{-# LANGUAGE CPP #-}
#if __GLASGOW_HASKELL__ >= 702
{-# LANGUAGE Trustworthy #-}
#endif
module System.Random.SplitMix32 (
SMGen,
nextWord32,
nextWord64,
nextTwoWord32,
nextInt,
nextDouble,
nextFloat,
nextInteger,
splitSMGen,
bitmaskWithRejection32,
bitmaskWithRejection32',
bitmaskWithRejection64,
bitmaskWithRejection64',
mkSMGen,
initSMGen,
newSMGen,
seedSMGen,
seedSMGen',
unseedSMGen,
) where
import Data.Bits (complement, shiftL, shiftR, xor, (.&.), (.|.))
import Data.Bits.Compat
(countLeadingZeros, finiteBitSize, popCount, zeroBits)
import Data.IORef (IORef, atomicModifyIORef, newIORef)
import Data.Word (Word32, Word64)
import System.IO.Unsafe (unsafePerformIO)
import System.Random.SplitMix.Init
#if defined(__HUGS__) || !MIN_VERSION_base(4,8,0)
import Data.Word (Word)
#endif
#ifndef __HUGS__
import Control.DeepSeq (NFData (..))
#endif
data SMGen = SMGen {-# UNPACK #-} !Word32 {-# UNPACK #-} !Word32
deriving Int -> SMGen -> ShowS
[SMGen] -> ShowS
SMGen -> String
(Int -> SMGen -> ShowS)
-> (SMGen -> String) -> ([SMGen] -> ShowS) -> Show SMGen
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> SMGen -> ShowS
showsPrec :: Int -> SMGen -> ShowS
$cshow :: SMGen -> String
show :: SMGen -> String
$cshowList :: [SMGen] -> ShowS
showList :: [SMGen] -> ShowS
Show
#ifndef __HUGS__
instance NFData SMGen where
rnf :: SMGen -> ()
rnf (SMGen Word32
_ Word32
_) = ()
#endif
instance Read SMGen where
readsPrec :: Int -> ReadS SMGen
readsPrec Int
d String
r = Bool -> ReadS SMGen -> ReadS SMGen
forall a. Bool -> ReadS a -> ReadS a
readParen (Int
d Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
10) (\String
r0 ->
[ (Word32 -> Word32 -> SMGen
SMGen Word32
seed Word32
gamma, String
r3)
| (String
"SMGen", String
r1) <- ReadS String
lex String
r0
, (Word32
seed, String
r2) <- Int -> ReadS Word32
forall a. Read a => Int -> ReadS a
readsPrec Int
11 String
r1
, (Word32
gamma, String
r3) <- Int -> ReadS Word32
forall a. Read a => Int -> ReadS a
readsPrec Int
11 String
r2
, Word32 -> Bool
forall a. Integral a => a -> Bool
odd Word32
gamma
]) String
r
nextWord32 :: SMGen -> (Word32, SMGen)
nextWord32 :: SMGen -> (Word32, SMGen)
nextWord32 (SMGen Word32
seed Word32
gamma) = (Word32 -> Word32
mix32 Word32
seed', Word32 -> Word32 -> SMGen
SMGen Word32
seed' Word32
gamma)
where
seed' :: Word32
seed' = Word32
seed Word32 -> Word32 -> Word32
forall a. Num a => a -> a -> a
+ Word32
gamma
nextWord64 :: SMGen -> (Word64, SMGen)
nextWord64 :: SMGen -> (Word64, SMGen)
nextWord64 SMGen
s0 = (Word32 -> Word64
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word32
w0 Word64 -> Int -> Word64
forall a. Bits a => a -> Int -> a
`shiftL` Int
32 Word64 -> Word64 -> Word64
forall a. Bits a => a -> a -> a
.|. Word32 -> Word64
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word32
w1, SMGen
s2)
where
(Word32
w0, SMGen
s1) = SMGen -> (Word32, SMGen)
nextWord32 SMGen
s0
(Word32
w1, SMGen
s2) = SMGen -> (Word32, SMGen)
nextWord32 SMGen
s1
nextTwoWord32 :: SMGen -> (Word32, Word32, SMGen)
nextTwoWord32 :: SMGen -> (Word32, Word32, SMGen)
nextTwoWord32 SMGen
s0 = (Word32
w0, Word32
w1, SMGen
s2) where
(Word32
w0, SMGen
s1) = SMGen -> (Word32, SMGen)
nextWord32 SMGen
s0
(Word32
w1, SMGen
s2) = SMGen -> (Word32, SMGen)
nextWord32 SMGen
s1
nextInt :: SMGen -> (Int, SMGen)
nextInt :: SMGen -> (Int, SMGen)
nextInt SMGen
g | Bool
isBigInt = (Int, SMGen)
int64
| Bool
otherwise = (Int, SMGen)
int32
where
int32 :: (Int, SMGen)
