Date: 5 November 91 Message No: 034
To: TeX implementors and distributors
From: Barbara Beeton
Subject: Messages from DEK, part 3
The third installment of DEK's September comments.
########################################################################
TeX -- size of \smash'ed boxes
Date: 24 Jun 91 18:56:42
From: jeffrey%se.chalmers.cs@se.sunet.sunic
Authorised-User: Alan Jeffrey
To: cet1@uk.ac.cam.phx
Subject: Odd TeX behaviour
Dear Chris,
Here's something I asked texhax a few days ago---barbara wrote back,
and suggested I ask you about it. Since you were so helpful in
finding that MF bug last year I thought you'd be a good person to ask.
The problem is what happens if you put a smashed box in a script for a
displaystyle mathop, for example:
$$ \sum^{\smash{\vrule height 1in depth 1in}} $$
produces the same as if the \smash weren't there. In general, if you
take a box, change its size, and put it in a displaystyle mathop
script, the size-changing info is lost. So:
\setbox0\hbox{...}
\ht0=...
\dp0=...
$$ \sum^{\box0} $$
is the same as
\setbox0\hbox{...}
$$ \sum^{\box0} $$
This isn't a bug, since in Appendix G, para. 13a, DEK says
Set box $x$ to the superscript field...
set box $y$ to the nucleus field...
set box $z$ to the subscript field...
Rebox all three of these boxes to width $\max(w(x),w(y),w(z))$.
As far as I can tell, in doing this reboxing, the outermost level of
box information is thrown away, and in particular the \ht and \dp
information goes with it.
So it's not a bug, but it's certainly not what you'd expect!
Alan.
Alan Jeffrey Tel: +46 31 72 10 98 jeffrey@cs.chalmers.se
Department of Computer Sciences, Chalmers University, Gothenburg, Sweden
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Date: Thu, 27 Jun 91 16:14:31 BST
From: Chris Thompson
To: Alan Jeffrey
Subject: Re: [Odd TeX behaviour]
Dear Alan,
Thank you for your description of the odd effects with \smash in
the limits of a \mathop. I *think* that Don Knuth has covered himself
against the possibility of these effects being bugs, but the situation
is in fact even odder than your examples illustrate.
As you point out, in
$$ \sum^{\smash{\vrule height 1in depth 1in}} $$
the superscript gets unsmashed by the reboxing described in step 13a
of Appendix A: in terms of code, the call of |rebox| (section 715)
from |make_op| (section 750). One can prevent the recalculation of
the height and depth by
$$ \sum^{\hbox{$\smash{\vrule height 1in depth 1in}$}} $$
or the like.
However, in
$$ \sum^{\smash{\vrule width 20pt height 1in depth 1in}} $$
the smashing remains in effect! This is because |rebox| does not
unpack and repack the box contents if the width is already what
is required. I suppose that this is implied by the description of
the `subroutine that ``reboxes'' a given box to a given width' on
page 442 of the TeXbook, but it certain isn't explicitly stated.
|rebox| also doesn't rebox if the box contents are the empty list;
it simply changes the width to that required. This means that any
explictly set \ht and \dp will survive in this case. (This would
happen in the case of a \(h|v)phantom, I think.) I can't find any
mention at all of this in Appendix G.
Altogether, The situation seems extremely messy, even if it is
according to spec. I think (Barbara?) that it should be brought to
Don's attention, at least. A cleaner spec would be that |rebox|
always preserves the height and depth, but I suppose that might be
an incompatible change.
Chris Thompson
-------
Date: Fri, 28 Jun 91 09:44:11 +0200
From: Alan Jeffrey
Subject: Note about reboxing.
