# [luatex] Strange cost in pagebreaking.

Paul Isambert zappathustra at free.fr
Thu Oct 17 17:15:15 CEST 2013

```For those interested, I’ve brought up the issue on texhax, hoping to find an
explanation for that behavior:
http://tug.org/pipermail/texhax/2013-October/020605.html

Best,
Paul

Paul Isambert <zappathustra at free.fr> a écrit:
> Thank you Luigi (still trying to make me read C code :) ),
> Thank you Taco (though I believed you could reverse-engineer
> a .tex source from a .log file),
> and thank you Ulrike (who set me on the right track),
>
> Indeed the problem came from insertions (it was so obvious that they
> might be involved that I somehow refused to see it, nor did I mention
> it): when you split an insertion at penalty X, then X is added to the
> cost of the pagebreak calculation (in \insertpenalties). Now if an
> insertion must be split, a penalty of -10000 is added at the end of
> its box so TeX is sure to find a feasible breakpoint. My insertions
> were split at the end (I’d designed them hastily and forgotten to
> define the associated \dimen, plus they were fully unbreakable boxes),
> and I had two classes of insertion, hence twice -10000.
>
> So \insertpenalties was -20000, and the strange thing is that the
> cost of a breakpoint is (generally) calculated as badness + penalty +
> insertpenalties, unless the penalty is < -10000, in which case the
> cost is that penalty (which forces pagebreak); but if that penalty is
> less than \insertpenalties (as was the case for me), the best
> breakpoint is before it, in my log at line 17:
>
> 16. % t=197.27 plus 2.0fil g=498.47559 b=0 p=150 c=-19850     < c = b+p+\insertpenalties
> 17. % t=209.27 plus 2.0fil g=498.47559 b=0 p=0 c=-20000#      < c = b+p+\insertpenalties
> 18. % t=209.27 plus 3.0fil g=498.47559 b=0 p=-11000 c=-11000  < c = p, and forces break
>
> That behavior is slightly surprising, but it is so in legacy TeX. So
> I’ll try to find the rationale behind it, and if I find none, I’ll
> declare it a bug in TeX (ha ha).
>
> Thanks to all, and sorry for the noise,
> Paul
>
> Ulrike Fischer <luatex at nililand.de> a écrit:
> > Am Tue, 15 Oct 2013 22:08:58 +0200 schrieb Paul Isambert:
> >
> > > Hello all,
> > >
> > > I¢ve encountered a problem which I definitely can¢t solve. It looks
> > > like a TeX problem, but since I really can¢t see what¢s going on I
> > > suspect a LuaTeX bug. Unfortunately the problem is extremely sensitive
> > > to simple changes, and so I can¢t even compare with a PDFTeX
> > > compilation. (And since there is a lot of my own code involved, I
> > > cannot do a minimal example either.)
> > >
> > > Here¢s what \tracingpages returns in my log file (until the current
> > > page is deemed good):
> > >
> > > 1.  %% goal height=569.05511, max depth=4.0
> > > 2.  % split251 to 0.0,38.12 p=-10000
> > > 3.  % split252 to 0.0,103.05 p=-10000
> > > 4.  % t=0.0 g=498.47559 b=10000 p=0 c=100000#
> > > 5.  % t=22.0 g=498.47559 b=10000 p=150 c=100000#
> > > 6.  % t=45.22 g=498.47559 b=10000 p=0 c=100000#
> > > 7.  % t=70.16 g=498.47559 b=10000 p=0 c=100000#
> > > 8.  % t=93.27 g=498.47559 b=10000 p=150 c=100000#
> > > 9.  % t=105.27 g=498.47559 b=10000 p=0 c=100000#
> > > 10. % t=121.27 plus 1.0fil g=498.47559 b=0 p=150 c=-19850#
> > > 11. % t=133.27 plus 1.0fil g=498.47559 b=0 p=0 c=-20000#
> > > 12. % t=145.27 plus 1.0fil g=498.47559 b=0 p=0 c=-20000#
> > > 13. % t=157.27 plus 1.0fil g=498.47559 b=0 p=150 c=-19850
> > > 14. % t=169.27 plus 1.0fil g=498.47559 b=0 p=0 c=-20000#
> > > 15. % t=185.27 plus 2.0fil g=498.47559 b=0 p=150 c=-19850
> > > 16. % t=197.27 plus 2.0fil g=498.47559 b=0 p=150 c=-19850
> > > 17. % t=209.27 plus 2.0fil g=498.47559 b=0 p=0 c=-20000#
> > > 18. % t=209.27 plus 3.0fil g=498.47559 b=0 p=-11000 c=-11000
> > >
> > > What bothers me is line 10 and following: where does the cost of
> > > -20000 comes from? There is no penalty of that value for each of those
> > > line, so I really can¢t see how it can be computed (since, basically,
> > > the cost of a breakpoint is badness + penalty).
> >
> > The cost are badness+penalty+\insertpenalties where \insertpenalties
> > is more or less (see page 122-126 of the texbook) the sum of the
> > split penalties. But the costs are only calculated when the badness
> > is <10000.
> >
> > You have two splits:
> >
> > > 2.  % split251 to 0.0,38.12 p=-10000
> > > 3.  % split252 to 0.0,103.05 p=-10000
> >
> > with penalties of -10000 and so  in line 10 when the badness is 0
> > their penalties are added to the costs.
> >
> > So the main question is where is the source of the split penalties.
> >
> > With
> > \interfootnotelinepenalty=-10000
> > \lipsum[1]\footnote{\lipsum[1]}
> > \lipsum[1]\footnote{\lipsum[1]}
> > \lipsum[1]\footnote{\lipsum[1]}
> > \lipsum[1]\footnote{\lipsum[1]}
> > \lipsum[1]\footnote{\lipsum[1]}
> >
> > I get
> >
> > % split253 to 42.00006,31.45 p=-10000
> > % t=323.80014 plus 7.0 minus 2.0 g=334.3502 b=341 p=0 c=-9659#
> >
> > But that is not the default value, and I don't know how to get two
> > splits.
> >
> > --
> > Ulrike Fischer
> > http://www.troubleshooting-tex.de/
> >
>

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