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authorNorbert Preining <norbert@preining.info>2021-05-27 03:01:40 +0000
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+TeX 3.14159 and other updates -- file 2 of 2
+
+########################################################################
+
+>>> plain.tex
+
+ +++ \oalign and \d{}
+
+[ the following two reports, from j"org knappen and petr sojka,
+ cover the same territory, but with different proposals for fixing
+[ dek -- ^^^^^^^^^^^^^^ _different_ bugs in the same territory
+]
+ the problem. i've included both since both looked reasonable to me.
+]
+-------
+Newsgroups: comp.text.tex
+Date: 17 May 1992 20:28:21 +0000 (GMT)
+[ dek -- 1992 again -- I changed \d in 1993 but never had heard of this
+]
+Organization: Computer Science Dept, University of Tennesee, Knoxville
+From: eijkhout@cupid.cs.utk.edu (Victor Eijkhout)
+Subject: Re: \d{}
+
+In article <01GK1PHMODB48WWBZV@VzdmzA.ZDV.Uni-Mainz.DE>,
+ KNAPPEN@VKPMZD.KPH.Uni-Mainz.de (J%org Knappen) writes:
+|> The following line
+|>
+|> Das ist ein Test von (\d{}) \verb:(\d{}):
+|>
+|> runs through TeX without any error messages, but produces an underdot which
+|> is more than 300pt left off the paper.
+
+About 1000pt left of the opening bracket to be a bit more precise.
+
+|> \d{ } also fails, \d{\ } works and
+|> produces a dot under ``nothing''.
+|>
+|> The test above turns out to be a driver's test, too. Two of four
+|> dvi-drivers (on our VAX/VMS-system) did not complain nor show the mistake
+|> in output.
+
+What mistake? How can a device driver know that your printer doesn'
+have paper 1 meter wide? (With the margin only 20 cm from the right
+paper edge :-)
+
+|> I consider the facts above as a misfeature (not to say bug).
+
+I consider the posting above as uninformed.
+
+But seriously, one might wonder what happens here.
+
+Watch this:
+
+This is TeX, C Version 3.0
+(/usr/local/lib/TeX/inputs/nul.tex
+LaTeX Version 2.09 <7 Dec 1989>
+)
+*\show\d
+> \d=macro:
+->\protect \pd .
+<*> \show\d
+
+? i\show\pd
+> \pd=macro:
+#1->\oalign {#1\crcr \hidewidth .\hidewidth }.
+<insert> \show\pd
+
+(Yes, that's true, I run TeX interactively. I must be just about
+the only one on earth to do this.)
+
+This tells you that \d is essentially a macro with one argument.
+You give it the empty argument, so it expands to
+ \oalign { \crcr \hidewidth .\hidewidth }
+
+Now, \oalign is essentially \halign, and we know (otherwise look it up)
+that \crcr only gives a new line if there was a line to terminate.
+Which there isn't in this case, so we get
+ \halign { \hidewidth .\hidewidth }
+[ dek -- ^ \preamble\cr
+]
+
+and since \hidewidth is \hskip -1000pt plus 1fil, you have managed to
+move the . 1000pt left of where you intended it to be.
+
+All of this does make me wonder a bit, though. Why did Knuth use \hidewidth?
+Well obviously so that you could put objects under 'nothing'.
+[ dek -- under very _narrow_ things
+]
+But why then \crcr and not just \cr? Well, probably he foresaw
+that people might want to put stuff under more than one line, so both
+\d{a\cr b} and \d{a\cr b\cr} had to give the same result.
+
+Hey, waddaya know! Everything is logical after all!
+
+|> Yours, J"org Knappen.
+
+Victor.
+-------
+X-ListName: TeX-Related Network Discussion List <INFO-TeX@SHSU.edu>
+Date: 21 May 1992 12:46 +0000 (GMT)
+From: J%org Knappen <KNAPPEN@VKPMZD.KPH.Uni-Mainz.de>
+Subject: Again \d{}, with a bug fix
+
+ Dear samretanoj,
+
+ After reading Victor's posting carefully, the following bug fix comes to my
+ mind:
+\def\d#1{\oalign{\null#1\crcr\hidewidth.\hidewidth}}
+[ dek -- ^^^^^ \relax is better
+]
+ (Barbara, are you listening? Please forward it to DEK)
+
+ It passes the following tests:
+Teste \d{}, \d{ }, \d{\ }!
+
+Mehr Tests: \d{a\cr b} und \d{a\cr b\cr}!
+\bye
+ An analogous fix should be done to \b, both in plain.tex and lplain.tex.
+
+ On drivers:
+ here is how a good driver (Brian {Hamilton Kelly}'s DVItoLN03) behaves:
+This is DVItoLN03, Vax/VMS Version 4.0-3
+[Some more message stuff deleted (JK)]
+Warning: Characters '' set off paper
+( x = -3768..-3768, y = 342 ) - ignored
+Warning: Characters '.' set off paper
+( x = -3768..-3756, y = 342 ) - ignored
+[153] Warning: Page wider than TeX reported by 510.2450pt
+
+ Yours, J"org Knappen.
+
+ P.S. Originally, I asked my question on the info-tex mailing list. The most
+ valuable contributions were only sent to the news group comp.text.tex.
+ Fortunately since one month I have also access to news...I must have missed
+ much before, even follow-ups to my own postings!
+-------
+Date: 12 Jan 1995 22:55:33 +0100 (MET)
+From: Petr Sojka <sojka@daeron.ics.muni.cz>
+Organization: Masaryk University, Brno, The Czech Republic
+Subject: Bug in plain.tex -- please pass to DEK
+
+Barbara,
+
+here is what I consider as a bug of plain.tex:
+You read there:
+
+% This is the plain TeX format that's described in The TeXbook.
+% N.B.: A version number is defined at the very end of this file;
+% please change that number whenever the file is modified!
+% And don't modify the file under any circumstances.
+
+...
+
+\def\oalign#1{\leavevmode\vtop{\baselineskip\z@skip \lineskip.25ex%
+ \ialign{##\crcr#1\crcr}}} % put characters over each other
+\def\ooalign{\lineskiplimit-\maxdimen \oalign}
+\def\sh@ft#1{\dimen\z@.00#1ex\multiply\dimen\z@\fontdimen1\font
+ \kern-.0156\dimen\z@} % compensate for slant in lowered accents
+\def\d#1{\oalign{#1\crcr\hidewidth\sh@ft{08}.\hidewidth}}
+\def\b#1{\oalign{#1\crcr\hidewidth\sh@ft{29}%
+ \vbox to.2ex{\hbox{\char22}\vss}\hidewidth}}
+\def\c#1{\setbox\z@\hbox{#1}\ifdim\ht\z@=1ex\accent24 #1%
+ \else{\ooalign{\unhbox\z@\crcr\hidewidth\char24\hidewidth}}\fi}
+\def\copyright{{\ooalign{\hfil\raise.07ex\hbox{c}\hfil\crcr\mathhexbox20D}}}
+
+Simply saying, Don forgot setting of \lineskiplimit to zero
+in \oalign as one of the line vertical spacing parameters
+besides \baselineskip and \lineskip
+ I found this bug when having set globally \lineskiplimit to
+-2dd and setting e.g. \d{a}. What a surprise -- the dot
+wasn't there! Or what do you expect to see with simple
+file saying
+\lineskiplimit-2dd\d a\bye
+? Dot below a or `in a'?
+
+Will I be sent a check?
+
+Petr Sojka <sojka@muni.cz>
+-------
+(reply, 12 Jan 1995)
+yep, you're right. it's a bug.
+the dot doesn't disappear, exactly, it just hides "in" the a.
+\b b does kind of the same thing, but \c c is protected because
+it uses \ooalign.
+
+yes, i think you'll get a check for this one, though i predict
+it'll be just a small one, 'cuz the big ones only get awarded
+for bugs in tex(.web) itself.
