| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file LICENSE in the 'random' repository) |
| Maintainer | libraries@haskell.org |
| Stability | stable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
System.Random
Description
This library deals with the common task of pseudo-random number generation.
Synopsis
- class RandomGen g where
- next :: g -> (Int, g)
- genWord8 :: g -> (Word8, g)
- genWord16 :: g -> (Word16, g)
- genWord32 :: g -> (Word32, g)
- genWord64 :: g -> (Word64, g)
- genWord32R :: Word32 -> g -> (Word32, g)
- genWord64R :: Word64 -> g -> (Word64, g)
- genShortByteString :: Int -> g -> (ShortByteString, g)
- genRange :: g -> (Int, Int)
- split :: g -> (g, g)
- uniform :: (RandomGen g, Uniform a) => g -> (a, g)
- uniformR :: (RandomGen g, UniformRange a) => (a, a) -> g -> (a, g)
- genByteString :: RandomGen g => Int -> g -> (ByteString, g)
- class Random a where
- class Uniform a
- class UniformRange a
- class Finite a
- data StdGen
- mkStdGen :: Int -> StdGen
- initStdGen :: MonadIO m => m StdGen
- getStdRandom :: MonadIO m => (StdGen -> (a, StdGen)) -> m a
- getStdGen :: MonadIO m => m StdGen
- setStdGen :: MonadIO m => StdGen -> m ()
- newStdGen :: MonadIO m => m StdGen
- randomIO :: (Random a, MonadIO m) => m a
- randomRIO :: (Random a, MonadIO m) => (a, a) -> m a
Introduction
This module provides type classes and instances for the following concepts:
- Pure pseudo-random number generators
RandomGenis an interface to pure pseudo-random number generators.StdGen, the standard pseudo-random number generator provided in this library, is an instance ofRandomGen. It uses the SplitMix implementation provided by the splitmix package. Programmers may, of course, supply their own instances ofRandomGen.
Usage
In pure code, use uniform and uniformR to generate pseudo-random values
with a pure pseudo-random number generator like StdGen.
>>>:{let rolls :: RandomGen g => Int -> g -> [Word] rolls n = take n . unfoldr (Just . uniformR (1, 6)) pureGen = mkStdGen 137 in rolls 10 pureGen :: [Word] :} [4,2,6,1,6,6,5,1,1,5]
To run use a monadic pseudo-random computation in pure code with a pure
pseudo-random number generator, use runStateGen and its variants.
>>>:{let rollsM :: StatefulGen g m => Int -> g -> m [Word] rollsM n = replicateM n . uniformRM (1, 6) pureGen = mkStdGen 137 in runStateGen_ pureGen (rollsM 10) :: [Word] :} [4,2,6,1,6,6,5,1,1,5]
Pure number generator interface
Pseudo-random number generators come in two flavours: pure and monadic.
RandomGen: pure pseudo-random number generators- These generators produce
a new pseudo-random value together with a new instance of the
pseudo-random number generator.
Pure pseudo-random number generators should implement
splitif they are splittable, that is, if there is an efficient method to turn one generator into two. The pseudo-random numbers produced by the two resulting generators should not be correlated. See [1] for some background on splittable pseudo-random generators. StatefulGen: monadic pseudo-random number generators- See System.Random.Stateful module
class RandomGen g where Source #
RandomGen is an interface to pure pseudo-random number generators.
StdGen is the standard RandomGen instance provided by this library.
Since: 1.0.0
Methods
next :: g -> (Int, g) Source #
Deprecated: No longer used
Returns an Int that is uniformly distributed over the range returned by
genRange (including both end points), and a new generator. Using next
is inefficient as all operations go via Integer. See
here for
more details. It is thus deprecated.
Since: 1.0.0
genWord8 :: g -> (Word8, g) Source #
genWord16 :: g -> (Word16, g) Source #
genWord32 :: g -> (Word32, g) Source #
genWord64 :: g -> (Word64, g) Source #
genWord32R :: Word32 -> g -> (Word32, g) Source #
genWord32R upperBound g returns a Word32 that is uniformly
distributed over the range [0, upperBound].
