module Statistics.RandomVariate
(
Gen
, Variate(..)
, normal
, create
, initialize
, withSystemRandom
, uniformArray
) where
#if defined(__GLASGOW_HASKELL__) && !defined(__HADDOCK__)
#include "MachDeps.h"
#endif
import Control.Exception (IOException, catch)
import Control.Monad (ap, unless)
import Control.Monad.ST (ST, runST)
import Data.Array.Vector
import Data.Bits ((.&.), (.|.), xor)
import Data.IORef (atomicModifyIORef, newIORef)
import Data.Int (Int8, Int16, Int32, Int64)
import Data.Ratio ((%), numerator)
import Data.Time.Clock.POSIX (getPOSIXTime)
import Data.Word (Word, Word8, Word16, Word32, Word64)
import Foreign.Marshal.Alloc (allocaBytes)
import Foreign.Marshal.Array (peekArray)
import GHC.Base (Int(I#))
import GHC.Word (Word64(W64#), uncheckedShiftL64#, uncheckedShiftRL64#)
import Prelude hiding (catch)
import System.CPUTime (cpuTimePrecision, getCPUTime)
import System.IO (IOMode(..), hGetBuf, hPutStrLn, stderr, withBinaryFile)
import System.IO.Unsafe (unsafePerformIO)
class Variate a where
uniform :: Gen s -> ST s a
instance Variate Int8 where
uniform = f where f = uniform1 fromIntegral
instance Variate Int16 where
uniform = f where f = uniform1 fromIntegral
instance Variate Int32 where
uniform = f where f = uniform1 fromIntegral
instance Variate Int64 where
uniform = f where f = uniform2 wordsTo64Bit
instance Variate Word8 where
uniform = f where f = uniform1 fromIntegral
instance Variate Word16 where
uniform = f where f = uniform1 fromIntegral
instance Variate Word32 where
uniform = uniformWord32
instance Variate Word64 where
uniform = f where f = uniform2 wordsTo64Bit
instance Variate Bool where
uniform = f where f = uniform1 wordToBool
instance Variate Float where
uniform = f where f = uniform1 wordToFloat
instance Variate Double where
uniform = f where f = uniform2 wordsToDouble
instance Variate Int where
#if WORD_SIZE_IN_BITS < 64
uniform = f where f = uniform1 fromIntegral
#else
uniform = f where f = uniform2 wordsTo64Bit
#endif
instance Variate Word where
#if WORD_SIZE_IN_BITS < 64
uniform = f where f = uniform1 fromIntegral
#else
uniform = f where f = uniform2 wordsTo64Bit
#endif
instance Variate Integer where
uniform = f where f g = do
u <- uniform g
return $! fromIntegral (u :: Int)
instance (Variate a, Variate b) => Variate (a,b) where
uniform = f where f g = (,) `fmap` uniform g `ap` uniform g
instance (Variate a, Variate b, Variate c) => Variate (a,b,c) where
uniform = f where f g = (,,) `fmap` uniform g `ap` uniform g `ap` uniform g
instance (Variate a, Variate b, Variate c, Variate d) => Variate (a,b,c,d) where
uniform = f
