base-4.15.1.0: GHC/Word.hs

{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE CPP, NoImplicitPrelude, BangPatterns, MagicHash, UnboxedTuples #-}
{-# OPTIONS_HADDOCK not-home #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  GHC.Word
-- Copyright   :  (c) The University of Glasgow, 1997-2002
-- License     :  see libraries/base/LICENSE
--
-- Maintainer  :  cvs-ghc@haskell.org
-- Stability   :  internal
-- Portability :  non-portable (GHC Extensions)
--
-- Sized unsigned integral types: 'Word', 'Word8', 'Word16', 'Word32', and
-- 'Word64'.
--
-----------------------------------------------------------------------------

#include "MachDeps.h"

module GHC.Word (
    Word(..), Word8(..), Word16(..), Word32(..), Word64(..),

    -- * Shifts
    uncheckedShiftL64#,
    uncheckedShiftRL64#,

    -- * Byte swapping
    byteSwap16,
    byteSwap32,
    byteSwap64,

    -- * Bit reversal
    bitReverse8,
    bitReverse16,
    bitReverse32,
    bitReverse64,

    -- * Equality operators
    -- | See GHC.Classes#matching_overloaded_methods_in_rules
    eqWord, neWord, gtWord, geWord, ltWord, leWord,
    eqWord8, neWord8, gtWord8, geWord8, ltWord8, leWord8,
    eqWord16, neWord16, gtWord16, geWord16, ltWord16, leWord16,
    eqWord32, neWord32, gtWord32, geWord32, ltWord32, leWord32,
    eqWord64, neWord64, gtWord64, geWord64, ltWord64, leWord64
    ) where

import Data.Bits
import Data.Maybe

#if WORD_SIZE_IN_BITS < 64
import GHC.IntWord64
#endif

import GHC.Base
import GHC.Enum
import GHC.Num
import GHC.Real
import GHC.Ix
import GHC.Show

------------------------------------------------------------------------
-- type Word8
------------------------------------------------------------------------

-- Word8 is represented in the same way as Word. Operations may assume
-- and must ensure that it holds only values from its logical range.

data {-# CTYPE "HsWord8" #-} Word8 = W8# Word#
-- ^ 8-bit unsigned integer type

-- See GHC.Classes#matching_overloaded_methods_in_rules
-- | @since 2.01
instance Eq Word8 where
    (==) = eqWord8
    (/=) = neWord8

eqWord8, neWord8 :: Word8 -> Word8 -> Bool
eqWord8 (W8# x) (W8# y) = isTrue# (x `eqWord#` y)
neWord8 (W8# x) (W8# y) = isTrue# (x `neWord#` y)
{-# INLINE [1] eqWord8 #-}
{-# INLINE [1] neWord8 #-}

-- | @since 2.01
instance Ord Word8 where
    (<)  = ltWord8
    (<=) = leWord8
    (>=) = geWord8
    (>)  = gtWord8

{-# INLINE [1] gtWord8 #-}
{-# INLINE [1] geWord8 #-}
{-# INLINE [1] ltWord8 #-}
{-# INLINE [1] leWord8 #-}
gtWord8, geWord8, ltWord8, leWord8 :: Word8 -> Word8 -> Bool
(W8# x) `gtWord8` (W8# y) = isTrue# (x `gtWord#` y)
(W8# x) `geWord8` (W8# y) = isTrue# (x `geWord#` y)
(W8# x) `ltWord8` (W8# y) = isTrue# (x `ltWord#` y)
(W8# x) `leWord8` (W8# y) = isTrue# (x `leWord#` y)

-- | @since 2.01
instance Show Word8 where
    showsPrec p x = showsPrec p (fromIntegral x :: Int)

-- | @since 2.01
instance Num Word8 where
    (W8# x#) + (W8# y#)    = W8# (narrow8Word# (x# `plusWord#` y#))
    (W8# x#) - (W8# y#)    = W8# (narrow8Word# (x# `minusWord#` y#))
    (W8# x#) * (W8# y#)    = W8# (narrow8Word# (x# `timesWord#` y#))
    negate (W8# x#)        = W8# (narrow8Word# (int2Word# (negateInt# (word2Int# x#))))
    abs x                  = x
    signum 0               = 0
    signum _               = 1
    fromInteger i          = W8# (narrow8Word# (integerToWord# i))

-- | @since 2.01
instance Real Word8 where
    toRational x = toInteger x % 1

-- | @since 2.01
instance Enum Word8 where
    succ x
        | x /= maxBound = x + 1
        | otherwise     = succError "Word8"
    pred x
        | x /= minBound = x - 1
        | otherwise     = predError "Word8"
    toEnum i@(I# i#)
        | i >= 0 && i <= fromIntegral (maxBound::Word8)
                        = W8# (int2Word# i#)
        | otherwise     = toEnumError "Word8" i (minBound::Word8, maxBound::Word8)
    fromEnum (W8# x#)   = I# (word2Int# x#)
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFrom #-}
    enumFrom            = boundedEnumFrom
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThen #-}
    enumFromThen        = boundedEnumFromThen

-- | @since 2.01
instance Integral Word8 where
    quot    (W8# x#) y@(W8# y#)
        | y /= 0                  = W8# (x# `quotWord#` y#)
        | otherwise               = divZeroError
    rem     (W8# x#) y@(W8# y#)
        | y /= 0                  = W8# (x# `remWord#` y#)
        | otherwise               = divZeroError
    div     (W8# x#) y@(W8# y#)
        | y /= 0                  = W8# (x# `quotWord#` y#)
        | otherwise               = divZeroError
    mod     (W8# x#) y@(W8# y#)
        | y /= 0                  = W8# (x# `remWord#` y#)
        | otherwise               = divZeroError
    quotRem (W8# x#) y@(W8# y#)
        | y /= 0                  = case x# `quotRemWord#` y# of
                                    (# q, r #) ->
                                        (W8# q, W8# r)
        | otherwise               = divZeroError
    divMod  (W8# x#) y@(W8# y#)
        | y /= 0                  = (W8# (x# `quotWord#` y#), W8# (x# `remWord#` y#))
        | otherwise               = divZeroError
    toInteger (W8# x#)            = IS (word2Int# x#)

