Fix or not? XeTeX’s botched radical construction

[RuixiZhang42]

unicode-math/um-code-compat.dtx

Line 60 in 184a23b

\box_ht:N \l_tmpa_box - \@@_radical_vgap:N ##1

According to um-code-fontparam.dtx, \@@_radical_vgap:N \displaystyle ultimately expands to \fontdimen 60 \textfont 2~ for XeTeX. But this is wrong.

As I wrote in the XeTeX mailing list, running

% plain XeTeX
\def\tmp#1{\textfont#1\ten \scriptfont#1\seven
 \scriptscriptfont#1\five}
\def\showfontdimen#1{\immediate\write-1{#1:
 \the\fontdimen#1\textfont2}}
\def\test#1{\font\ten="[#1.otf]:script=math" at 10pt
 \font\seven="[#1.otf]:script=math;+ssty=0" at 7pt
 \font\five="[#1.otf]:script=math;+ssty=1" at 5pt
 \tmp0\tmp1\tmp2\tmp3%
 \noindent#1\par
 \immediate\write-1{--- #1 ---}%
 \showfontdimen{5}%
 \showfontdimen{16}%
 \showfontdimen{48}%
 \showfontdimen{54}%
 \showfontdimen{57}%
 \showfontdimen{61}%
 \setbox0\hbox{$\displaystyle E$}%
 \setbox2\hbox{$\displaystyle\kern-\nulldelimiterspace
  \Uradical255 0 {E}$}%
 \immediate\write-1{displaystyle diff:
  \the\dimexpr\ht2-\ht0}%
 \showfontdimen{60}%
}
\test{texgyrebonum-math}
\test{texgyredejavu-math}
\test{texgyrepagella-math}
\test{texgyreschola-math}
\test{texgyretermes-math}
\test{STIXTwoMath-Regular}
\bye

yields

--- texgyrebonum-math ---
5: 4.85pt
16: 4.7pt
48: 0.72pt
54: 0.72pt
57: 0.72pt
61: 0.72pt
displaystyle diff: 1.89499pt
60: 1.05pt
--- texgyredejavu-math ---
5: 5.19pt
16: 5.39pt
48: 0.64pt
54: 0.52pt
57: 0.52pt
61: 0.52pt
displaystyle diff: 1.98749pt
60: 0.96pt
--- texgyrepagella-math ---
5: 4.69pt
16: 5.0pt
48: 0.6pt
54: 0.6pt
57: 0.6pt
61: 0.6pt
displaystyle diff: 1.85pt
60: 1.2pt
--- texgyreschola-math ---
5: 4.66pt
16: 4.86pt
48: 0.7pt
54: 0.7pt
57: 0.7pt
61: 0.7pt
displaystyle diff: 1.915pt
60: 1.0pt
--- texgyretermes-math ---
5: 4.5pt
16: 4.7pt
48: 0.52pt
54: 0.52pt
57: 0.52pt
61: 0.52pt
displaystyle diff: 1.69499pt
60: 1.4pt
--- STIXTwoMath-Regular ---
5: 4.73pt
16: 4.8pt
48: 0.68pt
54: 0.68pt
57: 0.68pt
61: 0.68pt
displaystyle diff: 1.87999pt
60: 1.7pt

meaning that when XeTeX constructs radicals in display style, it NEVER uses \fontdimen60. Instead, XeTeX uses 0.25 \fontdimen16 + \fontdimen48 as the vertical gap for radicals in display style. Similar issues exist for Overbar and Underbar constructions.

To me, this is clearly an upstream issue. But should unicode-math try to accommodate this?

[wspr]

I think it's unlikely that we'll see a fix for this in XeTeX, so I'd be happy to accomodate for it in unicode-math. Is there a sensible patch for what unicode-math is doing here? This part of the code is quite old and likely wasn't extensively tested at the time it was written

[RuixiZhang42]

Is there a sensible patch for what unicode-math is doing here?

