1 -----------------------------------------------------------------------------
3 -- Module : System.Random
4 -- Copyright : (c) The University of Glasgow 2001
5 -- License : BSD-style (see the file libraries/base/LICENSE)
7 -- Maintainer : libraries@haskell.org
9 -- Portability : portable
13 -----------------------------------------------------------------------------
20 -- * The 'RandomGen' class, and the 'StdGen' generator
22 RandomGen(next, split, genRange)
26 -- * The 'Random' class
27 , Random ( random, randomR,
31 -- * The global random number generator
48 import CPUTime ( getCPUTime )
49 import Foreign.Ptr ( Ptr, nullPtr )
51 import System.CPUTime ( getCPUTime )
52 import System.Time ( getClockTime, ClockTime(..) )
54 import Data.Char ( isSpace, chr, ord )
55 import System.IO.Unsafe ( unsafePerformIO )
57 import Numeric ( readDec )
59 -- The standard nhc98 implementation of Time.ClockTime does not match
60 -- the extended one expected in this module, so we lash-up a quick
63 data ClockTime = TOD Integer ()
64 foreign import ccall "time.h time" readtime :: Ptr () -> IO Int
65 getClockTime :: IO ClockTime
66 getClockTime = do t <- readtime nullPtr; return (TOD (toInteger t) ())
71 This library deals with the common task of pseudo-random
72 number generation. The library makes it possible to generate
73 repeatable results, by starting with a specified initial random
74 number generator; or to get different results on each run by using the
75 system-initialised generator, or by supplying a seed from some other
78 The library is split into two layers:
80 * A core /random number generator/ provides a supply of bits. The class
81 'RandomGen' provides a common interface to such generators.
83 * The class 'Random' provides a way to extract particular values from
84 a random number generator. For example, the 'Float' instance of 'Random'
85 allows one to generate random values of type 'Float'.
87 This implementation uses the Portable Combined Generator of L'Ecuyer
88 ["System.Random\#LEcuyer"] for 32-bit computers, transliterated by
89 Lennart Augustsson. It has a period of roughly 2.30584e18.
93 -- | The class 'RandomGen' provides a common interface to random number
96 class RandomGen g where
98 -- |The 'next' operation returns an 'Int' that is uniformly distributed
99 -- in the range returned by 'genRange' (including both end points),
100 -- and a new generator.
101 next :: g -> (Int, g)
103 -- |The 'split' operation allows one to obtain two distinct random number
104 -- generators. This is very useful in functional programs (for example, when
105 -- passing a random number generator down to recursive calls), but very
106 -- little work has been done on statistically robust implementations of
107 -- 'split' (["System.Random\#Burton", "System.Random\#Hellekalek"]
108 -- are the only examples we know of).
111 -- |The 'genRange' operation yields the range of values returned by
114 -- It is required that:
116 -- * If @(a,b) = 'genRange' g@, then @a < b@.
118 -- * 'genRange' is not strict.
120 -- The second condition ensures that 'genRange' cannot examine its
121 -- argument, and hence the value it returns can be determined only by the
122 -- instance of 'RandomGen'. That in turn allows an implementation to make
123 -- a single call to 'genRange' to establish a generator's range, without
124 -- being concerned that the generator returned by (say) 'next' might have
125 -- a different range to the generator passed to 'next'.
126 genRange :: g -> (Int,Int)
129 genRange g = (minBound,maxBound)
131 {- |The "System.Random" library provides one instance of 'RandomGen', the
132 abstract data type 'StdGen'.
134 The 'StdGen' instance of 'RandomGen' has a 'genRange' of at least 30 bits.
136 The result of repeatedly using 'next' should be at least as statistically
137 robust as the /Minimal Standard Random Number Generator/ described by
138 ["System.Random\#Park", "System.Random\#Carta"].
139 Until more is known about implementations of 'split', all we require is
140 that 'split' deliver generators that are (a) not identical and
141 (b) independently robust in the sense just given.
143 The 'Show' and 'Read' instances of 'StdGen' provide a primitive way to save the
144 state of a random number generator.
145 It is required that @'read' ('show' g) == g@.
147 In addition, 'read' may be used to map an arbitrary string (not necessarily one
148 produced by 'show') onto a value of type 'StdGen'. In general, the 'read'
149 instance of 'StdGen' has the following properties:
151 * It guarantees to succeed on any string.
153 * It guarantees to consume only a finite portion of the string.
155 * Different argument strings are likely to result in different results.