+[ i didn't discover the earlier report until after i'd replied;
+ too bad. ]
+-------
+
+ ----------------------------------------------------------------------
+
+ +++ hyphenation inhibited by struts
+
+Date: 06 Jan 1994 12:04:38 +0100
+From: Piet van Oostrum <piet@cs.ruu.nl>
+Subject: Bug in TeX
+
+Barbara,
+
+Could you forward the following to Knuth (I suppose you still act as a
+forwarding agent).
+
+I consider the following a bug in TeX (in fact in the Plain macros):
+
+The first and last words in a footnote are never hyphenated.
+
+This is because plain TeX inserts struts, which are rules, and as these are
+adjacent to the first and last words, they inhibit hyphenation.
+
+The solution is to insert \hskip0pt\relax between the struts and the text.
+In fact I think it would be better to include this in the definition of
+\strut.
+
+The solution to Exercise 22.8 has the same deficiency.
+
+Piet* van Oostrum, Dept of Computer Science, Utrecht University,
+Padualaan 14, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands.
+-------
+[ dek -- I believe it is also true that the first word of _any_
+ paragraph is not hyphenated. (I prefer actually to
+ disable hyphens on the final word; but anyway this change
+ is far too drastic to be contemplated at this time.)
+]
+(reply, 06 Jan 1994)
+piet,
+thanks for your report.
+i'll forward it to knuth, but i know his response:
+this isn't a real bug; it's an unfortunate feature, and if he
+had thought about it in 1984, he probably would have done what
+you suggest. but tex/plain/etc. are now frozen, and he's not
+going to make any changes except for indisputable bugs.
+
+he will probably also suggest that you write this up for tugboat.
+so i will beat him to it -- would you write this up in a form
+suitable for the "warnings" column? this would best take the
+form of a brief, clear description (the description in your
+message is certainly clear enough) with an example or two
+showing "before" and "after". let me know what you think.
+-------
+Date: 07 Jan 1994 09:44:09 +0100
+From: Piet van Oostrum <piet@cs.ruu.nl>
+Subject: Re: Bug in TeX
+
+>>>>> bbeeton <BNB@MATH.AMS.ORG> (BB) writes:
+
+BB> piet,
+BB> thanks for your report.
+BB> i'll forward it to knuth, but i know his response: [...]
+
+I'll just wait for DEK's response and then write a warning article about
+it. Thanks for your effort.
+-------
+[ dek -- I certainly agree that he should make such a contribution to
+ _Warnings_.
+ NB. There is an \allowhyphens macro [in Appendix D, not in plain]
+]
+
+ ----------------------------------------------------------------------
+
+ +++ TeXbook, page 363, in \endinsert
+
+Date: 09 Feb 1994 12:29:08 +0100 (MET)
+From: vieth@convex.rz.uni-duesseldorf.de (Ulrik Vieth)
+Organization: Heinrich-Heine-Universitaet Duesseldorf
+Subject: Re: for Knuth: minor typo in MFbook
+
+Hi Barbara,
+
+after I printed out all the errata files yesterday, I've checked it
+again. Here is what I found out:
+
+[ this turned out to have been resolved, but i've left the comment
+ in the report for background. ]
+The METAFONTbook, 5th printing, March 1990 is quite a strange mixture.
+[ dek -- royal foulup in _many_ printings. Ask Phyllis for copies
+ of letters I wrote to A-W when i first noticed it ...
+]
+It does include the changes from errata.five (1989) and errata.six
+until 3/13/90, excluding those dated 3/24/90 or later. It does *not*
+include the changes from errata.three nor those from errata.four,
+unless they happen to fall on pages affected by the later changes.
+My conclusion that some of the changes from 3/87 were done, was just
+a conincidence since most of them were index corrections on pages
+that were changed again in 1989--1990. I'll try to locate a newer
+printing of the METAFONTbook next week at the DANTE meeting to check
+if they have been done in subsequent printings. However, I couldn't
+find any note about the 6th printing in my copy of errata.three.
+There seem to be different of that file around.
+
+[ this is the problem that still remains ... ]
+OK, so far about the METAFONTbook. When I was at it, I also checked
+my copy of the TeXbook, 18th printing, May 1990. Here, there were
+no serious problems. It includes the changes from errata.six until
+3/24/90, so it was completed sliightly later than the METAFONTbook,
+5th printing. The only small problem I found was the change on page
+A363, dated 8/12/89, that should have been in, but isn't. I'll try
+[ dek -- he's correct ... this never made it into print.
+]
+to investigate this in a newer printing as well, but there might be
+the odd chance that it came too late when the bunch of changes
+dated 3/12/89 were send off and was forgotten with the next bunch
+a few months later. In any case, I'll try to find out.
+
+Greetings, Ulrik Vieth.
+-------
+
+i found this bug for page a363 in errata.six:
+
+ \bugonpage A363, lines 8--9 from the bottom (12/8/89)
+
+ {\ninepoint\parindent=0pt
+ | \if@mid \dimen@=\ht0 \advance\dimen@ by\dp\z@ |%
+ |\advance\dimen@ by12\p@|\parbreak%
+ | \advance\dimen@ by\pagetotal \advance\dimen@ by-\pageshrink|
+ \par}
+[ dek * ]
+-------
+Date: 18 Feb 1994 18:23:06 +0100 (MET)
+From: vieth@convex.rz.uni-duesseldorf.de (Ulrik Vieth)
+Subject: Re: for Knuth: minor typo in MFbook
+
+Hi Barbara,
+
+I have just returned from the DANTE meeting, where I found a copy of
+the 7th printing of the METAFONTbook to check. It appears to me that
+the changes from errata.three and errata.four that were missing in
+the 5th printing are finally in there. So the problem I reported is
+mostly solved.
+
+About the TeXbook: I've noticed that the famous duplicated exercise bug
+that was still present in the 22nd printing (final version) has been
+corrected in the 23rd printing. However the change on page A363 (8/12/89)
+is missing there as well. Of course it is in plain.tex 3.0 or later, but
+apparently page A363 has not been updated in the 18th printing or any
+other printing since then. So I guess this is indeed a problem for Knuth
+and Addison-Wesley. Although my first problem has disappeared in the end,
+this has led to the discovery of another problem still pending, so it
+was worthwhile after all.
+[ dek -- \check
+]
+
+Ulrik Vieth.
+-------
+
+<<< end plain.tex
+
+************************************************************************
+
+>>> Metafont
+
+ +++ arithmetic overflow with z=whatever[z',z'']
+
+Date: Mon, 9 May 94 14:44:46 WETDST
+From: Tomek Przechlewski <tomasz@panda.bg.univ.gda.pl>
+Subject: Bug in Metafont?
+
+Dear Barbara,
+
+I am passing the request of my friend Bogus{\l}aw
+Jackowski (you have met him in Aston last year). He cannot find the
+explanation of MF performance in the example appended below.
+
+Could you answer why in quite similar situations there are
+so different outcomes. Is this a bug in Metafont or a feature?
+
+I look forward to hearing from you
+
+--Tomek Przechlewski
+
+% ===================================================================
+
+%
+% \rm{}The following simple \MF\ program yielded unexpected (to me) results:
+%
+z1=whatever[(0,328),(100,329-eps)];
+z2=whatever[(0,328),(100,329)];
+z3=whatever[(0,328),(100,329+eps)];
+z4=whatever[(0,328),(100,329+2eps)];
+showdependencies;
+end.
+%%\def\~{\kern.15em}
+%
+% \rm{}The log file produced by, e.\~g., sbMF reads as follows:
+%
+% This is METAFONT, Version 2.71(c)sb13 (preloaded base=plain 93.5.6)
+% 23 JUL 1993 17:22
+%%%% originally the ampersand was not preceded by the slash, of course
+% ** \&plain aritover.mf
+% (aritover.mf
+% ! Arithmetic overflow.
+% l.5 ...atever[(0,328),(100,329)]
+% ;
+% ?
+% ! Arithmetic overflow.
+% l.6 ...er[(0,328),(100,329+eps)]
+% ;
+% ?
+% ! Arithmetic overflow.
+% l.6 ...r[(0,328),(100,329+eps)];
+%
+% ?