My LaTeX3 skills are deteriorating… But I imagine the patch would look something like (unicode-math does not map \fontdimen16 to a named command):

%    \begin{macrocode}
%<*XE>
\@@_after_package:nNn { mathtools } \@@_patch_mathtools_A:
  {
    \cs_set_nopar:Npn \MT_cramped_internal:Nn ##1 ##2
     {
       \hbox_set:Nn \l_tmpa_box
         {
           \color@setgroup \c_math_toggle_token \m@th
             ##1
             \tex_kern:D - \nulldelimiterspace % changed
             \Uradical 255 ~ 0 ~ { ##2 } % changed
           \c_math_toggle_token \color@endgroup
         }
       \box_set_ht:Nn \l_tmpa_box
         { % change begins
           \box_ht:N \l_tmpa_box - (
           \cs_if_eq:NNTF ##1 \displaystyle
             { .25 \fontdimen 16 \textfont 2 + \@@_fraction_rule:N \displaystyle }
             { \@@_radical_vgap:N ##1 } % need further testing
           )
         } % change ends
       \mode_leave_vertical: % added
       { } \box_use_drop:N \l_tmpa_box % changed
     }
  }
%</XE>
%    \end{macrocode}

Still need further testing for \textstyle, \scriptstyle, and \scriptscriptstyle to determine whether \@@_radical_vgap:N ##1 is enough or not.

Edit: Change \@@_fraction_rule:N ##1 to \@@_fraction_rule:N \displaystyle. Also, using .25 \fontdimen 16 \textfont 2 or \fontdimen 16 \textfont 2 / 4 depends on whether XeTeX truncates (div in the engine source code?) or rounds (floating point arithmetic?).

[RuixiZhang42]

Still need further testing for \textstyle, \scriptstyle, and \scriptscriptstyle to determine whether \@@_radical_vgap:N ##1 is enough or not.

No 🤔🫠, apparently.

Upon further digging, XeTeX never uses \fontdimen59 either 😂. It uses five quarters of \fontdimen48 as vertical gap in \textstyle, \scriptstyle, and \scriptscriptstyle. To accommodate, one says

           \cs_if_eq:NNTF ##1 \displaystyle
             { .25 \fontdimen 16 \textfont 2 + \@@_fraction_rule:N \displaystyle } % WTH?!
             { 1.25 \@@_fraction_rule:N ##1 } % WTH?!

The syntax is .25 \fontdimen 16 \textfont 2 and 1.25 \@@_fraction_rule:N ##1, NOT \fontdimen 16 \textfont 2 / 4 and \@@_fraction_rule:N ##1 * 5 / 4.

Testing code (using 100.33333pt, 70.33333pt, and 50.33333pt):

% plain XeTeX
\def\tmp#1{\textfont#1\hundred \scriptfont#1\seventy
 \scriptscriptfont#1\fifty}
\def\showfontdimen#1{\immediate\write-1{#1:
 \the\fontdimen#1\textfont2}}
\def\checkfont#1{\font\hundred="[#1.otf]:script=math" at 100.33333pt
 \font\seventy="[#1.otf]:script=math;+ssty=0" at 70.33333pt
 \font\fifty="[#1.otf]:script=math;+ssty=1" at 50.33333pt
 \tmp0\tmp1\tmp2\tmp3%
 \noindent#1\par
 \immediate\write-1{--- #1 ---}}
\def\testradical#1{\setbox0\hbox{$#1E\mathsurround=0pt $}%
 \setbox2\hbox{$#1\kern-\nulldelimiterspace
  \Uradical255 0 {E}\mathsurround=0pt $}%
 \ifx#1\displaystyle
  \ht2=\dimexpr
   \ht2-(.25\fontdimen16\textfont2+\fontdimen48\textfont2)\relax
 \else
  \ht2=\dimexpr\ht2-1.25\fontdimen48
   \ifx#1\textstyle
    \textfont
   \else
    \ifx#1\scriptstyle
     \scriptfont
    \else
     \scriptscriptfont
    \fi
   \fi 2\relax
 \fi
 \immediate\write-1{radical \string#1:
  wd diff \number\dimexpr\wd2-\wd0,
  ht diff \number\dimexpr\ht2-\ht0,
  dp diff \number\dimexpr\dp2-\dp0.}%
}
\checkfont{texgyrebonum-math}
\testradical\displaystyle \testradical\textstyle
\testradical\scriptstyle  \testradical\scriptscriptstyle
\checkfont{texgyredejavu-math}
\testradical\displaystyle \testradical\textstyle
\testradical\scriptstyle  \testradical\scriptscriptstyle
\checkfont{texgyrepagella-math}
\testradical\displaystyle \testradical\textstyle
\testradical\scriptstyle  \testradical\scriptscriptstyle
\checkfont{texgyreschola-math}
\testradical\displaystyle \testradical\textstyle
\testradical\scriptstyle  \testradical\scriptscriptstyle
\checkfont{texgyretermes-math}
\testradical\displaystyle \testradical\textstyle
\testradical\scriptstyle  \testradical\scriptscriptstyle
\checkfont{STIXTwoMath-Regular}
\testradical\displaystyle \testradical\textstyle
\testradical\scriptstyle  \testradical\scriptscriptstyle
\bye