-- | @since 2.01
instance Bounded Word8 where
    minBound = 0
    maxBound = 0xFF

-- | @since 2.01
instance Ix Word8 where
    range (m,n)         = [m..n]
    unsafeIndex (m,_) i = fromIntegral (i - m)
    inRange (m,n) i     = m <= i && i <= n

-- | @since 2.01
instance Bits Word8 where
    {-# INLINE shift #-}
    {-# INLINE bit #-}
    {-# INLINE testBit #-}
    {-# INLINE popCount #-}

    (W8# x#) .&.   (W8# y#)   = W8# (x# `and#` y#)
    (W8# x#) .|.   (W8# y#)   = W8# (x# `or#`  y#)
    (W8# x#) `xor` (W8# y#)   = W8# (x# `xor#` y#)
    complement (W8# x#)       = W8# (x# `xor#` mb#)
        where !(W8# mb#) = maxBound
    (W8# x#) `shift` (I# i#)
        | isTrue# (i# >=# 0#) = W8# (narrow8Word# (x# `shiftL#` i#))
        | otherwise           = W8# (x# `shiftRL#` negateInt# i#)
    (W8# x#) `shiftL`       (I# i#)
        | isTrue# (i# >=# 0#) = W8# (narrow8Word# (x# `shiftL#` i#))
        | otherwise           = overflowError
    (W8# x#) `unsafeShiftL` (I# i#) =
        W8# (narrow8Word# (x# `uncheckedShiftL#` i#))
    (W8# x#) `shiftR`       (I# i#)
        | isTrue# (i# >=# 0#) = W8# (x# `shiftRL#` i#)
        | otherwise           = overflowError
    (W8# x#) `unsafeShiftR` (I# i#) = W8# (x# `uncheckedShiftRL#` i#)
    (W8# x#) `rotate`       (I# i#)
        | isTrue# (i'# ==# 0#) = W8# x#
        | otherwise  = W8# (narrow8Word# ((x# `uncheckedShiftL#` i'#) `or#`
                                          (x# `uncheckedShiftRL#` (8# -# i'#))))
        where
        !i'# = word2Int# (int2Word# i# `and#` 7##)
    bitSizeMaybe i            = Just (finiteBitSize i)
    bitSize i                 = finiteBitSize i
    isSigned _                = False
    popCount (W8# x#)         = I# (word2Int# (popCnt8# x#))
    bit                       = bitDefault
    testBit                   = testBitDefault

-- | @since 4.6.0.0
instance FiniteBits Word8 where
    {-# INLINE countLeadingZeros #-}
    {-# INLINE countTrailingZeros #-}
    finiteBitSize _ = 8
    countLeadingZeros  (W8# x#) = I# (word2Int# (clz8# x#))
    countTrailingZeros (W8# x#) = I# (word2Int# (ctz8# x#))

{-# RULES
"fromIntegral/Word8->Word8"   fromIntegral = id :: Word8 -> Word8
"fromIntegral/Word8->Integer" fromIntegral = toInteger :: Word8 -> Integer
"fromIntegral/a->Word8"       fromIntegral = \x -> case fromIntegral x of W# x# -> W8# (narrow8Word# x#)
"fromIntegral/Word8->a"       fromIntegral = \(W8# x#) -> fromIntegral (W# x#)
  #-}

{-# RULES
"properFraction/Float->(Word8,Float)"
    properFraction = \x ->
                      case properFraction x of {
                        (n, y) -> ((fromIntegral :: Int -> Word8) n, y :: Float) }
"truncate/Float->Word8"
    truncate = (fromIntegral :: Int -> Word8) . (truncate :: Float -> Int)
"floor/Float->Word8"
    floor    = (fromIntegral :: Int -> Word8) . (floor :: Float -> Int)
"ceiling/Float->Word8"
    ceiling  = (fromIntegral :: Int -> Word8) . (ceiling :: Float -> Int)
"round/Float->Word8"
    round    = (fromIntegral :: Int -> Word8) . (round  :: Float -> Int)
  #-}

{-# RULES
"properFraction/Double->(Word8,Double)"
    properFraction = \x ->
                      case properFraction x of {
                        (n, y) -> ((fromIntegral :: Int -> Word8) n, y :: Double) }
"truncate/Double->Word8"
    truncate = (fromIntegral :: Int -> Word8) . (truncate :: Double -> Int)
"floor/Double->Word8"
    floor    = (fromIntegral :: Int -> Word8) . (floor :: Double -> Int)
"ceiling/Double->Word8"
    ceiling  = (fromIntegral :: Int -> Word8) . (ceiling :: Double -> Int)
"round/Double->Word8"
    round    = (fromIntegral :: Int -> Word8) . (round  :: Double -> Int)
  #-}

------------------------------------------------------------------------
-- type Word16
------------------------------------------------------------------------

-- Word16 is represented in the same way as Word. Operations may assume
-- and must ensure that it holds only values from its logical range.

data {-# CTYPE "HsWord16" #-} Word16 = W16# Word#
-- ^ 16-bit unsigned integer type

-- See GHC.Classes#matching_overloaded_methods_in_rules
-- | @since 2.01
instance Eq Word16 where
    (==) = eqWord16
    (/=) = neWord16

eqWord16, neWord16 :: Word16 -> Word16 -> Bool
eqWord16 (W16# x) (W16# y) = isTrue# (x `eqWord#` y)
neWord16 (W16# x) (W16# y) = isTrue# (x `neWord#` y)
{-# INLINE [1] eqWord16 #-}
{-# INLINE [1] neWord16 #-}

-- | @since 2.01
instance Ord Word16 where
    (<)  = ltWord16
    (<=) = leWord16
    (>=) = geWord16
    (>)  = gtWord16

{-# INLINE [1] gtWord16 #-}
{-# INLINE [1] geWord16 #-}
{-# INLINE [1] ltWord16 #-}
{-# INLINE [1] leWord16 #-}
gtWord16, geWord16, ltWord16, leWord16 :: Word16 -> Word16 -> Bool
(W16# x) `gtWord16` (W16# y) = isTrue# (x `gtWord#` y)
(W16# x) `geWord16` (W16# y) = isTrue# (x `geWord#` y)
(W16# x) `ltWord16` (W16# y) = isTrue# (x `ltWord#` y)
(W16# x) `leWord16` (W16# y) = isTrue# (x `leWord#` y)

