237,          # \jmath
+    0x7D => 0x2118,         # \wp
+    0x7E => [0x20D7,-729,0],# \vec
+  ],
+};
+
+$map{cmbsy10} = {
+  "Main-Bold" => [
+    [0,1] => 0x2212,        # -
+    1 => 0x22C5,            # \cdot
+    2 => 0xD7,              # \times
+    3 => 0x2217,            # \ast
+    4 => 0xF7,              # \div
+    5 => 0x22C4,            # \diamond
+    6 => 0xB1,              # \pm
+    7 => 0x2213,            # \mp
+    [8,0xC] => 0x2295,      # \oplus, \ominus, \otimes, \oslash, \odot
+    0xD => 0x25EF,          # \bigcirc
+    [0xE,0xF] => 0x2218,    # \circ, \bullet
+
+    0x10 => 0x224D,         # \asymp
+    0x11 => 0x2261,         # \equiv
+    [0x12,0x13] => 0x2286,  # \subseteq, \supseteq
+    [0x14,0x15] => 0x2264,  # \leq, \geq
+    [0x16,0x17] => 0x2AAF,  # \preceq, \succeq
+    0x18 => 0x223C,         # \sim
+    0x19 => 0x2248,         # \approx
+    [0x1A,0x1B] => 0x2282,  # \subset, \supset
+    [0x1C,0x1D] => 0x226A,  # \ll, \gg
+    [0x1E,0x1F] => 0x227A,  # \prec, \succ
+
+    0x20 => 0x2190,         # \leftarrow
+    0x21 => 0x2192,         # \rightarrow
+    0x22 => 0x2191,         # \uparrow
+    0x23 => 0x2193,         # \downarrow
+    0x24 => 0x2194,         # \leftrightarrow
+    0x25 => 0x2197,         # \nearrow
+    0x26 => 0x2198,         # \searrow
+    0x27 => 0x2243,         # \simeq
+
+    0x28 => 0x21D0,         # \Leftarrow
+    0x29 => 0x21D2,         # \Rightarrow
+    0x2A => 0x21D1,         # \Uparrow
+    0x2B => 0x21D3,         # \Downarrow
+    0x2C => 0x21D4,         # \Leftrightarrow
+    0x2D => 0x2196,         # \nwarrow
+    0x2E => 0x2199,         # \swarrow
+    0x2F => 0x221D,         # \propto
+
+    0x30 => 0x2032,         # \prime
+    0x31 => 0x221E,         # \infty
+    0x32 => 0x2208,         # \in
+    0x33 => 0x220B,         # \ni
+    0x34 => 0x25B3,         # \bigtriangleup and \triangle
+    0x35 => 0x25BD,         # \bigtriangledown
+    0x36 => [0x338,-894,0], # \not (combining)
+
+    0x38 => 0x2200,         # \forall
+    0x39 => 0x2203,         # \exists
+    0x3A => 0xAC,           # \neg
+    0x3B => 0x2205,         # \emptyset
+    0x3C => 0x211C,         # \Re
+    0x3D => 0x2111,         # \Im
+    0x3E => 0x22A4,         # \top
+    0x3F => 0x22A5,         # \bot
+
+    0x40 => 0x2135,         # \aleph
+
+    0x5B => 0x222A,         # \cup
+    0x5C => 0x2229,         # \cap
+    0x5D => 0x228E,         # \uplus
+    [0x5E,0x5F] => 0x2227,  # \wedge, \vee
+
+    [0x60,0x61] => 0x22A2,  # \vdash, \dashv
+    [0x62,0x63] => 0x230A,  # \lfloor, \rfloor
+    [0x64,0x65] => 0x2308,  # \lceil, \rceil
+    0x66 => 0x7B,           # {
+    0x67 => 0x7D,           # }
+    [0x68,0x69] => 0x27E8,  # \langle, \rangle
+    0x6A => 0x7C,           # |
+    0x6A => 0x2223,         # \vert
+    0x6B => 0x2225,         # \Vert
+    0x6C => 0x2195,         # \updownarrow
+    0x6D => 0x21D5,         # \Updownarrow
+    0x6E => 0x5C,           # \backslash
+    0x6E => 0x2216,         # \setminus
+    0x6F => 0x2240,         # \wr
+
