XPath - Java XPath result unexpected

Question

I have noticed something strange. This is my XML

<Items>
    <Item>
        <Name>A</Name>
        <Amount>0.0012</Amount>
        <Quantity>17</Quantity>
        <TotalAmount>0.0204</TotalAmount>
    </Item>
    <Item>
        <Name>B</Name>
        <Amount>1</Amount>
        <Quantity>2</Quantity>
        <TotalAmount>2</TotalAmount>
    </Item>
    <Item>
        <Name>C</Name>
        <Amount>3</Amount>
        <Quantity>2</Quantity>
        <TotalAmount>6</TotalAmount>
    </Item>
</Items>

And this is the XPath that I used

/Items/Item[((Amount * Quantity) != TotalAmount)]/Name

This XPath had to print the name of the item whose TotalAmount!= Product(Amount, Quantity).

I get the value A. But I do not understand why this is happening Because 0.0012 * 17 = 0.0204

And if I remove Item 'A', then I do not get a result.

The same goes for newer versions of XPath as well

for $x in /Items/Item[((Amount * Quantity) != TotalAmount)] return $x/Name

I'm using Saxon 9 in Java.

Can someone explain why this is happening.

Martin Honnen · Accepted Answer · 2017-02-23 18:35:17Z

Try using xs:decimal/xs:integer for better precision: /Items/Item[((xs:decimal(Amount) * xs:integer(Quantity)) != TotalAmount)]/Name.

If you look at http://xsltransform.net/94AbWBV which does

<xsl:transform xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="2.0" xmlns:xs="http://www.w3.org/2001/XMLSchema"
    exclude-result-prefixes="xs">

    <xsl:strip-space elements="*"/>
    <xsl:output indent="yes"/>

    <xsl:template match="/">
      <results>
          <names-precise>
            <xsl:value-of select="/Items/Item[((xs:decimal(Amount) * xs:integer(Quantity)) != TotalAmount)]/Name"/>
          </names-precise>
          <names-imprecise>
              <xsl:value-of select="/Items/Item[((Amount * Quantity) != TotalAmount)]/Name"/>
          </names-imprecise>
          <xsl:apply-templates/>
      </results>

    </xsl:template>

    <xsl:template match="@*|node()">
        <xsl:copy>
            <xsl:apply-templates select="@*|node()"/>
        </xsl:copy>
    </xsl:template>

    <xsl:template match="Item">
        <xsl:copy>
            <xsl:apply-templates/>
            <double-computation>
                <xsl:value-of select="Amount * Quantity"/>
            </double-computation>
            <decimal-computation>
                <xsl:value-of select="xs:decimal(Amount) * xs:integer(Quantity)"/>
            </decimal-computation>
        </xsl:copy>
    </xsl:template>
</xsl:transform>

you can see that the default floating point arithmetic used does not suffice to compute the exact result:

<results>
   <names-precise/>
   <names-imprecise>A</names-imprecise>
   <Items>
      <Item>
         <Name>A</Name>
         <Amount>0.0012</Amount>
         <Quantity>17</Quantity>
         <TotalAmount>0.0204</TotalAmount>
         <double-computation>0.020399999999999998</double-computation>
         <decimal-computation>0.0204</decimal-computation>
      </Item>
      <Item>
         <Name>B</Name>
         <Amount>1</Amount>
         <Quantity>2</Quantity>
         <TotalAmount>2</TotalAmount>
         <double-computation>2</double-computation>
         <decimal-computation>2</decimal-computation>
      </Item>
      <Item>
         <Name>C</Name>
         <Amount>3</Amount>
         <Quantity>2</Quantity>
         <TotalAmount>6</TotalAmount>
         <double-computation>6</double-computation>
         <decimal-computation>6</decimal-computation>
      </Item>
   </Items>
</results>

The same imprecision exists in other language like Javascript using the IEEE double number format:

document.getElementById('result').textContent = 0.0012 * 17;

<p>Result of <code>0.0012 * 17</code> with Javascript is <code id="result"></code>.</p>

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