[texhax] Horizontal Footnotes in Critical Editions

Alexander I Rozhenko roj at front.ru
Fri Sep 9 03:26:37 CEST 2005

Hi all,

I have compared some cases of the \MFL at floathook calculation formula on the
relative error in assumption that \normalbaselineskip = 10pt and
\columnwidth = 200pt.

(1) In the ideal case

\normalbaselineskip * 65536 / \columnwidth

the relative error is near 1/64 %.

(2) In the Knuth's case

(\normalbaselineskip * 1024) / \columnwidth * 64

the relative error is near 1 %.

(3) In the following case

(\normalbaselineskip * 256)  /  (\columnwidth  /  256)

the relative error is a sum of two errors: 1/4 + 1/4 = 1/2 %. The first one
is an error of division the \columnwidth by 256 and the last one is a error
of final division.

When \normalbaselineskip increases, the relative errors in all cases
decrease (in the last formula only second error decrease). When \columnwidth
increases, the relative errors of the first and the second formula increase,
but the error of the last formula changes more interesting: its first error
decreases and last error increases.

I think the last formula is better than Knuth's proposal in all practical
cases. It works for \normalbaselineskip < 64pt and has lesser error than the
second formula.

The final correction will look as follows:

@tempdima \normalbaselineskip
\multiply \@tempdima 256
\@tempdimb \columnwidth
\divide \@tempdimb 256
\divide \@tempdima \@tempdimb

Alexander I Rozhenko

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