I've been v happy with Divvy for many years. It's not auto-tiling, but it's perfect for for my purposes. Quick cmd-shift-arrow puts a window in [top 1/2, bottom 1/2, left 1/2, right 1/2] or cmd-shift-enter [for fullscreen] (across 2 monitors)... it's exactly right for me to avoid ever reaching for the mouse to position windows.