+% y4=0.01001x4+328
+% y3=0.01001x3+327.83998
+% y2=0.01x2+327.68
+% y1=0.01x1+328 )
+%
+% \rm{}Although Phil Taylor's opinion is that ``.\~.\~. the `bug' appears
+% \rm{}to be a feature; the error message is well-defined, and `help' gives
+% \rm{}a sensible diagnostic .\~.\~.'' I can hardly agree that this is OK.
+% \rm{}Good luck to everybody using equations of the form |z=whatever[z',z'']|.
+%
+% \rm{}Bogus\l{}aw Jackowski
+% \rm{}ul. Tatrza\'nska 6/1
+% \rm{}80-331 Gda\'nsk, Poland.
+%
+%
+% \rm{}P.\~S. For the first time I came up against this situation on 4 III 1993
+% \rm{}(the equation was |z=whatever[(37.0092,419.22664),(280.3105,417.96634)]|).
+% \rm{}Since that time I had ``a pleasure'' of encountering it several times. BJ.
+%%\let\makefootline\empty\end
+-------
+Date: Tue, 17 May 94 12:46:02 WETDST
+From: Tomek Przechlewski <tomasz@panda.bg.univ.gda.pl>
+Subject: B. Jackowki's replay
+
+Dear Barbara,
+
+thank you for your responding to Tomek's mail.
+
+> ...there was another report about METAFONT arithmetic overflow just
+> last week...
+
+Both error messages which are the subject of Pierre MacKay's response
+have nothing to do with the METAFONT's behavior I had to struggle with:
+
+1.
+> alpha=diag_ratio(4,stem2-stem3+stem4,y1-y2,x8r-x1l+mid_corr-2apex_corr);
+
+The `diag_ratio' macro does not make any use of `whatever[...]' construction,
+while my troubles are strictly connected with this construction.
+
+2.
+>z4=z5+whatever*(150u,h);
+
+Here the `! Arithmetic overflow' error occurs because the value of expression
+`150u' is too large: for cminch font u=223.51988 at 2540 dpi, hence the
+product would be about 33528, which is the number too large for METAFONT
+(her actual infinity is 32767.99998). So, once again, `whatever[...]'
+construction is not to blame.
+
+In my example I am using fairly ``regular'' numbers (ranging from zero to
+about 300) and, moreover, the behavior of METAFONT seems to be numerically
+instable, as changing the numbers by `eps' (in plain METAFONT eps=0.00049)
+has apparent impact on `! Arithmetic overflow' error.
+
+Of course, I am not in a position to insist on prof. Knuth to change
+METAFONT, neither I wish to overload him with unnecessary work. Nevertheless,
+I would be happy to learn at least when such a situation may occur; then it
+will perhaps become clear how to avoid it.
+
+Cheers. Jacko
+
+PS: and Tomek.
+-------
+[ message forwarded to chris thompson, but no response ]
+
+ ----------------------------------------------------------------------
+
+ +++ several reports from Bogus{\l}aw Jackowski
+
+Date: 18 Oct 1994 16:06:45 +0100 (MET)
+From: Wlodek Bzyl <matwb@halina.univ.gda.pl>
+Subject: errors of TeX, MF (from B. Jackowski)
+
+Hi, Barbara,
+
+This file contains actually five different files put together to facilitate
+electronic transmission and maintenance. Files are separated by `-=-=-= ...'
+lines. All of them contain remarks concerning may-be-bugs in various
+D. E. Kunth's products. If the authorship of a remark is not stated
+explicitly, this means that it is mine (BJ's).
+
+ Bogus\l{}aw Jackowski
+ ul. Tatrza\'nska 6/1
+ 80-331 Gda\'nsk, Poland
+
+
+ SYNOPSIS
+
+1) File ARITOVER.MF: describes troubles with METAFONT's arithmetical overflow
+ in context of linear equations; I've already sent this file to you,
+ but for the completeness reason I put it along with other messages.
+ To see the problem you can compile the file with METAFONT and/or
+ to print it using MFT utility with PL.MFT data (enclosed separately).
+
+ Perhaps Phil Taylor is right that what I regard as a bug is merely
+ a feature. If so, I would gladly learn how to avoid the problems
+ which this `feature' may cause.
+
+2) File SHUFFLED.TEX: discusses the problem of validity of the
+ ``shuffled binary property'' of METAFONT operation `intersectiontimes.'
+ This file can be compiled using TeX + MANMAC macros.
+
+3) File CSCSPU.CH: contains a minor change to the METAFONT sources
+ of the CM fonts.
+
+4) File ITALD.CH: contains a minor change to the METAFONT sources
+ of the CM fonts.
+
+5) File 2R1Q2TXB.TEX: contains two minor remarks (possibly out of date)
+ and one question concerning misprintings in The TeXbook. This file
+ can be compiled using TeX + MANMAC macros.
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FILE ARITOVER.MF
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+%
+% \rm{}The following simple \MF\ program yielded unexpected (to me) results:
+%
+z1=whatever[(0,328),(100,329-eps)];
+
+% [ text removed; complete message appears above ]
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% END OF FILE ARITOVER.MF
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FILE SHUFFLED.TEX
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\let\MFmanual=\!
+\input manmac \vsize24cm \pageheight\vsize
+\def\rhead{Chapter 14. Paths}
+\def\MFbook#1{%
+ {\def\MF{{\manual 89:;}\-{\manual <=>:\/}}% slant the logo
+ \sl The~\MF book#1}}
+\pageno137 \proofmodefalse
+
+\vdots
+
+\bigskip
+
+[ dek -- p137
+]
+\ddanger If the paths intersect more than once, \MF\ has a somewhat
+peculiar way of deciding what times $(t,u)$ should be reported by
+`$p$~intersectiontimes~$q$'. Suppose $p$ has length~$m$ and $q$ has
+length~$n$. \ (Paths of length~0 are first changed into motionless paths
+of length~1.) \ \MF\ proceeds to examine subpath~$(k,k+1)$ of~$p$
+versus subpath~$(l,l+1)$ of~$q$, for $k=0$, \dots,~$m-1$ and $l=0$,
+\dots,~$n-1$, with $l$ varying most rapidly. This reduces the general
+problem to the special case of paths of length~1, and the times $(t,u)$
+for the first such intersection found are added to $(k,l)$. But within
+paths of length~1 the search for intersection times is somewhat
+different: Instead of reporting the ``lexicographically smallest'' pair
+$(t,u)$ that corresponds to an intersection, \MF\ finds the $(t,u)$
+whose ``^{shuffled binary}'' representation $(.t_1u_1t_2u_2\ldots\,)_2$
+is minimum, where $(.t_1t_2\ldots\,)_2$ and $(.u_1u_2\ldots\,)_2$ are
+the radix-2 representations of $t$ and~$u$.
+
+\bigskip
+
+\vdots
+
+\bigskip
+
+\tenpoint
+
+This is what \MFbook\/ says on page 137. Then follows Exercise 14.17 which
+makes use of the ``shuffled binary property.'' Alas, the ``shuffled binary
+property'' does not hold. Consider a path $p=(a,b)\dashto(c,d)$. One would
+expect that the result of `$p$~\null intersectiontimes~\null reverse~$p$'
+should be $(0,1)$, as the shuffled binary representation is for this case
+$(.01010\ldots\,)_2$ which is the {\it minimum\/} of the shuffled binary
+representations for pairs $(x,1-x)$, ${0\le x\le1}$.
+
+Indeed, most likely the result will be like that (sometimes within some
+accuracy). But if there exist \MF\ numbers $c'$~and~$d'$ such that
+$c$~and~$d$ are of the form ${c=a+3c'}$ and ${d=a+3d'}$, the result is
+[ dek -- ^ b
+]
+astonishingly~$(0.5,0.5)$. This apparently contradicts the quoted statement
+as the shuffled binary representation of $(0.5,0.5)$ is $(.11)_2$ which is
+the {\it maximum\/} of the shuffled binary representations for pairs
+$(x,1-x)$, ${0\le x\le1}$.
