System.Random.Stateful

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>>> :seti -Wno-deprecations>>> unpack . fst . genByteString 10 $ pureGen[51,123,251,37,49,167,90,109,1,4]

Gets the global pseudo-random number generator. Extracts the contents of globalStdGen

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)[1,1,1,4,5,6,1,2,2,5]

This is an outdated function and it is recommended to switch to its equivalent applyAtomicGen instead, possibly with the globalStdGen if relying on the global state is acceptable.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)[2,1,1,5,4,3,6,6,3,2]

Initialize StdGen using system entropy (i.e. /dev/urandom) when it is available, while falling back on using system time as the seed.

Applies split to the current global pseudo-random generator globalStdGen, updates it with one of the results, and returns the other.

A variant of randomM that uses the global pseudo-random number generator globalStdGen.

>>> import Data.Int>>> randomIO :: IO Int32114794456

This function is equivalent to getStdRandom random and is included in this interface for historical reasons and backwards compatibility. It is recommended to use uniformM instead, possibly with the globalStdGen if relying on the global state is acceptable.

>>> import System.Random.Stateful>>> uniformM globalStdGen :: IO Int32-1768545016

A variant of randomRM that uses the global pseudo-random number generator globalStdGen

>>> randomRIO (2020, 2100) :: IO Int2028

Similar to randomIO, this function is equivalent to getStdRandom randomR and is included in this interface for historical reasons and backwards compatibility. It is recommended to use uniformRM instead, possibly with the globalStdGen if relying on the global state is acceptable.

>>> import System.Random.Stateful>>> uniformRM (2020, 2100) globalStdGen :: IO Int2044

Sets the global pseudo-random number generator. Overwrites the contents of globalStdGen

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})

You can use type applications to disambiguate the type of the generated numbers:

>>> :seti -XTypeApplications>>> uniform @Bool pureGen(True,StdGen {unStdGen = SMGen 11285859549637045894 7641485672361121627})

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 (unpack)>>> let pureGen = mkStdGen 137>>> unpack . fst $ uniformByteString 10 pureGen[51,123,251,37,49,167,90,109,1,4]

Fill in a slice of a mutable byte array with randomly generated bytes. This function does not fail, instead it clamps the offset and number of bytes to generate into a valid range.

Produce a list of the supplied length with elements generated uniformly.

See uniformListM for a stateful counterpart.

Examples

>>> let gen = mkStdGen 2023>>> import Data.Word (Word16)>>> uniformList 5 gen :: ([Word16], StdGen)([56342,15850,25292,14347,13919],StdGen {unStdGen = SMGen 6446154349414395371 1920468677557965761})

Produce a list of the supplied length with elements generated uniformly.

See uniformListM for a stateful counterpart.

Examples

>>> let gen = mkStdGen 2023>>> uniformListR 10 (20, 30) gen :: ([Int], StdGen)([26,30,27,24,30,25,27,21,27,27],StdGen {unStdGen = SMGen 12965503083958398648 1920468677557965761})

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})

You can use type applications to disambiguate the type of the generated numbers:

>>> :seti -XTypeApplications>>> uniformR @Int (1, 4) pureGen(4,StdGen {unStdGen = SMGen 11285859549637045894 7641485672361121627})

Produce an infinite list of pseudo-random values in a specified range. Same as uniforms, integrates nicely with list fusion. There is no way to recover the final generator, therefore either use split before calling uniformRs or use uniformListR instead.

Similar to randomRs, except it relies on UniformRange type class instead of Random.

Examples

>>> let gen = mkStdGen 2023>>> take 5 $ uniformRs (10, 100) gen :: [Int][32,86,21,57,39]

Shuffle elements of a list in a uniformly random order.

Examples

>>> uniformShuffleList "ELVIS" $ mkStdGen 252("LIVES",StdGen {unStdGen = SMGen 17676540583805057877 5302934877338729551})

Produce an infinite list of pseudo-random values. Integrates nicely with list fusion. Naturally, there is no way to recover the final generator, therefore either use split before calling uniforms or use uniformList instead.

