{-|
  IP routing table is a tree of 'AddrRange'
  to search one of them on the longest
  match base. It is a kind of TRIE with one
  way branching removed. Both IPv4 and IPv6
  are supported.
-}
module Data.IP.RouteTable.Internal where

import Control.Applicative ((<$>),(<*>),pure)
import Control.Monad
import Data.Bits
import Data.Foldable (Foldable(..))
import Data.IP.Addr
import Data.IP.Op
import Data.IP.Range
import Data.IntMap (IntMap, (!))
import qualified Data.IntMap as IM (fromList)
import Data.Monoid
import Data.Traversable
import Data.Word
import Prelude hiding (lookup)

----------------------------------------------------------------

{-|
  A class to contain IPv4 and IPv6.
-}
class Addr a => Routable a where
    {-|
      The 'intToTBit' function takes 'Int' and returns an 'Routable' address
      whose only n-th bit is set.
    -}
    intToTBit   :: Int -> a
    {-|
      The 'isZero' function takes an 'Routable' address and an test bit
      'Routable' address and returns 'True' is the bit is unset,
      otherwise returns 'False'.
    -}
    isZero :: a -> a -> Bool

instance Routable IPv4 where
    intToTBit = intToTBitIPv4
    isZero a b = a `masked` b == IP4 0

instance Routable IPv6 where
    intToTBit = intToTBitIPv6
    isZero a b = a `masked` b == IP6 (0,0,0,0)

----------------------------------------------------------------
--
-- Test Bit
--

intToTBitIPv4 :: Int -> IPv4
intToTBitIPv4 len = IP4 (intToTBitsIPv4 ! len)

intToTBitIPv6 :: Int -> IPv6
intToTBitIPv6 len = IP6 (intToTBitsIPv6 ! len)

intToTBitsWord32 :: [Word32]
intToTBitsWord32 = iterate (`shift` (-1)) 0x80000000

intToTBitsIPv4 :: IntMap IPv4Addr
intToTBitsIPv4 = IM.fromList $ zip [0..32] intToTBitsWord32

intToTBitsIPv6 :: IntMap IPv6Addr
intToTBitsIPv6 = IM.fromList $ zip [0..128] bs
  where
    bs = b1 ++ b2 ++ b3 ++ b4 ++ b5
    b1 = map (\vbit -> (vbit,all0,all0,all0)) intToTBits
    b2 = map (\vbit -> (all0,vbit,all0,all0)) intToTBits
    b3 = map (\vbit -> (all0,all0,vbit,all0)) intToTBits
    b4 = map (\vbit -> (all0,all0,all0,vbit)) intToTBits
    b5 =              [(all0,all0,all0,all0)]
    intToTBits = take 32 intToTBitsWord32
    all0 = 0x00000000

----------------------------------------------------------------

{-|
  The Tree structure for IP routing table based on TRIE with
  one way branching removed. This is an abstract data type,
  so you cannot touch its inside. Please use 'insert' or 'lookup', instead.
-}
data IPRTable k a =
    Nil
  | Node !(AddrRange k) !k !(Maybe a) !(IPRTable k a) !(IPRTable k a)
  deriving (Eq, Show)

----------------------------------------------------------------

{-|
  The 'empty' function returns an empty IP routing table.

>>> (empty :: IPRTable IPv4 ()) == fromList []
True
-}
empty :: Routable k => IPRTable k a
empty = Nil

instance Functor (IPRTable k) where
    fmap _ Nil = Nil
    fmap f (Node r a mv b1 b2) = Node r a (f <$> mv) (fmap f b1) (fmap f b2)

instance Foldable (IPRTable k) where
    foldMap _ Nil = mempty
    foldMap f (Node _ _ mv b1 b2) = foldMap f mv <> foldMap f b1 <> foldMap f b2

instance Traversable (IPRTable k) where
    traverse _ Nil = pure Nil
    traverse f (Node r a mv b1 b2) = Node r a <$> traverse f mv <*> traverse f b1 <*> traverse f b2

----------------------------------------------------------------

{-|
  The 'insert' function inserts a value with a key of 'AddrRange' to 'IPRTable'
  and returns a new 'IPRTable'.

>>> (insert ("127.0.0.1" :: AddrRange IPv4) () empty) == fromList [("127.0.0.1",())]
True
-}
insert :: (Routable k) => AddrRange k -> a -> IPRTable k a -> IPRTable k a
insert k1 v1 Nil = Node k1 tb1 (Just v1) Nil Nil
  where
    tb1 = keyToTestBit k1
insert k1 v1 s@(Node k2 tb2 v2 l r)
  | k1 == k2  = Node k1 tb1 (Just v1) l r
  | k2 >:> k1 = if isLeft k1 tb2 then
                    Node k2 tb2 v2 (insert k1 v1 l) r
                  else
                    Node k2 tb2 v2 l (insert k1 v1 r)
  | k1 >:> k2 = if isLeft k2 tb1 then
                    Node k1 tb1 (Just v1) s Nil
                  else
                    Node k1 tb1 (Just v1) Nil s
  | otherwise = let n = Node k1 tb1 (Just v1) Nil Nil
                in link n s
  where
    tb1 = keyToTestBit k1

link :: Routable k => IPRTable k a -> IPRTable k a -> IPRTable k a
link s1@(Node k1 _ _ _ _) s2@(Node k2 _ _ _ _)
  | isLeft k1 tbg = Node kg tbg Nothing s1 s2
  | otherwise     = Node kg tbg Nothing s2 s1
  where
    kg = glue 0 k1 k2
    tbg = keyToTestBit kg
link _ _ = error "link"

glue :: (Routable k) => Int -> AddrRange k -> AddrRange k -> AddrRange k
glue n k1 k2
  | addr k1 `masked` mk == addr k2 `masked` mk = glue (n + 1) k1 k2
  | otherwise = makeAddrRange (addr k1) (n - 1)
  where
    mk = intToMask n

keyToTestBit :: Routable k => AddrRange k -> k
keyToTestBit = intToTBit . mlen

isLeft :: Routable k => AddrRange k -> k -> Bool
isLeft adr = isZero (addr adr)

----------------------------------------------------------------

{-|
  The 'delete' function deletes a value by a key of 'AddrRange' from 'IPRTable'
  and returns a new 'IPRTable'.