+
+Here you have a little \MF\ program which can produce arbitrarily many
+`|>>|~|(0.5,0.5)|' messages on your terminal:
+
+ \begintt
+ path p; numeric a,b,c,d,n; n:=10;
+ for i:=1 upto n:
+ a:=uniformdeviate 1000; b:=uniformdeviate 1000;
+ c:=a+3uniformdeviate 1000; d:=b+3uniformdeviate 1000;
+ p:=(a,b)--(c,d);
+ show p intersectiontimes reverse p;
+ endfor
+ \endtt
+
+\medskip
+
+My basic question is: does the above specification cover all exceptions
+from the shuffled binary property?
+
+Also, I wonder whether it is a ``white lie,'' or a mistake in \MFbook,
+or---God forbid!---a bug in \MF\kern.1em?
+
+[ dek -- ANSWER:
+ This is an interesting question (but you could have figured it
+ out from the program. I admit that the documentation is ``terse'',
+ but the algorithm is pretty enough to reward a close look.)
+ In fact we _do_ get the minimum shuffled binary, which happens
+ to be not .0101010101... but .001111111111... [even smaller!];
+ which gives (0.5,0.5).
+ The point .001111111111 seems to lie on both curves only when
+ there is absolutely no truncation error, and I believe this
+ happens if and only if the control points z_0 .. controls z,
+ and z_2 .. z_3 satisfy z_1 - z_0 = z_2 - z_1 = z_3 - z_2 .
+ Otherwise it's necessary to go to the next higher case.
+ Of course the intersection point routine is not intended for
+ such curves -- it is supposed to -|- find genuine crossing points.
+]
+
+\bigskip
+
+\rightline{\vbox{\halign{#\hss\cr
+\it June 10, 1994\cr
+\noalign{\medskip}
+Bogus\l{}aw Jackowski\cr
+ul. Tatrza\'nska 6/1\cr
+80-331 Gda¤sk\cr
+Poland\cr
+}}}
+
+\end
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% END OF FILE SHUFFLED.TEX
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FILE CSCSPU.CH
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+% Following a change in ROMANU.MF I would suggest a similar change
+% in CSCSPU.MF:
+%
+@x
+bulb(3,4,5); % bulb
+@y
+[ dek -- $2.56
+]
+pickup tiny.nib; bulb(3,4,5); % bulb
+@z
+%
+% The original version of CSCSPU generates bad ``dotless'' small cap `j'
+% in Computer Concrete CCCSC10 font.
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% END OF FILE CSCSPU.CH
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FILE ITALD.CH
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+% The non-zero depth of the italic digit seven was noticed by 12 years old
+% Joanna Ry\'cko. I cannot see any reason for keeping this state of the art.
+% It seems that the following change in ITALD.MF would be appropriate:
+@x
+beginchar("7",9u#,fig_height#,desc_depth#);
+@y
+beginchar("7",9u#,fig_height#,0);
+@z
+
+[ dek -- I have sworn not to change the TFM files ever again. So this
+ curious glitch is permanent. (Long ago _all_ italic digits had
+ the same descender. Later I corrected everything but the 7;
+ we can live with it.
+]
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% END OF FILE ITALD.CH
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% FILE 2R1Q2TXB.TEX
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+\input manmac \vsize24cm \pageheight\vsize
+\proofmodefalse
+\def\rhead{}
+\def\rightheadline{}
+\font\bsl cmbxsl10
+
+\centerline{\bf Two Remarks and One Question}
+\centerline{\bf Concerning \bsl The \TeX book}
+
+\bigskip
+
+% [ this one has been fixed ]
+1)\enspace Noticed by Marek Ry\'cko: In the eighteenth printing of {\sl The
+\TeX book\/} Exercise~8.7 appears twice (one after the other).
+
+\bigskip
+
+2)\enspace Noticed by Marek Ry\'cko: In the source of {\sl The \TeX book\/}
+(incorporating the final corrections made in 1993) on the page~31 a space
+precedes improperly the word `\TeX' just after the verbatim quotation:
+[ dek -- $2.56
+]
+
+\medskip
+
+\noindent `[\dots] after typing something like this:
+\begintt
+! Undefined control sequence.
+l.2 \vship
+ 1in
+?
+\endtt
+\def\storypage{24} % listing of story.tex
+\TeX\ begins its error messages with `|!|', and it shows what it was
+reading at the time of the error by displaying two lines of context~[\dots]'
+
+\medskip
+
+\tolerance1000
+The reason for this is that after the verbatim quotation there is a command
+|\def\storypage{24}|, and there is a space after it.
+[ dek -- ^^^^^^ This command is in fact redundant -- I moved it to
+ manmac.tex but forgot to delete it from texbook.tex
+]
+
+\bigskip
+
+3)\enspace The ``problem'' raised during the Euro\TeX'94 meeting in Gda\'nsk,
+Poland: What is the proper spelling of Addison$\,*\,$Wesley: Addison-Wesley
+(back of the cover of {\sl The \TeX book}, prepared probably by the
+publisher) or Addison Wesley (the~source of {\sl The \TeX book\/}), or both?
+
+[ dek -- They flip-flopped several times during the 80s, as they had
+ different chief graphic designers for their ``corporate image''.
+ I couldn't keep up.
+]
+
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+% END OF FILE 2R1Q2TXB.TEX
+%-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+-------
+
+<<< end Metafont
+
+************************************************************************
+
+>>> CM fonts
+
+ +++ missing "cmchar"s in bigdel.mf
+
+Date: Sat, 07 Mar 92 15:23:59 GMT
+From: Chris Thompson <CET1@phoenix.cambridge.ac.uk>
+Cc: REH10@phoenix.cambridge.ac.uk
+Subject: Missing "cmchar"s in bigdel.mf
+
+Barbara,
+
+[ dek -- E95,E97 $2.56
+]
+Robert Hunt (reh10@phx.cam.ac.uk) has pointed out that in bigdel.mf
+the expected "cmchar"s on line 596 (character `077) and line 645
+(character `167) are missing. (As "cmchar" is usually a no-op, this
+only matters if you are trying to play the sort of games described
+on pp.312-313 of the METAFONTbook.) It seems to be just an oversight:
+perhaps you can add it to DEK's list?
+
+Chris Thompson
+JANET: cet1@uk.ac.cam.phx
+-------
+
+ ----------------------------------------------------------------------
+
+ +++ shaved_stem vs. cap_stem in greeku.mf
+
+Date: 14 May 1993 17:38:30 -0300 (BST)
+From: Chris Thompson <CET1@phx.cam.ac.uk>
+To: Barbara Beeton <BNB@MATH.AMS.ORG>
+Cc: Robert Hunt <REH10@phx.cam.ac.uk>
+Subject: Re: [Minor CM fonts bug]
+
+Barbara,
+
+Robert Hunt reports the following:
+> Line 196 of greeku.mf, which currently reads
+[ dek -- E187,E189 $2.56
+]
+>
+> lft x1l=lft x2l=hround(.5w-.5cap_stem); top y1=h; bot y2=0;
+>
+> should read
+>
+> lft x1l=lft x2l=hround(.5w-.5shaved_stem); top y1=h; bot y2=0;
+>
+> Exactly the same bug also occurs on line 215. (These are in the
+[ dek -- ^^^ 216
+]
+> character programs for capital Phi and Psi respectively.)
+
+This looks right to me: at some stage 'shaved_stem' was introduced
+to these programs instead of 'cap_stem', but these two occurrences
+were missed.
+
+Chris Thompson
+Cambridge University Computing Service
+-------
+
+ ----------------------------------------------------------------------
+
+ +++ miscellanea from Robert Hunt, mostly in CM sources
+
+Date: 29 Mar 1994 21:01:42 -0300 (BST)
+From: Robert Hunt <REH10@phx.cam.ac.uk>
+Cc: Chris Thompson <CET1@phx.cam.ac.uk>
+Subject: TeX bugs
+
+Dear Barbara,
+
+I've been saving up several bugs I've found in the Computer Modern sources, the
+METAFONTbook and Plain TeX for quite a while, and am now sending them on to you
+for DEK. Perhaps you could add them to his list of things to look at next time
+he reviews TeX etc. - I fully realise that this probably won't be for some
+quite considerable time!