-- | @since 2.01
instance Show Word16 where
    showsPrec p x = showsPrec p (fromIntegral x :: Int)

-- | @since 2.01
instance Num Word16 where
    (W16# x#) + (W16# y#)  = W16# (narrow16Word# (x# `plusWord#` y#))
    (W16# x#) - (W16# y#)  = W16# (narrow16Word# (x# `minusWord#` y#))
    (W16# x#) * (W16# y#)  = W16# (narrow16Word# (x# `timesWord#` y#))
    negate (W16# x#)       = W16# (narrow16Word# (int2Word# (negateInt# (word2Int# x#))))
    abs x                  = x
    signum 0               = 0
    signum _               = 1
    fromInteger i          = W16# (narrow16Word# (integerToWord# i))

-- | @since 2.01
instance Real Word16 where
    toRational x = toInteger x % 1

-- | @since 2.01
instance Enum Word16 where
    succ x
        | x /= maxBound = x + 1
        | otherwise     = succError "Word16"
    pred x
        | x /= minBound = x - 1
        | otherwise     = predError "Word16"
    toEnum i@(I# i#)
        | i >= 0 && i <= fromIntegral (maxBound::Word16)
                        = W16# (int2Word# i#)
        | otherwise     = toEnumError "Word16" i (minBound::Word16, maxBound::Word16)
    fromEnum (W16# x#)  = I# (word2Int# x#)
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFrom #-}
    enumFrom            = boundedEnumFrom
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThen #-}
    enumFromThen        = boundedEnumFromThen

-- | @since 2.01
instance Integral Word16 where
    quot    (W16# x#) y@(W16# y#)
        | y /= 0                    = W16# (x# `quotWord#` y#)
        | otherwise                 = divZeroError
    rem     (W16# x#) y@(W16# y#)
        | y /= 0                    = W16# (x# `remWord#` y#)
        | otherwise                 = divZeroError
    div     (W16# x#) y@(W16# y#)
        | y /= 0                    = W16# (x# `quotWord#` y#)
        | otherwise                 = divZeroError
    mod     (W16# x#) y@(W16# y#)
        | y /= 0                    = W16# (x# `remWord#` y#)
        | otherwise                 = divZeroError
    quotRem (W16# x#) y@(W16# y#)
        | y /= 0                  = case x# `quotRemWord#` y# of
                                    (# q, r #) ->
                                        (W16# q, W16# r)
        | otherwise                 = divZeroError
    divMod  (W16# x#) y@(W16# y#)
        | y /= 0                    = (W16# (x# `quotWord#` y#), W16# (x# `remWord#` y#))
        | otherwise                 = divZeroError
    toInteger (W16# x#)             = IS (word2Int# x#)

-- | @since 2.01
instance Bounded Word16 where
    minBound = 0
    maxBound = 0xFFFF

-- | @since 2.01
instance Ix Word16 where
    range (m,n)         = [m..n]
    unsafeIndex (m,_) i = fromIntegral (i - m)
    inRange (m,n) i     = m <= i && i <= n

-- | @since 2.01
instance Bits Word16 where
    {-# INLINE shift #-}
    {-# INLINE bit #-}
    {-# INLINE testBit #-}
    {-# INLINE popCount #-}

    (W16# x#) .&.   (W16# y#)  = W16# (x# `and#` y#)
    (W16# x#) .|.   (W16# y#)  = W16# (x# `or#`  y#)
    (W16# x#) `xor` (W16# y#)  = W16# (x# `xor#` y#)
    complement (W16# x#)       = W16# (x# `xor#` mb#)
        where !(W16# mb#) = maxBound
    (W16# x#) `shift` (I# i#)
        | isTrue# (i# >=# 0#)  = W16# (narrow16Word# (x# `shiftL#` i#))
        | otherwise            = W16# (x# `shiftRL#` negateInt# i#)
    (W16# x#) `shiftL`       (I# i#)
        | isTrue# (i# >=# 0#)  = W16# (narrow16Word# (x# `shiftL#` i#))
        | otherwise            = overflowError
    (W16# x#) `unsafeShiftL` (I# i#) =
        W16# (narrow16Word# (x# `uncheckedShiftL#` i#))
    (W16# x#) `shiftR`       (I# i#)
        | isTrue# (i# >=# 0#)  = W16# (x# `shiftRL#` i#)
        | otherwise            = overflowError
    (W16# x#) `unsafeShiftR` (I# i#) = W16# (x# `uncheckedShiftRL#` i#)
    (W16# x#) `rotate`       (I# i#)
        | isTrue# (i'# ==# 0#) = W16# x#
        | otherwise  = W16# (narrow16Word# ((x# `uncheckedShiftL#` i'#) `or#`
                                            (x# `uncheckedShiftRL#` (16# -# i'#))))
        where
        !i'# = word2Int# (int2Word# i# `and#` 15##)
    bitSizeMaybe i            = Just (finiteBitSize i)
    bitSize i                 = finiteBitSize i
    isSigned _                = False
    popCount (W16# x#)        = I# (word2Int# (popCnt16# x#))
    bit                       = bitDefault
    testBit                   = testBitDefault

-- | @since 4.6.0.0
instance FiniteBits Word16 where
    {-# INLINE countLeadingZeros #-}
    {-# INLINE countTrailingZeros #-}
    finiteBitSize _ = 16
    countLeadingZeros  (W16# x#) = I# (word2Int# (clz16# x#))
    countTrailingZeros (W16# x#) = I# (word2Int# (ctz16# x#))

-- | Reverse order of bytes in 'Word16'.
--
-- @since 4.7.0.0
byteSwap16 :: Word16 -> Word16
byteSwap16 (W16# w#) = W16# (narrow16Word# (byteSwap16# w#))