where f g = (,,,) `fmap` uniform g `ap` uniform g `ap` uniform g
`ap` uniform g
wordsTo64Bit :: Integral a => Word32 -> Word32 -> a
wordsTo64Bit a b =
fromIntegral ((fromIntegral a `shiftL` 32) .|. fromIntegral b)
wordToBool :: Word32 -> Bool
wordToBool i = (i .&. 1) /= 0
wordToFloat :: Word32 -> Float
wordToFloat x = (fromIntegral i * m_inv_32) + 0.5 + m_inv_33
where m_inv_33 = 1.16415321826934814453125e-10
m_inv_32 = 2.3283064365386962890625e-10
i = fromIntegral x :: Int32
wordsToDouble :: Word32 -> Word32 -> Double
wordsToDouble x y = (fromIntegral a * m_inv_32 + (0.5 + m_inv_53) +
fromIntegral (b .&. 0xFFFFF) * m_inv_52)
where m_inv_52 = 2.220446049250313080847263336181640625e-16
m_inv_53 = 1.1102230246251565404236316680908203125e-16
m_inv_32 = 2.3283064365386962890625e-10
a = fromIntegral x :: Int32
b = fromIntegral y :: Int32
newtype Gen s = Gen (MUArr Word32 s)
ioff, coff :: Int
ioff = 256
coff = 257
create :: ST s (Gen s)
create = initialize defaultSeed
initialize :: UArr Word32 -> ST s (Gen s)
initialize seed = do
q <- newMU 258
fill q
writeMU q ioff 255
writeMU q coff 362436
return (Gen q)
where fill q = go 0 where
go i | i == 256 = return ()
| otherwise = writeMU q i s >> go (i+1)
where s | i >= fini = if fini == 0
then indexU defaultSeed i
else indexU defaultSeed i `xor`
indexU seed (i `mod` fini)
| otherwise = indexU seed i
fini = lengthU seed
withTime :: (forall s. Gen s -> ST s a) -> IO a
withTime act = do
c <- (numerator . (%cpuTimePrecision)) `fmap` getCPUTime
t <- toRational `fmap` getPOSIXTime
let n = fromIntegral (numerator t) :: Word64
seed = [fromIntegral c, fromIntegral n, fromIntegral (n `shiftR` 32)]
return . runST $ initialize (toU seed) >>= act
withSystemRandom :: (forall s. Gen s -> ST s a) -> IO a
withSystemRandom act = tryRandom `catch` \(_::IOException) -> do
seen <- atomicModifyIORef warned ((,) True)
unless seen $ do
hPutStrLn stderr ("Warning: Couldn't open " ++ show random)
hPutStrLn stderr ("Warning: using system clock for seed instead " ++
"(quality will be lower)")
withTime act
where tryRandom = do
let nbytes = 1024
ws <- allocaBytes nbytes $ \buf -> do
nread <- withBinaryFile random ReadMode $
\h -> hGetBuf h buf nbytes
peekArray (nread `div` 4) buf
return . runST $ initialize (toU ws) >>= act
random = "/dev/urandom"
warned = unsafePerformIO $ newIORef False
shiftL :: Word64 -> Int -> Word64
shiftL (W64# x#) (I# i#) = W64# (x# `uncheckedShiftL64#` i#)
shiftR :: Word64 -> Int -> Word64
shiftR (W64# x#) (I# i#) = W64# (x# `uncheckedShiftRL64#` i#)
nextIndex :: Integral a => a -> Int
nextIndex i = fromIntegral j
where j = fromIntegral (i+1) :: Word8
