diff --git a/Statistics/RandomVariate.hs b/Statistics/RandomVariate.hs --- a/Statistics/RandomVariate.hs +++ b/Statistics/RandomVariate.hs @@ -1,473 +1,6 @@ -{-# LANGUAGE BangPatterns, CPP, DeriveDataTypeable, MagicHash, Rank2Types, - ScopedTypeVariables #-} --- | --- Module : Statistics.RandomVariate --- Copyright : (c) 2009 Bryan O'Sullivan --- License : BSD3 --- --- Maintainer : bos@serpentine.com --- Stability : experimental --- Portability : portable --- --- Pseudo-random variate generation. - module Statistics.RandomVariate ( - -- * Types - Gen - , Seed - , Variate(..) - -- * Other distributions - , normal - -- * Creation - , create - , initialize - , withSystemRandom - -- * State management - , save - , restore - -- * Helper functions - , uniformArray - -- * References - -- $references + module System.Random.MWC ) 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.Typeable (Typeable) -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) - --- | The class of types for which we can generate uniformly --- distributed random variates. --- --- The uniform PRNG uses Marsaglia's MWC256 (also known as MWC8222) --- multiply-with-carry generator, which has a period of 2^8222 and --- fares well in tests of randomness. It is also extremely fast, --- between 2 and 3 times faster than the Mersenne Twister. --- --- /Note/: Marsaglia's PRNG is not known to be cryptographically --- secure, so you should not use it for cryptographic operations. -class Variate a where - -- | Generate a single uniformly distributed random variate. The - -- range of values produced varies by type: - -- - -- * For fixed-width integral types, the type's entire range is - -- used. - -- - -- * For floating point numbers, the range (0,1] is used. Zero is - -- explicitly excluded, to allow variates to be used in - -- statistical calculations that require non-zero values - -- (e.g. uses of the 'log' function). - -- - -- * The range of random 'Integer' variates is the same as for - -- 'Int'. - -- - -- To generate a 'Float' variate with a range of [0,1), subtract - -- 2**(-33). To do the same with 'Double' variates, subtract - -- 2**(-53). - uniform :: Gen s -> ST s a - --- Thanks to Duncan Coutts for finding the pattern below for --- strong-arming GHC 6.10's inliner into behaving itself. This makes --- a 2x difference to performance compared to the following: --- --- > uniform = uniform1 fromIntegral - -instance Variate Int8 where - uniform = f where f = uniform1 fromIntegral - {-# INLINE f #-} - -instance Variate Int16 where - uniform = f where f = uniform1 fromIntegral - {-# INLINE f #-} - -instance Variate Int32 where - uniform = f where f = uniform1 fromIntegral - {-# INLINE f #-} - -instance Variate Int64 where - uniform = f where f = uniform2 wordsTo64Bit - {-# INLINE f #-} - -instance Variate Word8 where - uniform = f where f = uniform1 fromIntegral - {-# INLINE f #-} - -instance Variate Word16 where - uniform = f where f = uniform1 fromIntegral - {-# INLINE f #-} - -instance Variate Word32 where - uniform = uniformWord32 - -instance Variate Word64 where - uniform = f where f = uniform2 wordsTo64Bit - {-# INLINE f #-} - -instance Variate Bool where - uniform = f where f = uniform1 wordToBool - {-# INLINE f #-} - -instance Variate Float where - uniform = f where f = uniform1 wordToFloat - {-# INLINE f #-} - -instance Variate Double where - uniform = f where f = uniform2 wordsToDouble - {-# INLINE f #-} - -instance Variate Int where -#if WORD_SIZE_IN_BITS < 64 - uniform = f where f = uniform1 fromIntegral -#else - uniform = f where f = uniform2 wordsTo64Bit -#endif - {-# INLINE f #-} - -instance Variate Word where -#if WORD_SIZE_IN_BITS < 64 - uniform = f where f = uniform1 fromIntegral -#else - uniform = f where f = uniform2 wordsTo64Bit -#endif - {-# INLINE f #-} - -instance Variate Integer where - uniform = f where f g = do - u <- uniform g - return $! fromIntegral (u :: Int) - {-# INLINE f #-} - -instance (Variate a, Variate b) => Variate (a,b) where - uniform = f where f g = (,) `fmap` uniform g `ap` uniform g - {-# INLINE f #-} - -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 - {-# INLINE f #-} - -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 - {-# INLINE f #-} - -wordsTo64Bit :: Integral a => Word32 -> Word32 -> a -wordsTo64Bit a b = - fromIntegral ((fromIntegral a `shiftL` 32) .|. fromIntegral b) -{-# INLINE wordsTo64Bit #-} - -wordToBool :: Word32 -> Bool -wordToBool i = (i .&. 