{-# RULES
"fromIntegral/Word8->Word16"   fromIntegral = \(W8# x#) -> W16# x#
"fromIntegral/Word16->Word16"  fromIntegral = id :: Word16 -> Word16
"fromIntegral/Word16->Integer" fromIntegral = toInteger :: Word16 -> Integer
"fromIntegral/a->Word16"       fromIntegral = \x -> case fromIntegral x of W# x# -> W16# (narrow16Word# x#)
"fromIntegral/Word16->a"       fromIntegral = \(W16# x#) -> fromIntegral (W# x#)
  #-}

{-# RULES
"properFraction/Float->(Word16,Float)"
    properFraction = \x ->
                      case properFraction x of {
                        (n, y) -> ((fromIntegral :: Int -> Word16) n, y :: Float) }
"truncate/Float->Word16"
    truncate = (fromIntegral :: Int -> Word16) . (truncate :: Float -> Int)
"floor/Float->Word16"
    floor    = (fromIntegral :: Int -> Word16) . (floor :: Float -> Int)
"ceiling/Float->Word16"
    ceiling  = (fromIntegral :: Int -> Word16) . (ceiling :: Float -> Int)
"round/Float->Word16"
    round    = (fromIntegral :: Int -> Word16) . (round  :: Float -> Int)
  #-}

{-# RULES
"properFraction/Double->(Word16,Double)"
    properFraction = \x ->
                      case properFraction x of {
                        (n, y) -> ((fromIntegral :: Int -> Word16) n, y :: Double) }
"truncate/Double->Word16"
    truncate = (fromIntegral :: Int -> Word16) . (truncate :: Double -> Int)
"floor/Double->Word16"
    floor    = (fromIntegral :: Int -> Word16) . (floor :: Double -> Int)
"ceiling/Double->Word16"
    ceiling  = (fromIntegral :: Int -> Word16) . (ceiling :: Double -> Int)
"round/Double->Word16"
    round    = (fromIntegral :: Int -> Word16) . (round  :: Double -> Int)
  #-}

------------------------------------------------------------------------
-- type Word32
------------------------------------------------------------------------

-- Word32 is represented in the same way as Word.
#if WORD_SIZE_IN_BITS > 32
-- Operations may assume and must ensure that it holds only values
-- from its logical range.

-- We can use rewrite rules for the RealFrac methods

{-# RULES
"properFraction/Float->(Word32,Float)"
    properFraction = \x ->
                      case properFraction x of {
                        (n, y) -> ((fromIntegral :: Int -> Word32) n, y :: Float) }
"truncate/Float->Word32"
    truncate = (fromIntegral :: Int -> Word32) . (truncate :: Float -> Int)
"floor/Float->Word32"
    floor    = (fromIntegral :: Int -> Word32) . (floor :: Float -> Int)
"ceiling/Float->Word32"
    ceiling  = (fromIntegral :: Int -> Word32) . (ceiling :: Float -> Int)
"round/Float->Word32"
    round    = (fromIntegral :: Int -> Word32) . (round  :: Float -> Int)
  #-}

{-# RULES
"properFraction/Double->(Word32,Double)"
    properFraction = \x ->
                      case properFraction x of {
                        (n, y) -> ((fromIntegral :: Int -> Word32) n, y :: Double) }
"truncate/Double->Word32"
    truncate = (fromIntegral :: Int -> Word32) . (truncate :: Double -> Int)
"floor/Double->Word32"
    floor    = (fromIntegral :: Int -> Word32) . (floor :: Double -> Int)
"ceiling/Double->Word32"
    ceiling  = (fromIntegral :: Int -> Word32) . (ceiling :: Double -> Int)
"round/Double->Word32"
    round    = (fromIntegral :: Int -> Word32) . (round  :: Double -> Int)
  #-}

#endif

data {-# CTYPE "HsWord32" #-} Word32 = W32# Word#
-- ^ 32-bit unsigned integer type

-- See GHC.Classes#matching_overloaded_methods_in_rules
-- | @since 2.01
instance Eq Word32 where
    (==) = eqWord32
    (/=) = neWord32

eqWord32, neWord32 :: Word32 -> Word32 -> Bool
eqWord32 (W32# x) (W32# y) = isTrue# (x `eqWord#` y)
neWord32 (W32# x) (W32# y) = isTrue# (x `neWord#` y)
{-# INLINE [1] eqWord32 #-}
{-# INLINE [1] neWord32 #-}

-- | @since 2.01
instance Ord Word32 where
    (<)  = ltWord32
    (<=) = leWord32
    (>=) = geWord32
    (>)  = gtWord32

{-# INLINE [1] gtWord32 #-}
{-# INLINE [1] geWord32 #-}
{-# INLINE [1] ltWord32 #-}
{-# INLINE [1] leWord32 #-}
gtWord32, geWord32, ltWord32, leWord32 :: Word32 -> Word32 -> Bool
(W32# x) `gtWord32` (W32# y) = isTrue# (x `gtWord#` y)
(W32# x) `geWord32` (W32# y) = isTrue# (x `geWord#` y)
(W32# x) `ltWord32` (W32# y) = isTrue# (x `ltWord#` y)
(W32# x) `leWord32` (W32# y) = isTrue# (x `leWord#` y)

-- | @since 2.01
instance Num Word32 where
    (W32# x#) + (W32# y#)  = W32# (narrow32Word# (x# `plusWord#` y#))
    (W32# x#) - (W32# y#)  = W32# (narrow32Word# (x# `minusWord#` y#))
    (W32# x#) * (W32# y#)  = W32# (narrow32Word# (x# `timesWord#` y#))
    negate (W32# x#)       = W32# (narrow32Word# (int2Word# (negateInt# (word2Int# x#))))
    abs x                  = x
    signum 0               = 0
    signum _               = 1
    fromInteger i          = W32# (narrow32Word# (integerToWord# i))

