<?xml version="1.0" encoding="iso-8859-1"?>
 <reference id="ref.gmp">
  <title>GMP functions</title>
  <titleabbrev>GMP</titleabbrev>
  <partintro>
   <simpara>
    These functions allow you to work with arbitrary-length integers
    using GNU <acronym>MP</acronym> library. In order to have these
    functions available, you must compile PHP with
    <acronym>GMP</acronym> support by using the <option
    role="configure">--with-gmp</option> option.
   </simpara>
   <simpara>
    You can download the <acronym>GMP</acronym> library from <ulink
    url="&url.gmp;">&url.gmp;</ulink>.  This site also has the
    <acronym>GMP</acronym> manual available.
   </simpara>
   <simpara>
    You will need GMP version 2 or better to use these functions. Some
    functions may require more recent version of the GMP library.
   </simpara>
   <simpara>
    These functions have been added in PHP 4.0.4. 
   </simpara>
   <note>
    <para>
     Most GMP functions accept GMP number arguments, defined as
     <literal>resource</literal> below. However, most of these
     functions will accept also numeric and string arguments, given
     it's possible to convert the latter to number. Also, if there's
     faster function that can operate on integer arguments, it would
     be used instead of slower function when supplied arguments are
     integers. This is done transparently, so the bootom line is that
     you can use integers in every function that expects GMP
     number. See also <function>gmp_init</function> function.
    </para>
   </note>
   <para>
    <example>
     <title>Factorial function using GMP</title>
     <programlisting role="php">
&lt;?php
function fact ($x) {
    if ($x <= 1) 
        return 1;
    else
        return gmp_mul ($x, fact ($x-1));
}

print gmp_strval (fact (1000)) . "\n";
?>
     </programlisting>
    </example>
   </para>
   <para>
    This will calculate factiorial of 1000 (pretty big number)
    very fast.
   </para>
  </partintro>

  <refentry id="function.gmp-init">
   <refnamediv>
    <refname>gmp_init</refname>
    <refpurpose>Create GMP number</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_init</methodname>
      <methodparam><type>mixed</type><parameter>number</parameter></methodparam>
     </methodsynopsis>
    <para>
     Creates a GMP number from integer or string. String
     representation can be decimal or hexadecimal. In the latter case,
     the string should start with <literal>0x</literal>.
    </para>
    <para>
     <example>
      <title>Creating GMP number</title>
      <programlisting role="php">
&lt;?php
    $a = gmp_init (123456);
    $b = gmp_init ("0xFFFFDEBACDFEDF7200");
?>
      </programlisting>
     </example>
    </para>
    <note>
     <para>
      It is not necessary to call this function if you want to use
      integer or string in place of GMP number in GMP functions, like
      <function>gmp_add</function>. Function arguments are
      automatically converted to GMP numbers, if such conversion is
      possible and needed, using the same rules as
      <function>gmp_init</function>.
     </para>
    </note>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-intval">
   <refnamediv>
    <refname>gmp_intval</refname>
    <refpurpose>Convert GMP number to integer</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_intval</methodname>
     <methodparam><type>resource</type><parameter>gmpnumber</parameter></methodparam>
     </methodsynopsis>
    <para>
     This function allows to convert GMP number to integer.
     <warning>
      <simpara> 
       This function returns useful result only if the number actually
       fits the PHP integer (i.e., signed long type). If you want just
       to print the GMP number, use <function>gmp_strval</function>.
      </simpara>
     </warning>
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-strval">
   <refnamediv>
    <refname>gmp_strval</refname>
    <refpurpose>Convert GMP number to string</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>string</type><methodname>gmp_strval</methodname>
     <methodparam><type>resource</type><parameter>gmpnumber</parameter></methodparam>
     <methodparam choice="opt"><type>int</type><parameter>base</parameter></methodparam>
     </methodsynopsis>
    <para>
     Convert GMP number to string representation in base
     <parameter>base</parameter>. The default base is 10.  Allowed
     values for the base are from 2 to 36.
