----------------------------------------------------------------------------- -- | -- Module : System.Random -- Copyright : (c) The University of Glasgow 2001 -- License : BSD-style (see the file libraries/base/LICENSE) -- -- Maintainer : libraries@haskell.org -- Stability : stable -- Portability : portable -- -- This library deals with the common task of pseudo-random number -- generation. The library makes it possible to generate repeatable -- results, by starting with a specified initial random number generator, -- or to get different results on each run by using the system-initialised -- generator or by supplying a seed from some other source. -- -- The library is split into two layers: -- -- * A core /random number generator/ provides a supply of bits. -- The class 'RandomGen' provides a common interface to such generators. -- The library provides one instance of 'RandomGen', the abstract -- data type 'StdGen'. Programmers may, of course, supply their own -- instances of 'RandomGen'. -- -- * The class 'Random' provides a way to extract values of a particular -- type from a random number generator. For example, the 'Float' -- instance of 'Random' allows one to generate random values of type -- 'Float'. -- -- This implementation uses the Portable Combined Generator of L'Ecuyer -- ["System.Random\#LEcuyer"] for 32-bit computers, transliterated by -- Lennart Augustsson. It has a period of roughly 2.30584e18. -- ----------------------------------------------------------------------------- module System.Random ( -- $intro -- * Random number generators RandomGen(next, split, genRange) -- ** Standard random number generators , StdGen , mkStdGen -- ** The global random number generator -- $globalrng , getStdRandom , getStdGen , setStdGen , newStdGen -- * Random values of various types , Random ( random, randomR, randoms, randomRs, randomIO, randomRIO ) -- * References -- $references ) where import Prelude import Data.Int #ifdef __NHC__ import CPUTime ( getCPUTime ) import Foreign.Ptr ( Ptr, nullPtr ) import Foreign.C ( CTime, CUInt ) #else import System.CPUTime ( getCPUTime ) import System.Time ( getClockTime, ClockTime(..) ) #endif import Data.Char ( isSpace, chr, ord ) import System.IO.Unsafe ( unsafePerformIO ) import Data.IORef import Numeric ( readDec ) -- The standard nhc98 implementation of Time.ClockTime does not match -- the extended one expected in this module, so we lash-up a quick -- replacement here. #ifdef __NHC__ data ClockTime = TOD Integer Integer foreign import ccall "time.h time" readtime :: Ptr CTime -> IO CTime getClockTime :: IO ClockTime getClockTime = do CTime t <- readtime nullPtr; return (TOD (toInteger t) 0) #endif -- | The class 'RandomGen' provides a common interface to random number -- generators. -- -- Minimal complete definition: 'next' and 'split'. class RandomGen g where -- |The 'next' operation returns an 'Int' that is uniformly distributed -- in the range returned by 'genRange' (including both end points), -- and a new generator. next :: g -> (Int, g) -- |The 'split' operation allows one to obtain two distinct random number -- generators. This is very useful in functional programs (for example, when -- passing a random number generator down to recursive calls), but very -- little work has been done on statistically robust implementations of -- 'split' (["System.Random\#Burton", "System.Random\#Hellekalek"] -- are the only examples we know of). split :: g -> (g, g) -- |The 'genRange' operation yields the range of values returned by -- the generator. -- -- It is required that: -- -- * If @(a,b) = 'genRange' g@, then @a < b@. -- -- * 'genRange' always returns a pair of defined 'Int's. -- -- The second condition ensures that 'genRange' cannot examine its -- argument, and hence the value it returns can be determined only by the -- instance of 'RandomGen'. That in turn allows an implementation to make -- a single call to 'genRange' to establish a generator's range, without -- being concerned that the generator returned by (say) 'next' might have -- a different range to the generator passed to 'next'. -- -- The default definition spans the full range of 'Int'. genRange :: g -> (Int,Int) -- default method genRange _ = (minBound, maxBound) {- | The 'StdGen' instance of 'RandomGen' has a 'genRange' of at least 30 bits. The result of repeatedly using 'next' should be at least as statistically robust as the /Minimal Standard Random Number Generator/ described by ["System.Random\#Park", "System.Random\#Carta"]. Until