int32 = case SMGen -> (Word32, SMGen)
nextWord32 SMGen
g of
(Word32
w, SMGen
g') -> (Word32 -> Int
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word32
w, SMGen
g')
int64 :: (Int, SMGen)
int64 = case SMGen -> (Word64, SMGen)
nextWord64 SMGen
g of
(Word64
w, SMGen
g') -> (Word64 -> Int
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word64
w, SMGen
g')
isBigInt :: Bool
isBigInt :: Bool
isBigInt = Int -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize (Int
forall a. HasCallStack => a
undefined :: Int) Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
32
nextDouble :: SMGen -> (Double, SMGen)
nextDouble :: SMGen -> (Double, SMGen)
nextDouble SMGen
g = case SMGen -> (Word64, SMGen)
nextWord64 SMGen
g of
(Word64
w64, SMGen
g') -> (Word64 -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Word64
w64 Word64 -> Int -> Word64
forall a. Bits a => a -> Int -> a
`shiftR` Int
11) Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
doubleUlp, SMGen
g')
nextFloat :: SMGen -> (Float, SMGen)
nextFloat :: SMGen -> (Float, SMGen)
nextFloat SMGen
g = case SMGen -> (Word32, SMGen)
nextWord32 SMGen
g of
(Word32
w32, SMGen
g') -> (Word32 -> Float
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Word32
w32 Word32 -> Int -> Word32
forall a. Bits a => a -> Int -> a
`shiftR` Int
8) Float -> Float -> Float
forall a. Num a => a -> a -> a
* Float
floatUlp, SMGen
g')
nextInteger :: Integer -> Integer -> SMGen -> (Integer, SMGen)
nextInteger :: Integer -> Integer -> SMGen -> (Integer, SMGen)
nextInteger Integer
lo Integer
hi SMGen
g = case Integer -> Integer -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Integer
lo Integer
hi of
Ordering
LT -> let (Integer
i, SMGen
g') = Integer -> SMGen -> (Integer, SMGen)
nextInteger' (Integer
hi Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
- Integer
lo) SMGen
g in (Integer
i Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
+ Integer
lo, SMGen
g')
Ordering
EQ -> (Integer
lo, SMGen
g)
Ordering
GT -> let (Integer
i, SMGen
g') = Integer -> SMGen -> (Integer, SMGen)
nextInteger' (Integer
lo Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
- Integer
hi) SMGen
g in (Integer
i Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
+ Integer
hi, SMGen
g')
nextInteger' :: Integer -> SMGen -> (Integer, SMGen)
nextInteger' :: Integer -> SMGen -> (Integer, SMGen)
nextInteger' Integer
range = SMGen -> (Integer, SMGen)
loop
where
leadMask :: Word32
restDigits :: Word
(Word32
leadMask, Word
restDigits) = Word -> Integer -> (Word32, Word)
go Word
0 Integer
range where
go :: Word -> Integer -> (Word32, Word)
go :: Word -> Integer -> (Word32, Word)
go Word
n Integer
x | Integer
x Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
< Integer
two32 = (Word32 -> Word32
forall a. Bits a => a -> a
complement Word32
forall a. Bits a => a
zeroBits Word32 -> Int -> Word32
forall a. Bits a => a -> Int -> a
`shiftR` Word32 -> Int
forall b. FiniteBits b => b -> Int
countLeadingZeros (Integer -> Word32
forall a. Num a => Integer -> a
fromInteger Integer
x :: Word32), Word
n)
| Bool
otherwise = Word -> Integer -> (Word32, Word)
go (Word
n Word -> Word -> Word
forall a. Num a => a -> a -> a
+ Word
1) (Integer
x Integer -> Int -> Integer
forall a. Bits a => a -> Int -> a
`shiftR` Int
32)
generate :: SMGen -> (Integer, SMGen)
generate :: SMGen -> (Integer, SMGen)
generate SMGen
g0 =
let (Word32
x, SMGen
g') = SMGen -> (Word32, SMGen)
nextWord32 SMGen
g0
x' :: Word32
x' = Word32
x Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
.&. Word32
leadMask
in Integer -> Word -> SMGen -> (Integer, SMGen)
go (Word32 -> Integer
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word32
x') Word
restDigits SMGen
g'
where
go :: Integer -> Word -> SMGen -> (Integer, SMGen)
go :: Integer -> Word -> SMGen -> (Integer, SMGen)
go Integer
acc Word
0 SMGen
g = Integer
acc Integer -> (Integer, SMGen) -> (Integer, SMGen)
forall a b. a -> b -> b
`seq` (Integer
acc, SMGen
g)
go Integer
acc Word
n SMGen
g =
let (Word32
x, SMGen
g') = SMGen -> (Word32, SMGen)
nextWord32 SMGen
g
in Integer -> Word -> SMGen -> (Integer, SMGen)
go (Integer
acc Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
* Integer
two32 Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
+ Word32 -> Integer
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word32
x) (Word
n Word -> Word -> Word
forall a. Num a => a -> a -> a
- Word
1) SMGen
g'
loop :: SMGen -> (Integer, SMGen)
loop SMGen
g = let (Integer
x, SMGen
g') = SMGen -> (Integer, SMGen)
generate SMGen
g
in if Integer
x Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
> Integer
range
then SMGen -> (Integer, SMGen)
loop SMGen
g'
else (Integer
x, SMGen
g')
two32 :: Integer
two32 :: Integer
two32 = Integer
2 Integer -> Int -> Integer
forall a b. (Num a, Integral b) => a -> b -> a
^ (Int
32 :: Int)
splitSMGen :: SMGen -> (SMGen, SMGen)
splitSMGen :: SMGen -> (SMGen, SMGen)
splitSMGen (SMGen Word32
seed Word32
gamma) =
(Word32 -> Word32 -> SMGen
SMGen Word32
seed'' Word32
gamma, Word32 -> Word32 -> SMGen
SMGen (Word32 -> Word32
mix32 Word32
seed') (Word32 -> Word32
mixGamma Word32
seed''))
where
seed' :: Word32
seed' = Word32
seed Word32 -> Word32 -> Word32
forall a. Num a => a -> a -> a
+ Word32
gamma
seed'' :: Word32
seed'' = Word32
seed' Word32 -> Word32 -> Word32
forall a. Num a => a -> a -> a
+ Word32
gamma
goldenGamma :: Word32
goldenGamma :: Word32
goldenGamma = Word32
0x9e3779b9
floatUlp :: Float
floatUlp :: Float
floatUlp = Float
1.0 Float -> Float -> Float
forall a. Fractional a => a -> a -> a
/ Word32 -> Float
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Word32
1 Word32 -> Int -> Word32
forall a. Bits a => a -> Int -> a
`shiftL` Int
24 :: Word32)
doubleUlp :: Double
doubleUlp :: Double
doubleUlp = Double
1.0 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Word64 -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Word64
1 Word64 -> Int -> Word64
forall a. Bits a => a -> Int -> a
`shiftL` Int
53 :: Word64)
#if defined(__GHCJS__) && defined(OPTIMISED_MIX32)
foreign import javascript unsafe
"var x0 = $1 ^ $1 >>> 16; var x1 = x0 & 0xffff; var x2 = (((x0 >>> 16 & 0xffff) * 0x0000ca6b + x1 * 0x000085eb & 0xffff) << 16) + x1 * 0x0000ca6b; var x3 = x2 ^ x2 >>> 13; var x4 = x3 & 0xffff; var x5 = (((x3 >>> 16 & 0xffff) * 0x0000ae35 + x4 * 0x0000c2b2 & 0xffff) << 16) + x4 * 0x0000ae35; $r = (x5 ^ x5 >>> 16) | 0;"
mix32 :: Word32 -> Word32
foreign import javascript unsafe
"var x0 = $1 ^ $1 >>> 16; var x1 = x0 & 0xffff; var x2 = (((x0 >>> 16 & 0xffff) * 0x00006ccb + x1 * 0x000069ad & 0xffff) << 16) + x1 * 0x00006ccb; var x3 = x2 ^ x2 >>> 13; var x4 = x3 & 0xffff; var x5 = (((x3 >>> 16 & 0xffff) * 0x0000b5b3 + x4 * 0x0000cd9a & 0xffff) << 16) + x4 * 0x0000b5b3; $r = (x5 ^ x5 >>> 16) | 0;"
mix32variant13 :: Word32 -> Word32
#else
mix32 :: Word32 -> Word32
mix32 :: Word32 -> Word32
mix32 Word32
z0 =
let z1 :: Word32
z1 = Int -> Word32 -> Word32 -> Word32
shiftXorMultiply Int