{\obeylines
{\bf Reboxing math operator scripts in display style}
Alan Jeffrey and Chris Thompson
27 June 1991}
\hsize 31pc
{\obeyspaces\global\let =\ }
\catcode`\[=\active \catcode`\]=\active
\def[{\bgroup\par\medskip\tt\obeylines\catcode`\$11\catcode`\\11
\catcode`\{11\catcode`\}11\catcode`\^11\obeylines\obeyspaces}
\def]{\egroup\par\medskip\noindent\ignorespaces}
\def\com#1{{\tt\string#1}}
\medskip\noindent
It turns out that \TeX's algorithm for setting subscripts and
superscripts of limited operators has a rather odd feature. If you
say:
[
$$ \sum^{\vrule height 2ex depth 2ex}
\sum^{\smash{\vrule height 2ex depth 2ex}}
\sum^{\hbox{\smash{\vrule height 2ex depth 2ex}}} $$
]
then you get:
$$ \sum^{\vrule height 2ex depth 2ex}
\sum^{\smash{\vrule height 2ex depth 2ex}}
\sum^{\hbox{\smash{\vrule height 2ex depth 2ex}}} $$
That is, the \com\smash\ has no effect unless it is contained inside
another \com\hbox. In Appendix~G, para 13a of {\it The \TeX book}, the
specification for reboxing a limited script is given as:
{\medskip\narrower\noindent
Set box $x$ to the superscript field in style $C{\uparrow}$; set box
$y$ to the nucleus field in style $C$; and set box $z$ to the
subscript field in style $C{\downarrow}$. Rebox all three of these
boxes to width $\max(w(x), w(y), w(z))$.\par}
\medskip\noindent
It appears that this reboxing (performed by {\bf rebox} \S715) loses
the outermost level of box information. This is confirmed by:
[
$$ \sum^{\vrule width 20pt height 2ex depth 2ex}
\sum^{\smash{\vrule width 20pt height 2ex depth 2ex}}
\sum^{\hbox{\smash{\vrule width 20pt height 2ex depth 2ex}}} $$
]
which produces:
$$ \sum^{\vrule width 20pt height 2ex depth 2ex}
\sum^{\smash{\vrule width 20pt height 2ex depth 2ex}}
\sum^{\hbox{\smash{\vrule width 20pt height 2ex depth 2ex}}} $$
So when the script does not require reboxing, its height and depth are
not lost.
The situation seems rather messy, albeit according to spec. A cleaner
8specification would be that {\bf rebox} should preserve height and
depth, but this may be an incompatible change.
[ dek: _Correct_ _analysis_ ]
\medskip
\line{\hfil\it Alan Jeffrey}
\line{\hfil\it Chris Thompson}
\bye
-------
[ Here's another view of the same problem. ]
Date: Tue, 6 Aug 91 18:55:35 EDT
From: barr@triples.math.mcgill.ca
To: info-tex@SHSU.edu
Subject: problem with Tex
Can anyone explain the discontinuity in the following, or how to make
the dots go into an intermediate position?
Michael Barr
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .75em{\hss$\textstyle.$}}%
_{\hbox to .75em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .75em{$\textstyle.\hss$}}%
_{\hbox to .75em{\hss\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}}
$A\ldiv B\rdiv C$
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .76em{\hss$\textstyle.$}}%
_{\hbox to .76em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .76em{$\textstyle.\hss$}}%
_{\hbox to .76em{\hss\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}}
$A\ldiv B\rdiv C$
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .77em{\hss$\textstyle.$}}%
_{\hbox to .77em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .77em{$\textstyle.\hss$}}%
_{\hbox to .77em{\hss\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}}
$A\ldiv B\rdiv C$
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .78em{\hss$\textstyle.$}}%
_{\hbox to .78em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .78em{$\textstyle.\hss$}}%
_{\hbox to .78em{\hss\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}}
$A\ldiv B\rdiv C$
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .79em{\hss$\textstyle.$}}%
_{\hbox to .79em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .79em{$\textstyle.\hss$}}%
_{\hbox to .79em{\hss\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}}
$A\ldiv B\rdiv C$
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .80em{\hss$\textstyle.$}}%
_{\hbox to .80em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hbox to .80em{$\textstyle.\hss$}}%
_{\hbox to .80em{\hss\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}}
$A\ldiv B\rdiv C$
\bye
-------
Date: Tue, 6 Aug 91 21:54 PDT
From: Donald Arseneau
To: info-tex@SHSU.edu
Subject: Re: problem with positioning of mathop limits
Michael Barr (barr%triples.math.mcgill.ca) had a problem with jumps
in the placement of the limits on an operator.
