WordPress get the first and the last post ID

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PHP

WordPress

When displaying a single post I have previous / next links. This works but I would like the 'next' link to point to the first post when the last post is displayed and the 'previous' link to point to the latest post when the first post is displayed. According to the documentation get_boundary_post() should be able to get the first or the last post. Here is what is in my single.php:

<?php
	$prev_post = get_adjacent_post( true, '', true );
	$next_post = get_adjacent_post( true, '', false );
	if($next_post == '')
	{
		$next_post = get_boundary_post();
	}
	if($prev_post == '')
	{
		$prev_post = get_boundary_post(); //???
	}
	$prev_post_id = $prev_post->ID;
	$next_post_id = $next_post->ID;   

<a href="<?php echo get_permalink($prev_post); ?>">previous</a>
<a href="<?php echo get_permalink($next_post); ?>">next</a>

?>

Getting the first post link for the last post works, but getting the latest post link for the first post doesn't. I'm not sure how to call get_boundary_post() to get the latest post, I've tried to set its 'start' parameter to false (default is true) but the link still points to the first post.