# Macro vs counter: How to store and operate with numbers in TeX without using (too many) counters

I need to store and use a large amount of integers (a little bit of "programming with `TeX`"), but I know that TeX has a limited (up to 256) number of counters that can be used simultaneously. How to work with these numbers using macros? I need basic numerical operations and comparison.

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Related (duplicate?) question: Using counters or macros. –  Alan Munn May 15 '12 at 17:33
I agree with @AlanMunn that this seems to be a duplicate. Note that you can (re-)define "constants" using `\chardef` and `\mathchardef` which act basically like counters without needing a register. You can't add to them like with counter, however. –  Martin Scharrer May 15 '12 at 17:41
@AlanMunn: I read the topic you mentioned, but I still did not get an answer to my question, that is, how to use integers stored in macros as if they were numbers stored in counters. –  digital-Ink May 15 '12 at 17:42
Could you explain in more detail what exactly you need? You can define integer "constants" with `\mathchardef\myconstant=<integer>`. With e-TeX you can use e.g. `\mathchardef\myotherconstant=\numexpr \myconstant + 1 \relax` to add one to this "constant", etc., but `\myconstant=1` doesn't work. A benefit is that it is a terminated number and TeX will not expand further tokens to look for more potential digits like it does with macros. –  Martin Scharrer May 15 '12 at 17:49
@MartinScharrer: Ok, I will try to use \mathchardef. Maybe I was not carefull enough when reading the ralated post, this may be consider as a duplicate. –  digital-Ink May 15 '12 at 17:54

There is no real limitation nowadays if you use `pdftex` (or `pdflatex`), because the engine has 32768 count registers. The only problem is to persuade the allocation macros to use the whole set. In LaTeX this is obtained by loading (as early as possible, that is, immediately after `\documentclass`) the `etex` package.

If you use constants less than "8000 = 32768, they can be conveniently stored with `\mathchardef`:

``````\mathchardef\myconst=12000
``````

allows you to use `\myconst` in every place where TeX is expecting a `<number>` (as part of its syntax rules).

Note. A trick such as

``````\mathchardef\myconstant=\numexpr \myconstant + 1 \relax
``````

doesn't work. This is because of a security precaution taken by TeX during assignments. When one says

``````\mathchardef\myconstant=...
``````

the token `\myconstant` is temporarily set to `\relax`, so it can't be used in the following `\numexpr`. In that case one has to use a temporary storage bin:

``````\mathchardef\myconstant=42
...
\mathchardef\mytempconstant=\myconstant
\mathchardef\myconstant=\numexpr\mytempconstant+1\relax
``````

However, such computations are rather inefficient.

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+1 Could you also add an calculation example like the one in my comment above? –  Martin Scharrer May 15 '12 at 17:54
@MartinScharrer Did you try it? You can't use it in that way. –  egreg May 15 '12 at 18:04
No, I didn't actually tried it. It's funny. Apparently the macro definition is already changed (`\relax`'ed?) before the right-hand side is evaluated, which is very unusual. Anyway, `\mathchardef\temp=\numexpr \myconstant + 1 \relax \mathchardef\myconstant=\temp` works fine. –  Martin Scharrer May 15 '12 at 18:12
:-) I should reload the post before adding comments ... –  Martin Scharrer May 15 '12 at 18:14