Since: 1.2.0
genWord64R :: Word64 -> g -> (Word64, g) Source #
genWord64R upperBound g returns a Word64 that is uniformly
distributed over the range [0, upperBound].
Since: 1.2.0
genShortByteString :: Int -> g -> (ShortByteString, g) Source #
genShortByteString n g returns a ShortByteString of length n
filled with pseudo-random bytes.
Since: 1.2.0
Instances
uniform :: (RandomGen g, Uniform a) => g -> (a, g) Source #
Generates a value uniformly distributed over all possible values of that type.
This is a pure version of uniformM.
Examples
>>>import System.Random>>>let pureGen = mkStdGen 137>>>uniform pureGen :: (Bool, StdGen)(True,StdGen {unStdGen = SMGen 11285859549637045894 7641485672361121627})
Since: 1.2.0
uniformR :: (RandomGen g, UniformRange a) => (a, a) -> g -> (a, g) Source #
Generates a value uniformly distributed over the provided range, which is interpreted as inclusive in the lower and upper bound.
uniformR (1 :: Int, 4 :: Int)generates values uniformly from the set \(\{1,2,3,4\}\)uniformR (1 :: Float, 4 :: Float)generates values uniformly from the set \(\{x\;|\;1 \le x \le 4\}\)
The following law should hold to make the function always defined:
uniformR (a, b) = uniformR (b, a)
This is a pure version of uniformRM.
Examples
>>>import System.Random>>>let pureGen = mkStdGen 137>>>uniformR (1 :: Int, 4 :: Int) pureGen(4,StdGen {unStdGen = SMGen 11285859549637045894 7641485672361121627})
Since: 1.2.0
genByteString :: RandomGen g => Int -> g -> (ByteString, g) Source #
Generates a ByteString of the specified size using a pure pseudo-random
number generator. See uniformByteStringM for the monadic version.
Examples
>>>import System.Random>>>import Data.ByteString>>>let pureGen = mkStdGen 137>>>unpack . fst . genByteString 10 $ pureGen[51,123,251,37,49,167,90,109,1,4]
Since: 1.2.0
The class of types for which random values can be generated. Most
instances of Random will produce values that are uniformly distributed on the full
range, but for those types without a well-defined "full range" some sensible default
subrange will be selected.
Random exists primarily for backwards compatibility with version 1.1 of
this library. In new code, use the better specified Uniform and
UniformRange instead.
Since: 1.0.0
Minimal complete definition
Nothing
Methods
randomR :: RandomGen g => (a, a) -> g -> (a, g) Source #
Takes a range (lo,hi) and a pseudo-random number generator g, and returns a pseudo-random value uniformly distributed over the closed interval [lo,hi], together with a new generator. It is unspecified what happens if lo>hi, but usually the values will simply get swapped.
>>>let gen = mkStdGen 2021>>>fst $ randomR ('a', 'z') gen't'>>>fst $ randomR ('z', 'a') gen't'
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.
There is no requirement to follow the Ord instance and the concept of range can be
defined on per type basis. For example product types will treat their values
independently:
>>>fst $ randomR (('a', 5.0), ('z', 10.0)) $ mkStdGen 2021('t',6.240232662366563)
In case when a lawful range is desired uniformR should be used
instead.
Since: 1.0.0
default randomR :: (RandomGen g, UniformRange a) => (a, a) -> g -> (a, g) Source #
random :: RandomGen g => g -> (a, g) Source #
The same as randomR, but using a default range determined by the type:
- For bounded types (instances of
Bounded, such asChar), the range is normally the whole type. - For floating point types, the range is normally the closed interval
[0,1]. - For
Integer, the range is (arbitrarily) the range ofInt.
Since: 1.0.0
randomRs :: RandomGen g => (a, a) -> g -> [a] Source #
Plural variant of randomR, producing an infinite list of
pseudo-random values instead of returning a new generator.
Since: 1.0.0
randoms :: RandomGen g => g -> [a] Source #
Plural variant of random, producing an infinite list of
pseudo-random values instead of returning a new generator.