    </para>
    <para>
     <example>
      <title>Converting GMP number to string</title>
      <programlisting role="php">
&lt;?php
    $a = gmp_init("0x41682179fbf5");
    printf ("Decimal: %s, 36-based: %s", gmp_strval($a), gmp_strval($a,36));
?>
      </programlisting>
     </example>
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-add">
   <refnamediv>
    <refname>gmp_add</refname>
    <refpurpose>Add numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_add</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Add two GMP numbers. The result will be GMP number representing
     the sum of the arguments.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-sub">
   <refnamediv>
    <refname>gmp_sub</refname>
    <refpurpose>Subtract numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_sub</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Subtract <parameter>b</parameter> from <parameter>a</parameter>
     and returns the result.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-mul">
   <refnamediv>
    <refname>gmp_mul</refname>
    <refpurpose>Multiply numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_mul</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Multiplies <parameter>a</parameter> by <parameter>b</parameter>
     and returns the result.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-div-q">
   <refnamediv>
    <refname>gmp_div_q</refname>
    <refpurpose>Divide numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_div_q</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     <methodparam choice="opt"><type>int</type><parameter>round</parameter></methodparam>
     </methodsynopsis>
    <para>
     Divides <parameter>a</parameter> by <parameter>b</parameter> and
     returns the integer result. The result rounding is defined by the
     <parameter>round</parameter>, which can have the following
     values:
     <itemizedlist>
      <listitem>
       <simpara>
        <parameter>GMP_ROUND_ZERO</parameter>: The result is truncated
        towards 0.
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        <parameter>GMP_ROUND_PLUSINF</parameter>: The result is
        rounded towards <literal>+infinity</literal>.
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        <parameter>GMP_ROUND_MINUSINF</parameter>: The result is
        rounded towards <literal>-infinity</literal>.
       </simpara>
      </listitem>
     </itemizedlist>
    </para>
    <simpara>
     This function can also be called as <function>gmp_div</function>.
    </simpara>
    <para>
     See also <function>gmp_div_r</function>,
     <function>gmp_div_qr</function>
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-div-r">
   <refnamediv>
    <refname>gmp_div_r</refname>
    <refpurpose>Remainder of the division of numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_div_r</methodname>
     <methodparam><type>resource</type><parameter>n</parameter></methodparam>
     <methodparam><type>resource</type><parameter>d</parameter></methodparam>
     <methodparam choice="opt"><type>int</type><parameter>round</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates remainder of the integer division of
     <parameter>n</parameter> by <parameter>d</parameter>. The
     remainder has the sign of the <parameter>n</parameter> argument,
     if not zero.
    </para>
    <para>
     See the <function>gmp_div_q</function> function for description
     of the <parameter>round</parameter> argument.
    </para>
    <para>
     See also <function>gmp_div_q</function>,
     <function>gmp_div_qr</function>
    </para>
   </refsect1>
  </refentry>
 
  <refentry id="function.gmp-div-qr">
   <refnamediv>
    <refname>gmp_div_qr</refname>
    <refpurpose>Divide numbers and get quotient and remainder</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>array</type><methodname>gmp_div_qr</methodname>
      <methodparam><type>resource</type><parameter>n</parameter></methodparam>
      <methodparam><type>resource</type><parameter>d</parameter></methodparam>
      <methodparam choice="opt"><type>int</type><parameter>round</parameter></methodparam>
     </methodsynopsis>
    <para>
     The function divides <parameter>n</parameter> by
     <parameter>d</parameter> and returns array, with the first
     element being <literal>[n/d]</literal> (the integer result of the
     division) and the second being <literal>(n - [n/d] * d)</literal>
     (the remainder of the division).
    </para>
    <para>
     See the <function>gmp_div_q</function> function for description
     of the <parameter>round</parameter> argument.
    </para>
    <para>
     <example>
      <title>Division of GMP numbers</title>
      <programlisting role="php">
&lt;?php
    $a = gmp_init ("0x41682179fbf5");
    $res = gmp_div_qr ($a, "0xDEFE75");
    printf("Result is: q - %s, r - %s", 
            gmp_strval ($res[0]), gmp_strval ($res[1]));
?>
      </programlisting>
     </example>
    </para>
    <para>
     See also <function>gmp_div_q</function>,
     <function>gmp_div_r</function>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-div">
   <refnamediv>
    <refname>gmp_div</refname>
    <refpurpose>Divide numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_divexact</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     This function is an alias to <function>gmp_div_q</function>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-mod">
   <refnamediv>
    <refname>gmp_mod</refname>
    <refpurpose>Modulo operation</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_mod</methodname>
      <methodparam><type>resource</type><parameter>n</parameter></methodparam>
      <methodparam><type>resource</type><parameter>d</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates <parameter>n</parameter> modulo
     <parameter>d</parameter>. The result is always non-negative, the
