Here you may test different items per page configuration to understand its behavior.
$params['items_per_page_init'] = false; // no items per page
$params['items_per_page_init'] = '10,20,50,100'; // show options 10,20,50,100
$params['items_per_page_init'] = '$i*50'; // show options with the formula $i*50 i.e. 50,100,150,...
$params['items_per_page_all'] = false; // no show all option
$params['items_per_page_all'] = 'Show all'; // show all option with the text 'Show all'
$params['items_per_page_all'] = '#TOTAL_ITEMS#'; // show all option with the total of items value
$params['items_per_page_url'] = 'alert(\'#ID# - #PAGE# - #ITEMS_PER_PAGE# - #TOTAL_ITEMS#\')'; // javascript code triggered with the onchange event of the select box