Scale option doesn't fully work with LuaLaTeX

[eg9]

Consider the following example

\documentclass{article}

\usepackage{unicode-math}
\setmathfont[Scale=2.8]{latinmodern-math.otf}

\begin{document}

\[\nu_e + \beta^+\]

\end{document}

The placement of the superscript is incorrect with LuaLaTeX, while it is correct with XeLaTeX. The box is shifted by -3.62994pt with LuaLaTeX, by -10.16402pt with XeLaTeX, meaning that the scaling is not applied to the relevant parameter.

Subscripts are OK (however, XeLaTeX seems to be using a larger shifting down, but it's another matter).

See http://tex.stackexchange.com/questions/232320/superscript-placement-using-unicode-math-with-scaling for reference.

[eg9]

The issue now also appear with XeLaTeX.

[RuixiZhang42]

As of 2019/01/21, with the newest unicode-math in the working branch (v0.8m), the above MWE produces wrong outputs under both engines:

Problem analysis

During my test toward latex3/fontspec#349, I realized where this problem came from. The legacy font dimensions’ setups for families 2 and 3 are wrong, because they are simply based on Scale=1.00001 and Scale=0.99999.

Thus, technically only the math font with Scale=1 are “truly” setup correctly. For those who uses Scale=MatchLowercase or Scale=MatchUppercase, this problem is not noticeable because those scaling factors are likely to be around 1.

Possible solution

If I changed Scale=1.00001 and Scale=0.99999 in um-code-main.dtx to Scale=2.800028 and Scale=2.799972, respectively, I got the following outputs, which seem to be correct:

Therefore, loading the same OpenType math font for the second and the third times should use scale factors which look like the following:

Scale=1.00001 * <user specified scale> % for family 2

and

Scale=0.99999 * <user specified scale> % for family 3

[wspr]

Oh wow, that’s a good find. Thanks very much! Currently when a fontspec user says “Scale=1.1” then “Scale=1.2”, the final scaling taken is (maybe of course) “1.2”. But they could be cumulative. What do you think about the idea for “Scale=1.1,Scale=1.2” to result in a scaling factor of “1.32” ? This would allow a fontspec solution to fix the u-m problem, and mean that u-m doesn’t need to hook into internals of fontspec. Alternatively, I could add a new fontspec feature “Scale*” (or “Rescale” ?) that does the cumulative operation. This would be better for backwards compatibility in fontspec, I supposed.

[wspr]

I like the idea of fixing this in fontspec; see: latex3/fontspec#350

[RuixiZhang42]

@wspr To be honest, I do not like the new scaling idea, because I think it will cause unnecessary confusion. A “cumulative” scale doesn’t sound right (to me at least). If a new key were to be introduced, I would suggest CompoundScale as in “compound interest”, which implies that the operation is multiplicative.

I do like the current “override”-style method of Scale as I believe it’s clearer. After all, it is unicode-math that needs to load a single math font thrice, so we are really just dealing with a unicode-math problem.

I also thought about an “additive” approach rather than a “multiplicative” one, i.e.,

<user scale> ± ε   v.s.   <user scale> * ( 1 ± ε )

Any thoughts?

[wspr]

I didn't go with the additive scale largely because I didn't think having two approaches would be that useful. (Personally I think additive works better for something in absolute units like "fontsize = fontsize +2pt".)

And although I really liked CompoundScale as a name I went with ScaleAgain as it struck me as I was implementing the feature; I thought it would be memorable and the name captures exactly what it's doing :)

[RuixiZhang42]

Maybe the internal TeX rounding error won’t be a problem, but I think it’s worth mentioning here before the next release. Consider the following example:

\documentclass{article}
\usepackage{unicode-math}

\newcommand*\temp{0.7}% Play around with scale here

\setmainfont{texgyrepagella-regular.otf}[Scale=\temp]
\setmathfont{texgyrepagella-math.otf}[Scale=\temp]
\begin{document}
$\mathstrut$%
\the\numexpr\fontdimen6\font\par
\the\numexpr\fontdimen6\textfont2, family~2\par
\the\numexpr\fontdimen6\textfont3, family~3
\end{document}

which shows that families 2 and 3 are loaded at 458760sp and 458750sp, where the size of family 3 coincides with the text font 458750sp. Similar issue may appear under different “principle” scaling factors:

Scale	0.7	0.8	0.9	1.0	1.1	1.2
text em	458750	524290	589820	655360	720900	786430
family 2 em	458760	524290 (?)	589830	655370	720900 (?)	786440
family 3 em	458750 (?)	524280	589820 (?)	655350	720890	786420

I hope this will not cause any real problem as TeX forbids loading the same font at the same scale more than once.

On another note, Scale=MatchLowercase and Scale=MatchUppercase usually result in non-simple fraction scaling factors, so the em’s are likely to be truly different.

[RuixiZhang42]

BTW, the log file says that s*[<final scale>] are indeed different, so maybe the font is being loaded differently after all. It’s just that the em’s happen to be not distinguishable.