+    0x70 => [0x221A,0,760], # \surd    ### adjust position so font doesn't have a large depth
+    0x71 => 0x2A3F,         # \amalg
+    0x72 => 0x2207,         # \nabla
+    0x73 => 0x222B,         # \int
+    0x74 => 0x2294,         # \sqcup
+    0x75 => 0x2293,         # \sqcap
+    [0x76,0x77] => 0x2291,  # \sqsubseteq, \sqsupseteq
+
+    [0x79,0x7A] => 0x2020,  # \dagger, \ddagger
+
+    0x7C => 0x2663,         # \clubsuit
+    0x7D => 0x2662,         # \diamondsuit
+    0x7E => 0x2661,         # \heartsuit
+    0x7F => 0x2660,         # \spadesuit
+  ],
+
+  "Math-BoldItalic" => [
+    0x36 => 0x2F            # \not
+  ],
+};
+
+$map{msam10} = {
+  "Main-Regular" => [
+    0x5C => 0x2220,         # \angle
+  ],
+
+  "Main-Bold" => [
+    0x5C => 0x2220,         # \angle (emboldened below)
+  ],
+
+  "AMS" => [
+    0x00 => 0x22A1,         # \boxdot
+    0x01 => 0x229E,         # \boxplus
+    0x02 => 0x22A0,         # \boxtimes
+    0x03 => 0x25A1,         # \square
+    0x04 => 0x25A0,         # \blacksquare
+    0x05 => 0x22C5,         # \centerdot
+    0x06 => 0x25CA,         # \lozenge
+    0x07 => 0x29EB,         # \blacklozenge
+    0x08 => 0x21BB,         # \circlearrowright
+    0x09 => 0x21BA,         # \circlearrowleft
+    0x0A => 0x21CC,         # \rightleftharpoons
+    0x0B => 0x21CB,         # \leftrightharpoons
+    0x0C => 0x229F,         # \boxminus
+    0x0D => 0x22A9,         # \Vdash
+    0x0E => 0x22AA,         # \Vvdash
+    0x0F => 0x22A8,         # \vDash
+    0x10 => 0x21A0,         # \twoheadrightarrow
+    0x11 => 0x219E,         # \twoheadleftarrow
+    0x12 => 0x21C7,         # \leftleftarrows
+    0x13 => 0x21C9,         # \rightrightarrows
+    0x14 => 0x21C8,         # \upuparrows
+    0x15 => 0x21CA,         # \downdownarrows
+    0x16 => 0x21BE,         # \upharpoonright
+    0x17 => 0x21C2,         # \downharpoonright
+    0x18 => 0x21BF,         # \upharpoonleft
+    0x19 => 0x21C3,         # \downharpoonleft
+    0x1A => 0x21A3,         # \rightarrowtail
+    0x1B => 0x21A2,         # \leftarrowtail
+    0x1C => 0x21C6,         # \leftrightarrows
+    0x1D => 0x21C4,         # \rightleftarrows
+    0x1E => 0x21B0,         # \Lsh
+    0x1F => 0x21B1,         # \Rsh
+    0x20 => 0x21DD,         # \rightsquigarrow
+    0x21 => 0x21AD,         # \leftrightsquigarrow
+    0x22 => 0x21AB,         # \looparrowleft
+    0x23 => 0x21AC,         # \looparrowright
+    0x24 => 0x2257,         # \circeq
+    0x25 => 0x227F,         # \succsim
+    0x26 => 0x2273,         # \gtrsim
+    0x27 => 0x2A86,         # \gtrapprox
+    0x28 => 0x22B8,         # \multimap
+    0x29 => 0x2234,         # \therefore
+    0x2A => 0x2235,         # \because
+    0x2B => 0x2251,         # \doteqdot
+    0x2C => 0x225C,         # \triangleq
+    0x2D => 0x227E,         # \precsim
+    0x2E => 0x2272,         # \lesssim
+    0x2F => 0x2A85,         # \lessapprox
+    0x30 => 0x2A95,         # \eqslantless
+    0x31 => 0x2A96,         # \eqslantgtr
+    0x32 => 0x22DE,         # \curlyeqprec
+    0x33 => 0x22DF,         # \curlyeqsucc