+[ dek - ^^^^^^^^^^^^^^^ ^^^^
+]
+
+This message is, I'm afraid, rather long, but I thought it'd be better to send
+you everything in one go rather than split it up into lots of separate
+messages. Each of the bugs is separated by a line of ------'s below.
+[ dek -- well done
+]
+
+Thanks & best wishes,
+Robert Hunt.
+
+ ------------------------------------------------------------------------------
+
+There seems to be a recurrent error in the code for the various Computer Modern
+[ dek -- OK on pE481
+]
+integral signs. For example, in the code for the \displaystyle integral sign in
+bigop.mf, the line
+ lft x5r=hround(.5w-.5stem);
+[ dek -- E113, E115 $2.56
+ four places in bigop.mf
+ " " " ebigop.mf
+]
+should actually read
+ lft x5r=hround(.5w-.5max_size);
+as the character is max_size pixels wide at z5. (In fact, the stem parameter
+does not feature in the program for this character in any other way!) Similar
+comments apply to all the other sizes and styles of integral signs.
+
+ ------------------------------------------------------------------------------
+
+In the code for the Computer Modern partial differential sign in italms.mf, the
+line
+ path p; p=pulled_super_arc.l(3,4)(pull);
+[ dek -- E233 $2.56
+]
+should be replaced by
+ path p; {{interim superness:=more_super; p=pulled_super_arc.l(3,4)(pull)}};
+
+ ------------------------------------------------------------------------------
+
+In symbol.mf, the code for the Computer Modern elementary division operator has
+a bug causing the dots to be drawn with diameter dot_size+rule_thickness rather
+than dot_size. (It's clear that they're meant to be of diameter dot_size
+[ dek -- ^^^^^ No, the dots are the correct size but the
+ defs of x_3,y_3 are inappropriate
+ E438 $2.56
+]
+because of the definition of x3.) The reason that the code doesn't work is that
+pos doesn't know the breadth of rule.nib, so doesn't subtract anything off from
+[ dek -- currentbreadth is in fact set from the pickup fine.nib of the
+ integral sigh (by chance) -- I should make my intentions clear,
+ without changing the character image that I got by luck.
+]
+dot_size. Various fixes are possible (such as changing the font_setup routine
+in cmbase.mf to define breadth_[rule.nib]=rule_thickness), but the simplest
+seems to be to insert a line saying "pickup fine.nib;" just after the draw
+command.
+
+ ------------------------------------------------------------------------------
+
+There seems to be an error in the syntax definition for <path expression> on
+page 213 of the METAFONTbook (and also in the simplified definition on page
+129). I hope that I haven't embarrassed myself by misunderstanding it!
+
+The syntax as given doesn't seem to allow "(0,0)..(1,0)" as a
+<path expression>. A <path join> (".." here, with empty direction specifiers)
+must be followed by either "cycle" or <path tertiary>. A <path tertiary> must
+start with a <path primary>. But "(1,0)" cannot be a <path primary>, as it is
+[ dek -- C129 $2.56
+]
+not a <path argument> or <path variable>, nor is it "(<path expression>)"
+(since "1,0" without the brackets is not a valid <path expression>).
+[ dek -- <pair tertiary< movves from subexpr level to tertiary level
+]
+
+ ------------------------------------------------------------------------------
+
+There is a low-resolution anomaly that arises in the Computer Modern equals
+sign and several other such characters. Each of the bars of "=" is meant to be
+drawn by an identical _circular_ pen. However, at low resolutions (e.g.,
+300dpi, with mode CanonCX) the character can often turn out looking like the
+following:
+
+ xxxxxxxxxxxx
+ xxxxxxxxxxxxxx
+
+ xxxxxxxxxxxxxx
+ xxxxxxxxxxxx
+
+which doesn't have the symmetry one would expect at the end-points of the
+lines. This is due to the way in which the heights of the two bars are chosen;
+the centre-points of the bars are at heights math_axis+.5spread and
+math_axis-.5spread. Now math_axis has been chosen to be a good.y position for
+rule.nib, and spread has been chosen to be an integer+eps; but this means that
+if spread is an _odd_ integer (+eps) then the edges of the nib when it draws
+the two bars are at almost exactly the _least_ optimal heights for drawing!
+(I.e., an integer+.5+1/2eps.) This results in a loss of vertical symmetry at
+the end-points of each bar.
+
+My suggested solution for this is to ensure that spread is always an even
+integer (apart from the correction of size eps), as follows:
+ def compute_spread(expr normal_spread,big_spread)=
+ spread#:=math_spread[normal_spread,big_spread];
+ spread:=2ceiling(spread#*hppp/2)+2eps; enddef;
+[ dek -- E491 $2.56 ^ I left this out. _I_ _don't_ _know_
+ _why_, but it caused the equal isgn to look like
+ xxx---x
+ xx---x
+
+ xx---x
+ xxx---x
+ quite asymmetric!
+ I don't have time to fool around, but I guess this definition
+ is an improvement even though the 2eps should've been
+ good too ...
+ +0 OK
+ +eps OK
+ +2eps NG
+ +3eps NG
+ +1/3 NG
+]
+This does have the disadvantage that at very low resolutions characters can end
+up being rather widely spread.
+
+ ------------------------------------------------------------------------------
+
+The character "H" in font cmssdc10, at pixels_per_inch=300 and mag=magstep1
+(the other parameters are unimportant), demonstrates a rounding problem which
+is in fact present in a very great number of the Computer Modern character
+definitions. At the top and bottom left of the left-hand stem, a pixel has been
+cut out; but on the right of the left-hand stem, and on both sides of the
+right-hand stem, these pixels are filled in. This makes the character very
+asymmetric.
+
+The problem is caused because the stem is drawn with a pen of non-zero
+thickness which is turning a corner, and because of a nicety which is discussed
+in the METAFONTbook on the top of page 200. Basically, the line
+ lft x1l=lft x2l=hround max(2u,3u-.5cap_stem); x3=x4=w-x1;
+in the definition of "H" in romanu.mf should be replaced by the two lines
+ lft x1l=lft x2l=hround max(2u,3u-.5cap_stem)-eps;
+ rt x3r=rt x4r=w-hround max(2u,3u-.5cap_stem);
+(or something equivalent to these two). We want to avoid the vertices of the
+"tiny" pen polygon (which is being used to draw the character) passing through
+any ambiguous points whenever it turns a corner, and to do that we want its
+centre to lie at a half-integer minus eps whenever it's at the left-hand side
+of a stroke region, and at a half-integer (exactly) when it's at the right-hand
+side of a stroke. (By "half-integer" here I mean either an integer or an
+integer plus 1/2, dependent on the breadth of the "tiny" nib.) Since the "pos"
+command of cmbase sets the distance between x$l and x$r to be an integer plus
+eps (because the breadth of the tiny pen is set to an integer minus eps by the
+font_setup routine), the command "lft x1l=hround(...)-eps" sets lft x1l to an
+integer minus eps and rt x1r to exactly an integer; whereas "rt
+x3r=hround(...)" sets rt x3r to an integer and lft x3l to an integer minus eps.
+These commands therefore ensure that the stroke will have left-right symmetry.
+
+So the general rule which seems to be required is that in many of the CM
+programs,
+ lft x$l=hround(...);
+should be replaced by
+ lft x$l=hround(...)-eps;
+whereas
+ rt x$r=hround(...);
+should be left alone. Unfortunately this isn't a hard-and-fast rule, so would
+be difficult to do automatically; in particular, commands such as
+ lft x$l=w-rt x$$r=hround(...);
+need to be split into two statements.
+
+In fact, even the METAFONT logo font itself is subject to this problem! The "F"
+character in logo.mf can suffer from asymmetry of the top bar, with pixels
+being lost at the left-hand side (the right-hand side being alright). A quick
+solution would seem to be to set leftstemloc to an integer minus eps instead of
+exactly an integer, but I haven't checked this carefully to make sure it would
+work correctly.