>>> delete "127.0.0.1" (insert "127.0.0.1" () empty) == (empty :: IPRTable IPv4 ())
True
-}
delete :: (Routable k) => AddrRange k -> IPRTable k a -> IPRTable k a
delete _ Nil = Nil
delete k1 s@(Node k2 tb2 v2 l r)
  | k1 == k2  = node k2 tb2 Nothing l r
  | k2 >:> k1 = if isLeft k1 tb2 then
                    node k2 tb2 v2 (delete k1 l) r
                  else
                    node k2 tb2 v2 l (delete k1 r)
  | otherwise = s

node :: (Routable k) => AddrRange k -> k -> Maybe a -> IPRTable k a -> IPRTable k a -> IPRTable k a
node _ _ Nothing Nil r = r
node _ _ Nothing l Nil = l
node k tb v      l   r = Node k tb v l r

----------------------------------------------------------------

{-|
  The 'lookup' function looks up 'IPRTable' with a key of 'AddrRange'.
  If a routing information in 'IPRTable' matches the key, its value
  is returned.

>>> let v4 = ["133.4.0.0/16","133.5.0.0/16","133.5.16.0/24","133.5.23.0/24"] :: [AddrRange IPv4]
>>> let rt = fromList $ zip v4 v4
>>> lookup "127.0.0.1" rt
Nothing
>>> lookup "133.3.0.1" rt
Nothing
>>> lookup "133.4.0.0" rt
Just 133.4.0.0/16
>>> lookup "133.4.0.1" rt
Just 133.4.0.0/16
>>> lookup "133.5.16.0" rt
Just 133.5.16.0/24
>>> lookup "133.5.16.1" rt
Just 133.5.16.0/24
-}
lookup :: Routable k => AddrRange k -> IPRTable k a -> Maybe a
lookup k s = search k s Nothing

search :: Routable k => AddrRange k -> IPRTable k a -> Maybe a -> Maybe a
search _ Nil res = res
search k1 (Node k2 tb2 Nothing l r) res
  | k1 == k2  = res
  | k2 >:> k1 = if isLeft k1 tb2 then
                    search k1 l res
                  else
                    search k1 r res
  | otherwise = res
search k1 (Node k2 tb2 vl l r) res
  | k1 == k2  = vl
  | k2 >:> k1 = if isLeft k1 tb2 then
                    search k1 l vl
                  else
                    search k1 r vl
  | otherwise = res

----------------------------------------------------------------

{-|
  The 'findMatch' function looks up 'IPRTable' with a key of 'AddrRange'.
  If the key matches routing informations in 'IPRTable', they are
  returned.

>>> let v4 = ["133.4.0.0/16","133.5.0.0/16","133.5.16.0/24","133.5.23.0/24"] :: [AddrRange IPv4]
>>> let rt = fromList $ zip v4 $ repeat ()
>>> findMatch "133.4.0.0/15" rt :: [(AddrRange IPv4,())]
[(133.4.0.0/16,()),(133.5.0.0/16,()),(133.5.16.0/24,()),(133.5.23.0/24,())]
-}

findMatch :: MonadPlus m => Routable k => AddrRange k -> IPRTable k a -> m (AddrRange k, a)
findMatch _ Nil = mzero
findMatch k1 (Node k2 _ Nothing l r)
  | k1 >:> k2 = findMatch k1 l `mplus` findMatch k1 r
  | k2 >:> k1 = findMatch k1 l `mplus` findMatch k1 r
  | otherwise = mzero
findMatch k1 (Node k2 _ (Just vl) l r)
  | k1 >:> k2 = return (k2, vl) `mplus` findMatch k1 l `mplus` findMatch k1 r
  | k2 >:> k1 = findMatch k1 l `mplus` findMatch k1 r
  | otherwise = mzero

----------------------------------------------------------------

{-|
  The 'fromList' function creates a new IP routing table from
  a list of a pair of 'IPrange' and value.
-}
fromList :: Routable k => [(AddrRange k, a)] -> IPRTable k a
fromList = foldl' (\s (k,v) -> insert k v s) empty

{-|
  The 'toList' function creates a list of a pair of 'AddrRange' and
  value from an IP routing table.
-}
toList :: Routable k => IPRTable k a -> [(AddrRange k, a)]
toList = foldt toL []
  where
    toL Nil xs = xs
    toL (Node _ _ Nothing  _ _) xs = xs
    toL (Node k _ (Just a) _ _) xs = (k,a) : xs

----------------------------------------------------------------

foldt :: (IPRTable k a -> b -> b) -> b -> IPRTable k a -> b
foldt _ v Nil = v
foldt func v rt@(Node _ _ _ l r) = foldt func (foldt func (func rt v) l) r