16 Word32
0x85ebca6b Word32
z0
z2 :: Word32
z2 = Int -> Word32 -> Word32 -> Word32
shiftXorMultiply Int
13 Word32
0xc2b2ae35 Word32
z1
z3 :: Word32
z3 = Int -> Word32 -> Word32
shiftXor Int
16 Word32
z2
in Word32
z3
mix32variant13 :: Word32 -> Word32
mix32variant13 :: Word32 -> Word32
mix32variant13 Word32
z0 =
let z1 :: Word32
z1 = Int -> Word32 -> Word32 -> Word32
shiftXorMultiply Int
16 Word32
0x69ad6ccb Word32
z0
z2 :: Word32
z2 = Int -> Word32 -> Word32 -> Word32
shiftXorMultiply Int
13 Word32
0xcd9ab5b3 Word32
z1
z3 :: Word32
z3 = Int -> Word32 -> Word32
shiftXor Int
16 Word32
z2
in Word32
z3
shiftXor :: Int -> Word32 -> Word32
shiftXor :: Int -> Word32 -> Word32
shiftXor Int
n Word32
w = Word32
w Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
`xor` (Word32
w Word32 -> Int -> Word32
forall a. Bits a => a -> Int -> a
`shiftR` Int
n)
shiftXorMultiply :: Int -> Word32 -> Word32 -> Word32
shiftXorMultiply :: Int -> Word32 -> Word32 -> Word32
shiftXorMultiply Int
n Word32
k Word32
w = Int -> Word32 -> Word32
shiftXor Int
n Word32
w Word32 -> Word32 -> Word32
forall a. Num a => a -> a -> a
* Word32
k
#endif
mixGamma :: Word32 -> Word32
mixGamma :: Word32 -> Word32
mixGamma Word32
z0 =
let z1 :: Word32
z1 = Word32 -> Word32
mix32variant13 Word32
z0 Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
.|. Word32
1
n :: Int
n = Word32 -> Int
forall a. Bits a => a -> Int
popCount (Word32
z1 Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
`xor` (Word32
z1 Word32 -> Int -> Word32
forall a. Bits a => a -> Int -> a
`shiftR` Int
1))
in if Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
12
then Word32
z1
else Word32
z1 Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
`xor` Word32
0xaaaaaaaa
bitmaskWithRejection32 :: Word32 -> SMGen -> (Word32, SMGen)
bitmaskWithRejection32 :: Word32 -> SMGen -> (Word32, SMGen)
bitmaskWithRejection32 Word32
0 = String -> SMGen -> (Word32, SMGen)
forall a. HasCallStack => String -> a
error String
"bitmaskWithRejection32 0"
bitmaskWithRejection32 Word32
n = Word32 -> SMGen -> (Word32, SMGen)
bitmaskWithRejection32' (Word32
n Word32 -> Word32 -> Word32
forall a. Num a => a -> a -> a
- Word32
1)
{-# INLINEABLE bitmaskWithRejection32 #-}
bitmaskWithRejection64 :: Word64 -> SMGen -> (Word64, SMGen)
bitmaskWithRejection64 :: Word64 -> SMGen -> (Word64, SMGen)
bitmaskWithRejection64 Word64
0 = String -> SMGen -> (Word64, SMGen)
forall a. HasCallStack => String -> a
error String
"bitmaskWithRejection64 0"
bitmaskWithRejection64 Word64
n = Word64 -> SMGen -> (Word64, SMGen)
bitmaskWithRejection64' (Word64
n Word64 -> Word64 -> Word64
forall a. Num a => a -> a -> a
- Word64
1)
{-# INLINEABLE bitmaskWithRejection64 #-}
bitmaskWithRejection32' :: Word32 -> SMGen -> (Word32, SMGen)
bitmaskWithRejection32' :: Word32 -> SMGen -> (Word32, SMGen)
bitmaskWithRejection32' Word32
range = SMGen -> (Word32, SMGen)
go where
mask :: Word32
mask = Word32 -> Word32
forall a. Bits a => a -> a
complement Word32
forall a. Bits a => a
zeroBits Word32 -> Int -> Word32
forall a. Bits a => a -> Int -> a
`shiftR` Word32 -> Int
forall b. FiniteBits b => b -> Int
countLeadingZeros (Word32
range Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
.|. Word32
1)
go :: SMGen -> (Word32, SMGen)
go SMGen
g = let (Word32
x, SMGen
g') = SMGen -> (Word32, SMGen)
nextWord32 SMGen
g
x' :: Word32
x' = Word32
x Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
.&. Word32
mask
in if Word32
