ip-1.4.0: src/Net/IPv6.hs
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE InstanceSigs #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE CPP #-}
{-# OPTIONS_GHC -Wall #-}
module Net.IPv6
( -- * Convert
ipv6
, fromOctets
, fromWord16s
, fromWord32s
, fromTupleWord16s
, fromTupleWord32s
, toWord16s
, toWord32s
-- * Special IP Addresses
, any
, loopback
-- * Textual Conversion
-- ** Text
, encode
, decode
, parser
-- ** Printing
, print
-- * IPv6 Ranges
-- ** Range functions
, range
, fromBounds
, normalize
, contains
, member
, lowerInclusive
, upperInclusive
-- ** Textual Conversion
-- *** Text
, encodeRange
, decodeRange
, parserRange
, printRange
-- * Types
, IPv6(..)
, IPv6Range(..)
) where
import Net.IPv4 (IPv4(..))
import qualified Net.IPv4 as IPv4
import Control.Applicative
import Control.Monad.Primitive
import Control.Monad.ST
import Data.Bits
import Data.ByteString (ByteString)
import Data.Char (chr)
import Data.List (intercalate, group)
import Data.Primitive.Addr
import Data.Primitive.ByteArray
import Data.Primitive.Types (Prim(..))
import Data.Text (Text)
import Data.Word
import GHC.Enum (predError, succError)
import GHC.Exts
import GHC.Generics (Generic)
import Numeric (showHex)
import Prelude hiding (any, print)
import Text.ParserCombinators.ReadPrec (prec,step)
import Text.Printf (printf)
import Text.Read (Read(..),Lexeme(Ident),lexP,parens)
import qualified Data.Aeson as Aeson
import qualified Data.Attoparsec.Text as AT
import qualified Data.Attoparsec.Text as Atto
import qualified Data.ByteString.Char8 as BC8
import qualified Data.Text as Text
import qualified Data.Text.IO as TIO
-- $setup
--
-- These are here to get doctest work.
--
-- >>> import qualified Prelude as P
-- >>> import qualified Data.Text.IO as T
-- >>> import Test.QuickCheck (Arbitrary(..))
-- >>> instance Arbitrary IPv6 where { arbitrary = IPv6 <$> arbitrary <*> arbitrary }
-- >>> instance Arbitrary IPv6Range where { arbitrary = IPv6Range <$> arbitrary <*> arbitrary }
--
-- | A 128-bit Internet Protocol version 6 address.
data IPv6 = IPv6
{ ipv6A :: {-# UNPACK #-} !Word64
, ipv6B :: {-# UNPACK #-} !Word64
} deriving (Eq,Ord)
-- | Since 'IPv6' has more inhabitants than 'Int', the
-- implementation of 'fromEnum' discards information.
-- Currently, 'enumFromThen' and 'enumFromThenTo' emit
-- an error, but this could be remedied if someone
-- wants to provide an implementation of them.
instance Enum IPv6 where
succ (IPv6 a b)
| a == maxBound && b == maxBound = succError "IPv6"
| otherwise =
case b + 1 of
0 -> IPv6 (a + 1) 0
s -> IPv6 a s
pred (IPv6 a b)
| a == 0 && b == 0 = predError "IPv6"
| otherwise =
case b of
0 -> IPv6 (a - 1) maxBound
_ -> IPv6 a (b - 1)
toEnum :: Int -> IPv6
toEnum i = IPv6 0 (toEnum i)
fromEnum :: IPv6 -> Int
fromEnum (IPv6 _ b) = fromEnum b
{-# INLINE enumFrom #-}
enumFrom x = unfoldrLast (Just maxBound) (\b -> if b < maxBound then Just (b,succ b) else Nothing) x
{-# INLINE enumFromTo #-}
enumFromTo x y = unfoldrLast (if x <= y then Just y else Nothing) (\b -> if b < y then Just (b,succ b) else Nothing) x
enumFromThen = error "IPv6 currently lacks an implementation of enumFromThen"
enumFromThenTo = error "IPv6 currently lacks an implementation of enumFromThenTo"
-- This is like unfoldr except that it adds an additional element
-- at the end.
