Subtleties when using \def and \ifnum conditionals

Question

I am having some difficultly comparing two numbers passed as arguments using \ifnum. Consider the command

\def\comparenum[#1,#2]
{
  \def\x{#1}
  \def\y{#2}
  \ifnum\x=\y
   TRUE
  \else
   FALSE
  \fi
}

\comparenum[1,1] gives TRUE as I would expect. However, if I replace the above with

\ifnum\x=\y
  1
\else
  0
\fi

The same call \comparenum[1,1] produces 0 (replacing \y with \y{}, or indeed #2 seems to fix this). What is the reason for this behaviour? I would like to use the second construction so that I can nest the statement inside another conditional as in the top answer to How to form “if … or … then” conditionals in TeX?

Answer 1

Your second code is equivalent to

\def\comparenum[#1,#2]{ \def\x{#1} \def\y{#1} \ifnum\x=\y1 \else0 \fi}

(because spaces and end-of-lines are ignored after a control word). Now you should be able to see the main problem with the code. When TeX evaluates the conditional, it needs two numbers and does full expansion until finding tokens that cannot be interpreted as digits.

So it expands \x and = stops the search for digits while also starting the lookup for the next number; \y is expanded and 1 follows. So the call \comparenum[1,1] translates into

\ifnum1=11 \else0 \fi

which of course returns false.

You solve the issue with

\def\comparenum[#1,#2]{%
  \def\x{#1}%
  \def\y{#1}%
  \ifnum\x=\y\relax
    1% 
  \else
    0%
  \fi
}

The \relax token stops the lookup for digits.

On the other hand, this construct is not expandable. You can make an expandable version with

\def\comparenum[#1,#2]{%
  \ifnum#1=#2\space
    1%
  \else
    0%
  \fi
}

The \space expands to a space token that stops \ifnum from looking up for more digits and is then ignored by rule. However, this would leave a space if used with a counter register. A safer version would be

\def\comparenum[#1,#2]{%
  \ifnum#1=\expandafter\id\expandafter{\number#2}\space
    1%
  \else
    0%
  \fi
}
\def\id#1{#1}

An e-TeX version would be simpler:

\def\comparenum[#1,#2]{%
  \ifnum#1=\numexpr#2\relax
    1%
  \else
    0%
  \fi
}

Please, note the % that protect the end-of-lines avoiding that they make spaces in the output.