> Can anyone explain the discontinuity in the following, or how to make
> the dots go into an intermediate position?
>
> \def\rdiv{\mathrel{\mathop
> {\hbox{\vrule height.55ex width0pt depth-.54ex
> \smash{\hbox{\mathsurround=0pt$-$}}}}%
> \limits^{\kern0pt\hbox to .77em{\hss$\textstyle.$}}%
> _{\kern0pt\hbox to .77em{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hss}}}}
>
I've seen that problem before (with someone else's problem) and I stick
by my explanation: an error in TeX. What I think is happening is a
misapplication of the unboxing explained on the first page of Appendix G:
"In case (c), the glue is set with no stretching or shrinking, and additional
level of hboxing is omitted if it turns out to be redundant." But when that
hbox has had its size (\ht, \wd, \dp) changed, or it is not set to its natural
width (to, spread) it is *NOT* redundant but gets omitted anyway!
The immediate solution to Michael Barr's problem is to put something
outside the measured box so it cannot be omitted. Change all
\hbox to
to
\kern0pt \hbox to
and it will work.
The discontinuity with the size of the measured hbox was very interesting.
In all cases the boxes for the limits were set to the width of "-", 7.777pt.
But TeX obviously did some measurement before discarding the important
level of boxing. For \hbox to Xpt, X < 7.7777, the limits were unboxed
and surrounded by \hss...\hss, giving in effect "\hss \hss . \hss", which
placed the dot 1/3 of the way across the minus sign. When X > 7.7777,
TeX thought the nucleus "-" was norrower than the limits and did not pad
the limits with \hss, leaving them as "\hss .". After unboxing and reboxing,
the limits could stretch only on one side leaving the dot at one edge of
the minus sign.
Donald Arseneau asnd@triumfcl (.bitnet)
asnd@reg.triumf.ca
-------
Date: Wed, 7 Aug 91 11:11:56 EDT
From: barr@triples.math.mcgill.ca (Michael Barr)
To: bnb@math.ams.com
Subject: more problems with boxes
If you don't subscribe to texinfo, you may have missed my query and
Donald Arsenault's reply. Briefly, I was having trouble with the
series:
... \def\rdiv{...} [ series as in message to info-tex ]
shose output changes discontinuously as the parameter changes from .77
to .78 (not coincidentally, the width of $-$ is .77777...em). This is
clearly more troubles with 13a on page 444, but I still couldn't see why
I wasn't getting growth before that. (In fact, the parameter could have
been 0 with no effect on the output, which I wasn't quite aware of,
although I knew that down to .3em it made no difference.) It turns out
that what is likely happening is explained by line -4 on page 441, which
Donald says he had run into before. Apparently, TeX' rules for deciding
what ``turns out to be redundant'' are not the same as you and I might
decide on. He suggested that what was happening is that TeX was
unboxing the \hbox and then implementing 13a (which he wasn't aware of,
or at least didn't mention) by reboxing it with an \hss on either side
so that the effect of my code was as if it said \hss\hss.\hss on one
side and vice versa on the other, which resulted in the dots exactly 1/3
of the way (or 2/3). At this point, I have come up with
\def\rdiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\hskip0pt plus3fil\textstyle.}%
_{\smash{\raise1.20ex\hbox{$\textstyle.$}}\hskip0pt plus3fil}}}
\def\ldiv{\mathrel{\mathop
{\hbox{\vrule height.55ex width0pt depth-.54ex
\smash{\hbox{\mathsurround=0pt$-$}}}}%
\limits^{\textstyle.\hskip0pt plus3fil}%
_{\hskip0pt plus3fil\smash{\raise1.20ex\hbox{$\textstyle.$}}}}}
which is simpler and allows fine control over the spacing.
If you have not yet asked DEK about the 13a problem, you might include
these observations. In any case, a little more explanation is clearly
wanting here. By the way, DA suggested (correctly) that a \kern0pt
would prevent the unboxing.
Allow me to second strongly Nelson Beebe's plea in the last three
paragraphs of his editorial in the most recent tugboat. I have now
spent most of a day getting through the texarcana in building one simple
little sign. The number of permutations of \smash and \raise I had to
try to get the vertical placement right (and only by eye, with no
guarantee it will be right at another point size), the amount of time
wasted on getting the horizontal placement right, they both seemed
infinite. It simply shouldn't be so hard to do something so simple.