unfoldrLast :: Maybe a -> (b -> Maybe (a, b)) -> b -> [a]
{-# INLINE unfoldrLast #-}
unfoldrLast a0 f b0 = build
(\c n ->
let go b = case f b of
Just (a, new_b) -> a `c` go new_b
Nothing -> case a0 of
Nothing -> n
Just x -> x `c` n
in go b0
)
instance Bounded IPv6 where
minBound = IPv6 0 0
maxBound = IPv6 maxBound maxBound
instance Show IPv6 where
showsPrec p addr = showParen (p > 10)
$ showString "ipv6 "
. showHexWord16 a
. showChar ' '
. showHexWord16 b
. showChar ' '
. showHexWord16 c
. showChar ' '
. showHexWord16 d
. showChar ' '
. showHexWord16 e
. showChar ' '
. showHexWord16 f
. showChar ' '
. showHexWord16 g
. showChar ' '
. showHexWord16 h
where
(a,b,c,d,e,f,g,h) = toWord16s addr
instance Prim IPv6 where
sizeOf# _ = 2# *# sizeOf# (undefined :: Word64)
alignment# _ = alignment# (undefined :: Word64)
indexByteArray# arr# i# =
let i = I# i#
arr = ByteArray arr#
in IPv6 (indexByteArray arr (2 * i + 0)) (indexByteArray arr (2 * i + 1))
readByteArray# :: forall s. () => MutableByteArray# s -> Int# -> State# s -> (# State# s, IPv6 #)
readByteArray# arr# i# = internal $ do
let i = I# i#
arr = MutableByteArray arr#
a <- readByteArray arr (2 * i + 0) :: ST s Word64
b <- readByteArray arr (2 * i + 1)
return (IPv6 a b)
writeByteArray# :: forall s. () => MutableByteArray# s -> Int# -> IPv6 -> State# s -> State# s
writeByteArray# arr# i# (IPv6 a b) = internal_ $ do
let i = I# i#
arr = MutableByteArray arr#
writeByteArray arr (2 * i + 0) a
writeByteArray arr (2 * i + 1) b :: ST s ()
setByteArray# arr# i# len# ident = go 0#
where
go ix# s0 = if isTrue# (ix# <# len#)
then case writeByteArray# arr# (i# +# ix#) ident s0 of
s1 -> go (ix# +# 1#) s1
else s0
indexOffAddr# :: Addr# -> Int# -> IPv6
indexOffAddr# addr# i# =
let i = I# i#
addr = Addr addr#
in IPv6 (indexOffAddr addr (2 * i + 0)) (indexOffAddr addr (2 * i + 1))
readOffAddr# :: forall s. () => Addr# -> Int# -> State# s -> (# State# s, IPv6 #)
readOffAddr# addr# i# = internal $ do
let i = I# i#
addr = Addr addr#
a <- readOffAddr addr (2 * i + 0) :: ST s Word64
b <- readOffAddr addr (2 * i + 1)
return (IPv6 a b)
writeOffAddr# :: forall s. () => Addr# -> Int# -> IPv6 -> State# s -> State# s
writeOffAddr# addr# i# (IPv6 a b) = internal_ $ do
let i = I# i#
addr = Addr addr#
writeOffAddr addr (2 * i + 0) a
writeOffAddr addr (2 * i + 1) b :: ST s ()
setOffAddr# addr# i# len# ident = go 0#
where
go ix# s0 = if isTrue# (ix# <# len#)
then case writeOffAddr# addr# (i# +# ix#) ident s0 of
s1 -> go (ix# +# 1#) s1
else s0
internal_ :: PrimBase m => m () -> State# (PrimState m) -> State# (PrimState m)
internal_ m s = case internal m s of
(# s', _ #) -> s'
print :: IPv6 -> IO ()
print = TIO.putStrLn . encode
showHexWord16 :: Word16 -> ShowS
showHexWord16 w =
showString "0x"
. showChar (nibbleToHex (unsafeShiftR (fromIntegral w) 12))
. showChar (nibbleToHex ((unsafeShiftR (fromIntegral w) 8) .&. 0xF))
. showChar (nibbleToHex ((unsafeShiftR (fromIntegral w) 4) .&. 0xF))
. showChar (nibbleToHex ((fromIntegral w) .&. 0xF))
-- invariant: argument must be less than 16
nibbleToHex :: Word -> Char
nibbleToHex w
