register.php, Registration.php, register.php, from http://www.php-login.net/ (minimal), and users.php from http://frug.github.io/AJAX-Chat/

register.php

<?php
// show potential errors / feedback (from registration object)
if (isset($registration)) {
    if ($registration->errors) {
        foreach ($registration->errors as $error) {
            echo $error;
        }
    }
    if ($registration->messages) {
        foreach ($registration->messages as $message) {
            echo $message;
        }
    }
}
?>
<title>Register</title>
<!-- register form -->
<form method="post" action="register.php" name="registerform">   
    
    <!-- the user name input field uses a HTML5 pattern check -->
    <label for="login_input_username">Desired Username</label>
    <input id="login_input_username" class="login_input" type="text" pattern="[a-zA-Z0-9]{2,64}" name="user_name" required />
    
    <br>
    <!-- the email input field uses a HTML5 email type check -->
    <label for="login_input_email">Your Email</label>    
    <input id="login_input_email" class="login_input" type="email" name="user_email" required />        
    
    <br>
    <label for="login_input_password_new">Password</label>
    <input id="login_input_password_new" class="login_input" type="password" name="user_password_new" pattern=".{6,}" required autocomplete="off" /> *Must be 6 or more characters.
    
    <br>
    <label for="login_input_password_repeat">Password Again</label>
    <input id="login_input_password_repeat" class="login_input" type="password" name="user_password_repeat" pattern=".{6,}" required autocomplete="off" />        
    <input type="submit"  name="register" value="Register" />
    
</form>


<!-- backlink -->
<a href="index.php">Back to the login page.</a>

<br>
<a href="http://localhost:8080/#">Take Me Home!</a>

Registration.php

<?php

include ('../../chat/lib/data/users.php');
include('../../chat/lib/custom.php');

/**
 * Class registration
 * handles the user registration
 */
class Registration
{
    /**
     * @var object $db_connection The database connection
     */
    private $db_connection = null;
    /**
     * @var array $errors Collection of error messages
     */
    public $errors = array();
    /**
     * @var array $messages Collection of success / neutral messages
     */
    public $messages = array();

    /**
     * the function "__construct()" automatically starts whenever an object of this class is created,
     * you know, when you do "$registration = new Registration();"
     */
    public function __construct()
    {
        if (isset($_POST["register"])) {
            $this->registerNewUser();
        }
    }

    /**
     * handles the entire registration process. checks all error possibilities
     * and creates a new user in the database if everything is fine
     */
    private function registerNewUser()
    {
        if (empty($_POST['user_name'])) {
            $this->errors[] = "Empty Username";
        } elseif (empty($_POST['user_password_new']) || empty($_POST['user_password_repeat'])) {
            $this->errors[] = "Empty Password";
        } elseif ($_POST['user_password_new'] !== $_POST['user_password_repeat']) {
            $this->errors[] = "Password and password repeat are not the same";
        } elseif (strlen($_POST['user_password_new']) < 6) {
            $this->errors[] = "Password has a minimum length of 6 characters";
        } elseif (strlen($_POST['user_name']) > 64 || strlen($_POST['user_name']) < 2) {
            $this->errors[] = "Username cannot be shorter than 2 or longer than 64 characters";
        } elseif (!preg_match('/^[a-z\d]{2,64}$/i', $_POST['user_name'])) {
            $this->errors[] = "Username does not fit the name scheme: only a-Z and numbers are allowed, 2 to 64 characters";
        } elseif (empty($_POST['user_email'])) {
            $this->errors[] = "Email cannot be empty";
        } elseif (strlen($_POST['user_email']) > 64) {
            $this->errors[] = "Email cannot be longer than 64 characters";
        } elseif (!filter_var($_POST['user_email'], FILTER_VALIDATE_EMAIL)) {
            $this->errors[] = "Your email address is not in a valid email format";
        } elseif (!empty($_POST['user_name'])
            && strlen($_POST['user_name']) <= 64
            && strlen($_POST['user_name']) >= 2
            && preg_match('/^[a-z\d]{2,64}$/i', $_POST['user_name'])
            && !empty($_POST['user_email'])
            && strlen($_POST['user_email']) <= 64
            && filter_var($_POST['user_email'], FILTER_VALIDATE_EMAIL)
            && !empty($_POST['user_password_new'])
            && !empty($_POST['user_password_repeat'])
            && ($_POST['user_password_new'] === $_POST['user_password_repeat'])
        ) {
            // create a database connection
            $this->db_connection = new mysqli(DB_HOST, DB_USER, DB_PASS, DB_NAME);

