What is the best practice for arithmetic operations specially for package/class writing?

Question

There are some possibilities to execute arithmetic operations inside a package or class.

TeX

TeX supports \advance, \multiply or \divide to execute arithmetic operations. However the syntax is more or less "needs getting used to". Example:

\@tempdima=35pt
\advance\@tempdima by 10pt
\divide\@tempdima by 5

eTeX

eTeX supports the commands \dimexpr and \numexpr. This simplify the example above as follows:

\@tempdima=\dimexpr (35pt+10pt)/5 \relax

LaTeX3

LaTeX3 can be compared with eTeX.

\dim_set:Nn \l_tmpa_dim { (35pt+10pt) / 5 }

---

Packages

I know there are some packages which allow arithmetic operations, too. E.g. calc or pgf. Those packages can be compared with eTeX, too.

---

---

However what is the recommended way of doing arithmetic operations inside a package/class? What are the benefits/drawbacks of the different approaches?

Answer 1

Time differences are not likely to really matter, the following test shows that tex primitives are fractionally faster than etex on my machine (and one would assume that latex3 or pgf or fp macros would be slower still). However 16^6 is a lot of operations and this file does nothing else. In a real document TeX spends time typesetting or opening or writing files, so minor differences in computational speed are not likely to matter.

What matters more is that the computations are different: addition and multiplication are the same but etex uses rounding rather than truncating division (which is sort of OK, but different for lengths but is fairly useless for integer counts) The test file produces

6.85713pt
6.85715pt

with the first value being from \divide and the second from etex /.

\makeatletter

\def\a{\@tempdima=38pt
\advance\@tempdima by 10pt
\divide\@tempdima by 7 }

\a\typeout{\the\@tempdima}

\def\b{\@tempdima=\dimexpr (38pt+10pt)/7 \relax}

\b\typeout{\the\@tempdima}

\def\c{\a\a\a\a\a\a\a\a\a\a\a\a\a\a\a\a}
%\def\c{\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b}
\def\d{\c\c\c\c\c\c\c\c\c\c\c\c\c\c\c\c}
\def\e{\d\d\d\d\d\d\d\d\d\d\d\d\d\d\d\d}
\def\f{\e\e\e\e\e\e\e\e\e\e\e\e\e\e\e\e}
\def\g{\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f}
\g\g\g\g\g\g\g\g\g\g\g\g\g\g\g\g
\stop

Times:

tex

real    0m18.979s
user    0m18.408s
sys     0m0.124s

etex

real    0m20.351s
user    0m19.749s
sys     0m0.124s

Answer 2

The biggest difference between traditional TeX computations and e-TeX extensions is that the latter allow for "on the fly" calculations, without assignments. This goes at the expense of speed, as \numexpr, \dimexpr and \glueexpr are slower than using registers.

However, in writing code, something like

\setlength\@tempdima        {\paperwidth}
\addtolength\@tempdima      {-\textwidth}
\setlength\oddsidemargin    {.5\@tempdima}
\addtolength\oddsidemargin  {-1in}
\setlength\marginparwidth   {.5\@tempdima}
\addtolength\marginparwidth {-\marginparsep}
\addtolength\marginparwidth {-0.4in}
\addtolength\marginparwidth {-.4in}

(this is found in size10.clo) could be translated into the perhaps clearer

\setlength\oddsidemargin{%
  \dimexpr (\paperwidth - \textwidth)/2 - 1in \relax
}
\setlength\marginparwidth{%
  \dimexpr (\paperwidth - \textwidth)/2 - \marginparsep - 0.4in - 0.4in \relax}

(the double -0.4in can be understood by comparing the similar assignments when the twoside option is in force).

Due to the small differences in the way operations are performed (e-TeX division rounds, while traditional TeX division with registers truncates), it's not feasible now to change the standard classes into using the easier syntax, because older documents would be affected.

To the contrary, so long as a new package sticks to one syntax, I'd say that a clearer method is to be preferred: the code is less obscure and more easily maintained.

In LaTeX3 parlance, the two assignments would become

\dim_set:Nn \oddsidemargin  { (\paperwidth - \textwidth)/2 - 1in }
\dim_set:Nn \marginparwidth { (\paperwidth - \textwidth)/2 - \marginparsep - 0.4in - 0.4in }

which is even clearer.