%
-% (c) The AQUA Project, Glasgow University, 1994-1996
+% (c) The AQUA Project, Glasgow University, 1997
%
-
\section[Word]{Module @Word@}
-This code is largely copied from the Hugs library of the same name.
+GHC implementation of the standard Hugs/GHC @Word@
+interface, types and operations over unsigned, sized
+quantities.
\begin{code}
{-# OPTIONS -fno-implicit-prelude #-}
-
module Word
- ( Word8
- , Word16
- , Word32
- , Word64
+ ( Word8 -- all abstract.
+ , Word16 -- instances: Eq, Ord
+ , Word32 -- Num, Bounded, Real,
+ , Word64 -- Integral, Ix, Enum,
+ -- Read, Show, Bits,
+ -- CCallable, CReturnable
+ -- (last two
+
, word8ToWord32 -- :: Word8 -> Word32
, word32ToWord8 -- :: Word32 -> Word8
, word16ToWord32 -- :: Word16 -> Word32
import PrelNum
import PrelRead
import Ix
-import Error
+import GHCerr ( error )
import Bits
import GHC
+import CCall
-----------------------------------------------------------------------------
-- The "official" coercion functions
intToWord32 (I# x) = W32# (int2Word# x)
word32ToInt (W32# x) = I# (word2Int# x)
+\end{code}
------------------------------------------------------------------------------
--- Word8
------------------------------------------------------------------------------
-
-newtype Word8 = W8 Word32
+\subsection[Word8]{The @Word8@ interface}
-word8ToWord32 (W8 x) = x .&. 0xff
-word32ToWord8 = W8
+The byte type @Word8@ is represented in the Haskell
+heap by boxing up a 32-bit quantity, @Word#@. An invariant
+for this representation is that the higher 24 bits are
+*always* zeroed out. A consequence of this is that
+operations that could possibly overflow have to mask
+out the top three bytes before building the resulting @Word8@.
-instance Eq Word8 where (==) = binop (==)
-instance Ord Word8 where compare = binop compare
+\begin{code}
+data Word8 = W8# Word#
+
+instance CCallable Word8
+instance CReturnable Word8
+
+word8ToWord32 (W8# x) = W32# x
+word32ToWord8 (W32# x) = W8# (wordToWord8# x)
+
+-- mask out upper three bytes.
+intToWord8# :: Int# -> Word#
+intToWord8# i# = (int2Word# i#) `and#` (int2Word# 0xff#)
+
+wordToWord8# :: Word# -> Word#
+wordToWord8# w# = w# `and#` (int2Word# 0xff#)
+
+instance Eq Word8 where
+ (W8# x) == (W8# y) = x `eqWord#` y
+ (W8# x) /= (W8# y) = x `neWord#` y
+
+instance Ord Word8 where
+ compare (W8# x#) (W8# y#) = compareWord# x# y#
+ (<) (W8# x) (W8# y) = x `ltWord#` y
+ (<=) (W8# x) (W8# y) = x `leWord#` y
+ (>=) (W8# x) (W8# y) = x `geWord#` y
+ (>) (W8# x) (W8# y) = x `gtWord#` y
+ max x@(W8# x#) y@(W8# y#) =
+ case (compareWord# x# y#) of { LT -> y ; EQ -> x ; GT -> x }
+ min x@(W8# x#) y@(W8# y#) =
+ case (compareWord# x# y#) of { LT -> x ; EQ -> x ; GT -> y }
+
+-- Helper function, used by Ord Word* instances.