            // change character set to utf8 and check it
            if (!$this->db_connection->set_charset("utf8")) {
                $this->errors[] = $this->db_connection->error;
            }

            // if no connection errors (= working database connection)
            if (!$this->db_connection->connect_errno) {

                // escaping, additionally removing everything that could be (html/javascript-) code
                $user_name = $this->db_connection->real_escape_string(strip_tags($_POST['user_name'], ENT_QUOTES));
                $user_email = $this->db_connection->real_escape_string(strip_tags($_POST['user_email'], ENT_QUOTES));

                $user_password = $_POST['user_password_new'];
		$plaintName = $user_name;
		$plainPassword = $user_password;
		
		createUser($plainName, $plainPassword);
		
	
	
                // crypt the user's password with PHP 5.5's password_hash() function, results in a 60 character
                // hash string. the PASSWORD_DEFAULT constant is defined by the PHP 5.5, or if you are using
                // PHP 5.3/5.4, by the password hashing compatibility library
                $user_password_hash = password_hash($user_password, PASSWORD_DEFAULT);

                // check if user already exists
                $sql = "SELECT * FROM users WHERE user_name = '" . $user_name . "';";
                $query_check_user_name = $this->db_connection->query($sql);

                if ($query_check_user_name->num_rows == 1) {
                    $this->errors[] = "Sorry, that user name is already taken. Please choose another one.";
                } else {
                    // write new user's data into database
                    $sql = "INSERT INTO users (user_name, user_password_hash, user_email)
                            VALUES('" . $user_name . "', '" . $user_password_hash . "', '" . $user_email . "');";
                    $query_new_user_insert = $this->db_connection->query($sql);

		

                    // if user has been added successfully
                    if ($query_new_user_insert) {
                        $this->messages[] = "Your account has been created successfully. You can now log in.";
			
                    } else {
                        $this->errors[] = "Sorry, your registration failed. Please go back and try again.";
                    }
                }
            } else {
                $this->errors[] = "Sorry, no database connection.";
            }
        } else {
            $this->errors[] = "An unknown error occurred.";
        }
    }
}

users.php

<?php
/*
 * @package AJAX_Chat
 * @author Sebastian Tschan
 * @copyright (c) Sebastian Tschan
 * @license Modified MIT License
 * @link https://blueimp.net/ajax/
 */

// List containing the registered chat users:
$users = array();
// Default guest user (don't delete this one):
$users[0] = array();
$users[0]['userRole'] = AJAX_CHAT_GUEST;
$users[0]['userName'] = null;
$users[0]['password'] = null;
$users[0]['channels'] = array(0);

// Sample admin user:
$users[1] = array();
$users[1]['userRole'] = AJAX_CHAT_ADMIN;
$users[1]['userName'] = 'admin';
$users[1]['password'] = 'admin';
$users[1]['channels'] = array(0,1);

// Sample moderator user:
$users[2] = array();
$users[2]['userRole'] = AJAX_CHAT_MODERATOR;
$users[2]['userName'] = 'moderator';
$users[2]['password'] = 'moderator';
$users[2]['channels'] = array(0,1);

// Sample registered user:
$users[3] = array();
$users[3]['userRole'] = AJAX_CHAT_USER;
$users[3]['userName'] = 'user';
$users[3]['password'] = 'user';
$users[3]['channels'] = array(0,1);

$users[4] = array();
$users[4]['userRole'] = AJAX_CHAT_USER;
$users[4]['userName'] = 'test17';
$users[4]['password'] = 'test17';
$users[4]['channels'] = array(0,1);

$users[4] = array();
$users[4]['userRole'] = AJAX_CHAT_USER;
$users[4]['userName'] = 'bglenney';
$users[4]['password'] = 'standrews';
$users[4]['channels'] = array(0,1);

function createUser($username, $password)
{     

	global $users;
	$newArray = "";
	$userlength = count($users) + 1;
	
	$newArray = sprintf("$users[%s] = array();", $userlength);
	$newArray .= sprintf("$users[%s]['userRole'] = AJAX_CHAT_USER;", $userlength);
	$newArray .= sprintf("$users[%s]['userName'] = \"%s\";", $userlength, $username);
	$newArray .= sprintf("$users[%s]['password'] = \"%s\";", $userlength, $password);
	$newArray .= sprintf("$users[%s]['channels'] = array(0,1);", $userlength);
	
	$fp = fopen('users.php', 'a');
	fwrite($fp, $newArray);
	fclose($fp);
	

}