Similar to randoms, except it relies on Uniform type class instead of Random

Examples

>>> let gen = mkStdGen 2023>>> import Data.Word (Word16)>>> take 5 $ uniforms gen :: [Word16][56342,15850,25292,14347,13919]

Constructs a StdGen deterministically from an Int seed. See mkStdGen64 for a Word64 variant that is architecture agnostic.

Constructs a StdGen deterministically from a Word64 seed.

The difference between mkStdGen is that mkStdGen64 will work the same on 64-bit and 32-bit architectures, while the former can only use 32-bit of information for initializing the psuedo-random number generator on 32-bit operating systems

Efficiently generates a sequence of pseudo-random bytes in a platform independent manner.

Construct a Seed from a ByteArray of expected length. Whenever ByteArray does not match the SeedSize specified by the pseudo-random generator, this function will fail.

Just like mkSeed, but uses ByteString as argument. Results in a memcopy of the seed.

Convert a Seed to a list of 64bit words.

Construct a seed from a list of 64-bit words. At most SeedSize many bytes will be used.

This is a function that shows the name of the generator type, which is useful for error reporting.

Get the expected size of the Seed in number bytes

Just like seedSize, except it accepts a proxy as an argument.

Unwrap the Seed and get the underlying ByteArray

Just like unSeed, but produced a ByteString. Results in a memcopy of the seed.

Helper function that allows for operating directly on the Seed, while supplying a function that uses the pseudo-random number generator that is constructed from that Seed.

Example

>>> :set -XTypeApplications>>> import System.Random>>> withSeed (nonEmptyToSeed (pure 2024) :: Seed StdGen) (uniform @Int)(1039666877624726199,Seed [0xe9, 0x07, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00])

Read the seed from a file and use it for constructing a pseudo-random number generator. After supplied action has been applied to the constructed generator, the resulting generator will be converted back to a seed and written to the same file.

Same as withSeed, except it is useful with monadic computation and frozen generators.

See withSeedMutableGen for a helper that also handles seeds for mutable pseduo-random number generators.

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.

A type class for data with a finite number of inhabitants. This type class is used in the default implementation of System.Random.Stateful.Uniform.

Users are not supposed to write instances of Finite manually. There is a default implementation in terms of Generic instead.

>>> :seti -XDeriveGeneric -XDeriveAnyClass>>> import GHC.Generics (Generic)>>> data MyBool = MyTrue | MyFalse deriving (Generic, Finite)>>> data Action = Code MyBool | Eat (Maybe Bool) | Sleep deriving (Generic, Finite)

RandomGen is an interface to pure pseudo-random number generators.

StdGen is the standard RandomGen instance provided by this library.

This is a binary form of pseudo-random number generator's state. It is designed to be safe and easy to use for input/output operations like restoring from file, transmitting over the network, etc.

Constructor is not exported, becasue it is important for implementation to enforce the invariant of the underlying byte array being of the exact same length as the generator has specified in SeedSize. Use mkSeed and unSeed to get access to the raw bytes in a safe manner.

Pseudo-random generators that can be split into two separate and independent psuedo-random generators should provide an instance for this type class.

Historically this functionality was included in the RandomGen type class in the split function, however, few pseudo-random generators possess this property of splittability. This lead the old split function being usually implemented in terms of error.

The standard pseudo-random number generator.

The class of types for which a uniformly distributed value can be drawn from all possible values of the type.

The class of types for which a uniformly distributed value can be drawn from a range.

Interface for converting a pure pseudo-random number generator to and from non-empty sequence of bytes. Seeds are stored in Little-Endian order regardless of the platform it is being used on, which provides cross-platform compatibility, while providing optimal performance for the most common platform type.

Conversion to and from a Seed serves as a building block for implementing serialization for any pure or frozen pseudo-random number generator.

