    {-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  XMonad.Layout.Dwindle
    -- Copyright   :  (c) Norbert Zeh <norbert.zeh@gmail.com>
    -- License     :  BSD3
    --
    -- Maintainer  :  Norbert Zeh <norbert.zeh@gmail.com>
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Three layouts: The first, 'Spiral', is a reimplementation of
    -- 'XMonad.Layout.Spiral.spiral' with, at least to me, more intuitive semantics.
    -- The second, 'Dwindle', is inspired by a similar layout in awesome and
    -- produces the same sequence of decreasing window sizes as Spiral but pushes
    -- the smallest windows into a screen corner rather than the centre.  The third,
    -- 'Squeeze' arranges all windows in one row or in one column, with
    -- geometrically decreasing sizes.
    --
    -----------------------------------------------------------------------------

    module XMonad.Layout.Dwindle ( -- * Usage
                                   -- $usage
                                   Dwindle(..)
                                 , Direction2D(..)
                                 , Chirality(..)
                                 ) where

    import Data.List ( unfoldr )
    import XMonad
    import XMonad.StackSet ( integrate, Stack )
    import XMonad.Util.Types ( Direction2D(..) )

    -- $usage
    -- This module can be used as follows:
    --
    -- > import XMonad.Layout.Dwindle
    --
    -- Then add something like this to your layouts:
    --
    -- > Dwindle R CW 1.5 1.1
    --
    -- or
    --
    -- > Spiral L CW 1.5 1.1
    --
    -- or
    --
    -- ^ Squeeze D 1.5 1.1
    --
    -- The first produces a layout that places the second window to the right of
    -- the first, the third below the second, the fourth to the right of the third,
    -- and so on.  The first window is 1.5 times as wide as the second one, the
    -- second is 1.5 times as tall as the third one, and so on.  Thus, the further
    -- down the window stack a window is, the smaller it is and the more it is
    -- pushed into the bottom-right corner.
    --
    -- The second produces a layout with the same window sizes but places the second
    -- window to the left of the first one, the third above the second one, the
    -- fourth to the right of the third one, and so on.
    --
    -- The third produces a layout that stacks windows vertically top-down with each
    -- window being 1.5 times as tall as the next.
    --
    -- In all three cases, the fourth (third, in the case of 'Squeeze') parameter,
    -- 1.1, is the factor by which the third parameter increases or decreases in
    -- response to Expand or Shrink messages.
    --
    -- For more detailed instructions on editing the layoutHook see:
    --
    -- "XMonad.Doc.Extending#Editing_the_layout_hook"

    -- | Layouts with geometrically decreasing window sizes.  'Spiral' and 'Dwindle'
    -- split the screen into a rectangle for the first window and a rectangle for
    -- the remaining windows, which is split recursively to lay out these windows.
    -- Both layouts alternate between horizontal and vertical splits.
    --
    -- In each recursive step, the split 'Direction2D' determines the placement of the
    -- remaining windows relative to the current window: to the left, to the right,
    -- above or below.  The split direction of the first split is determined by the
    -- first layout parameter.  The split direction of the second step is rotated 90
    -- degrees relative to the first split direction according to the second layout
    -- parameter of type 'Chirality'.  So, if the first split is 'R' and the second
    -- layout parameter is 'CW', then the second split is 'D'.
    --
    -- For the 'Spiral' layout, the same 'Chirality' is used for computing the split
    -- direction of each step from the split direction of the previous step.  For
    -- example, parameters 'R' and 'CW' produces the direction sequence 'R', 'D',
    -- 'L', 'U', 'R', 'D', 'L', 'U', ...
    --
    -- For the 'Dwindle' layout, the 'Chirality' alternates between 'CW' and 'CCW' in
    -- each step.  For example, parameters 'U' and 'CCW' produce the direction
    -- sequence 'U', 'L', 'U', 'L', ... because 'L' is the 'CCW' rotation of 'U' and
    -- 'U' is the 'CW' rotation of 'L'.
    --
    -- In each split, the current rectangle is split so that the ratio between the
    -- size of the rectangle allocated to the current window and the size of the
    -- rectangle allocated to the remaining windows is the third layout parameter.
    -- This ratio can be altered using 'Expand' and 'Shrink' messages.  The former
    -- multiplies the ratio by the fourth layout parameter.  The latter divides the
    -- ratio by this parameter.
    --
    -- 'Squeeze' does not alternate between horizontal and vertical splits and
    -- simply splits in the direction given as its first argument.
    --
    -- Parameters for both 'Dwindle' and 'Spiral':
    --
    -- * First split direction
    --
    -- * First split chirality
    --
    -- * Size ratio between rectangle allocated to current window and rectangle
    -- allocated to remaining windows
    --
    -- * Factor by which the size ratio is changed in response to 'Expand' or 'Shrink'
    -- messages
    --
    -- The parameters for 'Squeeze' are the same, except that there is no 'Chirality'
    -- parameter.
    data Dwindle a = Dwindle !Direction2D !Chirality !Rational !Rational
                   | Spiral  !Direction2D !Chirality !Rational !Rational
                   | Squeeze !Direction2D !Rational !Rational
                   deriving (Read, Show)