+    0x34 => 0x227C,         # \preccurlyeq
+    0x35 => 0x2266,         # \leqq
+    0x36 => 0x2A7D,         # \leqslant
+    0x37 => 0x2276,         # \lessgtr
+    0x38 => 0x2035,         # \backprime
+    0x39 => 0x2212,         # dahsed arrow extension
+    0x3A => 0x2253,         # \risingdotseq
+    0x3B => 0x2252,         # \fallingdotseq
+    0x3C => 0x227D,         # \succcurlyeq
+    0x3D => 0x2267,         # \geqq
+    0x3E => 0x2A7E,         # \geqslant
+    0x3F => 0x2277,         # \gtrless
+    0x40 => 0x228F,         # \sqsubset
+    0x41 => 0x2290,         # \sqsupset
+    0x42 => 0x22B3,         # \vartriangleright
+    0x43 => 0x22B2,         # \vartriangleleft
+    0x44 => 0x22B5,         # \trianglerighteq
+    0x45 => 0x22B4,         # \trianglelefteq
+    0x46 => 0x2605,         # \bigstar
+    0x47 => 0x226C,         # \between
+    0x48 => 0x25BC,         # \blacktriangledown
+    0x49 => 0x25B6,         # \blacktriangleright
+    0x4A => 0x25C0,         # \blacktriangleleft
+    0x4B => 0x2192,         # rightarrow
+    0x4C => 0x2190,         # leftarrow
+    0x4D => 0x25B3,         # \vartriangle
+    0x4E => 0x25B2,         # \blacktriangle
+    0x4F => 0x25BD,         # \triangledown
+    0x50 => 0x2256,         # \eqcirc
+    0x51 => 0x22DA,         # \lesseqgtr
+    0x52 => 0x22DB,         # \gtreqless
+    0x53 => 0x2A8B,         # \lesseqqgtr
+    0x54 => 0x2A8C,         # \gtreqqless
+    0x55 => 0x00A5,         # yen
+    0x56 => 0x21DB,         # \Rrightarrow
+    0x57 => 0x21DA,         # \Lleftarrow
+    0x58 => 0x2713,         # checkmark
+    0x59 => 0x22BB,         # \veebar
+    0x5A => 0x22BC,         # \barwedge
+    0x5B => 0x2A5E,         # \doublebarwedge
+    0x5C => 0x2220,         # \angle
+    0x5D => 0x2221,         # \measuredangle
+    0x5E => 0x2222,         # \sphericalangle
+    0x5F => 0x221D,         # \varpropto
+    0x60 => 0x2323,         # \smallsmile
+    0x61 => 0x2322,         # \smallfrown
+    0x62 => 0x22D0,         # \Subset
+    0x63 => 0x22D1,         # \Supset
+    0x64 => 0x22D3,         # \Cup
+    0x65 => 0x22D2,         # \Cap
+    0x66 => 0x22CF,         # \curlywedge
+    0x67 => 0x22CE,         # \curlyvee
+    0x68 => 0x22CB,         # \leftthreetimes
+    0x69 => 0x22CC,         # \rightthreetimes
+    0x6A => 0x2AC5,         # \subseteqq
+    0x6B => 0x2AC6,         # \supseteqq
+    0x6C => 0x224F,         # \bumpeq
+    0x6D => 0x224E,         # \Bumpeq
+    0x6E => 0x22D8,         # \lll
+    0x6F => 0x22D9,         # \ggg
+    0x70 => 0x250C,         # \ulcorner
+    0x71 => 0x2510,         # \urcorner
+    0x72 => 0x00AE,         # registered sign
+    0x73 => 0x24C8,         # \circledS
+    0x74 => 0x22D4,         # \pitchfork
+    0x75 => 0x2214,         # \dotplus
+    0x76 => 0x223D,         # \backsim
+    0x77 => 0x22CD,         # \backsimeq
+    0x78 => 0x2514,         # \llcorner
+    0x79 => 0x2518,         # \lrcorner
+    0x7A => 0x2720,         # maltese cross
+    0x7B => 0x2201,         # \complement