162 instance RandomGen StdGen where
166 instance Show StdGen where
167 showsPrec p (StdGen s1 s2) =
172 instance Read StdGen where
173 readsPrec _p = \ r ->
176 _ -> [stdFromString r] -- because it shouldn't ever fail.
179 (s1, r1) <- readDec (dropWhile isSpace r)
180 (s2, r2) <- readDec (dropWhile isSpace r1)
181 return (StdGen s1 s2, r2)
184 If we cannot unravel the StdGen from a string, create
185 one based on the string given.
187 stdFromString :: String -> (StdGen, String)
188 stdFromString s = (mkStdGen num, rest)
189 where (cs, rest) = splitAt 6 s
190 num = foldl (\a x -> x + 3 * a) 1 (map ord cs)
194 The function 'mkStdGen' provides an alternative way of producing an initial
195 generator, by mapping an 'Int' into a generator. Again, distinct arguments
196 should be likely to produce distinct generators.
198 Programmers may, of course, supply their own instances of 'RandomGen'.
200 mkStdGen :: Int -> StdGen -- why not Integer ?
202 | s < 0 = mkStdGen (-s)
203 | otherwise = StdGen (s1+1) (s2+1)
205 (q, s1) = s `divMod` 2147483562
206 s2 = q `mod` 2147483398
208 createStdGen :: Integer -> StdGen
210 | s < 0 = createStdGen (-s)
211 | otherwise = StdGen (fromInteger (s1+1)) (fromInteger (s2+1))
213 (q, s1) = s `divMod` 2147483562
214 s2 = q `mod` 2147483398
216 -- FIXME: 1/2/3 below should be ** (vs@30082002) XXX
219 With a source of random number supply in hand, the 'Random' class allows the
220 programmer to extract random values of a variety of types.
222 Minimal complete definition: 'randomR' and 'random'.
227 -- | Takes a range /(lo,hi)/ and a random number generator
228 -- /g/, and returns a random value uniformly distributed in the closed
229 -- interval /[lo,hi]/, together with a new generator. It is unspecified
230 -- what happens if /lo>hi/. For continuous types there is no requirement
231 -- that the values /lo/ and /hi/ are ever produced, but they may be,
232 -- depending on the implementation and the interval.
233 randomR :: RandomGen g => (a,a) -> g -> (a,g)
235 -- | The same as 'randomR', but using a default range determined by the type:
237 -- * For bounded types (instances of 'Bounded', such as 'Char'),
238 -- the range is normally the whole type.
240 -- * For fractional types, the range is normally the semi-closed interval
243 -- * For 'Integer', the range is (arbitrarily) the range of 'Int'.
244 random :: RandomGen g => g -> (a, g)
246 -- | Plural variant of 'randomR', producing an infinite list of
247 -- random values instead of returning a new generator.
248 randomRs :: RandomGen g => (a,a) -> g -> [a]
249 randomRs ival g = x : randomRs ival g' where (x,g') = randomR ival g
251 -- | Plural variant of 'random', producing an infinite list of
252 -- random values instead of returning a new generator.
253 randoms :: RandomGen g => g -> [a]
254 randoms g = (\(x,g') -> x : randoms g') (random g)
256 -- | A variant of 'randomR' that uses the global random number generator
257 -- (see "System.Random#globalrng").
258 randomRIO :: (a,a) -> IO a
259 randomRIO range = getStdRandom (randomR range)
261 -- | A variant of 'random' that uses the global random number generator
262 -- (see "System.Random#globalrng").
264 randomIO = getStdRandom random
267 instance Random Int where
268 randomR (a,b) g = randomIvalInteger (toInteger a, toInteger b) g
269 random g = randomR (minBound,maxBound) g
271 instance Random Char where
273 case (randomIvalInteger (toInteger (ord a), toInteger (ord b)) g) of
275 random g = randomR (minBound,maxBound) g
277 instance Random Bool where
279 case (randomIvalInteger (toInteger (bool2Int a), toInteger (bool2Int b)) g) of
280 (x, g) -> (int2Bool x, g)
288 random g = randomR (minBound,maxBound) g
290 instance Random Integer where
291 randomR ival g = randomIvalInteger ival g
292 random g = randomR (toInteger (minBound::Int), toInteger (maxBound::Int)) g
294 instance Random Double where
295 randomR ival g = randomIvalDouble ival id g
296 random g = randomR (0::Double,1) g
298 -- hah, so you thought you were saving cycles by using Float?