    -- | Rotation between consecutive split directions
    data Chirality = CW | CCW
                   deriving (Read, Show)

    instance LayoutClass Dwindle a where
        pureLayout (Dwindle dir rot ratio _) = dwindle alternate dir rot ratio
        pureLayout (Spiral  dir rot ratio _) = dwindle rotate    dir rot ratio
        pureLayout (Squeeze dir     ratio _) = squeeze           dir     ratio
        pureMessage (Dwindle dir rot ratio delta) =
          fmap (\ratio' -> Dwindle dir rot ratio' delta) . changeRatio ratio delta
        pureMessage (Spiral dir rot ratio delta) =
          fmap (\ratio' -> Spiral dir rot ratio' delta) . changeRatio ratio delta
        pureMessage (Squeeze dir ratio delta) =
          fmap (\ratio' -> Squeeze dir ratio' delta) . changeRatio ratio delta

    changeRatio :: Rational -> Rational -> SomeMessage -> Maybe Rational
    changeRatio ratio delta = fmap f . fromMessage
      where f Expand = ratio * delta
            f Shrink = ratio / delta

    dwindle :: AxesGenerator -> Direction2D -> Chirality -> Rational -> Rectangle -> Stack a ->
               [(a, Rectangle)]
    dwindle trans dir rot ratio rect st = unfoldr genRects (integrate st, rect, dirAxes dir, rot)
      where genRects ([],     _, _, _)  = Nothing
            genRects ([w],    r, a, rt) = Just ((w, r),  ([], r,   a,  rt))
            genRects ((w:ws), r, a, rt) = Just ((w, r'), (ws, r'', a', rt'))
              where (r', r'') = splitRect r ratio a
                    (a', rt') = trans a rt

    squeeze :: Direction2D -> Rational -> Rectangle -> Stack a -> [(a, Rectangle)]
    squeeze dir ratio rect st = zip wins rects
      where wins    = integrate st
            nwins   = length wins
            sizes   = take nwins $ unfoldr (\r -> Just (r * ratio, r * ratio)) 1
            totals' = 0 : zipWith (+) sizes totals'
            totals  = tail totals'
            splits  = zip (tail sizes) totals
            ratios  = reverse $ map (\(l, r) -> l / r) splits
            rects   = genRects rect ratios
            genRects r []     = [r]
            genRects r (x:xs) = r' : genRects r'' xs
              where (r', r'') = splitRect r x (dirAxes dir)

    splitRect :: Rectangle -> Rational -> Axes -> (Rectangle, Rectangle)
    splitRect (Rectangle x y w h) ratio (ax, ay) = (Rectangle x' y' w' h', Rectangle x'' y'' w'' h'')
      where portion = ratio / (ratio + 1)
            w1  = (round $ fi w * portion) :: Int
            w2  = fi w - w1
            h1  = (round $ fi h * portion) :: Int
            h2  = fi h - h1
            x'  = x + fi (negate ax * (1 - ax) * w2 `div` 2)
            y'  = y + fi (negate ay * (1 - ay) * h2 `div` 2)
            w'  = fi $ w1 + (1 - abs ax) * w2
            h'  = fi $ h1 + (1 - abs ay) * h2
            x'' = x + fi (ax * (1 + ax) * w1 `div` 2)
            y'' = y + fi (ay * (1 + ay) * h1 `div` 2)
            w'' = fi $ w2 + (1 - abs ax) * w1
            h'' = fi $ h2 + (1 - abs ay) * h1
            fi :: (Num b, Integral a) => a -> b
            fi  = fromIntegral

    type Axes          = (Int, Int)
    type AxesGenerator = Axes -> Chirality -> (Axes, Chirality)

    dirAxes :: Direction2D -> Axes
    dirAxes L = (-1,  0)
    dirAxes R = ( 1,  0)
    dirAxes U = ( 0, -1)
    dirAxes D = ( 0,  1)

    alternate :: AxesGenerator
    alternate = chDir alt

    rotate :: AxesGenerator
    rotate = chDir id

    chDir :: (Chirality -> Chirality) -> AxesGenerator
    chDir f (x, y) r = (a' r, r')
      where a' CW  = (-y,  x)
            a' CCW = ( y, -x)
            r' = f r

    alt :: Chirality -> Chirality
    alt CW  = CCW
    alt CCW = CW