The fact that adding a kern of 0pt changes everything is
incomprehensible. The facts that \smash requires, while \raise forbids
a brace following it are incomprehensible. The entire chapter on dirty
tricks is an indictment of the program. Almost everything in that
chapter is entirely reasonable and should have straightforward ways of
doing them, not be the subject of dirty tricks. The lack of a simple
reliable loop is unforgivable. A while ago, someone posed a question on
texhax about leaving a 2"x2" box in the lower right corner of each page.
So far as I know, this question got no answer, perhaps has NO reasonable
answer in tex as currently constituted. Certainly, I could think of
none. Nor could I think of any way of having one page narrower than
another. This sort of thing is not good if we expect TeX to grow.
Michael Barr
-------
Date: Wed, 07 Aug 91 15:32:12 BST
From: Chris Thompson
To: Barbara Beeton
Cc: Donald Arseneau ,
Michael Barr
Subject: Re: [[barr@triples.math.mcgill.ca: problem with Tex]]
This one is similar to the height&depth-losing problem you sent me
before, but I think this one *is* unambiguously covered by Appendix G,
unexpected though the effects may be.
The relevant section is 13a, where the reboxing of \mathop's with
limits is being described. (Code is in TeX module 750.) Reboxing is
decsribed in the middle of p.442 ("There's also a subroutine...").
The nucleus is this case is 7.7778pt wide; in the first few cases
the super- and sub-scripts are narrower, have \hss glue added on each
side, and are reboxed (losing the old specification). In the last few
cases, the nucleus is narrower and is reboxed, the super- and sub-
scripts being left alone. Because there is already \hss glue in the
boxes, adding more of the same fundamentally alters their appearence.
(Page 442 does warn about this when it says "it centers ... unless
infinite glue is present in addition to the newly added \hss".)
Donald Arseneau is, I suppose, right to quote (c) from p.441:
the problem is the (false?) optimizations that TeX performs in
math-to-hosizontal conversion when it removes the "outermost" level
of boxing on math node components. His suggested \kern0pt will indeed
prevent this, of course.
Donald is wrong, however, in saying
> In all cases the boxes for the limits were set to the width of "-", 7.777pt.
They are, in fact, so set only in the cases when the explicit widths
of the super- and sub-script boxes are smaller than this; in the last
three cases the boxes all end up as 7.8, 7.9 and 8.0pt wide (+/-
rounding errors from the conversions from "em" to "pt"). Easily verified
by using \showlists.
Chris Thompson
-------
(reply, 7 Aug 91, to all)
chris,
thanks for your analysis.
the effects here are so unexpected that i think the problem is
worth a good strong warning in tugboat. could you help me to
prepare such a warning, with a very simple example showing what
happens under the relevant circumstances, and what can be done
to avoid it? if i come up with the example, can you prepare the
prose, citing chapter and verse?
-- bb
-------
Date: Thu, 08 Aug 1991 02:25:27 PDT
From: Donald Arseneau
To: uk%\"CET1@PHOENIX.CAMBRIDGE.AC.UK\"@erich.triumf.ca
Subject: Re: [[barr@triples.math.mcgill.ca: problem with Tex]]
Arrrggghh!
I could have sworn I saw those little boxes staying at 7.77777pt.
I guess the description of reboxing on p442 is more complete, and it
doesn't require the box to be "redundant", just a hbox.
This behaviour of TeX certainly violates the principle that round-off
errors shouldn't produce gross differences in the output.
Donald
-------
[ As suggested above, I intend to follow up with Chris to get a
statement of the problem for publication as a warning in TUGboat. ]
[ dek: ^^^^^^^^^^^^^^^ right.
If these things had been brought up years ago, TeX might have
changed [e.g. rebox preserving height/depth, \smash always
adding another level of boxing <-- but that might overflow
memory]
The unboxing etc. turns out to be extremely important for
posting of superscripts on accented variables ...
Anyway, no changes now, on grounds of compatibility etc.
]
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[ end of message 034 ]
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