Calculating day of the week XSL - xslt-1.0

Question

Trying to calculate day of the week number from date. Found some examples in the internet, but instead of day of the week number i see this : NaN.
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:strip-space elements="*"/>
<xsl:output indent="yes"/>
<xsl:template match="node()">
<xsl:copy>
<xsl:apply-templates/>
</xsl:copy>
</xsl:template>
<xsl:template match="date">
<xsl:copy>
<xsl:call-template name="date-format">
<xsl:with-param name="date-time" select="."/>
</xsl:call-template>
</xsl:copy>
</xsl:template>
<xsl:template name="date-format">
<xsl:param name="date-time"/>
<xsl:param name="date" select="substring-before($date-time,'T')"/>
<xsl:param name="year" select="substring-before($date,'-')"/>
<xsl:param name="month"
select="substring-before(substring-after($date,'-'),'-')"/>
<xsl:param name="day" select="substring-after(substring-after($date,'-'),'-')"/>
<xsl:variable name="a" select="floor((14 - $month) div 12)"/>
<xsl:variable name="y" select="$year - $a"/>
<xsl:variable name="m" select="$month + 12 * $a - 2"/>
<xsl:value-of select="($day + $y + floor($y div 4) - floor($y div 100)
+ floor($y div 400) + floor((31 * $m) div 12)) mod 7"/>
</xsl:template>
</xsl:stylesheet>
.
<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet href="test2.xsl" type="text/xsl" ?>
<document>
<date>2013-01-01</date>
<date>2013-05-24</date>
<date>2013-12-25</date>
<date>1957-07-13</date>
<date>1776-07-04</date>
</document>

Answer 1

The following stylesheet:
XSLT 1.0
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="xml" version="1.0" encoding="UTF-8" indent="yes"/>
<xsl:strip-space elements="*"/>
<xsl:template match="date">
<xsl:call-template name="day-of-week">
<xsl:with-param name="date" select="."/>
</xsl:call-template>
</xsl:template>
<xsl:template name="day-of-week">
<xsl:param name="date"/>
<xsl:variable name="year" select="substring($date,1, 4)"/>
<xsl:variable name="month" select="substring($date, 6, 2)"/>
<xsl:variable name="day" select="substring($date, 9, 2)"/>
<xsl:variable name="a" select="floor((14 - $month) div 12)"/>
<xsl:variable name="y" select="$year + 4800 - $a"/>
<xsl:variable name="m" select="$month + 12*$a - 3"/>
<xsl:variable name="JDN" select="$day + floor((153*$m + 2) div 5) + 365*$y + floor($y div 4) - floor($y div 100) + floor($y div 400) - 32045" />
<xsl:value-of select="($JDN + 1) mod 7" />
</xsl:template>
</xsl:stylesheet>
when applied to your input example:
<document>
<date>2013-01-01</date>
<date>2013-05-24</date>
<date>2013-12-25</date>
<date>1957-07-13</date>
<date>1776-07-04</date>
</document>
will return the following result:
<?xml version="1.0" encoding="UTF-8"?>
25364
Note:
The main problem with your attempt is this:
<xsl:param name="date" select="substring-before($date-time,'T')"/>
Your input has dates, not date-times, and they do not contain "T".