+compareWord# :: Word# -> Word# -> Ordering
+compareWord# x# y#
+ | x# `ltWord#` y# = LT
+ | x# `eqWord#` y# = EQ
+ | otherwise = GT
instance Num Word8 where
- x + y = to (binop (+) x y)
- x - y = to (binop (-) x y)
- negate = to . negate . from
- x * y = to (binop (*) x y)
- abs x = x
- signum = signumReal
- fromInteger = to . integer2Word
- fromInt = intToWord8
+ (W8# x) + (W8# y) =
+ W8# (intToWord8# (word2Int# x +# word2Int# y))
+ (W8# x) - (W8# y) =
+ W8# (intToWord8# (word2Int# x -# word2Int# y))
+ (W8# x) * (W8# y) =
+ W8# (intToWord8# (word2Int# x *# word2Int# y))
+ negate w@(W8# x) =
+ if x' ==# 0#
+ then w
+ else W8# (int2Word# (0x100# -# x'))
+ where
+ x' = word2Int# x
+ abs x = x
+ signum = signumReal
+ fromInteger (J# a# s# d#) = W8# (intToWord8# (integer2Int# a# s# d#))
+ fromInt = intToWord8
instance Bounded Word8 where
- minBound = 0
- maxBound = 0xff
+ minBound = 0
+ maxBound = 0xff
instance Real Word8 where
- toRational x = toInteger x % 1
+ toRational x = toInteger x % 1
+-- Note: no need to mask results here
+-- as they cannot overflow.
instance Integral Word8 where
- x `div` y = to (binop div x y)
- x `quot` y = to (binop quot x y)
- x `rem` y = to (binop rem x y)
- x `mod` y = to (binop mod x y)
- x `quotRem` y = to2 (binop quotRem x y)
- divMod = quotRem
- toInteger = toInteger . from
- toInt = word8ToInt
+ div (W8# x) (W8# y) = W8# (x `quotWord#` y)
+ quot (W8# x) (W8# y) = W8# (x `quotWord#` y)
+ rem (W8# x) (W8# y) = W8# (x `remWord#` y)
+ mod (W8# x) (W8# y) = W8# (x `remWord#` y)
+ quotRem (W8# x) (W8# y) = (W8# (x `quotWord#` y), W8# (x `remWord#` y))
+ divMod (W8# x) (W8# y) = (W8# (x `quotWord#` y), W8# (x `remWord#` y))
+ toInteger (W8# x) = word2Integer# x
+ toInt x = word8ToInt x
instance Ix Word8 where
range (m,n) = [m..n]
index b@(m,n) i
- | inRange b i = word32ToInt (from (i - m))
- | otherwise = error "index: Index out of range"
+ | inRange b i = word8ToInt (i-m)
+ | otherwise = error (showString "Ix{Word8}.index: Index " .
+ showParen True (showsPrec 0 i) .
+ showString " out of range " $
+ showParen True (showsPrec 0 b) "")
inRange (m,n) i = m <= i && i <= n
instance Enum Word8 where
- toEnum = to . intToWord32
- fromEnum = word32ToInt . from
+ toEnum (I# i) = W8# (intToWord8# i)
+ fromEnum (W8# w) = I# (word2Int# w)
enumFrom c = map toEnum [fromEnum c .. fromEnum (maxBound::Word8)]
enumFromThen c d = map toEnum [fromEnum c, fromEnum d .. fromEnum (last::Word8)]
where last = if d < c then minBound else maxBound
instance Show Word8 where
showsPrec p = showInt
+--
+-- Word8s are represented by an (unboxed) 32-bit Word.
+-- The invariant is that the upper 24 bits are always zeroed out.
+--
instance Bits Word8 where
- x .&. y = to (binop (.&.) x y)
- x .|. y = to (binop (.|.) x y)
- x `xor` y = to (binop xor x y)
- complement = to . complement . from
- x `shift` i = to (from x `shift` i)
--- rotate
- bit = to . bit
- setBit x i = to (setBit (from x) i)
- clearBit x i = to (clearBit (from x) i)
- complementBit x i = to (complementBit (from x) i)
- testBit x i = testBit (from x) i
+ (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#` int2Word# 0xff#)
+ shift (W8# x#) i@(I# i#)
+ | i > 0 = W8# (wordToWord8# (shiftL# x# i#))
+ | otherwise = W8# (wordToWord8# (shiftRL# x# (negateInt# i#)))
+ w@(W8# x) `rotate` (I# i)
+ | i ==# 0# = w
+ | i ># 0# = W8# ((wordToWord8# (shiftL# x i')) `or#`
+ (shiftRL# (x `and#`
+ (int2Word# (0x100# -# pow2# i2)))
+ i2))
+ | otherwise = rotate w (I# (8# +# i))
+ where
+ i' = word2Int# (int2Word# i `and#` int2Word# 7#)
+ i2 = 8# -# i'
+
+ bit (I# i#)
+ | i# >=# 0# && i# <=# 7# = W8# (wordToWord8# (shiftL# (int2Word# 1#) i#))
+ | otherwise = 0 -- We'll be overbearing, for now..