     sign of <parameter>d</parameter> is ignored.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-divexact">
   <refnamediv>
    <refname>gmp_divexact</refname>
    <refpurpose>Exact division of numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_divexact</methodname>
      <methodparam><type>resource</type><parameter>n</parameter></methodparam>
      <methodparam><type>resource</type><parameter>d</parameter></methodparam>
     </methodsynopsis>
    <para>
     Divides <parameter>n</parameter> by <parameter>d</parameter>,
     using fast "exact division" algorithm. This function produces
     correct results only when it is known in advance that
     <parameter>d</parameter> divides <parameter>n</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-cmp">
   <refnamediv>
    <refname>gmp_cmp</refname>
    <refpurpose>Compare numbers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_cmp</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Returns positive value if <literal>a > b</literal>, zero if
     <literal>a = b</literal> and negative value if <literal>a &lt;
     b</literal>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-neg">
   <refnamediv>
    <refname>gmp_neg</refname>
    <refpurpose>Negate number</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_neg</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Returns -<parameter>a</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-abs">
   <refnamediv>
    <refname>gmp_abs</refname>
    <refpurpose>Absolute value</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_abs</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Returns absolute value of <parameter>a</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-sign">
   <refnamediv>
    <refname>gmp_sign</refname>
    <refpurpose>Sign of number</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_sign</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Return sign of <parameter>a</parameter> - 1 if
     <parameter>a</parameter> is positive and -1 if it's negative.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-fact">
   <refnamediv>
    <refname>gmp_fact</refname>
    <refpurpose>Factorial</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_fact</methodname>
      <methodparam><type>int</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates factorial (<literal>a!</literal>) of <parameter>a</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-sqrt">
   <refnamediv>
    <refname>gmp_sqrt</refname>
    <refpurpose>Square root</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_sqrt</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates square root of <parameter>a</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-sqrtrm">
   <refnamediv>
    <refname>gmp_sqrtrm</refname>
    <refpurpose>Square root with remainder</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>array</type><methodname>gmp_sqrtrm</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Returns array where first element is the integer square root of
     <parameter>a</parameter> (see also
     <function>gmp_sqrt</function>), and the second is the remainder
     (i.e., the difference between <parameter>a</parameter> and the
     first element squared).
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-perfect-square">
   <refnamediv>
    <refname>gmp_perfect_square</refname>
    <refpurpose>Perfect square check</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>bool</type><methodname>gmp_perfect_square</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Returns &true; if <parameter>a</parameter> is a prefect square,
     &false; otherwise.
    </para>
    <para>
     See also: <function>gmp_sqrt</function>,
     <function>gmp_sqrtrm</function>.  
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-pow">
   <refnamediv>
    <refname>gmp_pow</refname>
    <refpurpose>Raise number into power</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_pow</methodname>
      <methodparam><type>resource</type><parameter>base</parameter></methodparam>
      <methodparam><type>int</type><parameter>exp</parameter></methodparam>
     </methodsynopsis>
    <para>
     Raise <parameter>base</parameter> into power
     <parameter>exp</parameter>. The case of 0^0 yields
     1. <parameter>exp</parameter> cannot be negative.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-powm">
   <refnamediv>
    <refname>gmp_powm</refname>
    <refpurpose>Raise number into power with modulo</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_powm</methodname>
      <methodparam><type>resource</type><parameter>base</parameter></methodparam>
      <methodparam><type>resource</type><parameter>exp</parameter></methodparam>
      <methodparam><type>resource</type><parameter>mod</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculate (<parameter>base</parameter> raised into power
     <parameter>exp</parameter>) modulo <parameter>mod</parameter>. If
     <parameter>exp</parameter> is negative, result is undefined.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-prob-prime">
   <refnamediv>
    <refname>gmp_prob_prime</refname>
    <refpurpose>Check if number is "probably prime"</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_prob_prime</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam choice="opt"><type>int</type><parameter>reps</parameter></methodparam>
     </methodsynopsis>
    <para>
     If this function returns 0, <parameter>a</parameter> is
     definitely not prime. If it returns 1, then
     <parameter>a</parameter> is "probably" prime.  If it returns 2,
     then <parameter>a</parameter> is surely prime. Reasonable values
     of <parameter>reps</parameter> vary from 5 to 10 (default being
     10); a higher value lowers the probability for a non-prime to
     pass as a "probable" prime.