1) /= 0 -{-# INLINE wordToBool #-} - -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 -{-# INLINE wordToFloat #-} - -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 -{-# INLINE wordsToDouble #-} - --- | State of the pseudo-random number generator. -newtype Gen s = Gen (MUArr Word32 s) - -ioff, coff :: Int -ioff = 256 -coff = 257 - --- | Create a generator for variates using a fixed seed. -create :: ST s (Gen s) -create = initialize defaultSeed -{-# INLINE create #-} - --- | Create a generator for variates using the given seed, of which up --- to 256 elements will be used. For arrays of less than 256 --- elements, part of the default seed will be used to finish --- initializing the generator's state. --- --- Examples: --- --- > initialize (singletonU 42) --- --- > initialize (toU [4, 8, 15, 16, 23, 42]) --- --- If a seed contains fewer than 256 elements, it is first used --- verbatim, then its elements are 'xor'ed against elements of the --- default seed until 256 elements are reached. -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 -{-# INLINE initialize #-} - --- | An immutable snapshot of the state of a 'Gen'. -newtype Seed = Seed (UArr Word32) - deriving (Eq, Read, Show, Typeable) - --- | Save the state of a 'Gen', for later use by 'restore'. -save :: Gen s -> ST s Seed -save (Gen q) = Seed `fmap` unsafeFreezeAllMU q -{-# INLINE save #-} - --- | Create a new 'Gen' that mirrors the state of a saved 'Seed'. -restore :: Seed -> ST s (Gen s) -restore (Seed s) = newMU n >>= fill - where fill q = go 0 where - go !i | i >= n = return (Gen q) - | otherwise = writeMU q i (indexU s i) >> go (i+1) - n = lengthU s -{-# INLINE restore #-} - --- | Using the current time as a seed, perform an action that uses a --- random variate generator. This is a horrible fallback for Windows --- systems. -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 - --- | Seed a PRNG with data from the system's fast source of --- pseudo-random numbers (\"\/dev\/urandom\" on Unix-like systems), --- then run the given action. --- --- /Note/: on Windows, this code does not yet use the native --- Cryptographic API as a source of random numbers (it uses the system --- clock instead). As a result, the sequences it generates may not be --- highly independent. -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 - {-# NOINLINE warned #-} - --- | Unchecked 64-bit left shift. -shiftL :: Word64 -> Int -> Word64 -shiftL (W64# x#) (I# i#) = W64# (x# `uncheckedShiftL64#` i#) - --- | Unchecked 64-bit right shift. -shiftR :: Word64 -> Int -> Word64 -shiftR (W64# x#) (I# i#) = W64# (x# `uncheckedShiftRL64#` i#) - --- | Compute the next index into the state pool. This is simply --- addition modulo 256. -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 -{-# INLINE uniformWord32 #-} - -uniform1 :: (Word32 -> a) -> Gen s -> ST s a -uniform1 f gen = do - i <- uniformWord32 gen - return $! f i -{-# INLINE uniform1 #-} - -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 -{-# INLINE uniform2 #-} - --- | Generate an array of pseudo-random variates. This is not --- necessarily faster than invoking 'uniform' repeatedly in a loop, --- but it may be more convenient to use in some situations. -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) -{-# INLINE uniformArray #-} - --- | Generate a normally distributed random variate. --- --- The implementation uses Doornik's modified ziggurat algorithm. --- Compared to the ziggurat algorithm usually used, this is slower, --- but generates more independent variates that pass stringent tests --- of randomness. -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 ] - --- $references --- --- * Doornik, J.A. (2005) An improved ziggurat method to generate --- normal random samples. Mimeo, Nuffield College, University of --- Oxford. --- --- * Doornik, J.A. (2007) Conversion of high-period random numbers to --- floating point. --- /ACM Transactions on Modeling and Computer Simulation/ 17(1). --- --- --- * Marsaglia, G. (2003) Seeds for random number generators. --- /Communications of the ACM/ 46(5):90–93. --- --- --- * Thomas, D.B.; Leong, P.G.W.; Luk, W.; Villasenor, J.D. --- (2007). Gaussian random number generators. --- /ACM Computing Surveys/ 39(4). --- +import System.Random.MWC diff --git a/Statistics/Resampling.hs b/Statistics/Resampling.hs --- a/Statistics/Resampling.hs +++ b/Statistics/Resampling.hs @@ -21,7 +21,7 @@ import Data.Array.Vector import Data.Array.Vector.Algorithms.Intro (sort) import Statistics.Function (createU, indices) -import Statistics.RandomVariate (Gen, uniform) +import System.Random.MWC (Gen, uniform) import Statistics.Types (Estimator, Sample) -- | A resample drawn randomly, with replacement, from a set of data diff --git a/statistics.cabal b/statistics.cabal --- a/statistics.cabal +++ b/statistics.cabal @@ -1,5 +1,5 @@ name: statistics -version: 0.4.0 +version: 0.4.1 synopsis: A library of statistical types, data, and functions description: This library provides a number of common functions and types useful @@ -55,6 +55,7 @@ build-depends: base < 5, erf, + mwc-random, time, uvector >= 0.1.0.4, uvector-algorithms >= 0.2