299 instance Random Float where
300 random g = randomIvalDouble (0::Double,1) realToFrac g
301 randomR (a,b) g = randomIvalDouble (realToFrac a, realToFrac b) realToFrac g
303 mkStdRNG :: Integer -> IO StdGen
306 (TOD sec _) <- getClockTime
307 return (createStdGen (sec * 12345 + ct + o))
309 randomIvalInteger :: (RandomGen g, Num a) => (Integer, Integer) -> g -> (a, g)
310 randomIvalInteger (l,h) rng
311 | l > h = randomIvalInteger (h,l) rng
312 | otherwise = case (f n 1 rng) of (v, rng') -> (fromInteger (l + v `mod` k), rng')
323 f (n-1) (fromIntegral x + acc * b) g'
325 randomIvalDouble :: (RandomGen g, Fractional a) => (Double, Double) -> (Double -> a) -> g -> (a, g)
326 randomIvalDouble (l,h) fromDouble rng
327 | l > h = randomIvalDouble (h,l) fromDouble rng
329 case (randomIvalInteger (toInteger (minBound::Int), toInteger (maxBound::Int)) rng) of
333 fromDouble ((l+h)/2) +
334 fromDouble ((h-l) / realToFrac intRange) *
335 fromIntegral (x::Int)
340 intRange = toInteger (maxBound::Int) - toInteger (minBound::Int)
342 iLogBase :: Integer -> Integer -> Integer
343 iLogBase b i = if i < b then 1 else 1 + iLogBase b (i `div` b)
345 stdNext :: StdGen -> (Int, StdGen)
346 stdNext (StdGen s1 s2) = (z', StdGen s1'' s2'')
347 where z' = if z < 1 then z + 2147483562 else z
351 s1' = 40014 * (s1 - k * 53668) - k * 12211
352 s1'' = if s1' < 0 then s1' + 2147483563 else s1'
355 s2' = 40692 * (s2 - k' * 52774) - k' * 3791
356 s2'' = if s2' < 0 then s2' + 2147483399 else s2'
358 stdSplit :: StdGen -> (StdGen, StdGen)
359 stdSplit std@(StdGen s1 s2)
362 -- no statistical foundation for this!
363 left = StdGen new_s1 t2
364 right = StdGen t1 new_s2
366 new_s1 | s1 == 2147483562 = 1
369 new_s2 | s2 == 1 = 2147483398
372 StdGen t1 t2 = snd (next std)
374 -- The global random number generator
376 {- $globalrng #globalrng#
378 There is a single, implicit, global random number generator of type
379 'StdGen', held in some global variable maintained by the 'IO' monad. It is
380 initialised automatically in some system-dependent fashion, for example, by
381 using the time of day, or Linux's kernel random number generator. To get
382 deterministic behaviour, use 'setStdGen'.
385 -- |Sets the global random number generator.
386 setStdGen :: StdGen -> IO ()
387 setStdGen sgen = writeIORef theStdGen sgen
389 -- |Gets the global random number generator.
390 getStdGen :: IO StdGen
391 getStdGen = readIORef theStdGen
393 theStdGen :: IORef StdGen
394 theStdGen = unsafePerformIO $ do
398 -- |Applies 'split' to the current global random generator,
399 -- updates it with one of the results, and returns the other.
400 newStdGen :: IO StdGen
403 let (a,b) = split rng
407 {- |Uses the supplied function to get a value from the current global
408 random generator, and updates the global generator with the new generator
409 returned by the function. For example, @rollDice@ gets a random integer
413 > rollDice = getStdRandom (randomR (1,6))
417 getStdRandom :: (StdGen -> (a,StdGen)) -> IO a
420 let (v, new_rng) = f rng
426 1. FW #Burton# Burton and RL Page, /Distributed random number generation/,
427 Journal of Functional Programming, 2(2):203-212, April 1992.
429 2. SK #Park# Park, and KW Miller, /Random number generators -
430 good ones are hard to find/, Comm ACM 31(10), Oct 1988, pp1192-1201.
432 3. DG #Carta# Carta, /Two fast implementations of the minimal standard
433 random number generator/, Comm ACM, 33(1), Jan 1990, pp87-88.
435 4. P #Hellekalek# Hellekalek, /Don\'t trust parallel Monte Carlo/,
436 Department of Mathematics, University of Salzburg,
437 <http://random.mat.sbg.ac.at/~peter/pads98.ps>, 1998.
439 5. Pierre #LEcuyer# L'Ecuyer, /Efficient and portable combined random
440 number generators/, Comm ACM, 31(6), Jun 1988, pp742-749.
442 The Web site <http://random.mat.sbg.ac.at/> is a great source of information.