+
+Is it worth doing anything about this? It's a very minor problem, and to put it
+[ dek -- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ To raise this question is to answer it!
+]
+right would require an awful lot of changes to the Computer Modern source
+files. Unless some super-whazzo solution involving changing the "lft" macro
+(etc.) can be thought up, it would be a very large amount of work.
+
+ ------------------------------------------------------------------------------
+
+There are a number of infelicities and/or bugs in the Plain TeX format. I've
+listed some I know about below in approximately decreasing order of importance;
+some (especially near the end of the list) are a little esoteric.
+
+% The Plain TeX \skew macro does not work properly with variable-size accents
+% such as \widetilde. The following rewrite corrects that.
+[ dek -- And makes people wonder why divide by 2 instead of using half
+ the skew originally!
+]
+%
+\def\skew#1#2#3{{\muskip\z@#1mu\divide\muskip\z@\tw@ \mkern\muskip\z@
+ #2{\mkern-\muskip\z@{#3}\mkern\muskip\z@}\mkern-\muskip\z@}{}}
+[ dek -- p359 $2.56
+]
+%
+% The maths spacing inserted by \bmod is incorrect in script or scriptscript
+% styles, because \nonscript was not used.
+%
+\def\bmod{\nonscript\mskip-\medmuskip\mkern5mu
+ \mathbin{\rm mod}\penalty900\mkern5mu\nonscript\mskip-\medmuskip}
+[ dek -- p361 $2.56
+ I hope this won't mess up too many people who have already
+ compensated for this bug.
+]
+%
+% \displaylines does not work correctly if \tabskip happens to be non-zero when
+% it is called (for instance, if the user does an \halign of his own with a
+% non-zero \tabskip, just before using $$\displaylines{...}$$).
+%
+\def\displaylines#1{\displ@y \tabskip\z@skip
+ \halign{\hbox to\displaywidth{$\@lign\hfil\displaystyle##\hfil$}\crcr
+ #1\crcr}}
+[ dek -- p362 $2.56
+]
+%
+% If a maths display is started when \prevdepth=-1000pt, the \openup adjustment
+% which \displ@y automatically inserts before the first line of the display to
+% compensate for the change in the value of \baselineskip should be omitted.
+%
+\def\displ@y{\global\dt@ptrue\openup\jot\m@th
+ \everycr{\noalign{\ifdt@p \global\dt@pfalse \ifdim\prevdepth>-1000\p@
+ \vskip-\lineskiplimit \vskip\normallineskiplimit \fi
+ \else \penalty\interdisplaylinepenalty \fi}}}
+[ dek -- p362 $2.56
+ It is _very_ hard to reach this situation!
+ \noindent $$ \displaylines ... seems to be the simplese.
+]
+%
+% [ \d{} and \b{} were reported earlier; see above under >>> plain.tex;
+% this is the first report of \@vereq, i believe ]
+% The \d and \b accent macros don't work if the user has set \lineskiplimit to
+% a negative value, say around -2pt or less. The \@vereq macro (used only by
+[ dek -- esplicitly ^
+]
+% \cong) suffers from a similar problem.
+%
+\def\d#1{{\lineskiplimit\maxdimen\oalign{#1\crcr\hidewidth.\hidewidth}}}
+\def\b#1{{\lineskiplimit\maxdimen\oalign{#1\crcr
+ \hidewidth\vbox to.2ex{\hbox{\char22}\vss}\hidewidth}}}
+\def\@vereq#1#2{\lower.5\p@\vbox{\lineskiplimit\maxdimen\lineskip-.5\p@
+ \ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
+[ dek -- p360 $2.56
+]
+%
+% Several definitions in Plain TeX contain excess tokens (typically redundant
+% "=" signs, "by" keywords, etc.). Some (e.g. \m@th) are executed so frequently
+% that it's worth removing them, which the following definitions do.
+%
+% [ removed ]
+%
+% [ removed some suggested hyphenations
+%
+% [ removed some suggested enhancements to operators like \sin ]
+%
+% \settabs breaks spectacularly in the (somewhat unlikely) eventuality of it
+[ dek -- ^^^^^^^^^^^^^ agreed
+]
+% being followed by an \if; for example,
+% \settabs \ifdim\hsize<8in 3 \else 4 \fi\columns
+[ dek -- p354 $2.56
+]
+%
+\let\temp=\+ \let\+=\relax
+
+\def\sett@b{\ifx\next\+\def\nxt{\afterassignment\s@tt@b\let\nxt}%
+ \else\let\nxt\s@tcols\fi \let\next\relax \nxt}
+\def\s@tt@b{\let\nxt\relax\us@false\m@ketabbox}
+
+\let\+=\temp
+%
+% English authors would greatly prefer to use English spellings in their
+% command names!
+%
+% [ removed ]
+
+ ------------------------------------------------------------------------------
+
+[ additional bugs summarized; separate reports included above ]
+-------
+(reply, 29 Mar 1994)
+robert,
+thanks very much for your collection.
+
+a comment on plain.tex. knuth has communicated to me that he
+will never again change plain.tex ; here is his response to a
+suggestion sent to him in february 1993:
+
+ [ dek: These macros look very good but I cannot change plain TeX
+ any more at this late date. _Ever_._
+ (Wish I had thought of them in 1985!)
+ He should publish them in TUGboat.
+ ]
+
+presumably if there is a very bad and obscure bug *that doesn't
+take effect very often* he might consider making an exception,
+but his ideal now is that the entire tex system remain stable,
+permanently. his recommendation that remaining problems, and
+suggested improvements, be published in tugboat must be taken
+at face value. if i don't pay attention to such comments, and
+send in everything that's sent to me, i put myself in danger
+of incurring his severe displeasure, which would jeopardize my
+welcome to forward real bugs. if you really do want to submit
+these suggestions for plain.tex to him, you should do it yourself
+by regular post. his address is
+
+ Prof. Donald E. Knuth
+ Department of Computer Science
+ Stanford University
+ Stanford, CA 94305 U.S.A.
+
+you could mention that i wouldn't forward them, or not, as you
+wish. (i'll let you know what i do forward when i next put a
+package together; that should be within the coming month.)
+
+regarding the computer modern sources, he may feel the same way
+as about plain.tex, but it's never been tested.
+-------
+Date: 11 Apr 1994 21:42:27 -0300 (BST)
+From: Robert Hunt <REH10@phx.cam.ac.uk>
+To: bbeeton <BNB@MATH.AMS.ORG>, Chris Thompson <CET1@phx.cam.ac.uk>
+Subject: Re: TeX bugs
+
+Dear Barbara,
+
+Thanks for your message about my bug collection. I understand DEK's position on
+Plain TeX, that he doesn't want to change it any more, and will certainly
+respect that. (Though I suppose I would be grateful if when you forward the
+rest of my list to him, you would just add a one-liner saying that there used
+to be several Plain TeX bug-fixes there but that you've removed them with my
+co-operation for this very reason!)
+
+How would I go about publishing them in TUGboat? [...]
+-------
+
+[ dek -- Barbara, I relented this time only because his macros were elegant
+ and instructive and (with the exception of \bmod) unlikely to
+ make existing .tex files obsolete.
+ The \bmod bug is something I'm sure people have compensated for,
+ e.g., by inserting a thin space where it now will look better
+ without any such manual tuning up ...
+ but I decided the correction desirable anyway.
+
+ For example, I had to change the MS to Concrete Math in seven places.
+ We could tell people to put the old def of \bmod in their files
+ if they don't wish to change. (That's what I decided to do with
+ Concrete Math.)
+
+ I do expect to be EXTREMELY hardnosed about ANY future changes
+ to plain.tex, however. My thought is that this might as well be
+ the one last chance for changes -- since \d was so badly in need
+ of correction (four separate changes to it!)
+ Therefore, _please_ _keep_ telling people so exactly what you have
+ been telling them so kindly about the frozen-ness of plain.tex.
