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 <chapter id="language-extensions">

   <title>Language Extensions</title>

   <para>

     These language extensions are provided in the following namespace URI:

     <screen>

 http://www.juiblex.co.uk/ns/libxexpr

     </screen>

     People using this namespace are encouraged to use the libxexpr namespace

     prefix.

   </para>

   <sect1 id="libxexpr-pi">

     <title>Function &lt;pi&gt;</title>

     <simplesect>

       <title>Synopsis</title>

 	<para>

 	  <pi> returns the value of π.

 	</para>

     </simplesect>

     <simplesect>

       <title>Arguments</title>

 	<para>

 	  <pi> takes no arguments.

 	</para>

     </simplesect>

     <simplesect>

       <title>Return Values</title>

 	<para>

 	  <pi> returns the value of π.

 	</para>

     </simplesect>

     <example>

       <programlisting>

 &lt;libxexpr:pi/&gt; ≅ &lt;float&gt;3.14&lt;/float&gt;<!--

    --></programlisting>

     </example>

   </sect1>

   <sect1 id="libxexpr-sin">

     <title>Function &lt;sin&gt;</title>

     <simplesect>

       <title>Synopsis</title>

 	<para>

 	  <sin> computes the sine function.

 	</para>

     </simplesect>

     <simplesect>

       <title>Arguments</title>

 	<para>

 	  <sin> takes one argument: x. If no argument is given, an error

 	  occurs.

 	</para>

     </simplesect>

     <simplesect>

       <title>Return Values</title>

 	<para>

 	  <sin> returns the sine of its argument, given in radians.

 	  If the argument does not evaluate to a finite number,

 	  <sin> returns an indeterminate result.

 	</para>

     </simplesect>

     <example>

       <programlisting>

 <libxexpr:sin>

   <divide>

     <libxexpr:pi/>

     2

   </divide>

 &lt;/libxexpr:sin&gt; --> &lt;float&gt;1&lt;/float&gt;<!--

    --></programlisting>

     </example>

   </sect1>

   <sect1 id="libxexpr-atan">

     <title>Function &lt;atan&gt;</title>

     <simplesect>

       <title>Synopsis</title>

 	<para>

 	  <atan> computes the arc tangent function.

 	</para>

     </simplesect>

     <simplesect>

       <title>Arguments</title>

 	<para>

 	  <atan> takes two arguments: x and y. The y argument defaults to

 	  1. If the x argument is missing, an error occurs.

 	</para>

     </simplesect>

     <simplesect>

       <title>Return Values</title>

 	<para>

 	  <atan> returns the principal value of the arc tangent of its

 	  argument(s) in radians. If either argument is indeterminate,

 	  the result is also indeterminate.

 	</para>

 	<para>

 	  If two arguments are given, <atan> returns the arc tangent of

 	  y/x, using the signs of the two arguments to determine the quadrant

 	  of the result which will be in the range [-π, π]. If both arguments

 	  are 0, the result will also be 0.

 	</para>

 	<para>

 	  If only one argument is given, <atan> returns the arc tangent of

 	  its argument. The result will be in the range [-π/2, π/2].

 	</para>

     </simplesect>

     <example>

       <programlisting>

 &lt;libxexpr:atan&gt;1 0&lt;/libxexpr:atan&gt; --> &lt;float&gt;0&lt;/float&gt;<!--

    --></programlisting>

     </example>

   </sect1>

   <sect1 id="libxexpr-exp">

     <title>Function &lt;exp&gt;</title>

     <simplesect>

       <title>Synopsis</title>

 	<para>

 	  <exp> computes the base-e exponential function.

 	</para>

     </simplesect>

     <simplesect>

       <title>Arguments</title>

 	<para>

 	  <exp> takes zero or one argument: x.

 	</para>

     </simplesect>

     <simplesect>

       <title>Return Values</title>

 	<para>

 	  <exp> returns the value of e (the base of natural logarithms)

 	  raised to the power of its argument (or just e if no argument is

 	  supplied). If the argument does not evaluate to a finite number,

 	  <exp> returns an indeterminate result.

 	</para>

     </simplesect>

     <example>

       <programlisting>

 &lt;libxexpr:exp&gt;2&lt;/libxexpr:exp&gt; ≅ &lt;float&gt;7.389&lt;/float&gt;<!--

    --></programlisting>

     </example>

   </sect1>

   <sect1 id="libxexpr-log">

     <title>Function &lt;log&gt;</title>

     <simplesect>

       <title>Synopsis</title>

 	<para>

 	  <log> computes the natural logarithmic function.

 	</para>

     </simplesect>

     <simplesect>

       <title>Arguments</title>

 	<para>

 	  <log> takes one argument: x. If no argument is given, an error

 	  occurs.

 	</para>

     </simplesect>

     <simplesect>

       <title>Return Values</title>

 	<para>

 	  <log> returns the natural logarithm of its argument.

 	  If the argument does not evaluate to a positive finite number,

 	  <log> returns an indeterminate result.

 	</para>

     </simplesect>

     <example>

       <programlisting>

 <libxexpr:log>

   <libxexpr:exp>2</libxexpr:exp>

 &lt;/libxexpr:log&gt; --> &lt;float&gt;2&lt;/float&gt;<!--

    --></programlisting>

     </example>

   </sect1>

   <sect1 id="libxexpr-pow">

     <title>Function &lt;pow&gt;</title>

     <simplesect>

       <title>Synopsis</title>

 	<para>

 	  <pow> computes the value of its first argument raised to the

 	  power of its second argument.

 	</para>

     </simplesect>

     <simplesect>

       <title>Arguments</title>

 	<para>

 	  <pow> takes two arguments: x and y. If fewer arguments are

 	  given, an error occurs.

 	</para>

     </simplesect>

     <simplesect>

       <title>Return Values</title>

 	<para>

 	  <pow> returns the value of x (its first argument) raised to the

 	  power of y (its second argument).

 	</para>

 	<para>

 	  If x is a finite value less than 0, and y is a finite non-integer,

 	  <pow> returns an indeterminate result. 

 	</para>

 	<para>

 	  If the result overflows, <pow> returns an indeterminate result. 

 	</para>

 	<para>

 	  If result underflows, and is not representable, 0 is returned.

 	</para>

 	<para>

 	  Except as specified below, if either argument is indeterminate,

 	  the result is also indeterminate.

 	</para>

 	<para>

 	  If x is 1, the result is 1 (even if y is indeterminate).

 	</para>

 	<para>

 	  If y is 0, the result is 1 (even if x is indeterminate).

 	</para>

 	<para>

 	  If x is 0, and y is an odd integer greater than 0, the result is 0.

 	</para>

 	<para>

 	  If x is 0, and y greater than 0 and not an odd integer, the result

 	  is 0.

 	</para>

 	<para>

 	  If x is 0, and y is less than 0,

 	  <pow> returns an indeterminate result. 

 	</para>

     </simplesect>

     <example>

       <programlisting>

   &lt;libxexpr:pow&gt;10 2&lt;/libxexpr:pow&gt; --> &lt;float&gt;100&lt;/float&gt;<!--

    --></programlisting>

     </example>

   </sect1>

 </chapter>