Since: 1.0.0
Instances
| Random Bool Source # | |
| Random Char Source # | |
| Random Double Source # | Note - |
| Random Float Source # | Note - |
| Random Int Source # | |
| Random Int8 Source # | |
| Random Int16 Source # | |
| Random Int32 Source # | |
| Random Int64 Source # | |
| Random Integer Source # | |
| Random Word Source # | |
| Random Word8 Source # | |
| Random Word16 Source # | |
| Random Word32 Source # | |
| Random Word64 Source # | |
| Random CChar Source # | |
| Random CSChar Source # | |
| Random CUChar Source # | |
| Random CShort Source # | |
| Random CUShort Source # | |
| Random CInt Source # | |
| Random CUInt Source # | |
| Random CLong Source # | |
| Random CULong Source # | |
| Random CLLong Source # | |
| Random CULLong Source # | |
| Random CBool Source # | |
| Random CFloat Source # | Note - |
| Random CDouble Source # | Note - |
| Random CPtrdiff Source # | |
| Random CSize Source # | |
| Random CWchar Source # | |
| Random CSigAtomic Source # | |
Defined in System.Random Methods randomR :: RandomGen g => (CSigAtomic, CSigAtomic) -> g -> (CSigAtomic, g) Source # random :: RandomGen g => g -> (CSigAtomic, g) Source # randomRs :: RandomGen g => (CSigAtomic, CSigAtomic) -> g -> [CSigAtomic] Source # randoms :: RandomGen g => g -> [CSigAtomic] Source # | |
| Random CIntPtr Source # | |
| Random CUIntPtr Source # | |
| Random CIntMax Source # | |
| Random CUIntMax Source # | |
| (Random a, Random b) => Random (a, b) Source # | Note - |
| (Random a, Random b, Random c) => Random (a, b, c) Source # | Note - |
| (Random a, Random b, Random c, Random d) => Random (a, b, c, d) Source # | Note - |
Defined in System.Random | |
| (Random a, Random b, Random c, Random d, Random e) => Random (a, b, c, d, e) Source # | Note - |
| (Random a, Random b, Random c, Random d, Random e, Random f) => Random (a, b, c, d, e, f) Source # | Note - |
Defined in System.Random Methods randomR :: RandomGen g => ((a, b, c, d, e, f), (a, b, c, d, e, f)) -> g -> ((a, b, c, d, e, f), g) Source # random :: RandomGen g => g -> ((a, b, c, d, e, f), g) Source # randomRs :: RandomGen g => ((a, b, c, d, e, f), (a, b, c, d, e, f)) -> g -> [(a, b, c, d, e, f)] Source # randoms :: RandomGen g => g -> [(a, b, c, d, e, f)] Source # | |
| (Random a, Random b, Random c, Random d, Random e, Random f, Random g) => Random (a, b, c, d, e, f, g) Source # | Note - |
Defined in System.Random Methods randomR :: RandomGen g0 => ((a, b, c, d, e, f, g), (a, b, c, d, e, f, g)) -> g0 -> ((a, b, c, d, e, f, g), g0) Source # random :: RandomGen g0 => g0 -> ((a, b, c, d, e, f, g), g0) Source # randomRs :: RandomGen g0 => ((a, b, c, d, e, f, g), (a, b, c, d, e, f, g)) -> g0 -> [(a, b, c, d, e, f, g)] Source # randoms :: RandomGen g0 => g0 -> [(a, b, c, d, e, f, g)] Source # | |
The class of types for which a uniformly distributed value can be drawn from all possible values of the type.
Since: 1.2.0
Instances
class UniformRange a Source #
The class of types for which a uniformly distributed value can be drawn from a range.
Since: 1.2.0
Minimal complete definition
Instances
A type class for data with a finite number of inhabitants.
This type class is used
in default implementations of Uniform.
Users are not supposed to write instances of Finite manually.
There is a default implementation in terms of Generic instead.
>>>:set -XDeriveGeneric -XDeriveAnyClass>>>import GHC.Generics (Generic)>>>data MyBool = MyTrue | MyFalse deriving (Generic, Finite)>>>data Action = Code MyBool | Eat (Maybe Bool) | Sleep deriving (Generic, Finite)
Instances
Standard pseudo-random number generator
The standard pseudo-random number generator.
