Dividing dimensions to get a count

Question

Is there a way to divide two dimens and get a count? For example, if I have a box that doesn't fit on a single page, and I want to know the number of pages I'd need for the box (i.e., \heightofbox / \textheight), can I get that in a count, or in a macro without any trailing units?

Answer 1

You can directly truncate the division by the trick \counter=\length trick which would multiply the length (in pt) by 65536 to get an integer number of sp units (which egreg taught me). Then you can divide and obtain a truncated result.

\documentclass{article}
\newcount\mycounterA
\newcount\mycounterB

\mycounterA=\textheight\relax
\mycounterB=\dimexpr100cm\relax

\begin{document}

\the\mycounterA\par
\the\mycounterB\par

The result is : \divide\mycounterB by\mycounterA\the\mycounterB\par
\advance\mycounterB by 1%
Pages needed : \the\mycounterB

\end{document}

Answer 2

Calculations can be done with e-TeX's \dimexpr or \numexpr. In the following example, the first expression in \typeout calculates a real number, in the second expression the result is an integer number, rounded up:

\documentclass{article}
\newsavebox{\mybox}

\begin{document}
  \sbox\mybox{\rule{1pt}{3000pt}}
  \makeatletter
  \typeout{\strip@pt\dimexpr 1pt * \ht\mybox / \textheight\relax}
  \typeout{\the\numexpr(\ht\mybox + \textheight/2)/\textheight\relax}
  \makeatother
\end{document}

Result:

5.45454
6

Remarks:

• In a numerical context (e-)TeX treats dimen or length registers as numbers with unit sp (1pt = 65536sp).
• \strip@pt removes the unit pt from the result of \dimexpr.
• The e-TeX \...expr commands round the result. In your case you probably want ceiling. This is achieved by adding the half of the divisor.
• The expressions are expandable, thus it is easy to use them in counter assignments or inside \edef.

But these numbers should be taken with care:

• If the box contains something large, that is not breakable, then result would be an overfull \vbox instead of the calculated pages, reducing the count of pages.
• The box might contain stretchable glue that might occupy more space than calculated with the natural box height. There can be more pages than calculated.

For a more accurate calculation, the box could be split using \vsplit to get the number of pages needed. Depending on the application the number of pages could also be calculated by using page references.

Answer 3

The fp package can manage floating point operations, while \strip@pt is a core-macro that strips the dimension from a length. Here's a small example:

\documentclass{article}
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\newlength{\lengthA}\newlength{\lengthB}
\begin{document}
\setlength{\lengthA}{20em}
\verb|\lengthA: |\the\lengthA \par
\setlength{\lengthB}{5em}
\verb|\lengthB: |\the\lengthB \par
\bigskip

\makeatletter
\edef\valueA{\strip@pt\lengthA}
\edef\valueB{\strip@pt\lengthB}
\FPeval\result{\valueA/\valueB}
\verb|\lengthA/\lengthB: |\result
\end{document}

Answer 4

You can convert the dimensions to counters, wheras their division results to an truncated integer, but a simple division will give you problematic results. The division is: How often does q (\textwidth) go in p (\heightoftext)?
The mathematical formula would be ceil(p/q) (rounding up). As p and q are integer values (counters in TeX) we can implement the ceiling function with a little trick.
Let’s take a look at q = 4, p = 2, …, 9:

       p             │  9  8  7  6  5  4  3  │
─────────────────────┼───────────────────────┼────────────────────────────────────────
  int( p    / q)     │  2  2  1  1  1  1  0  │  what we get
 ceil( p    / q)     │  3  2  2  2  2  1  1  │  what we want
  int( p    / q) + 1 │  3  3  2  2  2  2  1  │  what works for p/q ≠ int(p/q)
  int((p–1) / q) + 1 │  3  2  2  2  2  1  1  │  = ceil(p/q)

The second last row needs to be shifted by one to get the actual ceiling function what we achieve by subtracting 1 from q.

\def\divideMeCount#1#2{%
    \countp=#1\relax%
    \advance\countp by -1\relax%
    \countq=#2\relax%
    \divide\countp by \countq\relax%
}

---

Another solution uses a loop effectively counting the pages:

\def\divideMeLoop#1#2{%
    \dimenp=#1\relax%
    \dimenq=#2\relax%
    \tempi=0\relax%
    \loop\advance\dimenp by -\dimenq\relax\advance\tempi by 1\relax%
    \ifdim\dimenp>0pt\relax\repeat%
}

Values

• \textheight = 550.0pt
• \heightofbox =
  • 1099pt
  • 1100pt
  • 1101pt

Code

\documentclass{article}
\newcount\countp
\newcount\countq
\newdimen\dimenp
\newdimen\dimenq
\newcount\tempi
\newdimen\heightofbox
\def\divideMeCount#1#2{%
    \countp=#1\relax%
    \advance\countp by -1\relax%
    \countq=#2\relax%
    \divide\countp by \countq\relax%
}
\def\divideMeLoop#1#2{%
    \dimenp=#1\relax%
    \dimenq=#2\relax%
    \tempi=0\relax%
    \loop\advance\dimenp by -\dimenq\relax\advance\tempi by 1\relax%
    \ifdim\dimenp>0pt\relax\repeat%
}
\usepackage{pgf}
\begin{document}
\heightofbox=1099pt\relax
\the\heightofbox/\the\textheight\par
{\bfseries Counters\par}
\divideMeCount{\heightofbox}{\textheight}
counpt+1=\number\numexpr\countp+1\relax\par
{\bfseries Dimensions (Loop)\par}
\divideMeLoop{\heightofbox}{\textheight}
tempi=\the\tempi\par
{\bfseries PGF (example)\par}
\pgfmathtruncatemacro{\result}{ceil(\heightofbox/\textheight)}
result=\result
\bigskip

\heightofbox=1100pt\relax
\the\heightofbox/\the\textheight\par
{\bfseries Counters\par}
\divideMeCount{\heightofbox}{\textheight}
counpt+1=\number\numexpr\countp+1\relax\par
{\bfseries Dimensions (Loop)\par}
\divideMeLoop{\heightofbox}{\textheight}
tempi=\the\tempi\par
{\bfseries PGF (example)\par}
\pgfmathtruncatemacro{\result}{ceil(\heightofbox/\textheight)}
result=\result
\bigskip

\heightofbox=1101pt\relax
\the\heightofbox/\the\textheight\par
{\bfseries Counters\par}
\divideMeCount{\heightofbox}{\textheight}
counpt+1=\number\numexpr\countp+1\relax\par
{\bfseries Dimensions (Loop)\par}
\divideMeLoop{\heightofbox}{\textheight}
tempi=\the\tempi\par
{\bfseries PGF (example)\par}
\pgfmathtruncatemacro{\result}{ceil(\heightofbox/\textheight)}
result=\result
\end{document}

Output