12

I have been trying to automate the production of stepped tables that contain conversion factors of all sorts. (See Protrusion of fractions in tabulars).

As part of this I have a rather convoluted macro to convert decimals to fractions. The algorithm works fairly well and sample output is shown below:

enter image description here

As I am trying to catch common fractions as those found in traditional units (1/12, 3/4, 1/60, 1/3 etc), I would like to be able to break out of the loop once a limit is reached. I have tested it using FPifgt or similar but I am getting problems with the double fi. Is there a way out of it?

The code is shown below (apologies for length):

\documentclass{article}
\usepackage{amsmath,fp}
\begin{document}
\makeatletter
\count@=1
\def\DecimalToFraction#1{
%helper macro
\FPset\zero{0}
\FPset\X{#1}

%% Set initial values
\FPadd\X{\X}{0.0000000001} % avoid overflows and divisions by zero
\FPset\Zi{\X}
\FPset\Di{1}
\FPset\Dprevious{0}
%% begin loop
\loop\ifnum\count@<13
%% numerator term
\FPtrunc\temp{\Zi}{0} 
\FPsub\temp{\Zi}{\temp}
%% inverse
\FPdiv\Znext{1}{\temp}
%% Find Dnext
\FPtrunc\IntZnext{\Znext}{0}
%% Di x Int{Zi+1}
\FPmul\temp{\Di}{\IntZnext}
\FPadd\temp{\Di}{\Dprevious}
\FPset\Dnext{\temp}
\FPround\Dnext{\Dnext}{0}

%%% Find Ni+1
\FPmul\temp{\X}{\Dnext}
\FPround\temp{\temp}{0}
\FPset\Nnext{\temp}

\FPdiv\ratio{\Nnext}{\Dnext}

\(Z_i=\Znext\to \Nnext/\Dnext =\ratio\)

\FPset{\Dprevious}{\Dnext}
\FPset{\Di}{\Dprevious}
\FPset{\Zi}{\Znext}

\advance\count@ by1
\repeat
%% end of loop

\gdef\NUM{\Nnext}
\gdef\DEN{\Dnext}

\makeatother
}

\def\Test#1{%
\DecimalToFraction{#1}
The number $#1=\frac{\NUM}{\DEN}$

}
\Test{0.375}
\end{document}
9
  • Why do you want to do something like this inside TeX? Surely a programming language designed for managing numbers would make more sense for this sort of task...
    – Seamus
    Mar 2, 2011 at 19:26
  • @Seamus Handling numbers through TeX is as easy as any language and you do not need to jump in an out of programs. Problem TeX does not offer a range of datastructures so the problems with if and loops etc. Mar 2, 2011 at 19:33
  • @Yiannis: TeX just tends to be a bit slow for that kind of things. :) Mar 2, 2011 at 19:36
  • @Yiannis so pick a language with the proper data structures? I'm all for doing stuff in TeX, but it seems like there are easier ways to achieve what you want outside of TeX...
    – Seamus
    Mar 2, 2011 at 19:37
  • 1
    @Bruno If you can come up with some good link lists and sorting it can be very useful. I have some prototypes for objects. I'll dig them out and post a few questions over the next couple of days. Mar 2, 2011 at 20:15

2 Answers 2

16

To abort the loop after the current iteration simply \let the internal \iterate macro to \relax. If you want to skip the rest of the loop code you can use a macro defined to \fi\iffalse for this (as Bruno already said).