+
+ setBit x i = x .|. bit i
+ clearBit x i = x .&. complement (bit i)
+ complementBit x i = x `xor` bit i
+
+ testBit (W8# x#) (I# i#)
+ | i# <# 8# && i# >=# 0# = (word2Int# (x# `and#` (shiftL# (int2Word# 1#) i#))) /=# 0#
+ | otherwise = False -- for now, this is really an error.
+
bitSize _ = 8
isSigned _ = False
------------------------------------------------------------------------------
--- Word16
------------------------------------------------------------------------------
+pow2# :: Int# -> Int#
+pow2# x# = word2Int# (shiftL# (int2Word# 1#) x#)
-newtype Word16 = W16 Word32
+\end{code}
+
+\subsection[Word16]{The @Word16@ interface}
-word16ToWord32 (W16 x) = x .&. 0xffff
-word32ToWord16 = W16
+The double byte type @Word16@ is represented in the Haskell
+heap by boxing up a machine word, @Word#@. An invariant
+for this representation is that only the lower 16 bits are
+`active', any bits above are {\em always} zeroed out.
+A consequence of this is that operations that could possibly
+overflow have to mask out anything above the lower two bytes
+before putting together the resulting @Word16@.
-instance Eq Word16 where (==) = binop (==)
-instance Ord Word16 where compare = binop compare
+\begin{code}
+data Word16 = W16# Word#
+instance CCallable Word16
+instance CReturnable Word16
+
+word16ToWord32 (W16# x) = W32# x
+word32ToWord16 (W32# x) = W16# (wordToWord16# x)
+
+-- mask out upper 16 bits.
+intToWord16# :: Int# -> Word#
+intToWord16# i# = ((int2Word# i#) `and#` (int2Word# 0xffff#))
+
+wordToWord16# :: Word# -> Word#
+wordToWord16# w# = w# `and#` (int2Word# 0xffff#)
+
+instance Eq Word16 where
+ (W16# x) == (W16# y) = x `eqWord#` y
+ (W16# x) /= (W16# y) = x `neWord#` y
+
+instance Ord Word16 where
+ compare (W16# x#) (W16# y#) = compareWord# x# y#
+ (<) (W16# x) (W16# y) = x `ltWord#` y
+ (<=) (W16# x) (W16# y) = x `leWord#` y
+ (>=) (W16# x) (W16# y) = x `geWord#` y
+ (>) (W16# x) (W16# y) = x `gtWord#` y
+ max x@(W16# x#) y@(W16# y#) =
+ case (compareWord# x# y#) of { LT -> y ; EQ -> x ; GT -> x }
+ min x@(W16# x#) y@(W16# y#) =
+ case (compareWord# x# y#) of { LT -> x ; EQ -> x ; GT -> y }
instance Num Word16 where
- x + y = to (binop (+) x y)
- x - y = to (binop (-) x y)
- negate = to . negate . from
- x * y = to (binop (*) x y)
- abs x = x
- signum = signumReal
- fromInteger = to . integer2Word
- fromInt = intToWord16
+ (W16# x) + (W16# y) =
+ W16# (intToWord16# (word2Int# x +# word2Int# y))
+ (W16# x) - (W16# y) =
+ W16# (intToWord16# (word2Int# x -# word2Int# y))
+ (W16# x) * (W16# y) =
+ W16# (intToWord16# (word2Int# x *# word2Int# y))
+ negate w@(W16# x) =
+ if x' ==# 0#
+ then w
+ else W16# (int2Word# (0x10000# -# x'))
+ where
+ x' = word2Int# x
+ abs x = x
+ signum = signumReal
+ fromInteger (J# a# s# d#) = W16# (intToWord16# (integer2Int# a# s# d#))
+ fromInt = intToWord16
instance Bounded Word16 where
- minBound = 0
- maxBound = 0xffff
+ minBound = 0
+ maxBound = 0xffff
instance Real Word16 where
toRational x = toInteger x % 1
instance Integral Word16 where
- x `div` y = to (binop div x y)
- x `quot` y = to (binop quot x y)
- x `rem` y = to (binop rem x y)
- x `mod` y = to (binop mod x y)
- x `quotRem` y = to2 (binop quotRem x y)
- divMod = quotRem
- toInteger = toInteger . from
- toInt = word16ToInt
+ div (W16# x) (W16# y) = W16# (x `quotWord#` y)
+ quot (W16# x) (W16# y) = W16# (x `quotWord#` y)
+ rem (W16# x) (W16# y) = W16# (x `remWord#` y)
+ mod (W16# x) (W16# y) = W16# (x `remWord#` y)
+ quotRem (W16# x) (W16# y) = (W16# (x `quotWord#` y), W16# (x `remWord#` y))
+ divMod (W16# x) (W16# y) = (W16# (x `quotWord#` y), W16# (x `remWord#` y))
+ toInteger (W16# x) = word2Integer# x
+ toInt x = word16ToInt x
instance Ix Word16 where
range (m,n) = [m..n]
index b@(m,n) i
- | inRange b i = word32ToInt (from (i - m))
- | otherwise = error "index: Index out of range"
+ | inRange b i = word16ToInt (i - m)
+ | otherwise = error (showString "Ix{Word16}.index: Index " .