It is not trivial to implement platform independence. For this reason this type class has two alternative ways of creating an instance for this class. The easiest way for constructing a platform indepent seed is by converting the inner state of a generator to and from a list of 64 bit words using toSeed64 and fromSeed64 respectively. In that case cross-platform support will be handled automaticaly.

>>> :set -XDataKinds -XTypeFamilies>>> import Data.Word (Word8, Word32)>>> import Data.Bits ((.|.), shiftR, shiftL)>>> import Data.List.NonEmpty (NonEmpty ((:|)))>>> data FiveByteGen = FiveByteGen Word8 Word32 deriving Show>>> :{instance SeedGen FiveByteGen where  type SeedSize FiveByteGen = 5  fromSeed64 (w64 :| _) =    FiveByteGen (fromIntegral (w64 `shiftR` 32)) (fromIntegral w64)  toSeed64 (FiveByteGen x1 x4) =    let w64 = (fromIntegral x1 `shiftL` 32) .|. fromIntegral x4     in (w64 :| []):}

>>> FiveByteGen 0x80 0x01020304FiveByteGen 128 16909060>>> fromSeed (toSeed (FiveByteGen 0x80 0x01020304))FiveByteGen 128 16909060>>> toSeed (FiveByteGen 0x80 0x01020304)Seed [0x04, 0x03, 0x02, 0x01, 0x80]>>> toSeed64 (FiveByteGen 0x80 0x01020304)549772722948 :| []

However, when performance is of utmost importance or default handling of cross platform independence is not sufficient, then an adventurous developer can try implementing conversion into bytes directly with toSeed and fromSeed.

Properties that must hold:

> fromSeed (toSeed gen) == gen

> fromSeed64 (toSeed64 gen) == gen

Note, that there is no requirement for every Seed to roundtrip, eg. this proprty does not even hold for StdGen:

>>> let seed = nonEmptyToSeed (0xab :| [0xff00]) :: Seed StdGen>>> seed == toSeed (fromSeed seed)False

Number of bytes that is required for storing the full state of a pseudo-random number generator. It should be big enough to satisfy the roundtrip property:

> fromSeed (toSeed gen) == gen

StatefulGen is an interface to monadic pseudo-random number generators.

This class is designed for mutable pseudo-random number generators that have a frozen imutable counterpart that can be manipulated in pure code.

It also works great with frozen generators that are based on pure generators that have a RandomGen instance.

Here are a few laws, which are important for this type class:

• Roundtrip and complete destruction on overwrite:

overwriteGen mg fg >> freezeGen mg = pure fg

• Modification of a mutable generator:

overwriteGen mg fg = modifyGen mg (const ((), fg)

• Freezing of a mutable generator:

freezeGen mg = modifyGen mg (fg -> (fg, fg))

Functionality for thawing frozen generators is not part of the FrozenGen class, becase not all mutable generators support functionality of creating new mutable generators, which is what thawing is in its essence. For this reason StateGen does not have an instance for this type class, but it has one for FrozenGen.

Here is an important law that relates this type class to FrozenGen

• Roundtrip and independence of mutable generators:

traverse thawGen fgs >>= traverse freezeGen = pure fgs

Runs a mutable pseudo-random number generator from its FrozenGen state.

Examples

>>> import Data.Int (Int8)>>> withMutableGen (IOGen (mkStdGen 217)) (uniformListM 5) :: IO ([Int8], IOGen StdGen)([-74,37,-50,-2,3],IOGen {unIOGen = StdGen {unStdGen = SMGen 4273268533320920145 15251669095119325999}})

Same as withMutableGen, but only returns the generated value.

Examples

>>> import System.Random.Stateful>>> let pureGen = mkStdGen 137>>> withMutableGen_ (IOGen pureGen) (uniformRM (1 :: Int, 6 :: Int))4

Just like withMutableGen, except uses a Seed instead of a frozen generator.