+    0x7C => 0x22BA,         # \intercal
+    0x7D => 0x229A,         # \circledcirc
+    0x7E => 0x229B,         # \circledast
+    0x7F => 0x229D,         # \circleddash
+  ],
+};
+
+$map{msbm10} = {
+  "Size4" => [
+    0x5B => 0x2C6,          # \widehat
+    0x5B => [0x302,-1889,0],# \widehat (combining)
+    0x5D => 0x2DC,          # \widetilde
+    0x5D => [0x303,-1889,0],# \widetilde (combining)
+  ],
+
+  "Main-Regular" => [
+    0x7E => 0x210F,         # \hbar
+  ],
+
+  "Main-Italic" => [
+    0x7D => 0x210F,         # \hbar (with slant)
+  ],
+
+  "AMS" => [
+    0x00 => 0xE00C,         # \lvertneqq
+    0x01 => 0xE00D,         # \gvertneqq
+    0x02 => 0x2270,         # \nleq
+    0x03 => 0x2271,         # \ngeq
+    0x04 => 0x226E,         # \nless
+    0x05 => 0x226F,         # \ngtr
+    0x06 => 0x2280,         # \nprec
+    0x07 => 0x2281,         # \nsucc
+    0x08 => 0x2268,         # \lneqq
+    0x09 => 0x2269,         # \gneqq
+    0x0A => 0xE010,         # \nleqslant
+    0x0B => 0xE00F,         # \ngeqslant
+    0x0C => 0x2A87,         # \lneq
+    0x0D => 0x2A88,         # \gneq
+    0x0E => 0x22E0,         # \npreceq
+    0x0F => 0x22E1,         # \nsucceq
+    0x10 => 0x22E8,         # \precnsim
+    0x11 => 0x22E9,         # \succnsim
+    0x12 => 0x22E6,         # \lnsim
+    0x13 => 0x22E7,         # \gnsim
+    0x14 => 0xE011,         # \nleqq
+    0x15 => 0xE00E,         # \ngeqq
+    0x16 => 0x2AB5,         # \precneqq
+    0x17 => 0x2AB6,         # \succneqq
+    0x18 => 0x2AB9,         # \precnapprox
+    0x19 => 0x2ABA,         # \succnapprox
+    0x1A => 0x2A89,         # \lnapprox
+    0x1B => 0x2A8A,         # \gnapprox
+    0x1C => 0x2241,         # \nsim
+    0x1D => 0x2246,         # \ncong
+    0x1E => 0x2571,         # \diagup
+    0x1F => 0x2572,         # \diagdown
+    0x20 => 0xE01A,         # \varsubsetneq
+    0x21 => 0xE01B,         # \varsupsetneq
+    0x22 => 0xE016,         # \nsubseteqq
+    0x23 => 0xE018,         # \nsupseteqq
+    0x24 => 0x2ACB,         # \subsetneqq
+    0x25 => 0x2ACC,         # \supsetneqq
+    0x26 => 0xE017,         # \varsubsetneqq
+    0x27 => 0xE019,         # \varsupsetneqq
+    0x28 => 0x228A,         # \subsetneq
+    0x29 => 0x228B,         # \supsetneq
+    0x2A => 0x2288,         # \nsubseteq
+    0x2B => 0x2289,         # \nsupseteq
+    0x2C => 0x2226,         # \nparallel
+    0x2D => 0x2224,         # \nmid
+    0x2E => 0xE006,         # \nshortmid
+    0x2F => 0xE007,         # \nshortparallel
+    0x30 => 0x22AC,         # \nvdash
+    0x31 => 0x22AE,         # \nVdash
+    0x32 => 0x22AD,         # \nvDash
+    0x33 => 0x22AF,         # \nVDash
+    0x34 => 0x22ED,         # \ntrianglerighteq
+    0x35 => 0x22EC,         # \ntrianglelefteq
+    0x36 => 0x22EA,         # \ntriangleleft
+    0x37 => 0x22EB,         # \ntriangleright
+    0x38 => 0x219A,         # \nleftarrow
+    0x39 => 0x219B,         # \nrightarrow
+    0x3A => 0x21CD,         # \nLeftarrow
+    0x3B => 0x21CF,         # \nRightarrow
+    0x3C => 0x21CE,         # \nLeftrightarrow
