How can I find out what pages my floats are on (without looking at every page of the document)?

Question

This question led to a new package:
chkfloat

Making small tweaks to my (two-column) document can result in my floats (both single and double columns) moving all over the place. I know that my document is more likely to look good if float F is on page P say, than if it is on page P+1. However, I have a long document and it is tiresome to check every page after each build to see if my floats have moved.

Therefore, I would like LaTeX to raise an error (or at least alert me in some way) if float F(n) is not on page P(n) where F(n) and P(n) are specified for some subset of my floats (I'd be happy with an answer that can deal with tracking one float to begin with though!). However, it is not possible to put checking code inside the floats themselves, because this code is executed when the floats are "read" rather than when they are "placed".

Even if I can tweak the float parameters so that the floats appear in locations I prefer, this would still be a useful automated test, so the focus of my question is not intended to be about float parameters, unless there are some magic parameters that force LaTeX to put the floats in approximate places that I specify (that is, floating places! --- not just 'here', which I assume is not possible for two column floats anyway).

Clearly, LaTeX does keep track of which floats appear on which page, as the \listoffigures can show this information. But I am not sure what's the best way of accessing that information myself to do the testing; is there a hook that gets called when a float is placed? Preferably the test would work in one run (note that the list of figures takes two runs to update), but this is not essential.

I've included a single-column MWE with a single float to play with. Changing the \lipsum range changes where the float gets placed. (If the double column nature makes a big difference, I can try to supply a modified MWE.)

\documentclass{article}
\usepackage[a4paper]{geometry}%don't trust MikTeX's defaults!
\usepackage{lipsum}
\begin{document}
    % choose which of the following two lines to use to configure where the float appears.
    \lipsum[1-5]% figure appears on page 2 if this line is used
    %\lipsum[1-4]% figure appears on page 1 if this line is used
    \begin{figure}
        \centering
        Hello world. I was typeset on page \thepage, but that may not be where I appear!

        \rule{4cm}{4cm}

        \caption{fig}
    \end{figure}
    ***Figure appeared in the text just above here.***

    \lipsum[5-8]
    \listoffigures
\end{document}

Answer 1

Different approach from JLDIaz. Just put the code between START HERE and END HERE by the end of yout preamble. The code is self-commented.

Remark: I made this into a package. Don't use this code directly, better get and use the package.

\documentclass{article}

% START HERE
\makeatletter
% tolerances
\PassOptionsToPackage{patch}{kvoptions}
\RequirePackage{kvoptions}
\DeclareStringOption{tolerance}
\def\chkfloat@tolerance{1}
\ProcessKeyvalOptions*
% store original macros \@float and \@caption
\let\chkfloat@float\@float
\let\chkfloat@caption\@caption
% make \@float remember the page where the float should be
\def\@float{\edef\chkfloat@page{\thepage}\chkfloat@float}
% make \@caption write to a file .fof the information about final page, original page and float caption
\def\@caption#1[#2]#3{\chkfloat@caption{#1}[#2]{#3}%
  \addtocontents{fof}{\protect\chkfloat@{\thepage}{\chkfloat@page}{\csname fnum@#1\endcsname: #2}}%
}
% checking macro
\def\chkfloat@#1#2#3{\ifnum#1>\numexpr#2+\chkfloat@tolerance\relax
  \begingroup\let\on@line\@gobble\def\nobreakspace{ }\GenericWarning{}{Float misplaced on pages #2->#1, #3}\endgroup
\fi
}
% process the file .fof
\@starttoc{fof}

\makeatother
% END HERE

\begin{document}

Hello world!

\begin{figure}[b]
FIGURE BOTTOM
\caption{Figure at bottom}
\end{figure}

\begin{figure}[p]
FIGURE PAGE
\caption{Figure at its page}
\end{figure}

\end{document}

Answer 2

Here is an idea. When you use the command \label next to a caption, LaTeX writes into the .aux file the figure number and the page number (the actual page number in which the figure appears). In addition it defines a macro which stores that page number, which can be retrieved with command \pageref.

The idea is to add to each figure a \label which specifies the page at which the figure should appear, as for example: \label{ShouldBeOnPage1}. An external script could read the -aux file and compare the name of the label with the value of its page number.

Even better, LaTeX can do this check at the end of the document. The following MWE provides the basic idea, but it only checks for a single figure. A proper solution would include a loop to check all the figures, but I lack the knowledge to implement the complete solution. You can manually specify each check as I did with the first figure:

\documentclass{article}
\usepackage[a4paper]{geometry}%don't trust MikTeX's defaults!
\usepackage{lipsum}

\def\CheckFloat#1{%  The macro which does the check for a single figure
% The parameter is the page number at which the figure should appear
\expandafter\ifx#1\pageref{ShouldBeOnPage#1}%
\relax
\else\GenericWarning{(Floats)}{Warning: A float which should appear on page #1 is misplaced (to page \pageref{ShouldBeOnPage#1})}
\fi
}


\AtEndDocument{% Manually do all checks
 \CheckFloat{1}
}

\begin{document}
% choose which of the following two lines to use to configure where the float appears.
\lipsum[1-5]% figure appears on page 2 if this line is used
%\lipsum[1-4]% figure appears on page 1 if this line is used
\begin{figure}
\centering
Hello world. I was typeset on page \thepage, but that may not be where I appear!

\rule{4cm}{4cm}

\caption{fig}\label{ShouldBeOnPage1}  % <----- Add this to the figures
\end{figure}
***Figure appeared in the text just above here.***

\lipsum[5-8]
\listoffigures
\end{document}

Running this example you get the warning:

Warning: A float which should appear on page 1 is misplaced (to page 2\hbox {})
 on input line 33.

Note that my code assumes a single figure per page. A proper solution would define a macro for each figure, based on the figure number, which stores the page at which the figure should appear, and create a label based also on the figure number and the expected page, which will provide the actual page via \pageref.

I know this is not a complete solution, but I hope this idea is worth and someone more skilled than me completes it.