more is known about implementations of 'split', all we require is that 'split' deliver generators that are (a) not identical and (b) independently robust in the sense just given. The 'Show' and 'Read' instances of 'StdGen' provide a primitive way to save the state of a random number generator. It is required that @'read' ('show' g) == g@. In addition, 'read' may be used to map an arbitrary string (not necessarily one produced by 'show') onto a value of type 'StdGen'. In general, the 'read' instance of 'StdGen' has the following properties: * It guarantees to succeed on any string. * It guarantees to consume only a finite portion of the string. * Different argument strings are likely to result in different results. -} data StdGen = StdGen Int32 Int32 instance RandomGen StdGen where next = stdNext split = stdSplit genRange _ = stdRange instance Show StdGen where showsPrec p (StdGen s1 s2) = showsPrec p s1 . showChar ' ' . showsPrec p s2 instance Read StdGen where readsPrec _p = \ r -> case try_read r of r'@[_] -> r' _ -> [stdFromString r] -- because it shouldn't ever fail. where try_read r = do (s1, r1) <- readDec (dropWhile isSpace r) (s2, r2) <- readDec (dropWhile isSpace r1) return (StdGen s1 s2, r2) {- If we cannot unravel the StdGen from a string, create one based on the string given. -} stdFromString :: String -> (StdGen, String) stdFromString s = (mkStdGen num, rest) where (cs, rest) = splitAt 6 s num = foldl (\a x -> x + 3 * a) 1 (map ord cs) {- | The function 'mkStdGen' provides an alternative way of producing an initial generator, by mapping an 'Int' into a generator. Again, distinct arguments should be likely to produce distinct generators. -} mkStdGen :: Int -> StdGen -- why not Integer ? mkStdGen s = mkStdGen32 $ fromIntegral s mkStdGen32 :: Int32 -> StdGen mkStdGen32 s | s < 0 = mkStdGen32 (-s) | otherwise = StdGen (s1+1) (s2+1) where (q, s1) = s `divMod` 2147483562 s2 = q `mod` 2147483398 createStdGen :: Integer -> StdGen createStdGen s = mkStdGen32 $ fromIntegral s -- FIXME: 1/2/3 below should be ** (vs@30082002) XXX {- | With a source of random number supply in hand, the 'Random' class allows the programmer to extract random values of a variety of types. Minimal complete definition: 'randomR' and 'random'. -} class Random a where -- | Takes a range /(lo,hi)/ and a random number generator -- /g/, and returns a random value uniformly distributed in the closed -- interval /[lo,hi]/, together with a new generator. It is unspecified -- what happens if /lo>hi/. For continuous types there is no requirement -- that the values /lo/ and /hi/ are ever produced, but they may be, -- depending on the implementation and the interval. randomR :: RandomGen g => (a,a) -> g -> (a,g) -- | The same as 'randomR', but using a default range determined by the type: -- -- * For bounded types (instances of 'Bounded', such as 'Char'), -- the range is normally the whole type. -- -- * For fractional types, the range is normally the semi-closed interval -- @[0,1)@. -- -- * For 'Integer', the range is (arbitrarily) the range of 'Int'. random :: RandomGen g => g -> (a, g) -- | Plural variant of 'randomR', producing an infinite list of -- random values instead of returning a new generator. randomRs :: RandomGen g => (a,a) -> g -> [a] randomRs ival g = x : randomRs ival g' where (x,g') = randomR ival g -- | Plural variant of 'random', producing an infinite list of -- random values instead of returning a new generator. randoms :: RandomGen g => g -> [a] randoms g = (\(x,g') -> x : randoms g') (random g) -- | A variant of 'randomR' that uses the global random number generator -- (see "System.Random#globalrng"). randomRIO :: (a,a) -> IO a randomRIO range = getStdRandom (randomR range) -- | A variant of 'random' that uses the global random number generator -- (see "System.Random#globalrng"). randomIO :: IO a randomIO = getStdRandom random instance Random Int where randomR (a,b) g = randomIvalInteger (toInteger a, toInteger b) g random g = randomR (minBound,maxBound) g instance Random Char where randomR (a,b) g = case (randomIvalInteger (toInteger (ord a), toInteger (ord b)) g) of (x,g') -> (chr x, g') random g = randomR (minBound,maxBound) g instance Random Bool where randomR (a,b) g = case (randomIvalInteger (toInteger (bool2Int a), toInteger (bool2Int b)) g) of (x, g') -> (int2Bool x, g') where bool2Int False = 0 bool2Int True = 1 int2Bool 0 = False int2Bool _ = True random g = randomR (minBound,maxBound) g instance Random Integer where