-- | @since 2.01
instance Enum Word32 where
    succ x
        | x /= maxBound = x + 1
        | otherwise     = succError "Word32"
    pred x
        | x /= minBound = x - 1
        | otherwise     = predError "Word32"
    toEnum i@(I# i#)
        | i >= 0
#if WORD_SIZE_IN_BITS > 32
          && i <= fromIntegral (maxBound::Word32)
#endif
                        = W32# (int2Word# i#)
        | otherwise     = toEnumError "Word32" i (minBound::Word32, maxBound::Word32)
#if WORD_SIZE_IN_BITS == 32
    fromEnum x@(W32# x#)
        | x <= fromIntegral (maxBound::Int)
                        = I# (word2Int# x#)
        | otherwise     = fromEnumError "Word32" x
    enumFrom            = integralEnumFrom
    enumFromThen        = integralEnumFromThen
    enumFromTo          = integralEnumFromTo
    enumFromThenTo      = integralEnumFromThenTo
#else
    fromEnum (W32# x#)  = I# (word2Int# x#)
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFrom #-}
    enumFrom            = boundedEnumFrom
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThen #-}
    enumFromThen        = boundedEnumFromThen
#endif

-- | @since 2.01
instance Integral Word32 where
    quot    (W32# x#) y@(W32# y#)
        | y /= 0                    = W32# (x# `quotWord#` y#)
        | otherwise                 = divZeroError
    rem     (W32# x#) y@(W32# y#)
        | y /= 0                    = W32# (x# `remWord#` y#)
        | otherwise                 = divZeroError
    div     (W32# x#) y@(W32# y#)
        | y /= 0                    = W32# (x# `quotWord#` y#)
        | otherwise                 = divZeroError
    mod     (W32# x#) y@(W32# y#)
        | y /= 0                    = W32# (x# `remWord#` y#)
        | otherwise                 = divZeroError
    quotRem (W32# x#) y@(W32# y#)
        | y /= 0                  = case x# `quotRemWord#` y# of
                                    (# q, r #) ->
                                        (W32# q, W32# r)
        | otherwise                 = divZeroError
    divMod  (W32# x#) y@(W32# y#)
        | y /= 0                    = (W32# (x# `quotWord#` y#), W32# (x# `remWord#` y#))
        | otherwise                 = divZeroError
    toInteger (W32# x#)
#if WORD_SIZE_IN_BITS == 32
        | isTrue# (i# >=# 0#)       = IS i#
        | otherwise                 = integerFromWord# x#
        where
        !i# = word2Int# x#
#else
                                    = IS (word2Int# x#)
#endif

-- | @since 2.01
instance Bits Word32 where
    {-# INLINE shift #-}
    {-# INLINE bit #-}
    {-# INLINE testBit #-}
    {-# INLINE popCount #-}

    (W32# x#) .&.   (W32# y#)  = W32# (x# `and#` y#)
    (W32# x#) .|.   (W32# y#)  = W32# (x# `or#`  y#)
    (W32# x#) `xor` (W32# y#)  = W32# (x# `xor#` y#)
    complement (W32# x#)       = W32# (x# `xor#` mb#)
        where !(W32# mb#) = maxBound
    (W32# x#) `shift` (I# i#)
        | isTrue# (i# >=# 0#)  = W32# (narrow32Word# (x# `shiftL#` i#))
        | otherwise            = W32# (x# `shiftRL#` negateInt# i#)
    (W32# x#) `shiftL`       (I# i#)
        | isTrue# (i# >=# 0#)  = W32# (narrow32Word# (x# `shiftL#` i#))
        | otherwise            = overflowError
    (W32# x#) `unsafeShiftL` (I# i#) =
        W32# (narrow32Word# (x# `uncheckedShiftL#` i#))
    (W32# x#) `shiftR`       (I# i#)
        | isTrue# (i# >=# 0#)  = W32# (x# `shiftRL#` i#)
        | otherwise            = overflowError
    (W32# x#) `unsafeShiftR` (I# i#) = W32# (x# `uncheckedShiftRL#` i#)
    (W32# x#) `rotate`       (I# i#)
        | isTrue# (i'# ==# 0#) = W32# x#
        | otherwise   = W32# (narrow32Word# ((x# `uncheckedShiftL#` i'#) `or#`
                                            (x# `uncheckedShiftRL#` (32# -# i'#))))
        where
        !i'# = word2Int# (int2Word# i# `and#` 31##)
    bitSizeMaybe i            = Just (finiteBitSize i)
    bitSize i                 = finiteBitSize i
    isSigned _                = False
    popCount (W32# x#)        = I# (word2Int# (popCnt32# x#))
    bit                       = bitDefault
    testBit                   = testBitDefault

-- | @since 4.6.0.0
instance FiniteBits Word32 where
    {-# INLINE countLeadingZeros #-}
    {-# INLINE countTrailingZeros #-}
    finiteBitSize _ = 32
    countLeadingZeros  (W32# x#) = I# (word2Int# (clz32# x#))
    countTrailingZeros (W32# x#) = I# (word2Int# (ctz32# x#))

{-# RULES
"fromIntegral/Word8->Word32"   fromIntegral = \(W8# x#) -> W32# x#
"fromIntegral/Word16->Word32"  fromIntegral = \(W16# x#) -> W32# x#
"fromIntegral/Word32->Word32"  fromIntegral = id :: Word32 -> Word32
"fromIntegral/Word32->Integer" fromIntegral = toInteger :: Word32 -> Integer
"fromIntegral/a->Word32"       fromIntegral = \x -> case fromIntegral x of W# x# -> W32# (narrow32Word# x#)
"fromIntegral/Word32->a"       fromIntegral = \(W32# x#) -> fromIntegral (W# x#)
  #-}

-- | @since 2.01
instance Show Word32 where
#if WORD_SIZE_IN_BITS < 33
    showsPrec p x = showsPrec p (toInteger x)
#else
    showsPrec p x = showsPrec p (fromIntegral x :: Int)
#endif


-- | @since 2.01
instance Real Word32 where
    toRational x = toInteger x % 1

-- | @since 2.01
instance Bounded Word32 where
    minBound = 0
    maxBound = 0xFFFFFFFF

-- | @since 2.01
instance Ix Word32 where
    range (m,n)         = [m..n]
    unsafeIndex (m,_) i = fromIntegral (i - m)
    inRange (m,n) i     = m <= i && i <= n

-- | Reverse order of bytes in 'Word32'.
--
-- @since 4.7.0.0
byteSwap32 :: Word32 -> Word32
byteSwap32 (W32# w#) = W32# (narrow32Word# (byteSwap32# w#))

------------------------------------------------------------------------
-- type Word64
------------------------------------------------------------------------