+    0x3D => 0x21AE,         # \nleftrightarrow
+    0x3E => 0x22C7,         # \divideontimes
+    0x3F => 0x2205,         # \varnothing
+    0x40 => 0x2204,         # \nexists
+
+    [0x41,0x5A] => 0x41,    # A-Z
+    0x5C => 0x2C6,          # \widehat
+    0x5C => [0x302,-2333,0],# \widehat (combining)
+    0x5E => 0x2DC,          # \widetilde
+    0x5E => [0x303,-2333,0],# \widetilde (combining)
+
+    0x60 => 0x2132,         # \Finv
+    0x61 => 0x2141,         # \Game
+    0x66 => 0x2127,         # \mho
+    0x67 => 0x00F0,         # \eth
+    0x68 => 0x2242,         # minus-tilde
+    0x69 => 0x2136,         # \beth
+    0x6A => 0x2137,         # \gimel
+    0x6B => 0x2138,         # \daleth
+    0x6C => 0x22D6,         # \lessdot
+    0x6D => 0x22D7,         # \gtrdot
+    0x6E => 0x22C9,         # \ltimes
+    0x6F => 0x22CA,         # \rtimes
+    0x70 => 0x2223,         # \shortmid
+    0x71 => 0x2225,         # \shortparallel
+    0x72 => 0x2216,         # \smallsetminus
+    0x73 => 0x223C,         # \thicksim
+    0x74 => 0x2248,         # \thickapprox
+    0x75 => 0x224A,         # \approxeq
+    0x76 => 0x2AB8,         # \succapprox
+    0x77 => 0x2AB7,         # \precapprox
+    0x78 => 0x21B6,         # \curvearrowleft
+    0x79 => 0x21B7,         # \curvearrowright
+    0x7A => 0x03DD,         # \digamma
+    0x7B => 0x03F0,         # \varkappa
+    0x7A => 0xE008,         # \digamma  (non-standard, for IE)
+    0x7B => 0xE009,         # \varkappa (non-standard, for IE)
+    0x7C => 0x006B,         # \Bbbk
+    0x7D => 0x210F,         # \hslash
+    0x7E => 0x0127,         # \hbar
+    0x7F => 0x220D,         # \backepsilon
+  ],
+};
+
+foreach $cmfont (keys %map) {
+    foreach $mjfont (keys %{$map{$cmfont}}) {
+        $style = $mjfont; $style =~ s/.*?(-|$)//; $style = "Regular" unless $style;
+        $family = $mjfont; $family =~ s/-.*//;
+        $fontname = "$family-$style";
+        @{$reverse{$fontname}{$cmfont}} = @{$map{$cmfont}{$mjfont}};
+    }
+}
+
+my %output;
+
+sub add_to_output {
+    my ($mjfont,$cmfont,$from,$to) = @_;
+
+    my $xshift = 0, $yshift = 0;
+
+    if (ref($to) eq "ARRAY") {
+        $xshift = $to->[1];
+        $yshift = $to->[2];
+        $to = $to->[0];
+    }
+
+    $data = {
+        "font" => $cmfont,
+        "char" => $from,
+        "xshift" => $xshift,
+        "yshift" => $yshift
+    };
+
+    $output{$mjfont}{$to} = $data;
+}
+
+foreach $mjfont (keys %reverse) {
+    foreach $cmfont (keys %{$reverse{$mjfont}}) {
+        @remap = @{$reverse{$mjfont}{$cmfont}};
+        while (defined($item = shift(@remap))) {
+            $remap = shift(@remap);
+
+            if (ref($item) eq "ARRAY") {
+                foreach $from ($item->[0]...$item->[1]) {
+                    $to = $from - $item->[0] + $remap;
+                    add_to_output($mjfont, $cmfont, $from, $to);
+                }
+            } else {
+                add_to_output($mjfont, $cmfont, $item, $remap);
+            }
+        }
+    }
+}
+
+print(encode_json(\%output));

