HTTP Auth for single WordPress page

functions.php

function http_auth_headers(){
	header('WWW-Authenticate: Basic realm="Web Page Restricted"');
        header('HTTP/1.0 401 Unauthorized');
        echo 'You must enter the correct credentials to access this page';
        exit;
}
add_action('template_redirect', 'add_http_auth_basic', 0);
function add_http_auth_basic(){
	$uri = 'contact';
	if(!is_admin()){
		global $wp;
		if($wp->request === $uri || strpos($wp->request, $uri.'/') !== false ){
			$user = HTTP_USER_NAME; 
			$pass = HTTP_USER_PASS; 
			if (!isset($_SERVER['PHP_AUTH_USER'])) {
				http_auth_headers();
			} else{
				if ($_SERVER['PHP_AUTH_USER'] !== $user && $_SERVER['PHP_AUTH_PW'] !== $pass) {
					http_auth_headers();
				}
			}
		}
	}
}