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Move PRNG out to mwc-random package.

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commit 44904fa93a474972556cc23c604307ff7797ffd1 1 parent 81681de
@bos authored
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471 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. <http://www.doornik.com/research/ziggurat.pdf>
---
--- * Doornik, J.A. (2007) Conversion of high-period random numbers to
--- floating point.
--- /ACM Transactions on Modeling and Computer Simulation/ 17(1).
--- <http://www.doornik.com/research/randomdouble.pdf>
---
--- * Marsaglia, G. (2003) Seeds for random number generators.
--- /Communications of the ACM/ 46(5):90&#8211;93.
--- <http://doi.acm.org/10.1145/769800.769827>
---
--- * Thomas, D.B.; Leong, P.G.W.; Luk, W.; Villasenor, J.D.
--- (2007). Gaussian random number generators.
--- /ACM Computing Surveys/ 39(4).
--- <http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/grng_acmcs07.pdf>
+import System.Random.MWC
View
2  Statistics/Resampling.hs
@@ -21,7 +21,7 @@ import Control.Monad.ST (ST)
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
View
1  statistics.cabal
@@ -55,6 +55,7 @@ library
build-depends:
base < 5,
erf,
+ mwc-random,
time,
uvector >= 0.1.0.4,
uvector-algorithms >= 0.2
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