Examples

Here is good example of how withSeedMutableGen can be used with withSeedFile, which uses a locally stored seed.

First we define a reportSeed function that will print the contents of a seed file as a list of bytes:

>>> import Data.ByteString as BS (readFile, writeFile, unpack)>>> :seti -XOverloadedStrings>>> let reportSeed fp = print . ("Seed: " <>) . show . BS.unpack =<< BS.readFile fp

Given a file path, write an StdGen seed into the file:

>>> :seti -XFlexibleContexts -XScopedTypeVariables>>> let writeInitSeed fp = BS.writeFile fp (unSeedToByteString (toSeed (mkStdGen 2025)))

Apply a StatefulGen monadic action that uses IOGen StdGen, restored from the seed in the given path:

>>> let withMutableSeedFile fp action = withSeedFile fp (\(seed :: Seed (IOGen StdGen)) -> withSeedMutableGen seed action)

Given a path and an action initialize the seed file and apply the action using that seed:

>>> let withInitSeedFile fp action = writeInitSeed fp *> reportSeed fp *> withMutableSeedFile fp action <* reportSeed fp

For the sake of example we will use a temporary directory for storing the seed. Here we report the contents of the seed file before and after we shuffle a list:

>>> import UnliftIO.Temporary (withSystemTempDirectory)>>> withSystemTempDirectory "random" (\fp -> withInitSeedFile (fp ++ "/seed.bin") (uniformShuffleListM [1..10]))"Seed: [183,178,143,77,132,163,109,14,157,105,82,99,148,82,109,173]""Seed: [60,105,117,203,187,138,69,39,157,105,82,99,148,82,109,173]"[7,5,4,3,1,8,10,6,9,2]

Just like withSeedMutableGen, except it doesn't return the final generator, only the resulting value. This is slightly more efficient, since it doesn't incur overhead from freezeing the mutable generator

Generates a pseudo-random value using monadic interface and Random instance.

Examples

>>> import System.Random.Stateful>>> let pureGen = mkStdGen 139>>> g <- newIOGenM pureGen>>> randomM g :: IO Double0.33775117339631733

You can use type applications to disambiguate the type of the generated numbers:

>>> :seti -XTypeApplications>>> randomM @Double g0.9156875994165681

Generates a pseudo-random value using monadic interface and Random instance.

Examples

>>> import System.Random.Stateful>>> let pureGen = mkStdGen 137>>> g <- newIOGenM pureGen>>> randomRM (1, 100) g :: IO Int52

You can use type applications to disambiguate the type of the generated numbers:

>>> :seti -XTypeApplications>>> randomRM @Int (1, 100) g2

Splits a pseudo-random number generator into two. Overwrites the mutable pseudo-random number generator with one of the immutable pseudo-random number generators produced by a split function and returns the other.

Splits a pseudo-random number generator into two. Overwrites the mutable wrapper with one of the resulting generators and returns the other as a new mutable generator.

The class of types for which a uniformly distributed value can be drawn from all possible values of the type.

A definition of Uniform for Finite types. If your data has several fields of sub-Word cardinality, this instance may be more efficient than one, derived via Generic and GUniform.

>>> :seti -XDeriveGeneric -XDeriveAnyClass>>> import GHC.Generics (Generic)>>> import System.Random.Stateful>>> data Triple = Triple Word8 Word8 Word8 deriving (Show, Generic, Finite)>>> instance Uniform Triple where uniformM = uniformViaFiniteM>>> gen <- newIOGenM (mkStdGen 42)>>> uniformListM 5 gen :: IO [Triple][Triple 60 226 48,Triple 234 194 151,Triple 112 96 95,Triple 51 251 15,Triple 6 0 208]

The class of types for which a uniformly distributed value can be drawn from a range.

Utilize Ord instance to decide if a value is within the range. Designed to be used for implementing isInRange

Utilize Enum instance to decide if a value is within the range. Designed to be used for implementing isInRange