| w < 10 = chr (fromIntegral (w + 48))
| otherwise = chr (fromIntegral (w + 87))
instance Read IPv6 where
readPrec = parens $ prec 10 $ do
Ident "ipv6" <- lexP
a <- step readPrec
b <- step readPrec
c <- step readPrec
d <- step readPrec
e <- step readPrec
f <- step readPrec
g <- step readPrec
h <- step readPrec
return (fromWord16s a b c d e f g h)
instance Aeson.ToJSON IPv6 where
toJSON = Aeson.String . encode
instance Aeson.FromJSON IPv6 where
parseJSON = Aeson.withText "IPv6" $ \t -> case decode t of
Nothing -> fail "invalid IPv6 address"
Just i -> return i
rightToMaybe :: Either a b -> Maybe b
rightToMaybe = either (const Nothing) Just
fromOctets ::
Word8 -> Word8 -> Word8 -> Word8
-> Word8 -> Word8 -> Word8 -> Word8
-> Word8 -> Word8 -> Word8 -> Word8
-> Word8 -> Word8 -> Word8 -> Word8
-> IPv6
fromOctets a b c d e f g h i j k l m n o p =
let !(w1,w2) = fromOctetsV6
(fromIntegral a) (fromIntegral b) (fromIntegral c) (fromIntegral d)
(fromIntegral e) (fromIntegral f) (fromIntegral g) (fromIntegral h)
(fromIntegral i) (fromIntegral j) (fromIntegral k) (fromIntegral l)
(fromIntegral m) (fromIntegral n) (fromIntegral o) (fromIntegral p)
in IPv6 w1 w2
-- | Create an 'IPv6' address from the eight 16-bit fragments that make
-- it up. This closely resembles the standard IPv6 notation, so
-- is used for the 'Show' instance. Note that this lacks the formatting
-- feature for suppress zeroes in an 'IPv6' address, but it should be
-- readable enough for hacking in GHCi.
--
-- >>> let addr = ipv6 0x3124 0x0 0x0 0xDEAD 0xCAFE 0xFF 0xFE00 0x1
-- >>> addr
-- ipv6 0x3124 0x0000 0x0000 0xdead 0xcafe 0x00ff 0xfe00 0x0001
-- >>> T.putStrLn (encode addr)
-- 3124::dead:cafe:ff:fe00:1
ipv6 ::
Word16 -> Word16 -> Word16 -> Word16
-> Word16 -> Word16 -> Word16 -> Word16
-> IPv6
ipv6 = fromWord16s
-- | An alias for the 'ipv6' smart constructor.
fromWord16s ::
Word16 -> Word16 -> Word16 -> Word16
-> Word16 -> Word16 -> Word16 -> Word16
-> IPv6
fromWord16s a b c d e f g h =
let !(w1,w2) = fromWord16sV6
(fromIntegral a) (fromIntegral b) (fromIntegral c) (fromIntegral d)
(fromIntegral e) (fromIntegral f) (fromIntegral g) (fromIntegral h)
in IPv6 w1 w2
-- | Convert an 'IPv6' to eight 16-bit words.
toWord16s :: IPv6 -> (Word16,Word16,Word16,Word16,Word16,Word16,Word16,Word16)
toWord16s (IPv6 a b) =
( fromIntegral (unsafeShiftR a 48)
, fromIntegral (unsafeShiftR a 32)
, fromIntegral (unsafeShiftR a 16)
, fromIntegral a
, fromIntegral (unsafeShiftR b 48)
, fromIntegral (unsafeShiftR b 32)
, fromIntegral (unsafeShiftR b 16)
, fromIntegral b
)
-- | Uncurried variant of 'fromWord16s'.
fromTupleWord16s :: (Word16,Word16,Word16,Word16,Word16,Word16,Word16,Word16) -> IPv6
fromTupleWord16s (a,b,c,d,e,f,g,h) = fromWord16s a b c d e f g h
-- | Build an 'IPv6' from four 32-bit words. The leftmost argument
-- is the high word and the rightword is the low word.
fromWord32s :: Word32 -> Word32 -> Word32 -> Word32 -> IPv6
fromWord32s a b c d =
let !(w1,w2) = fromWord32sV6
(fromIntegral a) (fromIntegral b) (fromIntegral c) (fromIntegral d)
in IPv6 w1 w2
-- | Uncurried variant of 'fromWord32s'.