#if WORD_SIZE_IN_BITS < 64

data {-# CTYPE "HsWord64" #-} Word64 = W64# Word64#
-- ^ 64-bit unsigned integer type

-- See GHC.Classes#matching_overloaded_methods_in_rules
-- | @since 2.01
instance Eq Word64 where
    (==) = eqWord64
    (/=) = neWord64

eqWord64, neWord64 :: Word64 -> Word64 -> Bool
eqWord64 (W64# x) (W64# y) = isTrue# (x `eqWord64#` y)
neWord64 (W64# x) (W64# y) = isTrue# (x `neWord64#` y)
{-# INLINE [1] eqWord64 #-}
{-# INLINE [1] neWord64 #-}

-- | @since 2.01
instance Ord Word64 where
    (<)  = ltWord64
    (<=) = leWord64
    (>=) = geWord64
    (>)  = gtWord64

{-# INLINE [1] gtWord64 #-}
{-# INLINE [1] geWord64 #-}
{-# INLINE [1] ltWord64 #-}
{-# INLINE [1] leWord64 #-}
gtWord64, geWord64, ltWord64, leWord64 :: Word64 -> Word64 -> Bool
(W64# x) `gtWord64` (W64# y) = isTrue# (x `gtWord64#` y)
(W64# x) `geWord64` (W64# y) = isTrue# (x `geWord64#` y)
(W64# x) `ltWord64` (W64# y) = isTrue# (x `ltWord64#` y)
(W64# x) `leWord64` (W64# y) = isTrue# (x `leWord64#` y)

-- | @since 2.01
instance Num Word64 where
    (W64# x#) + (W64# y#)  = W64# (int64ToWord64# (word64ToInt64# x# `plusInt64#` word64ToInt64# y#))
    (W64# x#) - (W64# y#)  = W64# (int64ToWord64# (word64ToInt64# x# `minusInt64#` word64ToInt64# y#))
    (W64# x#) * (W64# y#)  = W64# (int64ToWord64# (word64ToInt64# x# `timesInt64#` word64ToInt64# y#))
    negate (W64# x#)       = W64# (int64ToWord64# (negateInt64# (word64ToInt64# x#)))
    abs x                  = x
    signum 0               = 0
    signum _               = 1
    fromInteger i          = W64# (integerToWord64# i)

-- | @since 2.01
instance Enum Word64 where
    succ x
        | x /= maxBound = x + 1
        | otherwise     = succError "Word64"
    pred x
        | x /= minBound = x - 1
        | otherwise     = predError "Word64"
    toEnum i@(I# i#)
        | i >= 0        = W64# (wordToWord64# (int2Word# i#))
        | otherwise     = toEnumError "Word64" i (minBound::Word64, maxBound::Word64)
    fromEnum x@(W64# x#)
        | x <= fromIntegral (maxBound::Int)
                        = I# (word2Int# (word64ToWord# x#))
        | otherwise     = fromEnumError "Word64" x
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFrom #-}
    enumFrom            = integralEnumFrom
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThen #-}
    enumFromThen        = integralEnumFromThen
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromTo #-}
    enumFromTo          = integralEnumFromTo
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThenTo #-}
    enumFromThenTo      = integralEnumFromThenTo

-- | @since 2.01
instance Integral Word64 where
    quot    (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `quotWord64#` y#)
        | otherwise                 = divZeroError
    rem     (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `remWord64#` y#)
        | otherwise                 = divZeroError
    div     (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `quotWord64#` y#)
        | otherwise                 = divZeroError
    mod     (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `remWord64#` y#)
        | otherwise                 = divZeroError
    quotRem (W64# x#) y@(W64# y#)
        | y /= 0                    = (W64# (x# `quotWord64#` y#), W64# (x# `remWord64#` y#))
        | otherwise                 = divZeroError
    divMod  (W64# x#) y@(W64# y#)
        | y /= 0                    = (W64# (x# `quotWord64#` y#), W64# (x# `remWord64#` y#))
        | otherwise                 = divZeroError
    toInteger (W64# x#)             = integerFromWord64# x#

-- | @since 2.01
instance Bits Word64 where
    {-# INLINE shift #-}
    {-# INLINE bit #-}
    {-# INLINE testBit #-}
    {-# INLINE popCount #-}

    (W64# x#) .&.   (W64# y#)  = W64# (x# `and64#` y#)
    (W64# x#) .|.   (W64# y#)  = W64# (x# `or64#`  y#)
    (W64# x#) `xor` (W64# y#)  = W64# (x# `xor64#` y#)
    complement (W64# x#)       = W64# (not64# x#)
    (W64# x#) `shift` (I# i#)
        | isTrue# (i# >=# 0#)  = W64# (x# `shiftL64#` i#)
        | otherwise            = W64# (x# `shiftRL64#` negateInt# i#)
    (W64# x#) `shiftL`       (I# i#)
        | isTrue# (i# >=# 0#)  = W64# (x# `shiftL64#` i#)
        | otherwise            = overflowError
    (W64# x#) `unsafeShiftL` (I# i#) = W64# (x# `uncheckedShiftL64#` i#)
    (W64# x#) `shiftR`       (I# i#)
        | isTrue# (i# >=# 0#)  = W64# (x# `shiftRL64#` i#)
        | otherwise            = overflowError
    (W64# x#) `unsafeShiftR` (I# i#) = W64# (x# `uncheckedShiftRL64#` i#)
    (W64# x#) `rotate` (I# i#)
        | isTrue# (i'# ==# 0#) = W64# x#
        | otherwise            = W64# ((x# `uncheckedShiftL64#` i'#) `or64#`
                                       (x# `uncheckedShiftRL64#` (64# -# i'#)))
        where
        !i'# = word2Int# (int2Word# i# `and#` 63##)
    bitSizeMaybe i            = Just (finiteBitSize i)
    bitSize i                 = finiteBitSize i
    isSigned _                = False
    popCount (W64# x#)        = I# (word2Int# (popCnt64# x#))
    bit                       = bitDefault
    testBit                   = testBitDefault

-- give the 64-bit shift operations the same treatment as the 32-bit
-- ones (see GHC.Base), namely we wrap them in tests to catch the
-- cases when we're shifting more than 64 bits to avoid unspecified
-- behaviour in the C shift operations.

