Identity facebook autosignup

OK, I'm not a CS dev so don't be to harsh ... 

This is to auto signin facebook users on the first page they view under the following circumstances: 

(1) The user is using a tablet or desktop ( there'll be a separate a/b tested version for mobile users ) 
(2) The user has previously authorised the guardian app in facebook
(3) The user has not signed out in the last month.