fromTupleWord32s :: (Word32,Word32,Word32,Word32) -> IPv6
fromTupleWord32s (a,b,c,d) = fromWord32s a b c d
-- | Convert an 'IPv6' to four 32-bit words.
toWord32s :: IPv6 -> (Word32,Word32,Word32,Word32)
toWord32s (IPv6 a b) =
( fromIntegral (unsafeShiftR a 32)
, fromIntegral a
, fromIntegral (unsafeShiftR b 32)
, fromIntegral b
)
loopback :: IPv6
loopback = IPv6 0 1
any :: IPv6
any = IPv6 0 0
-- | Encodes the IP, using zero-compression on the leftmost-longest string of
-- zeroes in the address.
-- Per <https://tools.ietf.org/html/rfc5952#section-5 RFC 5952 Section 5>,
-- this uses mixed notation when encoding an IPv4-mapped IPv6 address:
--
-- >>> T.putStrLn $ encode $ fromWord16s 0xDEAD 0xBEEF 0x0 0x0 0x0 0x0 0x0 0x1234
-- dead:beef::1234
-- >>> T.putStrLn $ encode $ fromWord16s 0x0 0x0 0x0 0x0 0x0 0xFFFF 0x6437 0xA5B4
-- ::ffff:100.55.165.180
-- >>> T.putStrLn $ encode $ fromWord16s 0x0 0x0 0x0 0x0 0x0 0x0 0x0 0x0
-- ::
encode :: IPv6 -> Text
encode ip =
if isIPv4MappedAddress
-- This representation is RECOMMENDED by https://tools.ietf.org/html/rfc5952#section-5
then Text.pack "::ffff:" `mappend` IPv4.encode (IPv4.IPv4 (fromIntegral w7 `unsafeShiftL` 16 .|. fromIntegral w8))
else toText [w1, w2, w3, w4, w5, w6, w7, w8]
where
isIPv4MappedAddress = w1 == 0 && w2 == 0 && w3 == 0 && w4 == 0 && w5 == 0 && w6 == 0xFFFF
(w1, w2, w3, w4, w5, w6, w7, w8) = toWord16s ip
toText ws = Text.pack $ intercalate ":" $ expand 0 longestZ grouped
where
expand _ 8 _ = ["::"]
expand _ _ [] = []
expand i longest ((x, len):wsNext)
-- zero-compressed group:
| x == 0 && len == longest =
-- first and last need an extra colon since there's nothing
-- to concat against
(if i == 0 || (i+len) == 8 then ":" else "")
: expand (i+len) 0 wsNext
-- normal group:
| otherwise = replicate len (showHex x "") ++ expand (i+len) longest wsNext
longestZ = maximum . (0:) . map snd . filter ((==0) . fst) $ grouped
grouped = map (\x -> (head x, length x)) (group ws)
-- | Decode an IPv6 address. This accepts both standard IPv6
-- notation (with zero compression) and mixed notation for
-- IPv4-mapped IPv6 addresses.
decode :: Text -> Maybe IPv6
decode t = rightToMaybe (AT.parseOnly (parser <* AT.endOfInput) t)
parser :: Atto.Parser IPv6
parser = makeIP <$> ip
where
makeIP [w1, w2, w3, w4, w5, w6, w7, w8] = fromWord16s w1 w2 w3 w4 w5 w6 w7 w8
makeIP _ = error "Net.IPv6.parser: Implementation error. Please open a bug report."
