ceiling()

Description

ceiling() returns the smallest integer that is greater than or equal to its argument. It rounds a number up toward positive infinity. For positive numbers with a fractional part this means adding enough to reach the next integer; for negative numbers it rounds toward zero.

The argument is first converted to a number using the same rules as number(). If the argument is already an integer, it is returned unchanged. Special values (NaN, Infinity, -Infinity) pass through unmodified.

ceiling() is the complement of floor(). It is commonly used to compute the total number of pages needed to display a set of items, to round monetary amounts up to the next whole unit, or to ensure allocated space is never less than required.

Parameters

Return value

xs:double — the smallest integer value greater than or equal to the argument.

Examples

Total pages needed for a list of items

Input XML:

<?xml version="1.0" encoding="UTF-8"?>
<catalog>
  <item>A</item>
  <item>B</item>
  <item>C</item>
  <item>D</item>
  <item>E</item>
</catalog>

Stylesheet:

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
  <xsl:output method="xml" indent="yes"/>

  <xsl:variable name="pageSize" select="2"/>

  <xsl:template match="/catalog">
    <xsl:variable name="total" select="count(item)"/>
    <pagination>
      <total-items><xsl:value-of select="$total"/></total-items>
      <pages-needed><xsl:value-of select="ceiling($total div $pageSize)"/></pages-needed>
    </pagination>
  </xsl:template>
</xsl:stylesheet>

Output:

<pagination>
  <total-items>5</total-items>
  <pages-needed>3</pages-needed>
</pagination>

Ceiling of positive and negative numbers

Input XML:

<?xml version="1.0" encoding="UTF-8"?>
<values>
  <v>3.2</v>
  <v>-3.2</v>
  <v>4.0</v>
</values>

Stylesheet:

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
  <xsl:output method="xml" indent="yes"/>

  <xsl:template match="/values">
    <results>
      <xsl:for-each select="v">
        <ceiling of="{.}"><xsl:value-of select="ceiling(.)"/></ceiling>
      </xsl:for-each>
    </results>
  </xsl:template>
</xsl:stylesheet>

Output:

<results>
  <ceiling of="3.2">4</ceiling>
  <ceiling of="-3.2">-3</ceiling>
  <ceiling of="4.0">4</ceiling>
</results>

Notes

• ceiling(-3.2) returns -3, not -4. The direction is always toward positive infinity.
• If the argument is NaN, ceiling() returns NaN.
• If the argument is Infinity or -Infinity, the same infinity is returned unchanged.
• Like floor(), the return type is xs:double, so serialisation may show a trailing .0 on some processors.
• When dividing integers, use ceiling($a div $b) rather than ceiling($a) div $b; the latter rounds the numerator first and can produce incorrect results.

See also

• floor()
• round()
• number()