WordPress custom pagination with $wpdb->get_results

functions.php

<?php
$items_per_page = 2;
$page = isset( $_GET['cpage'] ) ? abs( (int) $_GET['cpage'] ) : 1;
$offset = ( $page * $items_per_page ) - $items_per_page;

$query = 'SELECT * FROM '.$table_name;

$total_query = "SELECT COUNT(1) FROM (${query}) AS combined_table";
$total = $wpdb->get_var( $total_query );

$results = $wpdb->get_results( $query.' ORDER BY id DESC LIMIT '. $offset.', '. $items_per_page, OBJECT );
/*
*
* Here goes the loop
*
***/
echo paginate_links( array(
                        'base' => add_query_arg( 'cpage', '%#%' ),
                        'format' => '',
                        'prev_text' => __('&laquo;'),
                        'next_text' => __('&raquo;'),
                        'total' => ceil($total / $items_per_page),
                        'current' => $page
                    ));