Abort at end of current iteration:

\documentclass{article}

\begin{document}

\newcount\mycount

\mycount=1

\loop\ifnum\mycount<13

 % Do calculation
 \typeout{Loop: \the\mycount}

 \ifnum\mycount>5
    \let\iterate\relax
 \fi
 \advance\mycount by 1\relax
\repeat

\end{document}

Abort immediately:

\documentclass{article}

\def\breakloop{\fi\iffalse}
\begin{document}

\newcount\mycount

\mycount=1

\loop\ifnum\mycount<13

 % Do calculation
 \typeout{Loop: \the\mycount}

 \ifnum\mycount>5
    \expandafter\breakloop
 \fi

 \typeout{ more }
 \advance\mycount by 1\relax
\repeat

\end{document}

Explanation:

First lets look at the (LaTeX) definitions of \loop and \repeat:

\loop:
\long macro:#1\repeat ->\def \iterate {#1\relax \expandafter \iterate \fi }\iterate \let \iterate \relax . 

\repeat:
\fi. 

As you see \loop stores everything between it and \repeat into \iterate which calls itself. This recursion implements the loop. The \expandafter ensures that no dangling \fis get accumulated. As long the loop \if... is true the text is executed, and \iterate is called again after the \fi. If the conditional is false everything until the \fi is skipped including the \expandafter. However if \iterate is changed to \relax the recursion stops independent of the conditional. Because this happens after the \fi no cleanup is required.

The \breakloop generates a \fi\iffalse. The \fi closes the loop conditional and the \iffalse makes TeX skip everything until the final \fi like the loop conditional would do.


If you need to use FP conditionals inside the loop you have to make them "skip save" first. The problem is that FP define own if switches as macros which aren't recognized when TeX skips over an false path. To fix this define macros like this

\def\xFPiflt#1#2{%
  \FPiflt{#1}{#2}%
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
}

Then use \xFPiflt\x\y{<true>}{<false>} instead of \FPiflt\x\y <true> \else <false> \fi.

7
  • @Martin thanks. It works nicely with \ifnum but not with the FP conditionals. Any idea? they have the same structure like ifnum. Mar 2, 2011 at 20:11
  • @Yiannis: Try to move \breakloop to the outside of the FP conditional e.g. by only executing \let\x\breakloop inside that conditional and later simply execute \x (which default to \empty or \relax otherwise). Mar 2, 2011 at 20:19
  • @Yiannis: I didn't know much about fp before, but I just saw that they use macros to define own \ifxxx switches which is incompatible with the skipping process of TeX! Can you give an example of a FP conditional inside a \loop? I don't think it will work at all. Mar 2, 2011 at 20:21
  • @Yiannis: See my updated answer on how to use FP conditionals inside \loop or \ifnum etc. Mar 2, 2011 at 20:34
  • @Martin I would post a new question tomorrow with a minimal, I think it would be better. Mar 2, 2011 at 20:39
5

The loop has the structure

\loop
...
\if...
...
\repeat

If you are between \if and \repeat, you can issue \fi\iffalse to close the current \if and skip all the text until \repeat (or rather, until a \fi that is produced by \loop...\repeat). This will not work if your loop is \loop...\if...\else...\repeat.

A more robust solution is to place \@gobble\mysentinel just before \repeat, and then use the following macro to go out of the loop:

\def\Iwanttobreakfree#1\mysentinel{\iffalse}

This will throw away all the tokens until \mysentinel, including \@gobble, and the \iffalse makes sure that the loop stops.

10
  • @bruno thanks, why do you add an argument to the macro Iwanttobreakfree ? Mar 2, 2011 at 19:42
  • Nice answer (and nice macro name)!
    – TH.
    Mar 2, 2011 at 19:45
  • @Yiannis: #1 will be all the tokens until \mysentinel: those that you want to get rid of (notice that #1 does not appear in the replacement text of Iwanttobreakfree). Mar 2, 2011 at 19:49
  • @Yiannis: This is how we do loops for expl3, using some slightly different names (\q_recursion_stop is the key marker), with the 'gobble' function having the catchy name \use_none_delimit_by_q_recursion_stop:w :-)
    – Joseph Wright
    Mar 2, 2011 at 20:03
  • 1
    @Bruno: I was not sure - I was more pointed at the name, as the 'use_none' sort-of explains about #1 :-)
    – Joseph Wright
    Mar 2, 2011 at 20:13

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