<?php
if ( ! is_user_logged_in() ) { // Display WordPress login form:
$args = array(
    'redirect' => admin_url(),
    'form_id' => 'loginform-custom',
    'label_username' => __( 'Username custom text' ),
    'label_password' => __( 'Password custom text' ),
    'label_remember' => __( 'Remember Me custom text' ),
    'label_log_in' => __( 'Log In custom text' ),
    'remember' => true
);
wp_login_form( $args );
} else { // If logged in:
wp_loginout( home_url() ); // Display "Log Out" link.
echo " | ";
wp_register('', ''); // Display "Site Admin" link.
}
?>

function wp_authenticate($username, $password) {
$username = sanitize_user($username);
$password = trim($password);

$user = apply_filters('authenticate', null, $username, $password);

if ( $user == null ) {
    $user = new WP_Error('authentication_failed', __('<strong>ERROR</strong>: Invalid username or incorrect password.'));
}

$ignore_codes = array('empty_username', 'empty_password');

if (is_wp_error($user) && !in_array($user->get_error_code(), $ignore_codes) ) {

    // Put your code here

}

return $user;
}