uniformWord32 :: Gen s -> ST s Word32
uniformWord32 (Gen q) = do
let a = 809430660 :: Word64
i <- nextIndex `fmap` readMU q ioff
c <- fromIntegral `fmap` readMU q coff
qi <- fromIntegral `fmap` readMU q i
let t = a * qi + c
t32 = fromIntegral t
writeMU q i t32
writeMU q ioff (fromIntegral i)
writeMU q coff (fromIntegral (t `shiftR` 32))
return t32
uniform1 :: (Word32 -> a) -> Gen s -> ST s a
uniform1 f gen = do
i <- uniformWord32 gen
return $! f i
uniform2 :: (Word32 -> Word32 -> a) -> Gen s -> ST s a
uniform2 f (Gen q) = do
let a = 809430660 :: Word64
i <- nextIndex `fmap` readMU q ioff
let j = nextIndex i
c <- fromIntegral `fmap` readMU q coff
qi <- fromIntegral `fmap` readMU q i
qj <- fromIntegral `fmap` readMU q j
let t = a * qi + c
t32 = fromIntegral t
c' = t `shiftR` 32
u = a * qj + c'
u32 = fromIntegral u
writeMU q i t32
writeMU q j u32
writeMU q ioff (fromIntegral j)
writeMU q coff (fromIntegral (u `shiftR` 32))
return $! f t32 u32
uniformArray :: (UA a, Variate a) => Gen s -> Int -> ST s (UArr a)
uniformArray gen n = newMU n >>= loop
where
loop mu = go 0
where go !i | i >= n = unsafeFreezeAllMU mu
| otherwise = uniform gen >>= writeMU mu i >> go (i+1)
normal :: Gen s -> ST s Double
normal gen = loop
where
loop = do
u <- (subtract 1 . (*2)) `fmap` uniform gen
ri <- uniform gen
let i = fromIntegral ((ri :: Word32) .&. 127)
bi = indexU blocks i
bj = indexU blocks (i+1)
if abs u < indexU ratios i
then return $! u * bi
else if i == 0
then normalTail (u < 0)
else do
let x = u * bi
xx = x * x
d = exp (0.5 * (bi * bi xx))
e = exp (0.5 * (bj * bj xx))
c <- uniform gen
if e + c * (d e) < 1
then return x
else loop
blocks = let f = exp (0.5 * r * r)
in (`snocU` 0) . consU (v/f) . consU r . unfoldU 126 go $ (r :*: f)
where
go (b :*: g) = JustS (h :*: (h :*: exp (0.5 * h * h)))
where h = sqrt (2 * log (v / b + g))
v = 9.91256303526217e-3
r = 3.442619855899
ratios = zipWithU (/) (tailU blocks) blocks
normalTail neg = tailing
where tailing = do
x <- ((/r) . log) `fmap` uniform gen
y <- log `fmap` uniform gen
if y * (2) < x * x
then tailing
else return $! if neg then x r else r x
defaultSeed :: UArr Word32
defaultSeed = toU [
0x7042e8b3, 0x06f7f4c5, 0x789ea382, 0x6fb15ad8, 0x54f7a879, 0x0474b184,
0xb3f8f692, 0x4114ea35, 0xb6af0230, 0xebb457d2, 0x47693630, 0x15bc0433,
0x2e1e5b18, 0xbe91129c, 0xcc0815a0, 0xb1260436, 0xd6f605b1, 0xeaadd777,
0x8f59f791, 0xe7149ed9, 0x72d49dd5, 0xd68d9ded, 0xe2a13153, 0x67648eab,
0x48d6a1a1, 0xa69ab6d7, 0x236f34ec, 0x4e717a21, 0x9d07553d, 0x6683a701,
0x19004315, 0x7b6429c5, 0x84964f99, 0x982eb292, 0x3a8be83e, 0xc1df1845,