shiftL64#, shiftRL64# :: Word64# -> Int# -> Word64#

a `shiftL64#` b  | isTrue# (b >=# 64#) = wordToWord64# 0##
                 | otherwise           = a `uncheckedShiftL64#` b

a `shiftRL64#` b | isTrue# (b >=# 64#) = wordToWord64# 0##
                 | otherwise           = a `uncheckedShiftRL64#` b

{-# RULES
"fromIntegral/Int->Word64"    fromIntegral = \(I#   x#) -> W64# (int64ToWord64# (intToInt64# x#))
"fromIntegral/Word->Word64"   fromIntegral = \(W#   x#) -> W64# (wordToWord64# x#)
"fromIntegral/Word64->Int"    fromIntegral = \(W64# x#) -> I#   (word2Int# (word64ToWord# x#))
"fromIntegral/Word64->Word"   fromIntegral = \(W64# x#) -> W#   (word64ToWord# x#)
"fromIntegral/Word64->Word64" fromIntegral = id :: Word64 -> Word64
  #-}

#else

-- Word64 is represented in the same way as Word.
-- Operations may assume and must ensure that it holds only values
-- from its logical range.

data {-# CTYPE "HsWord64" #-} Word64 = W64# Word#
-- ^ 64-bit unsigned integer type

-- See GHC.Classes#matching_overloaded_methods_in_rules
-- | @since 2.01
instance Eq Word64 where
    (==) = eqWord64
    (/=) = neWord64

eqWord64, neWord64 :: Word64 -> Word64 -> Bool
eqWord64 (W64# x) (W64# y) = isTrue# (x `eqWord#` y)
neWord64 (W64# x) (W64# y) = isTrue# (x `neWord#` y)
{-# INLINE [1] eqWord64 #-}
{-# INLINE [1] neWord64 #-}

-- | @since 2.01
instance Ord Word64 where
    (<)  = ltWord64
    (<=) = leWord64
    (>=) = geWord64
    (>)  = gtWord64

{-# INLINE [1] gtWord64 #-}
{-# INLINE [1] geWord64 #-}
{-# INLINE [1] ltWord64 #-}
{-# INLINE [1] leWord64 #-}
gtWord64, geWord64, ltWord64, leWord64 :: Word64 -> Word64 -> Bool
(W64# x) `gtWord64` (W64# y) = isTrue# (x `gtWord#` y)
(W64# x) `geWord64` (W64# y) = isTrue# (x `geWord#` y)
(W64# x) `ltWord64` (W64# y) = isTrue# (x `ltWord#` y)
(W64# x) `leWord64` (W64# y) = isTrue# (x `leWord#` y)

-- | @since 2.01
instance Num Word64 where
    (W64# x#) + (W64# y#)  = W64# (x# `plusWord#` y#)
    (W64# x#) - (W64# y#)  = W64# (x# `minusWord#` y#)
    (W64# x#) * (W64# y#)  = W64# (x# `timesWord#` y#)
    negate (W64# x#)       = W64# (int2Word# (negateInt# (word2Int# x#)))
    abs x                  = x
    signum 0               = 0
    signum _               = 1
    fromInteger i          = W64# (integerToWord# i)

-- | @since 2.01
instance Enum Word64 where
    succ x
        | x /= maxBound = x + 1
        | otherwise     = succError "Word64"
    pred x
        | x /= minBound = x - 1
        | otherwise     = predError "Word64"
    toEnum i@(I# i#)
        | i >= 0        = W64# (int2Word# i#)
        | otherwise     = toEnumError "Word64" i (minBound::Word64, maxBound::Word64)
    fromEnum x@(W64# x#)
        | x <= fromIntegral (maxBound::Int)
                        = I# (word2Int# x#)
        | otherwise     = fromEnumError "Word64" x

#if WORD_SIZE_IN_BITS < 64
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFrom #-}
    enumFrom            = integralEnumFrom
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThen #-}
    enumFromThen        = integralEnumFromThen
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromTo #-}
    enumFromTo          = integralEnumFromTo
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINE enumFromThenTo #-}
    enumFromThenTo      = integralEnumFromThenTo
#else
    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINABLE enumFrom #-}
    enumFrom w
        = map wordToWord64
        $ enumFrom (word64ToWord w)

    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINABLE enumFromThen #-}
    enumFromThen w s
        = map wordToWord64
        $ enumFromThen (word64ToWord w) (word64ToWord s)

    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINABLE enumFromTo #-}
    enumFromTo w1 w2
        = map wordToWord64
        $ enumFromTo (word64ToWord w1) (word64ToWord w2)

    -- See Note [Stable Unfolding for list producers] in GHC.Enum
    {-# INLINABLE enumFromThenTo #-}
    enumFromThenTo w1 s w2
        = map wordToWord64
        $ enumFromThenTo (word64ToWord w1) (word64ToWord s) (word64ToWord w2)

word64ToWord :: Word64 -> Word
word64ToWord (W64# w#) = (W# w#)

wordToWord64 :: Word -> Word64
wordToWord64 (W# w#) = (W64# w#)
#endif


-- | @since 2.01
instance Integral Word64 where
    quot    (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `quotWord#` y#)
        | otherwise                 = divZeroError
    rem     (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `remWord#` y#)
        | otherwise                 = divZeroError
    div     (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `quotWord#` y#)
        | otherwise                 = divZeroError
    mod     (W64# x#) y@(W64# y#)
        | y /= 0                    = W64# (x# `remWord#` y#)
        | otherwise                 = divZeroError
    quotRem (W64# x#) y@(W64# y#)
        | y /= 0                  = case x# `quotRemWord#` y# of
                                    (# q, r #) ->
                                        (W64# q, W64# r)
        | otherwise                 = divZeroError
    divMod  (W64# x#) y@(W64# y#)
        | y /= 0                    = (W64# (x# `quotWord#` y#), W64# (x# `remWord#` y#))
        | otherwise                 = divZeroError
    toInteger (W64# x#)
        | isTrue# (i# >=# 0#)       = IS i#
        | otherwise                 = integerFromWord# x#
        where
        !i# = word2Int# x#

