Slightly modified code for Swift 3.0
let calendar = NSCalendar.current as NSCalendar
// Replace the hour (time) of both dates with 00:00
let date1 = calendar.startOfDay(for: startDateTime)
let date2 = calendar.startOfDay(for: endDateTime)
let flags = NSCalendar.Unit.day
let components = calendar.components(flags, from: date1, to: date2, options: [])
return components.day!