ip = (Atto.char ':' *> Atto.char ':' *> doubleColon 0) <|> part 0
part :: Int -> Atto.Parser [Word16]
part n =
case n of
-- max 8 parts in an IPv6 address
7 -> pure <$> Atto.hexadecimal
-- after 6 parts it could end in IPv4 dotted notation
6 -> ipv4 <|> hexPart
_ -> hexPart
where
hexPart = (:)
<$> Atto.hexadecimal
<*> (Atto.char ':' *>
(
(Atto.char ':' *> doubleColon (n+1))
<|>
part (n+1)
)
)
doubleColon :: Int -> Atto.Parser [Word16]
doubleColon count = do
rest <- afterDoubleColon <|> pure []
let fillerLength = (8 - count - length rest)
if fillerLength <= 0
then fail "too many parts in IPv6 address"
else pure (replicate fillerLength 0 ++ rest)
-- after double colon, IPv4 dotted notation could appear anywhere
afterDoubleColon :: Atto.Parser [Word16]
afterDoubleColon =
ipv4 <|>
(:) <$> Atto.hexadecimal <*> ((Atto.char ':' *> afterDoubleColon) <|> pure [])
ipv4 :: Atto.Parser [Word16]
ipv4 = ipv4ToWord16s <$> IPv4.parser
ipv4ToWord16s :: IPv4 -> [Word16]
ipv4ToWord16s (IPv4 word) = [fromIntegral (word `unsafeShiftR` 16), fromIntegral (word .&. 0xFFFF)]
fromOctetsV6 ::
Word64 -> Word64 -> Word64 -> Word64
-> Word64 -> Word64 -> Word64 -> Word64
-> Word64 -> Word64 -> Word64 -> Word64
-> Word64 -> Word64 -> Word64 -> Word64
-> (Word64,Word64)
fromOctetsV6 a b c d e f g h i j k l m n o p =
( fromOctetsWord64 a b c d e f g h
, fromOctetsWord64 i j k l m n o p
)
fromWord16sV6 ::
Word64 -> Word64 -> Word64 -> Word64
-> Word64 -> Word64 -> Word64 -> Word64
-> (Word64,Word64)
fromWord16sV6 a b c d e f g h =
( fromWord16Word64 a b c d
, fromWord16Word64 e f g h
)
fromWord32sV6 :: Word64 -> Word64 -> Word64 -> Word64 -> (Word64,Word64)
fromWord32sV6 a b c d =
( fromWord32Word64 a b
, fromWord32Word64 c d
)
fromOctetsWord64 ::
Word64 -> Word64 -> Word64 -> Word64
-> Word64 -> Word64 -> Word64 -> Word64
-> Word64
fromOctetsWord64 a b c d e f g h = fromIntegral
( shiftL a 56
.|. shiftL b 48
.|. shiftL c 40
.|. shiftL d 32
.|. shiftL e 24
.|. shiftL f 16
.|. shiftL g 8
.|. h
)
fromWord16Word64 :: Word64 -> Word64 -> Word64 -> Word64 -> Word64
fromWord16Word64 a b c d = fromIntegral
( unsafeShiftL a 48
.|. unsafeShiftL b 32
.|. unsafeShiftL c 16
.|. d
)
fromWord32Word64 :: Word64 -> Word64 -> Word64
fromWord32Word64 a b = fromIntegral (unsafeShiftL a 32 .|. b)
data IPv6Range = IPv6Range
{ ipv6RangeBase :: {-# UNPACK #-} !IPv6
, ipv6RangeLength :: {-# UNPACK #-} !Word8
} deriving (Eq,Ord,Show,Read,Generic)
mask :: Word8 -> Word64
mask w = if w > 63
then 0xffffffffffffffff
else complement (shiftR 0xffffffffffffffff (fromIntegral w))
normalize :: IPv6Range -> IPv6Range
normalize (IPv6Range (IPv6 w1 w2) len) =
let len' = min len 128
norm
| len' < 64 = (IPv6Range (IPv6 (w1 .&. mask len') (w2 .&. mask 0)) len')
| otherwise = (IPv6Range (IPv6 (w1 .&. mask 64) (w2 .&. mask (len' - 64))) len')
in norm
encodeRange :: IPv6Range -> Text
encodeRange x = encode (ipv6RangeBase x) <> Text.pack "/" <> (Text.pack $ (show . fromEnum) $ ipv6RangeLength x)
decodeRange :: Text -> Maybe IPv6Range
decodeRange = rightToMaybe . AT.parseOnly (parserRange <* AT.endOfInput)
parserRange :: AT.Parser IPv6Range
parserRange = do
ip <- parser
_ <- AT.char '/'
theMask <- AT.decimal >>= limitSize
return (normalize (IPv6Range ip theMask))
where
limitSize i =
if i > 128
then fail "An IP range length must be between 0 and 128"
else return i
-- | Checks to see if an 'IPv6' address belongs in the 'IPv6Range'.