+ showParen True (showsPrec 0 i) .
+ showString " out of range " $
+ showParen True (showsPrec 0 b) "")
inRange (m,n) i = m <= i && i <= n
instance Enum Word16 where
- toEnum = to . intToWord32
- fromEnum = word32ToInt . from
+ toEnum (I# i) = W16# (intToWord16# i)
+ fromEnum (W16# w) = I# (word2Int# w)
enumFrom c = map toEnum [fromEnum c .. fromEnum (maxBound::Word16)]
enumFromThen c d = map toEnum [fromEnum c, fromEnum d .. fromEnum (last::Word16)]
where last = if d < c then minBound else maxBound
showsPrec p = showInt
instance Bits Word16 where
- x .&. y = to (binop (.&.) x y)
- x .|. y = to (binop (.|.) x y)
- x `xor` y = to (binop xor x y)
- complement = to . complement . from
- x `shift` i = to (from x `shift` i)
--- rotate
- bit = to . bit
- setBit x i = to (setBit (from x) i)
- clearBit x i = to (clearBit (from x) i)
- complementBit x i = to (complementBit (from x) i)
- testBit x i = testBit (from x) i
+ (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#` int2Word# 0xffff#)
+ shift (W16# x#) i@(I# i#)
+ | i > 0 = W16# (wordToWord16# (shiftL# x# i#))
+ | otherwise = W16# (shiftRL# x# (negateInt# i#))
+ w@(W16# x) `rotate` (I# i)
+ | i ==# 0# = w
+ | i ># 0# = W16# ((wordToWord16# (shiftL# x i')) `or#`
+ (shiftRL# (x `and#`
+ (int2Word# (0x10000# -# pow2# i2)))
+ i2))
+ | otherwise = rotate w (I# (16# +# i'))
+ where
+ i' = word2Int# (int2Word# i `and#` int2Word# 15#)
+ i2 = 16# -# i'
+ bit (I# i#)
+ | i# >=# 0# && i# <=# 15# = W16# (shiftL# (int2Word# 1#) i#)
+ | otherwise = 0 -- We'll be overbearing, for now..
+
+ setBit x i = x .|. bit i
+ clearBit x i = x .&. complement (bit i)
+ complementBit x i = x `xor` bit i
+
+ testBit (W16# x#) (I# i#)
+ | i# <# 16# && i# >=# 0# = (word2Int# (x# `and#` (shiftL# (int2Word# 1#) i#))) /=# 0#
+ | otherwise = False -- for now, this is really an error.
+
bitSize _ = 16
isSigned _ = False
------------------------------------------------------------------------------
--- Word32
---
--- This code assumes that Word# is 32-bits - which is true on a 32-bit
--- architecture, but will need to be updated for 64-bit architectures.
------------------------------------------------------------------------------
+\end{code}
+
+\subsection[Word32]{The @Word32@ interface}
-data Word32 = W32# Word# deriving (Eq, Ord)
+The quad byte type @Word32@ is represented in the Haskell
+heap by boxing up a machine word, @Word#@. An invariant
+for this representation is that any bits above the lower
+32 are {\em always} zeroed out. A consequence of this is that
+operations that could possibly overflow have to mask
+the result before building the resulting @Word16@.