x' Word32 -> Word32 -> Bool
forall a. Ord a => a -> a -> Bool
> Word32
range
then SMGen -> (Word32, SMGen)
go SMGen
g'
else (Word32
x', SMGen
g')
{-# INLINEABLE bitmaskWithRejection32' #-}
bitmaskWithRejection64' :: Word64 -> SMGen -> (Word64, SMGen)
bitmaskWithRejection64' :: Word64 -> SMGen -> (Word64, SMGen)
bitmaskWithRejection64' Word64
range = SMGen -> (Word64, SMGen)
go where
mask :: Word64
mask = Word64 -> Word64
forall a. Bits a => a -> a
complement Word64
forall a. Bits a => a
zeroBits Word64 -> Int -> Word64
forall a. Bits a => a -> Int -> a
`shiftR` Word64 -> Int
forall b. FiniteBits b => b -> Int
countLeadingZeros (Word64
range Word64 -> Word64 -> Word64
forall a. Bits a => a -> a -> a
.|. Word64
1)
go :: SMGen -> (Word64, SMGen)
go SMGen
g = let (Word64
x, SMGen
g') = SMGen -> (Word64, SMGen)
nextWord64 SMGen
g
x' :: Word64
x' = Word64
x Word64 -> Word64 -> Word64
forall a. Bits a => a -> a -> a
.&. Word64
mask
in if Word64
x' Word64 -> Word64 -> Bool
forall a. Ord a => a -> a -> Bool
> Word64
range
then SMGen -> (Word64, SMGen)
go SMGen
g'
else (Word64
x', SMGen
g')
{-# INLINEABLE bitmaskWithRejection64' #-}
seedSMGen
:: Word32
-> Word32
-> SMGen
seedSMGen :: Word32 -> Word32 -> SMGen
seedSMGen Word32
seed Word32
gamma = Word32 -> Word32 -> SMGen
SMGen Word32
seed (Word32
gamma Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
.|. Word32
1)
seedSMGen' :: (Word32, Word32) -> SMGen
seedSMGen' :: (Word32, Word32) -> SMGen
seedSMGen' = (Word32 -> Word32 -> SMGen) -> (Word32, Word32) -> SMGen
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Word32 -> Word32 -> SMGen
seedSMGen
unseedSMGen :: SMGen -> (Word32, Word32)
unseedSMGen :: SMGen -> (Word32, Word32)
unseedSMGen (SMGen Word32
seed Word32
gamma) = (Word32
seed, Word32
gamma)
mkSMGen :: Word32 -> SMGen
mkSMGen :: Word32 -> SMGen
mkSMGen Word32
s = Word32 -> Word32 -> SMGen
SMGen (Word32 -> Word32
mix32 Word32
s) (Word32 -> Word32
mixGamma (Word32
s Word32 -> Word32 -> Word32
forall a. Num a => a -> a -> a
+ Word32
goldenGamma))
initSMGen :: IO SMGen
initSMGen :: IO SMGen
initSMGen = (Word32 -> SMGen) -> IO Word32 -> IO SMGen
forall a b. (a -> b) -> IO a -> IO b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Word32 -> SMGen
mkSMGen IO Word32
initialSeed'
newSMGen :: IO SMGen
newSMGen :: IO SMGen
newSMGen = IORef SMGen -> (SMGen -> (SMGen, SMGen)) -> IO SMGen
forall a b. IORef a -> (a -> (a, b)) -> IO b
atomicModifyIORef IORef SMGen
theSMGen SMGen -> (SMGen, SMGen)
splitSMGen
theSMGen :: IORef SMGen
theSMGen :: IORef SMGen
theSMGen = IO (IORef SMGen) -> IORef SMGen
forall a. IO a -> a
unsafePerformIO (IO (IORef SMGen) -> IORef SMGen)
-> IO (IORef SMGen) -> IORef SMGen
forall a b. (a -> b) -> a -> b
$ IO SMGen
initSMGen IO SMGen -> (SMGen -> IO (IORef SMGen)) -> IO (IORef SMGen)
forall a b. IO a -> (a -> IO b) -> IO b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= SMGen -> IO (IORef SMGen)
forall a. a -> IO (IORef a)
newIORef
{-# NOINLINE theSMGen #-}
initialSeed' :: IO Word32
initialSeed' :: IO Word32
initialSeed' = do
Word64
w64 <- IO Word64
initialSeed
Word32 -> IO Word32
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (Word64 -> Word32
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Word64 -> Int -> Word64
forall a. Bits a => a -> Int -> a
shiftR Word64
w64 Int
32) Word32 -> Word32 -> Word32
forall a. Bits a => a -> a -> a
`xor` Word64 -> Word32
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word64
w64)