--
-- >>> let ip = ipv6 0x2001 0x0db8 0x0db8 0x1094 0x2051 0x0000 0x0000 0x0001
-- >>> let iprange mask = IPv6Range (ipv6 0x2001 0x0db8 0x0000 0x0000 0x0000 0x0000 0x0000 0x0001) mask
-- >>> contains (iprange 8) ip
-- True
-- >>> contains (iprange 48) ip
-- False
--
-- Typically, element-testing functions are written to take the element
-- as the first argument and the set as the second argument. This is intentionally
-- written the other way for better performance when iterating over a collection.
-- For example, you might test elements in a list for membership like this:
--
-- >>> let r = IPv6Range (ipv6 0x2001 0x0db8 0x0000 0x0000 0x0000 0x0000 0x0000 0x0001) 64
-- >>> fmap (contains r) (take 5 $ iterate succ $ ipv6 0x2001 0x0db8 0x0000 0x0000 0xffff 0xffff 0xffff 0xfffe)
-- [True,True,False,False,False]
--
-- The implementation of 'contains' ensures that (with GHC), the bitmask
-- creation and range normalization only occur once in the above example.
-- They are reused as the list is iterated.
contains :: IPv6Range -> IPv6 -> Bool
contains (IPv6Range (IPv6 wsubnetA wsubnetB) len) =
let lenA = if len > 64 then 64 else len
lenB = if len > 64 then len - 64 else 0
theMaskA = mask lenA
theMaskB = mask lenB
wsubnetNormalizedA = wsubnetA .&. theMaskA
wsubnetNormalizedB = wsubnetB .&. theMaskB
in \(IPv6 wA wB) ->
(wA .&. theMaskA) == wsubnetNormalizedA
&&
(wB .&. theMaskB) == wsubnetNormalizedB
-- | This is provided to mirror the interface provided by @Data.Set@. It
-- behaves just like 'contains' but with flipped arguments.
--
-- prop> member ip r == contains r ip
member :: IPv6 -> IPv6Range -> Bool
member = flip contains
-- | The inclusive lower bound of an 'IPv6Range'. This is conventionally
-- understood to be the broadcast address of a subnet. For example:
--
-- >>> T.putStrLn $ encode $ lowerInclusive $ IPv6Range (ipv6 0x2001 0x0db8 0x0000 0x0000 0x0000 0x0000 0x0000 0x0001) 25
-- 2001:d80::
--
-- Note that the lower bound of a normalized 'IPv4Range' is simply the
-- ip address of the range:
--
-- prop> lowerInclusive r == ipv6RangeBase (normalize r)
lowerInclusive :: IPv6Range -> IPv6
lowerInclusive (IPv6Range (IPv6 w1 w2) len) =
ipv6RangeBase (normalize (IPv6Range (IPv6 w1 w2) len))
upperInclusive :: IPv6Range -> IPv6
upperInclusive (IPv6Range (IPv6 w1 w2) len) =
let len' = min 128 len
theInvertedMask :: Word64
theInvertedMask = shiftR 0xffffffffffffffff (fromIntegral len')
theInvertedMask2 = shiftR 0xffffffffffffffff ((fromIntegral len')-64)
upper
| len' < 64 = IPv6 ((w1 .|. theInvertedMask)) ((w2 .|. shiftR 0xffffffffffffffff 0))
| otherwise = IPv6 (w1) (w2 .|. theInvertedMask2)
in upper
-- | This exists mostly for testing purposes.
printRange :: IPv6Range -> IO ()
printRange = TIO.putStrLn . encodeRange
range :: IPv6 -> Word8 -> IPv6Range
range addr len = normalize (IPv6Range addr len)
fromBounds :: IPv6 -> IPv6 -> IPv6Range
fromBounds (IPv6 a1 a2) (IPv6 b1 b2) =
normalize (IPv6Range (IPv6 a1 a2) (maskFromBounds a1 b1 a2 b2))
maskFromBounds :: Word64 -> Word64 -> Word64 -> Word64 -> Word8
maskFromBounds lo1 hi1 lo2 hi2 =
let x = countLeadingZeros (xor lo1 hi1)
check
| x < 64 = fromIntegral x
| otherwise = fromIntegral $ x + (countLeadingZeros (xor lo2 hi2))
in check