Why doesn't LaTeX implement single pass references?

Question

Example:

\documentclass{article}

\begin{document}


\section{Power series}\label{ps}

\begin{equation} \label{eq}
\sum_{i=0}^\infty a_i x^i.
\end{equation}

The equation \ref{eq} is a typical power series.

\section{Conclusion}
Look at Section~\ref{ps}.


\end{document}

In order to get the references, latex must be run twice, and an auxiliary file is created. Whereas, look at the following analogous (less verbose) OpTeX example:

\sec[ps] Power series 

$$
\sum_{i=0}^\infty a_i x^i. \eqmark[eq]
$$

The equation \ref[eq] is a typical power series.

\sec Conclusion
Look at Section~\ref[ps].

\bye

We need to run optex only once to get the references. Moreover, no auxiliary (.ref) file is created, because in this example references can be already resolved in one pass.

So, I don't understand why LaTeX always forces a two pass approach even when a single pass can work as well, and can deal with the most common kinds of references (future references are rarer).

Answer 1

"Why" questions are not easy to answer, especially as the original system was designed for machines with a tiny fraction of the memory that current machines have, but..

It is true, as you point out, that it would be possible in some cases for backward counter references to be resolved in one pass, but this would not be possible for page references and not possible for forward references.

Firstly it is worth noting that this makes absolutely no difference in practice, so it's just a theoretical question:

• If you are writing the file, very few people write the entire document in one session and just run latex once and use the pdf, so resolving cross references does not require any extra runs of latex. They are resolved by the time they need to be resolved.

• If you are processing a complete document that you have been given as source then usually it contains a table of contents or list of figures or references to a bibliography, so would take multiple passes to resolve all references even if \label was changed to allow backward \ref in a single pass.

Technically \label causes an ordered pair (or quadruple with hyperref) of data for the current counter and page reference to be saved. By saving them to the aux file and reading them back at the start, both values are either known or not and usable for forward or backward references. This simplifies the implementation and especially it simplifies documenting the behaviour.

Note that optex was designed in an era when machines had much more available memory and by a different person, so it is not that surprising that it takes different design decisions in some cases, neither is right or wrong.

The fact that latex is documented as a multipass system with data stored to the filesystem between passes rather than in memory is just an optimisation to give the user the possibility of just using a single pass after each edit. You could just as easily advertise it as a system that resolves all cross references (as latexmk or context do for example) by doing multiple runs as an "internal implementation detail" and resolving all cross references before returning a PDF to the user.

Answer 2

You start from a wrong point of view.

With OpTeX you do get a .ref file written, in case one run is insufficient to solve cross references, which can happen in two cases:

1. a future reference, or
2. a label has been set in the vicinity of a page break, and the page number at the time the label is seen is not the same as what is at output time.

The first case is clear. For the second case, consider

Some text to artificially push the section too near the page break.

\vskip\dimexpr\vsize-4\baselineskip\relax

\sec[ps] Power series 

$$
\sum_{i=0}^\infty a_i x^i. \eqmark[eq]
$$

The equation \ref[eq] is a typical power series.

\sec Conclusion
Look at Section~\ref[ps] at page~\pgref[ps].

\bye

and you'll see that a .ref file will be created. The log will contain

WARNING l.18: Try to rerun to get references right.

Due to the asynchronous mechanism of page breaking, there is no way to resolve cross references, even past ones, in one pass. As you see, even past references may need two passes.

If you just want back references to numbers and not to pages, then it should work even with hyperlinks, but it seems quite a big limitation.