[texhax] Horizontal Footnotes in Critical Editions

Uwe Lück uwe.lueck at web.de
Sat Sep 10 11:59:00 CEST 2005

At 03:26 09.09.05, Alexander I Rozhenko wrote:

>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

Great -- I cannot check this, but it convinces me that Alex really is a
numerics professional. (OK, it seems to be "theoretically" equivalent
and numerically very safe.) -- I'd like to know Robin Fairbank's problem
with footmisc and its solution, maybe it's relevant for a comparison.


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