+
+\begin{code}
+data Word32 = W32# Word#
+instance CCallable Word32
+instance CReturnable Word32
+
+instance Eq Word32 where
+ (W32# x) == (W32# y) = x `eqWord#` y
+ (W32# x) /= (W32# y) = x `neWord#` y
+
+instance Ord Word32 where
+ compare (W32# x#) (W32# y#) = compareWord# x# y#
+ (<) (W32# x) (W32# y) = x `ltWord#` y
+ (<=) (W32# x) (W32# y) = x `leWord#` y
+ (>=) (W32# x) (W32# y) = x `geWord#` y
+ (>) (W32# x) (W32# y) = x `gtWord#` y
+ max x@(W32# x#) y@(W32# y#) =
+ case (compareWord# x# y#) of { LT -> y ; EQ -> x ; GT -> x }
+ min x@(W32# x#) y@(W32# y#) =
+ case (compareWord# x# y#) of { LT -> x ; EQ -> x ; GT -> y }
instance Num Word32 where
- (+) = intop (+)
- (-) = intop (-)
- (*) = intop (*)
- negate (W32# x) = W32# (int2Word# (negateInt# (word2Int# x)))
- abs x = x
- signum = signumReal
- fromInteger = integer2Word
- fromInt (I# x) = W32# (int2Word# x)
-
-{-# INLINE intop #-}
-intop op x y = intToWord32 (word32ToInt x `op` word32ToInt y)
+ (W32# x) + (W32# y) =
+ W32# (intToWord32# (word2Int# x +# word2Int# y))
+ (W32# x) - (W32# y) =
+ W32# (intToWord32# (word2Int# x -# word2Int# y))
+ (W32# x) * (W32# y) =
+ W32# (intToWord32# (word2Int# x *# word2Int# y))
+#if WORD_SIZE_IN_BYTES > 4
+ negate w@(W32# x) =
+ if x' ==# 0#
+ then w
+ else W32# (intToWord32# (0x100000000# -# x'))
+ where
+ x' = word2Int# x
+#else
+ negate (W32# x) = W32# (intToWord32# (negateInt# (word2Int# x)))
+#endif
+ abs x = x
+ signum = signumReal
+ fromInteger (J# a# s# d#) = W32# (intToWord32# (integer2Int# a# s# d#))
+ fromInt (I# x) = W32# (intToWord32# x)
+ -- ToDo: restrict fromInt{eger} range.
+
+intToWord32# :: Int# -> Word#
+wordToWord32# :: Word# -> Word#
+
+#if WORD_SIZE_IN_BYTES > 4
+intToWord32# i# = (int2Word# i#) `and#` (int2Word# 0xffffffff)
+wordToWord32# w# = w# `and#` (int2Word# 0xffffffff)
+#else
+intToWord32# i# = int2Word# i#
+wordToWord32# w# = w#
+#endif
instance Bounded Word32 where
minBound = 0
+#if WORD_SIZE_IN_BYTES > 4
+ maxBound = 0xffffffff
+#else
maxBound = minBound - 1
+#endif
instance Real Word32 where
toRational x = toInteger x % 1
instance Integral Word32 where
- x `div` y = if x > 0 && y < 0 then quotWord (x-y-1) y
- else if x < 0 && y > 0 then quotWord (x-y+1) y
- else quotWord x y
- quot = quotWord
- rem = remWord
- x `mod` y = if x > 0 && y < 0 || x < 0 && y > 0 then
- if r/=0 then r+y else 0
- else
- r
- where r = remWord x y
- a `quotRem` b = (a `quot` b, a `rem` b)
- divMod x y = (x `div` y, x `mod` y)
- toInteger (W32# x) = int2Integer# (word2Int# x)
+ div x y = quotWord32 x y
+ quot x y = quotWord32 x y
+ rem x y = remWord32 x y
+ mod x y = remWord32 x y
+ quotRem a b = (a `quotWord32` b, a `remWord32` b)
+ divMod x y = quotRem x y
+ toInteger (W32# x) = word2Integer# x
toInt (W32# x) = I# (word2Int# x)
-{-# INLINE quotWord #-}
-{-# INLINE remWord #-}
-(W32# x) `quotWord` (W32# y) = W32# (x `quotWord#` y)
-(W32# x) `remWord` (W32# y) = W32# (x `remWord#` y)
+{-# INLINE quotWord32 #-}
+{-# INLINE remWord32 #-}
+(W32# x) `quotWord32` (W32# y) = W32# (x `quotWord#` y)
+(W32# x) `remWord32` (W32# y) = W32# (x `remWord#` y)
instance Ix Word32 where
range (m,n) = [m..n]
index b@(m,n) i
| inRange b i = word32ToInt (i - m)
- | otherwise = error "index: Index out of range"
+ | otherwise = error (showString "Ix{Word32}.index: Index " .