Instances
| Eq StdGen Source # | |
| Show StdGen Source # | |
| NFData StdGen Source # | |
Defined in System.Random.Internal | |
| RandomGen StdGen Source # | |
Defined in System.Random.Internal Methods next :: StdGen -> (Int, StdGen) Source # genWord8 :: StdGen -> (Word8, StdGen) Source # genWord16 :: StdGen -> (Word16, StdGen) Source # genWord32 :: StdGen -> (Word32, StdGen) Source # genWord64 :: StdGen -> (Word64, StdGen) Source # genWord32R :: Word32 -> StdGen -> (Word32, StdGen) Source # genWord64R :: Word64 -> StdGen -> (Word64, StdGen) Source # genShortByteString :: Int -> StdGen -> (ShortByteString, StdGen) Source # | |
initStdGen :: MonadIO m => m StdGen Source #
Initialize StdGen using system entropy (i.e. /dev/urandom) when it is
available, while falling back on using system time as the seed.
Since: 1.2.1
Global standard pseudo-random number generator
There is a single, implicit, global pseudo-random number generator of type
StdGen, held in a global mutable variable that can be manipulated from
within the IO monad. It is also available as
globalStdGen, therefore it is recommended to use the
new System.Random.Stateful interface to explicitly operate on the global
pseudo-random number generator.
It is initialised with initStdGen, although it is possible to override its
value with setStdGen. All operations on the global pseudo-random number
generator are thread safe, however in presence of concurrency they are
naturally become non-deterministic. Moreover, relying on the global mutable
state makes it hard to know which of the dependent libraries are using it as
well, making it unpredictable in the local context. Precisely of this reason,
the global pseudo-random number generator is only suitable for uses in
applications, test suites, etc. and is advised against in development of
reusable libraries.
It is also important to note that either using StdGen with pure functions
from other sections of this module or by relying on
runStateGen from stateful interface does not only
give us deterministic behaviour without requiring IO, but it is also more
efficient.
getStdRandom :: MonadIO m => (StdGen -> (a, StdGen)) -> m a Source #
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 produces a pseudo-random integer
between 1 and 6:
>>>rollDice = getStdRandom (randomR (1, 6))>>>replicateM 10 (rollDice :: IO Int)[5,6,6,1,1,6,4,2,4,1]
This is an outdated function and it is recommended to switch to its
equivalent applyAtomicGen instead, possibly with the
globalStdGen if relying on the global state is
acceptable.
>>>import System.Random.Stateful>>>rollDice = applyAtomicGen (uniformR (1, 6)) globalStdGen>>>replicateM 10 (rollDice :: IO Int)[4,6,1,1,4,4,3,2,1,2]
Since: 1.0.0
getStdGen :: MonadIO m => m StdGen Source #
Gets the global pseudo-random number generator. Extracts the contents of
globalStdGen
Since: 1.0.0
setStdGen :: MonadIO m => StdGen -> m () Source #
Sets the global pseudo-random number generator. Overwrites the contents of
globalStdGen
Since: 1.0.0
newStdGen :: MonadIO m => m StdGen Source #
Applies split to the current global pseudo-random generator
globalStdGen, updates it with one of the results,
and returns the other.
Since: 1.0.0
randomIO :: (Random a, MonadIO m) => m a Source #
A variant of randomM that uses the global
pseudo-random number generator globalStdGen.
>>>import Data.Int>>>randomIO :: IO Int32-1580093805
This function is equivalent to getStdRandom randomuniformM instead, possibly with
the globalStdGen if relying on the global state is
acceptable.
>>>import System.Random.Stateful>>>uniformM globalStdGen :: IO Int32-1649127057
Since: 1.0.0
randomRIO :: (Random a, MonadIO m) => (a, a) -> m a Source #
A variant of randomRM that uses the global
pseudo-random number generator globalStdGen
>>>randomRIO (2020, 2100) :: IO Int2040
Similar to randomIO, this function is equivalent to getStdRandom
randomRuniformRM instead, possibly with the
globalStdGen if relying on the global state is
acceptable.