    </para>
    <para>
     The function uses Miller-Rabin's probabilistic test.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-gcd">
   <refnamediv>
    <refname>gmp_gcd</refname>
    <refpurpose>Calculate GCD</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_gcd</methodname>
     <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculate greatest common divisor of <parameter>a</parameter> and
     <parameter>b</parameter>. The result is always positive even if
     either of or both input operands are negative.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-gcdext">
   <refnamediv>
    <refname>gmp_gcdext</refname>
    <refpurpose>Calculate GCD and multipliers</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>array</type><methodname>gmp_gcdext</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates g, s, and t, such that <literal>a*s + b*t = g =
     gcd(a,b)</literal>, where gcd is gretest common divisor. Returns
     array with respective elements g, s and t.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-invert">
   <refnamediv>
    <refname>gmp_invert</refname>
    <refpurpose>Inverse by modulo</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_invert</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Computes the inverse of <parameter>a</parameter> modulo
     <parameter>b</parameter>. Returns &false; if an inverse does not
     exist.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-legendre">
   <refnamediv>
    <refname>gmp_legendre</refname>
    <refpurpose>Legendre symbol</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_legendre</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>p</parameter></methodparam>
     </methodsynopsis>
    <para>
     Compute the
     <ulink url="http://www.utm.edu/research/primes/glossary/LegendreSymbol.html">
     Legendre symbol</ulink> of <parameter>a</parameter> and
     <parameter>p</parameter>. <parameter>p</parameter> should be odd
     and must be positive.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-jacobi">
   <refnamediv>
    <refname>gmp_jacobi</refname>
    <refpurpose>Jacobi symbol</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_jacobi</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>p</parameter></methodparam>
     </methodsynopsis>
    <para>
     Computes
     <ulink url="http://www.utm.edu/research/primes/glossary/JacobiSymbol.html">
     Jacobi symbol</ulink> of <parameter>a</parameter> and
     <parameter>p</parameter>. <parameter>p</parameter> should be odd
     and must be positive.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-random">
   <refnamediv>
    <refname>gmp_random</refname>
    <refpurpose>Random number</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_random</methodname>
      <methodparam><type>int</type><parameter>limiter</parameter></methodparam>
     </methodsynopsis>
    <para>
     Generate a random number. The number will be up to
     <parameter>limiter</parameter> words long. If
     <parameter>limiter</parameter> is negative, negative numbers are
     generated.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-and">
   <refnamediv>
    <refname>gmp_and</refname>
    <refpurpose>Logical AND</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_and</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates logical AND of two GMP numbers.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-or">
   <refnamediv>
    <refname>gmp_or</refname>
    <refpurpose>Logical OR</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_or</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates logical inclusive OR of two GMP numbers.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-xor">
   <refnamediv>
    <refname>gmp_xor</refname>
    <refpurpose>Logical XOR</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_xor</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Calculates logical exclusive OR (XOR) of two GMP numbers.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-setbit">
   <refnamediv>
    <refname>gmp_setbit</refname>
    <refpurpose>Set bit</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_setbit</methodname>
      <methodparam><type>resource</type><parameter>&amp;a</parameter></methodparam>
      <methodparam><type>int</type><parameter>index</parameter></methodparam>
      <methodparam choice="opt"><type>bool</type><parameter>set_clear</parameter></methodparam>
     </methodsynopsis>
    <para>
     Sets bit <parameter>index</parameter> in
     <parameter>a</parameter>. <parameter>set_clear</parameter>
     defines if the bit is set to 0 or 1. By default the bit is set to
     1.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-clrbit">
   <refnamediv>
    <refname>gmp_clrbit</refname>
    <refpurpose>Clear bit</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>resource</type><methodname>gmp_clrbit</methodname>
      <methodparam><type>resource</type><parameter>&amp;a</parameter></methodparam>
      <methodparam><type>int</type><parameter>index</parameter></methodparam>
     </methodsynopsis>
    <para>
     Clears (sets to 0) bit <parameter>index</parameter> in
     <parameter>a</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-scan0">
   <refnamediv>
    <refname>gmp_scan0</refname>
    <refpurpose>Scan for 0</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_scan0</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>int</type><parameter>start</parameter></methodparam>
     </methodsynopsis>
    <para>
     Scans <parameter>a</parameter>, starting with bit
     <parameter>start</parameter>, towards more significant bits,
     until the first clear bit is found. Returns the index of the
     found bit.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-scan1">
   <refnamediv>
    <refname>gmp_scan1</refname>
    <refpurpose>Scan for 1</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_scan1</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>int</type><parameter>start</parameter></methodparam>
     </methodsynopsis>
    <para>
     Scans <parameter>a</parameter>, starting with bit
     <parameter>start</parameter>, towards more significant bits,
     until the first set bit is found. Returns the index of the found
     bit.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-popcount">
   <refnamediv>
    <refname>gmp_popcount</refname>
    <refpurpose>Population count</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_popcount</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
     </methodsynopsis>
    <para>
     Return the population count of <parameter>a</parameter>.
    </para>
   </refsect1>
  </refentry>

  <refentry id="function.gmp-hamdist">
   <refnamediv>
    <refname>gmp_hamdist</refname>
    <refpurpose>Hamming distance</refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>gmp_hamdist</methodname>
      <methodparam><type>resource</type><parameter>a</parameter></methodparam>
      <methodparam><type>resource</type><parameter>b</parameter></methodparam>
     </methodsynopsis>
    <para>
     Returns the hamming distance between <parameter>a</parameter> and
     <parameter>a</parameter>. Both operands should be non-negative.
    </para>
   </refsect1>
  </refentry>

 </reference>

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