+ showParen True (showsPrec 0 i) .
+ showString " out of range " $
+ showParen True (showsPrec 0 b) "")
inRange (m,n) i = m <= i && i <= n
instance Enum Word32 where
showsPrec p = showInt
instance Bits Word32 where
- (.&.) = wordop and#
- (.|.) = wordop or#
- xor = wordop xor#
- complement x = x `xor` maxBound
+ (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
shift (W32# x) i@(I# i#)
- | i > 0 = W32# (shiftL# x i#)
- | otherwise = W32# (shiftRA# x (negateInt# i#))
- --rotate
- bit i = 1 `shift` i
+ | i > 0 = W32# (wordToWord32# (shiftL# x i#))
+ | otherwise = W32# (shiftRL# x (negateInt# i#))
+ w@(W32# x) `rotate` (I# i)
+ | i ==# 0# = w
+ | i ># 0# = W32# ((wordToWord32# (shiftL# x i')) `or#`
+ (shiftRL# (x `and#`
+ (int2Word# (word2Int# maxBound# -# pow2# i2 +# 1#)))
+ i2))
+ | otherwise = rotate w (I# (32# +# i))
+ where
+ i' = word2Int# (int2Word# i `and#` int2Word# 31#)
+ i2 = 32# -# i'
+ (W32# maxBound#) = maxBound
+
+ bit (I# i#)
+ | i# >=# 0# && i# <=# 31# = W32# (shiftL# (int2Word# 1#) i#)
+ | otherwise = 0 -- We'll be overbearing, for now..
+
setBit x i = x .|. bit i
clearBit x i = x .&. complement (bit i)
complementBit x i = x `xor` bit i
- testBit x i = (x .&. bit i) /= 0
+
+ testBit (W32# x#) (I# i#)
+ | i# <# 32# && i# >=# 0# = (word2Int# (x# `and#` (shiftL# (int2Word# 1#) i#))) /=# 0#
+ | otherwise = False -- for now, this is really an error.
bitSize _ = 32
isSigned _ = False
-{-# INLINE wordop #-}
-wordop op (W32# x) (W32# y) = W32# (x `op` y)
+\end{code}
------------------------------------------------------------------------------
--- Word64
------------------------------------------------------------------------------
+\subsection[Word64]{The @Word64@ interface}
+\begin{code}
data Word64 = W64 {lo,hi::Word32} deriving (Eq, Ord, Bounded)
w64ToInteger W64{lo,hi} = toInteger lo + 0x100000000 * toInteger hi
-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
--- Coercions - used to make the instance declarations more uniform
------------------------------------------------------------------------------
-
-class Coerce a where
- to :: Word32 -> a
- from :: a -> Word32
-
-instance Coerce Word8 where
- from = word8ToWord32
- to = word32ToWord8
-
-instance Coerce Word16 where
- from = word16ToWord32
- to = word32ToWord16
-
-binop :: Coerce word => (Word32 -> Word32 -> a) -> (word -> word -> a)
-binop op x y = from x `op` from y
-
-to2 :: Coerce word => (Word32, Word32) -> (word, word)
-to2 (x,y) = (to x, to y)
-
-integer2Word (J# a# s# d#) = W32# (int2Word# (integer2Int# a# s# d#))
-
------------------------------------------------------------------------------
-- Code copied from the Prelude
-----------------------------------------------------------------------------