randomR ival g = randomIvalInteger ival g random g = randomR (toInteger (minBound::Int), toInteger (maxBound::Int)) g instance Random Double where randomR ival g = randomIvalDouble ival id g random g = randomR (0::Double,1) g -- hah, so you thought you were saving cycles by using Float? instance Random Float where random g = randomIvalDouble (0::Double,1) realToFrac g randomR (a,b) g = randomIvalDouble (realToFrac a, realToFrac b) realToFrac g mkStdRNG :: Integer -> IO StdGen mkStdRNG o = do ct <- getCPUTime (TOD sec psec) <- getClockTime return (createStdGen (sec * 12345 + psec + ct + o)) randomIvalInteger :: (RandomGen g, Num a) => (Integer, Integer) -> g -> (a, g) randomIvalInteger (l,h) rng | l > h = randomIvalInteger (h,l) rng | otherwise = case (f n 1 rng) of (v, rng') -> (fromInteger (l + v `mod` k), rng') where k = h - l + 1 b = 2147483561 n = iLogBase b k f 0 acc g = (acc, g) f n' acc g = let (x,g') = next g in f (n' - 1) (fromIntegral x + acc * b) g' randomIvalDouble :: (RandomGen g, Fractional a) => (Double, Double) -> (Double -> a) -> g -> (a, g) randomIvalDouble (l,h) fromDouble rng | l > h = randomIvalDouble (h,l) fromDouble rng | otherwise = case (randomIvalInteger (toInteger (minBound::Int32), toInteger (maxBound::Int32)) rng) of (x, rng') -> let scaled_x = fromDouble ((l+h)/2) + fromDouble ((h-l) / realToFrac int32Range) * fromIntegral (x::Int32) in (scaled_x, rng') int32Range :: Integer int32Range = toInteger (maxBound::Int32) - toInteger (minBound::Int32) iLogBase :: Integer -> Integer -> Integer iLogBase b i = if i < b then 1 else 1 + iLogBase b (i `div` b) stdRange :: (Int,Int) stdRange = (0, 2147483562) stdNext :: StdGen -> (Int, StdGen) -- Returns values in the range stdRange stdNext (StdGen s1 s2) = (fromIntegral z', StdGen s1'' s2'') where z' = if z < 1 then z + 2147483562 else z z = s1'' - s2'' k = s1 `quot` 53668 s1' = 40014 * (s1 - k * 53668) - k * 12211 s1'' = if s1' < 0 then s1' + 2147483563 else s1' k' = s2 `quot` 52774 s2' = 40692 * (s2 - k' * 52774) - k' * 3791 s2'' = if s2' < 0 then s2' + 2147483399 else s2' stdSplit :: StdGen -> (StdGen, StdGen) stdSplit std@(StdGen s1 s2) = (left, right) where -- no statistical foundation for this! left = StdGen new_s1 t2 right = StdGen t1 new_s2 new_s1 | s1 == 2147483562 = 1 | otherwise = s1 + 1 new_s2 | s2 == 1 = 2147483398 | otherwise = s2 - 1 StdGen t1 t2 = snd (next std) -- The global random number generator {- $globalrng #globalrng# There is a single, implicit, global random number generator of type 'StdGen', held in some global variable maintained by the 'IO' monad. It is initialised automatically in some system-dependent fashion, for example, by using the time of day, or Linux's kernel random number generator. To get deterministic behaviour, use 'setStdGen'. -} -- |Sets the global random number generator. setStdGen :: StdGen -> IO () setStdGen sgen = writeIORef theStdGen sgen -- |Gets the global random number generator. getStdGen :: IO StdGen getStdGen = readIORef theStdGen theStdGen :: IORef StdGen theStdGen = unsafePerformIO $ do rng <- mkStdRNG 0 newIORef rng -- |Applies 'split' to the current global random generator, -- updates it with one of the results, and returns the other. newStdGen :: IO StdGen newStdGen = atomicModifyIORef theStdGen split {- |Uses the supplied function to get a value from the current global random generator, and updates the global generator with the new generator returned by the function. For example, @rollDice@ gets a random integer between 1 and 6: > rollDice :: IO Int > rollDice = getStdRandom (randomR (1,6)) -} getStdRandom :: (StdGen -> (a,StdGen)) -> IO a getStdRandom f = atomicModifyIORef theStdGen (swap . f) where swap (v,g) = (g,v) {- $references 1. FW #Burton# Burton and RL Page, /Distributed random number generation/, Journal of Functional Programming, 2(2):203-212, April 1992. 2. SK #Park# Park, and KW Miller, /Random number generators - good ones are hard to find/, Comm ACM 31(10), Oct 1988, pp1192-1201. 3. DG #Carta# Carta, /Two fast implementations of the minimal standard random number generator/, Comm ACM, 33(1), Jan 1990, pp87-88. 4. P #Hellekalek# Hellekalek, /Don\'t trust parallel Monte Carlo/, Department of Mathematics, University of Salzburg, <http://random.mat.sbg.ac.at/~peter/pads98.ps>, 1998. 5. Pierre #LEcuyer# L'Ecuyer, /Efficient and portable combined random number generators/, Comm ACM, 31(6), Jun 1988, pp742-749. The Web site <http://random.mat.sbg.ac.at/> is a great source of information. -}