OOPHP5 singleton database class

If i made my database class a singleton would I call it in the constructors of the classes it is required in?

Database class so far

[code=php]
<?php
class database
private $query;
private $results;

private static $database;

//connect to the database
private function __construct()
{
$this->link = mysql_connect($constants::DBHOST, $constants::DBUSER, $constants::DBPASS) or die(mysql_error());
mysql_select_db($constants::DBNAME) or die(mysql_error());
}

public static function singleton()
{
if (!isset(self::$database)) {
self::$database = new database();
}

return self::$database;
}

public function query($query)
{
$this->query = $query;
$this->execute();
}
//execute the mysql query
private function execute()
{
$this->results = mysql_query($this->query, $this->link) or die(mysql_error());
}

//protect against SQL injection attacks
public function antisql($data)
{
if (is_array($data))
{
foreach ($data as $name=>$value)
{
$data[$name] = mysql_real_escape_string($value);
}
}
else
{
$data = mysql_real_escape_string($data);
}
return $data;
}

//retrive the insert id
public function insertid()
{
return mysql_insert_id();
}

//return an array of results
public function returnArray()
{
return mysql_fetch_array($this->results);
}
}
[/code]

a quick knockup example of registration class

[code=php]
class registration
{

public function __construct()
{
$database = database::singleton();
}

public function checkunique($email)
{
$this->query(“SELECT * FROM `members` WHERE email=’$email'”);
}

public function add()
{
$this->query(“INSERT INTO `members` (`name`, `address`) VALUES (‘$name’, ‘$address’)”);
}
[/code]

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