0x3cf7b527, 0xb66a7d3f, 0xf93f6838, 0x736b1c85, 0x5f0825c1, 0x37e9904b,
0x724cd7b3, 0xfdcb7a46, 0xfdd39f52, 0x715506d5, 0xbd1b6637, 0xadabc0c0,
0x219037fc, 0x9d71b317, 0x3bec717b, 0xd4501d20, 0xd95ea1c9, 0xbe717202,
0xa254bd61, 0xd78a6c5b, 0x043a5b16, 0x0f447a25, 0xf4862a00, 0x48a48b75,
0x1e580143, 0xd5b6a11b, 0x6fb5b0a4, 0x5aaf27f9, 0x668bcd0e, 0x3fdf18fd,
0x8fdcec4a, 0x5255ce87, 0xa1b24dbf, 0x3ee4c2e1, 0x9087eea2, 0xa4131b26,
0x694531a5, 0xa143d867, 0xd9f77c03, 0xf0085918, 0x1e85071c, 0x164d1aba,
0xe61abab5, 0xb8b0c124, 0x84899697, 0xea022359, 0x0cc7fa0c, 0xd6499adf,
0x746da638, 0xd9e5d200, 0xefb3360b, 0x9426716a, 0xabddf8c2, 0xdd1ed9e4,
0x17e1d567, 0xa9a65000, 0x2f37dbc5, 0x9a4b8fd5, 0xaeb22492, 0x0ebe8845,
0xd89dd090, 0xcfbb88c6, 0xb1325561, 0x6d811d90, 0x03aa86f4, 0xbddba397,
0x0986b9ed, 0x6f4cfc69, 0xc02b43bc, 0xee916274, 0xde7d9659, 0x7d3afd93,
0xf52a7095, 0xf21a009c, 0xfd3f795e, 0x98cef25b, 0x6cb3af61, 0x6fa0e310,
0x0196d036, 0xbc198bca, 0x15b0412d, 0xde454349, 0x5719472b, 0x8244ebce,
0xee61afc6, 0xa60c9cb5, 0x1f4d1fd0, 0xe4fb3059, 0xab9ec0f9, 0x8d8b0255,
0x4e7430bf, 0x3a22aa6b, 0x27de22d3, 0x60c4b6e6, 0x0cf61eb3, 0x469a87df,
0xa4da1388, 0xf650f6aa, 0x3db87d68, 0xcdb6964c, 0xb2649b6c, 0x6a880fa9,
0x1b0c845b, 0xe0af2f28, 0xfc1d5da9, 0xf64878a6, 0x667ca525, 0x2114b1ce,
0x2d119ae3, 0x8d29d3bf, 0x1a1b4922, 0x3132980e, 0xd59e4385, 0x4dbd49b8,
0x2de0bb05, 0xd6c96598, 0xb4c527c3, 0xb5562afc, 0x61eeb602, 0x05aa192a,
0x7d127e77, 0xc719222d, 0xde7cf8db, 0x2de439b8, 0x250b5f1a, 0xd7b21053,
0xef6c14a1, 0x2041f80f, 0xc287332e, 0xbb1dbfd3, 0x783bb979, 0x9a2e6327,
0x6eb03027, 0x0225fa2f, 0xa319bc89, 0x864112d4, 0xfe990445, 0xe5e2e07c,
0xf7c6acb8, 0x1bc92142, 0x12e9b40e, 0x2979282d, 0x05278e70, 0xe160ba4c,
0xc1de0909, 0x458b9bf4, 0xbfce9c94, 0xa276f72a, 0x8441597d, 0x67adc2da,
0x6162b854, 0x7f9b2f4a, 0x0d995b6b, 0x193b643d, 0x399362b3, 0x8b653a4b,
0x1028d2db, 0x2b3df842, 0x6eecafaf, 0x261667e9, 0x9c7e8cda, 0x46063eab,
0x7ce7a3a1, 0xadc899c9, 0x017291c4, 0x528d1a93, 0x9a1ee498, 0xbb7d4d43,
0x7837f0ed, 0x34a230cc, 0x614a628d, 0xb03f93b8, 0xd72e3b08, 0x604c98db,
0x3cfacb79, 0x8b81646a, 0xc0f082fa, 0xd1f92388, 0xe5a91e39, 0xf95c756d,
0x1177742f, 0xf8819323, 0x5c060b80, 0x96c1cd8f, 0x47d7b440, 0xbbb84197,
0x35f749cc, 0x95b0e132, 0x8d90ad54, 0x5c3f9423, 0x4994005b, 0xb58f53b9,
0x32df7348, 0x60f61c29, 0x9eae2f32, 0x85a3d398, 0x3b995dd4, 0x94c5e460,
0x8e54b9f3, 0x87bc6e2a, 0x90bbf1ea, 0x55d44719, 0x2cbbfe6e, 0x439d82f0,
0x4eb3782d, 0xc3f1e669, 0x61ff8d9e, 0x0909238d, 0xef406165, 0x09c1d762,
0x705d184f, 0x188f2cc4, 0x9c5aa12a, 0xc7a5d70e, 0xbc78cb1b, 0x1d26ae62,
0x23f96ae3, 0xd456bf32, 0xe4654f55, 0x31462bd8 ]