+]
+
+ ----------------------------------------------------------------------
+
+ +++ cap_ess in cmmi12 and larger
+
+Date: 01 Feb 1994 18:17:07 +0100
+Reply-to: METAFONT Distribution List <metafont@ens.fr>
+From: KNAPPEN@VKPMZD.kph.Uni-Mainz.DE
+Subject: c-cmmi.mf (Sauter tools) revisited: Bug in cap_ess
+[ dek -- ^^^^^^^^^^^^ This is something I have nothing to do with...
+]
+
+Bug report in c-cmmi.mf
+
+At 17.28pt the middle part of the letter S in cmmi looks too thin. I have
+gone into the parameters and found the following formula for
+cap_ess (design_size>10, rest omitted):
+
+cap_ess#:=(-design_size*5 + 380)/360 pt#;
+
+this means that the parameter cap_ess# decreases with design_size and will
+reach zero at 76 pt! So why that decrease? Let's look at the Knuthian
+parameters for cmr, cmmi and cmti:
+
+font 5 6 7 8 9 10 12 (pt#)
+cmr 14 19 23 27 31 35 43 (1/36 pt#)
+cmmi 13.5 18.5 22.5 26 30 33 32
+cmti -- -- 21 24 27 31 34
+
+For all font but cmmi12, cap_ess of cmmi is between the values of cmr and
+cmti, but closer to the cmr value. It look as if for cmmi12 a value of 42
+was aimed at, but for some reasons 32 has become a feature of this font. If
+you look sharply at the S in cmmi12 (at 600dpi), you might find it a little
+too light besides the letter R, but this is at the edge of visibility (at
+least for my eye), therefore I'd never noticed it without looking at the
+parameters.
+[ dek -- As far as I know, there was no good formula for the ess widths;
+ I just played until they seemed right -- I defer to committee for
+ these things.
+]
+
+However, further decrease of cap_ess is a bad idea, it should increase
+again from design_size=12 on.
+
+Here a proposed formula for design_size>12, it yields 320/360 pt# at
+12 and increases then, never getting bigger then the cmr-value:
+
+(design_size*9 + 216) / 360pt#
+
+It will be, however, lower then the value of cap_ess in cmti.
+Since roman letters may appear in matematical formulae, the alignment
+to the cmr parameters is imho the more important case.
+
+Fortunately, a change in the parameter cap_ess does not affect the font
+metrics (or have I missed something?), therefore we can make a change here
+[ dek -- ^^^^^^^^^ true -- anybody can change to
+ heart's content
+]
+without disturbing documents using the Sauter fonts.
+
+Comments?
+
+Yours, J"org Knappen.
+-------
+
+ ----------------------------------------------------------------------
+
+ +++ possible glitch in cmbx5 and cmbx6
+
+Date: 15 Dec 1994 12:01:51 -0800 (PST)
+From: kinch@netcom.com (Richard J. Kinch)
+To: tex-implementors@MATH.AMS.ORG
+Subject: Bug in cmbx5 and cmbx6
+
+I believe there is a latent bug in Computer Modern cmbx5 and cmbx6.
+
+The meta-ness seems to degenerate at the 5-point optical size used in cmbx5.
+For example, digit "7" grows a wart on top, and serifs on glyphs like A, K, M,
+N, U, V, W, X, Y, and others are notched in the inside corners. The "7"
+problem is clearly visible at 300 dpi when magnified to cmbx5 at 37.15pt. The
+serif notching is not evident except at even larger magnifications. At normal
+size at 300 or 600 this is not necessarily visible.
+
+In C&T Volume E (Computer Modern Typefaces) on page 560 there is a sample of
+cmbx5. Under a 10x lens or so you can see extra ink on the top of the
+digit "7". I believe there is a one- or two-pixel wart on top of "7" in the
+cmbx6 sample, too.
+
+The problems are evident in proof-size printouts.
+
+I discovered this in converting the METAFONT shapes to Bezier outlines with my
+automatic converter, METAFOG. I saw the misshapen glyphs and puzzled for days
+thinking I had a bug in my converter.
+
+Richard Kinch
+-------
+
+[ dek -- It's okay to change the shapes of CM fonts as long as you don't
+ change the TFM files. I haven't time to fix this problem
+ since I don't consider enlarged cmbx an important font ...
+ I was unable to see the notches on the A, but I agree that the 7
+ [drawn outline of 7, with a lump on the top] looks cancerous.
+ Not a problem at the sizes intended. Ultrabold is where
+ meta-ness can be expected to break first.
+
+ (Congrats on METAFOG)
+]
+
+ ----------------------------------------------------------------------
+
+ +++ arithmetic overflow in CMinch
+
+Date: 05 May 1994 14:08:55 -0700
+From: mackay@cs.washington.edu (Pierre MacKay)
+To: BNB@MATH.AMS.ORG
+Cc: Bob@microprograms.com, mackay@cs.washington.edu, unixtex@u.washington.edu
+Subject: Arithmetic overflow in CMinch
+
+Bob Harris (bob@microprograms.com) got in touch with me a couple
+of days ago to report that it was not popssible to run
+cminch with a 2540dpi LinotypeThreeZeroZero mode_def.
+
+The letter W and the numeral 3 generate the
+! Arithmetic overflow
+message, and the problem is far too serious to
+be turned off with warningcheck:=0;
+even if you wanted to do that.
+
+The offending lines were easy enough to spot:
+ in romanu.mf one third of the way through "The letter W"
+[ dek -- E291 32\cents
+]
+
+alpha=diag_ratio(4,stem2-stem3+stem4,y1-y2,x8r-x1l+mid_corr-2apex_corr);
+
+ in romand.mf. halfway through "The numeral 3"
+
+z4=z5+whatever*(150u,h);
+
+Fortunately both of these statements generate ratios, so that the
+raw arguments can be reduced consistently with no change in the results.
+I extract from my email messages, slightly edited.
+
+ > Think of "whatever" (in this manifestation)
+ > as a path of infinite length along the angle
+ > specified by (150u,h)
+ > Since the angle (15u,0.1h) is exactly the same
+ > ---I checked it with expr.mf, and there is no
+ > loss of precision---there is the answer.
+ > Write the offending line as
+
+z4=z5+whatever*(15u,0.1h);
+
+ > The same trick that works for 3 works for W, though it requires a
+ > little more editing.
+
+alpha=diag_ratio(4,.1(stem2-stem3+stem4),
+ .1(y1-y2),.1(x8r-x1l+mid_corr-2apex_corr);
+[ dek -- This doesn't fit on page E113 and besides it is too kludgy --
+ bad style ...
+ What I shall really do is redefine diag_ratio -- it's pointless
+ to multiply by y and divide by y again!
+
+ > This has the effect of calculating on a dpi measure of 254, but since what
+ > we are looking for is a ratio, it makes no difference. I ran with
+ > both calculations using the ljfour mode (effectively that means one
+ > calculation at 600dpi and one at 60dpi) and got exactly the same ratio
+
+ > There is a small rounding difference in the 2540dpi file
+
+ > 600dpi gives a diag_ratio of 1.03595
+ > 2540 dpi gives a diag_ratio of 1.03609
+
+ > That may well be an artifact of some decisions in the parameter file.
+ > I doubt that .00014 is enough to worry about in this context.
+ > (The ratio that results after the ! arithmetic overflow is, of course,
+ > grossly out of line.
+
+I was a bit puzzled at first to explain why this hadn't showed up before,
+since I have made up fonts at 9600dpi and even 14454dpi, but the answer
+lies in the peculiarity of a 72.27pt font. Even a 17pt parameter file
+has to be run at magstep 3 before its em-square reaches 1000 pixels in
+width at 2540dpi. But there could be real problems with cmr17 at the
+9600dpi that Lance Carnes uses to derive his Chelgraph outlines from.
+
+I wonder if DEK would be interested in preempting this problem, since
+the solution is so painless, and will not affect TFM checksums.
