```{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}

-----------------------------------------------------------------------------
-- |
-- Copyright   :  (c) Joe Thornber <joe.thornber@gmail.com>
--
-- Maintainer  :  Joe Thornber <joe.thornber@gmail.com>
-- Stability   :  stable
-- Portability :  portable
--
-- Spiral adds a spiral tiling layout
--
-----------------------------------------------------------------------------

-- * Usage
-- \$usage
spiral
, spiralWithDir
, Rotation (..)
, Direction (..)
) where

import Data.Ratio

-- \$usage
--
-- > import Data.Ratio
--
--
-- > myLayouts =  spiral (1 % 1) ||| etc..
-- > main = xmonad defaultConfig { layoutHook = myLayouts }
--
-- For more detailed instructions on editing the layoutHook see:
--

fibs :: [Integer]
fibs = 1 : 1 : zipWith (+) fibs (tail fibs)

mkRatios :: [Integer] -> [Rational]
mkRatios (x1:x2:xs) = (x1 % x2) : mkRatios (x2:xs)
mkRatios _ = []

data Rotation = CW | CCW deriving (Read, Show)
data Direction = East | South | West | North deriving (Eq, Enum, Read, Show)

blend :: Rational -> [Rational] -> [Rational]
blend scale ratios = zipWith (+) ratios scaleFactors
where
len = length ratios
step = (scale - (1 % 1)) / (fromIntegral len)
scaleFactors = map (* step) . reverse . take len \$ [0..]

spiral :: Rational -> SpiralWithDir a
spiral = spiralWithDir East CW

spiralWithDir :: Direction -> Rotation -> Rational -> SpiralWithDir a
spiralWithDir = SpiralWithDir

data SpiralWithDir a = SpiralWithDir Direction Rotation Rational

instance LayoutClass SpiralWithDir a where
pureLayout (SpiralWithDir dir rot scale) sc stack = zip ws rects
where ws = integrate stack
ratios = blend scale . reverse . take (length ws - 1) . mkRatios \$ tail fibs
rects = divideRects (zip ratios dirs) sc
dirs  = dropWhile (/= dir) \$ case rot of
CW  -> cycle [East .. North]
CCW -> cycle [North, West, South, East]
handleMessage (SpiralWithDir dir rot scale) = return . fmap resize . fromMessage
where resize Expand = spiralWithDir dir rot \$ (21 % 20) * scale
resize Shrink = spiralWithDir dir rot \$ (20 % 21) * scale
description _ = "Spiral"

-- This will produce one more rectangle than there are splits details
divideRects :: [(Rational, Direction)] -> Rectangle -> [Rectangle]
divideRects [] r = [r]
divideRects ((r,d):xs) rect = case divideRect r d rect of
(r1, r2) -> r1 : (divideRects xs r2)

-- It's much simpler if we work with all Integers and convert to
-- Rectangle at the end.
data Rect = Rect Integer Integer Integer Integer

fromRect :: Rect -> Rectangle
fromRect (Rect x y w h) = Rectangle (fromIntegral x) (fromIntegral y) (fromIntegral w) (fromIntegral h)

toRect :: Rectangle -> Rect
toRect (Rectangle x y w h) = Rect (fromIntegral x) (fromIntegral y) (fromIntegral w) (fromIntegral h)

divideRect :: Rational -> Direction -> Rectangle -> (Rectangle, Rectangle)
divideRect r d rect = let (r1, r2) = divideRect' r d \$ toRect rect in
(fromRect r1, fromRect r2)

divideRect' :: Rational -> Direction -> Rect -> (Rect, Rect)
divideRect' ratio dir (Rect x y w h) =
case dir of
East -> let (w1, w2) = chop ratio w in (Rect x y w1 h, Rect (x + w1) y w2 h)
South -> let (h1, h2) = chop ratio h in (Rect x y w h1, Rect x (y + h1) w h2)
West -> let (w1, w2) = chop (1 - ratio) w in (Rect (x + w1) y w2 h, Rect x y w1 h)
North -> let (h1, h2) = chop (1 - ratio) h in (Rect x (y + h1) w h2, Rect x y w h1)

chop :: Rational -> Integer -> (Integer, Integer)
chop rat n = let f = ((fromIntegral n) * (numerator rat)) `div` (denominator rat) in
(f, n - f)
```