metrics/parse_tfm.py

@@ -0,0 +1,149 @@
+class CharInfoWord(object):
+    def __init__(self, word):
+        b1, b2, b3, b4 = (word >> 24,
+                          (word & 0xff0000) >> 16,
+                          (word & 0xff00) >> 8,
+                          word & 0xff)
+
+        self.width_index = b1
+        self.height_index = b2 >> 4
+        self.depth_index = b2 & 0x0f
+        self.italic_index = (b3 & 0b11111100) >> 2
+        self.tag = b3 & 0b11
+        self.remainder = b4
+
+
+class TfmCharMetrics(object):
+    def __init__(self, width, height, depth, italic):
+        self.width = width
+        self.height = height
+        self.depth = depth
+        self.italic_correction = italic
+
+
+class TfmFile(object):
+    def __init__(self, start_char, end_char, char_info, width_table,
+                 height_table, depth_table, italic_table):
+        self.start_char = start_char
+        self.end_char = end_char
+        self.char_info = char_info
+        self.width_table = width_table
+        self.height_table = height_table
+        self.depth_table = depth_table
+        self.italic_table = italic_table
+
+    def get_char_metrics(self, char_num):
+        if char_num < self.start_char or char_num > self.end_char:
+            raise RuntimeError("Invalid character number")
+
+        info = self.char_info[char_num + self.start_char]
+
+        return TfmCharMetrics(
+            self.width_table[info.width_index],
+            self.height_table[info.height_index],
+            self.depth_table[info.depth_index],
+            self.italic_table[info.italic_index])
+
+
+class TfmReader(object):
+    def __init__(self, f):
+        self.f = f
+
+    def read_byte(self):
+        return ord(self.f.read(1))
+
+    def read_halfword(self):
+        b1 = self.read_byte()
+        b2 = self.read_byte()
+        return (b1 << 8) | b2
+
+    def read_word(self):
+        b1 = self.read_byte()
+        b2 = self.read_byte()
+        b3 = self.read_byte()
+        b4 = self.read_byte()
+        return (b1 << 24) | (b2 << 16) | (b3 << 8) | b4
+
+    def read_fixword(self):
+        word = self.read_word()
+
+        neg = False
+        if word & 0x80000000:
+            neg = True
+            word = (-word & 0xffffffff)
+
+        return (-1 if neg else 1) * word / float(1 << 20)
+
+    def read_bcpl(self, length):
+        str_length = self.read_byte()
+        data = self.f.read(length - 1)
+        return data[:str_length]
+
+
+def read_tfm_file(file_name):
+    with open(file_name, 'rb') as f:
+        reader = TfmReader(f)
+
+        # file_size
+        reader.read_halfword()
+        header_size = reader.read_halfword()
+
+        start_char = reader.read_halfword()
+        end_char = reader.read_halfword()
+
+        width_table_size = reader.read_halfword()
+        height_table_size = reader.read_halfword()
+        depth_table_size = reader.read_halfword()
+        italic_table_size = reader.read_halfword()
+
+        # ligkern_table_size
+        reader.read_halfword()
+        # kern_table_size
+        reader.read_halfword()
+
+        # extensible_table_size
+        reader.read_halfword()
+        # parameter_table_size
+        reader.read_halfword()
+
+        # checksum
+        reader.read_word()
+        # design_size
+        reader.read_fixword()
+
+        if header_size > 2:
+            # coding_scheme
+            reader.read_bcpl(40)
+
+        if header_size > 12:
+            # font_family
+            reader.read_bcpl(20)
+
+        for i in range(header_size - 17):
+            reader.read_word()
+
+        char_info = []
+        for i in range(start_char, end_char + 1):
+            char_info.append(CharInfoWord(reader.read_word()))
+
+        width_table = []
+        for i in range(width_table_size):
+            width_table.append(reader.read_fixword())
+
+        height_table = []
+        for i in range(height_table_size):
+            height_table.append(reader.read_fixword())
+
+        depth_table = []
+        for i in range(depth_table_size):
+            depth_table.append(reader.read_fixword())
+
+        italic_table = []
+        for i in range(italic_table_size):
+            italic_table.append(reader.read_fixword())
+
+        # There is more information, like the ligkern, kern, extensible, and
+        # param table, but we don't need these for now
+
+        return TfmFile(start_char, end_char, char_info, width_table,
+                       height_table, depth_table, italic_table)

metrics/replace_line.py

@@ -0,0 +1,17 @@
+#!/usr/bin/env python2
+
+import sys
+
+with open("../fontMetrics.js", "r") as metrics:
+    old_lines = file.readlines(metrics)
+
+replace = sys.stdin.read()
+
+with open("../fontMetrics.js", "w") as output:
+    for line in old_lines:
+        if line.startswith("var metricMap"):
+            output.write("var metricMap = ")
+            output.write(replace)
+            output.write(";\n")
+        else:
+            output.write(line)

static/katex.less

@@ -179,10 +179,6 @@ big parens
         .baseline-align-hack-outer;
         text-align: left;
 
-        // The rendering of $y'$, for example, looks bad without this.
-        // TODO(alpert): Obviously incorrect. Figure out the proper fix here.
-        margin-left: 0.05em;
-
         .msup,
         .msub,
         .fix-ie {

test/huxley/Huxleyfile.json

@@ -129,5 +129,11 @@
         "name": "Rule",
         "screenSize": [1024, 768],
         "url": "http://localhost:7936/test/huxley/test.html?m=\\rule{1em}{0.5em}\\rule{1ex}{2ex}\\rule{1em}{1ex}\\rule{1em}{0.431ex}"
+    },
+
+    {
+        "name": "PrimeSpacing",
+        "screenSize": [1024, 768],
+        "url": "http://localhost:7936/test/huxley/test.html?m=f'+f_2'+f^{f'}"
     }
 ]

test/huxley/PrimeSpacing.hux/record.json

@@ -0,0 +1,5 @@
+[
+  {
+    "action": "screenshot"
+  }
+]