Log:

--- texgyrebonum-math ---
radical \displaystyle: wd diff 0, ht diff 0, dp diff 0.
radical \textstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptscriptstyle: wd diff 0, ht diff 0, dp diff 0.
--- texgyredejavu-math ---
radical \displaystyle: wd diff 0, ht diff 0, dp diff 0.
radical \textstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptscriptstyle: wd diff 0, ht diff 0, dp diff 0.
--- texgyrepagella-math ---
radical \displaystyle: wd diff 0, ht diff 0, dp diff 0.
radical \textstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptscriptstyle: wd diff 0, ht diff 0, dp diff 0.
--- texgyreschola-math ---
radical \displaystyle: wd diff 0, ht diff 0, dp diff 0.
radical \textstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptscriptstyle: wd diff 0, ht diff 0, dp diff 0.
--- texgyretermes-math ---
radical \displaystyle: wd diff 0, ht diff 0, dp diff 0.
radical \textstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptscriptstyle: wd diff 0, ht diff 0, dp diff 0.
--- STIXTwoMath-Regular ---
radical \displaystyle: wd diff 0, ht diff 0, dp diff 0.
radical \textstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptstyle: wd diff 0, ht diff 0, dp diff 0.
radical \scriptscriptstyle: wd diff 0, ht diff 0, dp diff 0.

[RuixiZhang42]

Okay, the plot thickens.

So far, I’ve only tested for non-existing radical in various OT math fonts, which is what \MT_cramped_internal:Nn uses to force cramped styles. Indeed, XeTeX makes up strange values as RadicalVGaps for non-existing radical. But the full picture seems to be:

OpenType MATH.MathConstants	Non-existing radical	Existing radical
.radicalVerticalGap	1.25\fontdimen48	\fontdimen59
.radicalDisplayStyleVerticalGap	.25\fontdimen16+\fontdimen48	\fontdimen60
.radicalRuleThickness	—	\fontdimen61
.radicalExtraAscender	—	\fontdimen61 (!)

So even for existing radical, XeTeX doesn’t use the correct \fontdimen62 as RadicalExtraAscender.

Anyway, only the non-existing radical construction is relevant here. But, for the sake of completeness, here’s the testing code for existing radical:

% plain XeTeX, for existing radical
\def\tmp#1{\textfont#1\ten \scriptfont#1\seven
 \scriptscriptfont#1\five}
\def\checkfont#1{\font\ten="[#1.otf]:script=math" at 10pt
 \font\seven="[#1.otf]:script=math;+ssty=0" at 7pt
 \font\five="[#1.otf]:script=math;+ssty=1" at 5pt
 \tmp0\tmp1\tmp2\tmp3%
 \noindent#1\par
 \immediate\write-1{--- #1 ---}}
\def\sqrt{\Uradical1 "221A }
\def\red{\special{color push rgb 1 0 0}\hrule\special{color pop}}
\def\choosemathfont#1{\ifx#1\scriptscriptstyle\scriptscriptfont
 \else\ifx#1\scriptstyle\scriptfont
  \else\textfont\fi\fi}
\def\test#1{% what XeTeX does with \Uradical
 \setbox2\hbox{$#1\sqrt{\mkern18mu}\mathsurround=0pt $}%
 \immediate\write-1{\string#1: ht \the\ht2, dp \the\dp2.}%
 % recreate the ht and the dp using a plain U+221A
 \setbox0\hbox{$#1\char"221A \mathsurround=0pt $}%
 \dimen0=.5\dimexpr % half for the bottom
  \ht0+\dp0 % this is the total height of U+221A
  -\fontdimen61 \choosemathfont#12 % take away RadicalRuleThickness
  \ifx#1\displaystyle
   -\fontdimen60 \textfont2 % take away RadicalDisplayStyleVGap
  \else
   -\fontdimen59 \choosemathfont#12 % take away RadicalVGap
  \fi\relax
 \dimen1=\dimexpr\ht0+\dp0-\dimen0 % this is the height up to rule
%  +\fontdimen62 \choosemathfont#12 % didn't add RadicalExtraAscender
  +\fontdimen61 \choosemathfont#12 % add RadicalRuleThickness
  \relax
 \immediate\write-1{formula: ht \the\dimen1, dp \the\dimen0.}%
 \hbox{\unhbox0\vbox{\red\box2}}}
\raggedbottom
\checkfont{latinmodern-math}
\test\displaystyle \test\textstyle
\test\scriptstyle  \test\scriptscriptstyle
\checkfont{texgyredejavu-math}
\test\displaystyle \test\textstyle
\test\scriptstyle  \test\scriptscriptstyle
\checkfont{STIXTwoMath-Regular}
\test\displaystyle \test\textstyle
\test\scriptstyle  \test\scriptscriptstyle
\bye

Log:

--- latinmodern-math ---
\displaystyle: ht 6.34pt, dp 4.06pt.
formula: ht 6.34pt, dp 4.06pt.
\textstyle: ht 5.84999pt, dp 4.55pt.
formula: ht 5.84999pt, dp 4.55pt.
\scriptstyle: ht 4.095pt, dp 3.185pt.
formula: ht 4.095pt, dp 3.185pt.
\scriptscriptstyle: ht 2.925pt, dp 2.275pt.
formula: ht 2.925pt, dp 2.275pt.
--- texgyredejavu-math ---
\displaystyle: ht 5.63002pt, dp 3.62999pt.
formula: ht 5.63002pt, dp 3.62999pt.
\textstyle: ht 5.63002pt, dp 3.62999pt.
formula: ht 5.63002pt, dp 3.62999pt.
\scriptstyle: ht 3.941pt, dp 2.541pt.
formula: ht 3.941pt, dp 2.541pt.
\scriptscriptstyle: ht 2.815pt, dp 1.815pt.
formula: ht 2.815pt, dp 1.815pt.
--- STIXTwoMath-Regular ---
\displaystyle: ht 7.805pt, dp 4.745pt.
formula: ht 7.805pt, dp 4.745pt.
\textstyle: ht 7.37999pt, dp 5.17pt.
formula: ht 7.37999pt, dp 5.17pt.
\scriptstyle: ht 5.166pt, dp 3.61899pt.
formula: ht 5.12401pt, dp 3.577pt.
\scriptscriptstyle: ht 3.69pt, dp 2.58499pt.
formula: ht 3.9325pt, dp 2.8275pt.

Notice that the test fails for STIX Two Math in \scriptstyle and \scriptscriptstyle; the dimensions don’t match. In addition to botching \fontdimen62, XeTeX also fails to substitute ssty=0 and ssty=1 variants of the radical glyph, causing the discrepancy (not relevant for non-existing radical).