>>>import System.Random.Stateful>>>uniformRM (2020, 2100) globalStdGen :: IO Int2079
Since: 1.0.0
Compatibility and reproducibility
Backwards compatibility and deprecations
Version 1.2 mostly maintains backwards compatibility with version 1.1. This has a few consequences users should be aware of:
- The type class
Randomis only provided for backwards compatibility. New code should useUniformandUniformRangeinstead. - The methods
nextandgenRangeinRandomGenare deprecated and only provided for backwards compatibility. New instances ofRandomGenshould implement word-based methods instead. See below for more information about how to write aRandomGeninstance. This library provides instances for
Randomfor some unbounded types for backwards compatibility. For an unbounded type, there is no way to generate a value with uniform probability out of its entire domain, so therandomimplementation for unbounded types actually generates a value based on some fixed range.For
Integer,randomgenerates a value in theIntrange. ForFloatandDouble,randomgenerates a floating point value in the range[0, 1).This library does not provide
Uniforminstances for any unbounded types.
Reproducibility
If you have two builds of a particular piece of code against this library, any deterministic function call should give the same result in the two builds if the builds are
- compiled against the same major version of this library
- on the same architecture (32-bit or 64-bit)
Notes for pseudo-random number generator implementors
How to implement RandomGen
Consider these points when writing a RandomGen instance for a given pure
pseudo-random number generator:
- If the pseudo-random number generator has a power-of-2 modulus, that is,
it natively outputs
2^nbits of randomness for somen, implementgenWord8,genWord16,genWord32andgenWord64. See below for more details. - If the pseudo-random number generator does not have a power-of-2
modulus, implement
nextandgenRange. See below for more details. - If the pseudo-random number generator is splittable, implement
split. If there is no suitable implementation,splitshould fail with a helpful error message.
How to implement RandomGen for a pseudo-random number generator with power-of-2 modulus
Suppose you want to implement a permuted congruential generator.
>>>data PCGen = PCGen !Word64 !Word64
It produces a full Word32 of randomness per iteration.
>>>import Data.Bits>>>:{let stepGen :: PCGen -> (Word32, PCGen) stepGen (PCGen state inc) = let newState = state * 6364136223846793005 + (inc .|. 1) xorShifted = fromIntegral (((state `shiftR` 18) `xor` state) `shiftR` 27) :: Word32 rot = fromIntegral (state `shiftR` 59) :: Word32 out = (xorShifted `shiftR` (fromIntegral rot)) .|. (xorShifted `shiftL` fromIntegral ((-rot) .&. 31)) in (out, PCGen newState inc) :}
>>>fst $ stepGen $ snd $ stepGen (PCGen 17 29)3288430965
You can make it an instance of RandomGen as follows:
>>>:{instance RandomGen PCGen where genWord32 = stepGen split _ = error "PCG is not splittable" :}
How to implement RandomGen for a pseudo-random number generator without a power-of-2 modulus
We do not recommend you implement any new pseudo-random number generators without a power-of-2 modulus.
Pseudo-random number generators without a power-of-2 modulus perform significantly worse than pseudo-random number generators with a power-of-2 modulus with this library. This is because most functionality in this library is based on generating and transforming uniformly pseudo-random machine words, and generating uniformly pseudo-random machine words using a pseudo-random number generator without a power-of-2 modulus is expensive.
The pseudo-random number generator from
L’Ecuyer (1988) natively
generates an integer value in the range [1, 2147483562]. This is the
generator used by this library before it was replaced by SplitMix in version
1.2.
>>>data LegacyGen = LegacyGen !Int32 !Int32>>>:{let legacyNext :: LegacyGen -> (Int, LegacyGen) legacyNext (LegacyGen s1 s2) = (fromIntegral z', LegacyGen 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' :}
You can make it an instance of RandomGen as follows:
>>>:{instance RandomGen LegacyGen where next = legacyNext genRange _ = (1, 2147483562) split _ = error "Not implemented" :}
References
- Guy L. Steele, Jr., Doug Lea, and Christine H. Flood. 2014. Fast splittable pseudorandom number generators. In Proceedings of the 2014 ACM International Conference on Object Oriented Programming Systems Languages & Applications (OOPSLA '14). ACM, New York, NY, USA, 453-472. DOI: https://doi.org/10.1145/2660193.2660195