-- | @since 2.01
instance Bits Word64 where
    {-# INLINE shift #-}
    {-# INLINE bit #-}
    {-# INLINE testBit #-}
    {-# INLINE popCount #-}

    (W64# x#) .&.   (W64# y#)  = W64# (x# `and#` y#)
    (W64# x#) .|.   (W64# y#)  = W64# (x# `or#`  y#)
    (W64# x#) `xor` (W64# y#)  = W64# (x# `xor#` y#)
    complement (W64# x#)       = W64# (x# `xor#` mb#)
        where !(W64# mb#) = maxBound
    (W64# x#) `shift` (I# i#)
        | isTrue# (i# >=# 0#)  = W64# (x# `shiftL#` i#)
        | otherwise            = W64# (x# `shiftRL#` negateInt# i#)
    (W64# x#) `shiftL`       (I# i#)
        | isTrue# (i# >=# 0#)  = W64# (x# `shiftL#` i#)
        | otherwise            = overflowError
    (W64# x#) `unsafeShiftL` (I# i#) = W64# (x# `uncheckedShiftL#` i#)
    (W64# x#) `shiftR`       (I# i#)
        | isTrue# (i# >=# 0#)  = W64# (x# `shiftRL#` i#)
        | otherwise            = overflowError
    (W64# x#) `unsafeShiftR` (I# i#) = W64# (x# `uncheckedShiftRL#` i#)
    (W64# x#) `rotate` (I# i#)
        | isTrue# (i'# ==# 0#) = W64# x#
        | otherwise            = W64# ((x# `uncheckedShiftL#` i'#) `or#`
                                       (x# `uncheckedShiftRL#` (64# -# i'#)))
        where
        !i'# = word2Int# (int2Word# i# `and#` 63##)
    bitSizeMaybe i            = Just (finiteBitSize i)
    bitSize i                 = finiteBitSize i
    isSigned _                = False
    popCount (W64# x#)        = I# (word2Int# (popCnt64# x#))
    bit                       = bitDefault
    testBit                   = testBitDefault

{-# RULES
"fromIntegral/a->Word64" fromIntegral = \x -> case fromIntegral x of W# x# -> W64# x#
"fromIntegral/Word64->a" fromIntegral = \(W64# x#) -> fromIntegral (W# x#)
  #-}

uncheckedShiftL64# :: Word# -> Int# -> Word#
uncheckedShiftL64#  = uncheckedShiftL#

uncheckedShiftRL64# :: Word# -> Int# -> Word#
uncheckedShiftRL64# = uncheckedShiftRL#

#endif

-- | @since 4.6.0.0
instance FiniteBits Word64 where
    {-# INLINE countLeadingZeros #-}
    {-# INLINE countTrailingZeros #-}
    finiteBitSize _ = 64
    countLeadingZeros  (W64# x#) = I# (word2Int# (clz64# x#))
    countTrailingZeros (W64# x#) = I# (word2Int# (ctz64# x#))

-- | @since 2.01
instance Show Word64 where
    showsPrec p x = showsPrec p (toInteger x)

-- | @since 2.01
instance Real Word64 where
    toRational x = toInteger x % 1

-- | @since 2.01
instance Bounded Word64 where
    minBound = 0
    maxBound = 0xFFFFFFFFFFFFFFFF

-- | @since 2.01
instance Ix Word64 where
    range (m,n)         = [m..n]
    unsafeIndex (m,_) i = fromIntegral (i - m)
    inRange (m,n) i     = m <= i && i <= n

-- | Reverse order of bytes in 'Word64'.
--
-- @since 4.7.0.0
#if WORD_SIZE_IN_BITS < 64
byteSwap64 :: Word64 -> Word64
byteSwap64 (W64# w#) = W64# (byteSwap64# w#)
#else
byteSwap64 :: Word64 -> Word64
byteSwap64 (W64# w#) = W64# (byteSwap# w#)
#endif

-- | Reverse the order of the bits in a 'Word8'.
--
-- @since 4.12.0.0
bitReverse8 :: Word8 -> Word8
bitReverse8 (W8# w#) = W8# (narrow8Word# (bitReverse8# w#))

-- | Reverse the order of the bits in a 'Word16'.
--
-- @since 4.12.0.0
bitReverse16 :: Word16 -> Word16
bitReverse16 (W16# w#) = W16# (narrow16Word# (bitReverse16# w#))

-- | Reverse the order of the bits in a 'Word32'.
--
-- @since 4.12.0.0
bitReverse32 :: Word32 -> Word32
bitReverse32 (W32# w#) = W32# (narrow32Word# (bitReverse32# w#))

-- | Reverse the order of the bits in a 'Word64'.
--
-- @since 4.12.0.0
#if WORD_SIZE_IN_BITS < 64
bitReverse64 :: Word64 -> Word64
bitReverse64 (W64# w#) = W64# (bitReverse64# w#)
#else
bitReverse64 :: Word64 -> Word64
bitReverse64 (W64# w#) = W64# (bitReverse# w#)
#endif

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

{-# RULES
"fromIntegral/Natural->Word8"
    fromIntegral = (fromIntegral :: Word -> Word8)  . naturalToWord
"fromIntegral/Natural->Word16"
    fromIntegral = (fromIntegral :: Word -> Word16) . naturalToWord
"fromIntegral/Natural->Word32"
    fromIntegral = (fromIntegral :: Word -> Word32) . naturalToWord
  #-}

{-# RULES
"fromIntegral/Word8->Natural"
    fromIntegral = naturalFromWord . (fromIntegral :: Word8  -> Word)
"fromIntegral/Word16->Natural"
    fromIntegral = naturalFromWord . (fromIntegral :: Word16 -> Word)
"fromIntegral/Word32->Natural"
    fromIntegral = naturalFromWord . (fromIntegral :: Word32 -> Word)
  #-}

#if WORD_SIZE_IN_BITS == 64
-- these RULES are valid for Word==Word64
{-# RULES
"fromIntegral/Natural->Word64"
    fromIntegral = (fromIntegral :: Word -> Word64) . naturalToWord
"fromIntegral/Word64->Natural"
    fromIntegral = naturalFromWord . (fromIntegral :: Word64 -> Word)
  #-}
#endif