How to set a length to the min of two other lengths?

Question

I have declared several lengths in my document: \bottomMargin \topMargin and \initialPaperHeight.

Right now, I am doing this

\AtEndDocument{%
\global\paperheight\dimexpr\pagetotal + \bottomMargin + \topMargin \relax
}

But, instead of setting \paperheight to \pagetotal + \bottomMargin + \topMargin, I would like to set \paperheight to the minimum of this value and of \initialPaperHeight. In pseudo-code, I would like to do

\paperheight = min(\initialPaperHeight, \pagetotal + \bottomMargin + \topMargin)

So, my question is: How should I do?

Answer 1

\AtEndDocument{%
  \ifdim\dimexpr \pagetotal + \bottomMargin + \topMargin < \initialPaperHeight \relax
    \global\paperheight\dimexpr \pagetotal + \bottomMargin + \topMargin
  \else
    \global\paperheight\initialPaperHeight
  \fi
}

However, to me it seems that you are trying to do something complicated here which you shouldn't need.

Answer 2

LaTeX3 has also a function for this:

\usepackage{expl3}

\ExplSyntaxOn

\global \paperheight = \dim_min:nn { \initialPaperHeight } { \pagetotal + \bottomMargin + \topMargin }

\ExplSyntaxOff

(untest because you gave no MWE …)