+-------
+
+ ----------------------------------------------------------------------
+
+ +++ sterling sign
+
+Date: 04 Jan 1995 00:29:37 +0100
+Reply-to: METAFONT Distribution List <metafont@ens.fr>
+From: Yannis Haralambous <Yannis.Haralambous@univ-lille1.fr>
+Subject: error in CM fonts
+
+IMHO the following error has to be corrected:
+
+In file italp.mf, character "Sterling sign", line -7, replace
+rt x9r=hround(w-u);
+[ dek -- E239 $2.56
+]
+by
+rt x9l=hround(w-u);
+Otherwise the results are bad in typewriter style and catastrophic in
+sans-serif. The funny thing is that I could _swear_ that on the image
+of the character the code is correct [probably a typo by Addison-Wesley].
+
+Yannis
+-------
+Date: 04 Jan 1995 10:35:54 +0100
+Reply-to: METAFONT Distribution List <metafont@ens.fr>
+From: Piet van Oostrum <piet@cs.ruu.nl>
+Subject: Re: error in CM fonts
+
+>>>>> Yannis Haralambous <Yannis.Haralambous@univ-lille1.fr> (YH) writes:
+
+YH> IMHO the following error has to be corrected:
+
+YH> In file italp.mf, character "Sterling sign", line -7, replace
+YH> rt x9r=hround(w-u);
+YH> by
+YH> rt x9l=hround(w-u);
+YH> Otherwise the results are bad in typewriter style and catastrophic in
+YH> sans-serif. The funny thing is that I could _swear_ that on the image
+YH> of the character the code is correct [probably a typo by Addison-Wesley].
+
+It can't be a typo by Addison Wesley, because it is in Knuth's original
+sources (AW didn't type, they got -- of course -- the source from Knuth).
+
+If you look at the image you can really see that it is generated by the x9r
+code, because the character sticks out a little bit to the right of the
+x=11 line. Notice that the x9r point is to the LEFT of the x9l point!!
+
+And yes, with your correction it looks much better in sans serif. In the
+[ dek -- ^^^^^^^^^^
+ what sans serif?? This char does not have a sans serif style
+ in the present design ... sans serif has no ``bulbs''
+]
+italic font, which is the only cm font where it is used, the difference
+[ dek -- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+]
+isn't very great because the x9r and x9l point are quite close top each
+other, whereas in the sans-serif case they are 1 u apart.
+ --
+Piet van Oostrum <piet@cs.ruu.nl>
+-------
+
+<<< end CM fonts
+
+************************************************************************
+
+>>> Fontware
+
+ +++ testfont.tex
+
+X-ListName: TeX-Related Network Discussion List <INFO-TeX@SHSU.edu>
+Date: 05 Feb 1993 20:44 +0000 (GMT)
+From: J%org Knappen <KNAPPEN@VKPMZD.KPH.Uni-Mainz.de>
+Subject: Bug in testfont.tex
+
+By chance I came across to notice a feature of testfont.tex, which I regard
+as a bug:
+
+In the \lowers and \uppers test, the kerning and ligature information is
+not used. Therefore it is not possible to adjust the spacing of a font
+using this tool. Since I know that some experts in macro expansion are
+aroung here, i think one of them will take the challenge to rewrite
+the routines of testfont.tex in order to be completely expandable and use
+the kerning.
+
+Yours, J"org Knappen.
+-------
+
+[ dek -- Font designers traditionally test without kerning (at least
+ they did when I worked with them in 80-85), but I suppose
+ such macros would be easy to write.
+]
+
+ ----------------------------------------------------------------------
+
+ +++ VPtoVF
+
+Date: 23 Aug 1993 10:08:20 +0200
+From: Armin.Koellner@RUBA.RZ.ruhr-uni-bochum.de
+Subject: VPtoVF bug report and some comments on the AMS fonts
+
+Dear Barbara Beeton,
+
+since you stated in one of your letters that you are the right person
+to get in contact with D.E.Knuth, I am sending to you a report of a
+bug in the web file VPtoVF (Version 1.2, 90/9/5) which I found when
+experimenting with ligature tables generated by a program written by
+myself:
+
+If a ligature table erroneously starts with a STOP command, VPtoVF
+will often destroy other data. This abnormal behaviour appears
+because the variable lk_step_ended is not initialized by program code
+to be FALSE, so that the conduct of the program depends on the random
+contents of the memory cell the variable inherits. I suggest to
+change the web file in order to correct this bug.
+
+Additionally, I would like to suggest some improvements on the AMS
+symbol fonts, and, as you are working for the AMS (I suppose), could
+you please give it to the font developer of your organisation? Thank
+you very much.
+
+When I experimented with a program which handles fonts by detecting
+their font coding scheme, I got stuck with the AMS symbol font series
+msam and msbm. At first I detected that in my version of these fonts
+(version="2.1a", date="15-OCT-1991") the series msbm* had no font
+coding scheme string at all! This happened because the file xbbold.mf
+ends with the token "end" instead of giving the control back to the
+file amsyb.mf which ends correctly with "bye". I think, this bug
+should be corrected.
+[ this bug was fixed shortly after receiving this report ]
+
+Secondly, the AMS symbol fonts have the same font coding scheme
+string as the cmsy* series, namely "TeX math symbols". This makes
+them indistinguishable when considering only this string. As far as
+[ dek -- not really needed for msam -- only for fonts used in
+ family 2, 3 ...
+]
+I understand, this special name is necessary for programs like TFtoPL
+and VFtoVP to handle the character coding and math symbol font
+parameters correctly. However, by reading the corresponding web files
+for these programs, I learned that they only consider the first 11
+characters of the font coding scheme string. Therefore, I suggest for
+the next version of your font series to name the font coding scheme
+"TeX math symbols by AMS, Part A" and "TeX math symbols by AMS,
+Part B", resp.
+[ dek -- good suggestion
+]
+
+Yours sincerely,
+Armin K\"ollner
+-------
+Date: 26 Aug 1993 12:54:58 -0300 (BST)
+From: Chris Thompson <CET1@phx.cam.ac.uk>
+Subject: Re: [[Armin.Keollner: VPtoVF bug report and some comments]]
+
+Barbara,
+
+Armin Kollner writes:
+> If a ligature table erroneously starts with a STOP command, VPtoVF
+ (or a SKIP command)
+> will often destroy other data. This abnormal behaviour appears
+> because the variable lk_step_ended is not initialized by program code
+> to be FALSE, so that the conduct of the program depends on the random
+> contents of the memory cell the variable inherits. I suggest to
+> change the web file in order to correct this bug.
+
+This is indeed a bug in the current versions of VPtoVF and PLtoTF.
+I found it rather difficult to demonstrate, as the uninitialised
+variable ends up as binary zero (typically = Pascal "false") on
+most systems. I did manage it eventually, though.
+
+[...]
+
+> Secondly, the AMS symbol fonts have the same font coding scheme
+> string as the cmsy* series, namely "TeX math symbols". This makes
+> them indistinguishable when considering only this string. As far as
+> I understand, this special name is necessary for programs like TFtoPL
+> and VFtoVP to handle the character coding and math symbol font
+> parameters correctly. However, by reading the corresponding web files
+> for these programs, I learned that they only consider the first 11
+> characters of the font coding scheme string. Therefore, I suggest for
+> the next version of your font series to name the font coding scheme
+> "TeX math symbols by AMS, Part A" and "TeX math symbols by AMS,
+> Part B", resp.
+
+It is true that PLtoTF and VPtoTF (currently!) test only the initial
+section of the coding scheme ("TEX MATH SY" or "TEX MATH EX", after
+upper casing) when setting |font_type|. The result is used to control
+the format used in the (V)PL output for various things (whether to
+use names or numbers for the higher-numbered FONTDIMENs, and whether
+to use D or C format for certain character numbers). This only affects
+human-readability, though: the semantic content is not affected.
+
+Quite how the "font coding scheme" should be used is far from obvious,
+but it is certainly arguable that the msam*/msbm* fonts do not have
+the same "coding scheme" as the cmsy* fonts, in the sense that
+characters at corresponding code positions are not, in any plausible
+sense the "same" meta-character. I don't know whether a change could
+really be said to make "use of these files ... more reliable" (to
+quote you), though.
+
+[...]
+
+Chris Thompson
+Cambridge University Computing Service
+-------
+
+<<< end Fontware
+
+************************************************************************