php-doc-en/reference/bc/functions/bcpowmod.xml

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  <refentry id="function.bcpowmod">
   <refnamediv>
    <refname>bcpowmod</refname>
    <refpurpose>
     Raise an arbitrary precision number to another, reduced by a specified modulus
    </refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>string</type><methodname>bcpowmod</methodname>
      <methodparam><type>string</type><parameter>x</parameter></methodparam>
      <methodparam><type>string</type><parameter>y</parameter></methodparam>
      <methodparam><type>string</type><parameter>modulus</parameter></methodparam>
      <methodparam choice="opt"><type>int</type><parameter>scale</parameter></methodparam>
     </methodsynopsis>
    <para>
     Use the fast-exponentiation method to raise <parameter>x</parameter> 
     to the power <parameter>y</parameter> with respect to the modulus
     <parameter>modulus</parameter>.  The optional
     <parameter>scale</parameter> can be used to set the number of
     digits after the decimal place in the result. 
    </para>
    <note>
     <para>
      Because this method uses the modulus operation, non-natural numbers
      may give unexpected results.  A natural number is any positive 
      non-zero integer.
     </para>
    </note>
   </refsect1>
   <refsect1>
    &reftitle.examples;
    <para>
     The following two statements are functionally identical.  The 
     <function>bcpowmod</function> version however, executes in 
     less time and can accept larger parameters.
     <informalexample>
      <programlisting role="php">
<![CDATA[
<?php
$a = bcpowmod($x, $y, $mod);

$b = bcmod(bcpow($x, $y), $mod);

// $a and $b are equal to each other. 

?>
]]>
      </programlisting>
     </informalexample>
    </para>
   </refsect1>
   <refsect1>
    &reftitle.seealso;
    <para>
     <function>bcpow</function>&listendand;
     <function>bcmod</function>.
    </para>
   </refsect1>
  </refentry>

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