<?xml version="1.0" encoding="utf-8"?>
<page xmlns="http://projectmallard.org/1.0/" type="guide" id="floor-ceil" xml:lang="de">

    <info>
        <link type="guide" xref="index#equation"/>
    
    <mal:credit xmlns:mal="http://projectmallard.org/1.0/" type="translator copyright">
      <mal:name>Jan Arne Petersen</mal:name>
      <mal:email>jap@gnome.org</mal:email>
      <mal:years>2007</mal:years>
    </mal:credit>
  
    <mal:credit xmlns:mal="http://projectmallard.org/1.0/" type="translator copyright">
      <mal:name>Christian Kirbach</mal:name>
      <mal:email>Christian.Kirbach@googlemail.com</mal:email>
      <mal:years>2008,2009,2010,2014,2015,2017,2021,2025</mal:years>
    </mal:credit>
  
    <mal:credit xmlns:mal="http://projectmallard.org/1.0/" type="translator copyright">
      <mal:name>Mario Blättermann</mal:name>
      <mal:email>mario.blaettermann@gmail.com</mal:email>
      <mal:years>2012, 2013, 2020</mal:years>
    </mal:credit>
  
    <mal:credit xmlns:mal="http://projectmallard.org/1.0/" type="translator copyright">
      <mal:name>Jakob Kramer</mal:name>
      <mal:email>jakob.kramer@gmx.de</mal:email>
      <mal:years>2010</mal:years>
    </mal:credit>
  
    <mal:credit xmlns:mal="http://projectmallard.org/1.0/" type="translator copyright">
      <mal:name>Tim Sabsch</mal:name>
      <mal:email>tim@sabsch.com</mal:email>
      <mal:years>2018</mal:years>
    </mal:credit>
  
    <mal:credit xmlns:mal="http://projectmallard.org/1.0/" type="translator copyright">
      <mal:name>Jürgen Benvenuti</mal:name>
      <mal:email>gastornis@posteo.org</mal:email>
      <mal:years>2023</mal:years>
    </mal:credit>
  </info>

	<title>Runden</title>

    <p>
    Nearest integer values tying away from zero are calculated using the [ and ] symbols or round <link xref="function">function</link>.
    </p>
    <example>
    <p>[0.5]</p>
    <p>round (0.5)</p>
    </example>

    <p>
    Nearest integer values toward -∞ also known as floor values are calculated using the ⌊ and ⌋ symbols or floor <link xref="function">function</link>.
    </p>
    <example>
    <p>
    ⌊0.5⌋
    </p>
    <p>floor (0.5)</p>
    </example>

    <p>
    Nearest integer values toward +∞ also known as ceiling values are calculated using the ⌈ and ⌉ symbols or ceil <link xref="function">function</link>.
    </p>
    <example>
    <p>
    ⌈0.5⌉
    </p>
    <p>ceil (0.5)</p>
    </example>

    <p>
    Nearest integer values toward 0 i.e. the integer components are calculated using int <link xref="function">function</link>.
    </p>
    <p>
    The fractional components are calculated using frac <link xref="function">function</link>.
    </p>
    <example>
    <p>int (0.5)</p>
    <p>frac (0.5)</p>
    </example>
</page>
