Modulerandom-1.3.1Haskell2010

System.Random

This library deals with the common task of pseudo-random number generation.

2 types
7 classes
33 values

Packagerandom-1.3.1
Exports46
LanguageHaskell2010
LicenceBSD-3-Clause
SourceRandom.hs

Introduction

0 declarations

This module provides type classes and instances for the following concepts:

Pure pseudo-random number generators

RandomGen

is an interface to pure pseudo-random number generators.

StdGen, the standard pseudo-random number generator provided in this library, is an instance of RandomGen. It uses the SplitMix implementation provided by the splitmix package. Programmers may, of course, supply their own instances of RandomGen.

Usage

0 declarations

In pure code, use uniform and uniformR to generate pseudo-random values with a pure pseudo-random number generator like StdGen.

Example1 expression

>>> :{let rolls :: RandomGen g => Int -> g -> [Word]    rolls n = fst . uniformListR n (1, 6)    pureGen = mkStdGen 137in    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.

Example1 expression

>>> :{let rollsM :: StatefulGen g m => Int -> g -> m [Word]    rollsM n = uniformListRM n (1, 6)    pureGen = mkStdGen 137in    runStateGen_ pureGen (rollsM 10) :: [Word]:}[4,2,6,1,6,6,5,1,1,5]

Pure number generator interface

8 declarations

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 split if 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

classclass RandomGen g where

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

StdGen is the standard RandomGen instance provided by this library.

Methods

genWord8 :: g -> (Word8, g)
Returns a Word8 that is uniformly distributed over the entire Word8 range.
genWord16 :: g -> (Word16, g)
Returns a Word16 that is uniformly distributed over the entire Word16 range.
genWord32 :: g -> (Word32, g)
Returns a Word32 that is uniformly distributed over the entire Word32 range.
genWord64 :: g -> (Word64, g)
Returns a Word64 that is uniformly distributed over the entire Word64 range.
genWord32R :: Word32 -> g -> (Word32, g)
genWord32R upperBound g returns a Word32 that is uniformly distributed over the range [0, upperBound].
genWord64R :: Word64 -> g -> (Word64, g)
genWord64R upperBound g returns a Word64 that is uniformly distributed over the range [0, upperBound].
unsafeUniformFillMutableByteArray :: MutableByteArray s -> Int -> Int -> g -> ST s g
Fill in the supplied MutableByteArray with uniformly generated random bytes. This function is unsafe because it is not required to do any bounds checking. For a safe variant use System.Random.Sateful.uniformFillMutableByteArrayM instead.
Default type class implementation uses defaultUnsafeUniformFillMutableByteArray.
split :: g -> (g, g)
Returns two distinct pseudo-random number generators.
Implementations should take care to ensure that the resulting generators are not correlated. Some pseudo-random number generators are not splittable. In that case, the split implementation should fail with a descriptive error message.

Instances8RandomGen, …

RandomGen StdGenDefined in random-1.3.1 · System.Random.Internal
RandomGen SMGenDefined in random-1.3.1 · System.Random.Internal
RandomGen SMGenDefined in random-1.3.1 · System.Random.Internal
RandomGen g => RandomGen (StateGen g)Defined in random-1.3.1 · System.Random.Internal
RandomGen g => RandomGen (AtomicGen g)Defined in random-1.3.1 · System.Random.Stateful
RandomGen g => RandomGen (IOGen g)Defined in random-1.3.1 · System.Random.Stateful
RandomGen g => RandomGen (STGen g)Defined in random-1.3.1 · System.Random.Stateful
RandomGen g => RandomGen (TGen g)Defined in random-1.3.1 · System.Random.Stateful

classclass RandomGen g => SplitGen g where

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.

Methods

splitGen :: g -> (g, g)
Returns two distinct pseudo-random number generators.
Implementations should take care to ensure that the resulting generators are not correlated.

Instances8SplitGen, …

SplitGen StdGenDefined in random-1.3.1 · System.Random.Internal
SplitGen SMGenDefined in random-1.3.1 · System.Random.Internal
SplitGen SMGenDefined in random-1.3.1 · System.Random.Internal
SplitGen g => SplitGen (StateGen g)Defined in random-1.3.1 · System.Random.Internal
SplitGen g => SplitGen (AtomicGen g)Defined in random-1.3.1 · System.Random.Stateful
SplitGen g => SplitGen (IOGen g)Defined in random-1.3.1 · System.Random.Stateful
SplitGen g => SplitGen (STGen g)Defined in random-1.3.1 · System.Random.Stateful
SplitGen g => SplitGen (TGen g)Defined in random-1.3.1 · System.Random.Stateful

valueuniform :: (Uniform a, RandomGen g) => g -> (a, g)

Generates a value uniformly distributed over all possible values of that type.

This is a pure version of uniformM.

Examples

Example3 expressions

>>> 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:

Example2 expressions

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

valueuniformR :: (UniformRange a, RandomGen g) => (a, a) -> g -> (a, g)

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

Example3 expressions

>>> 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:

Example2 expressions

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

classclass Random a where

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.

Methods

randomR :: RandomGen g => (a, a) -> g -> (a, g)
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.
Example3 expressions
```
>>> let gen = mkStdGen 26>>> fst $ randomR ('a', 'z') gen'z'>>> fst $ randomR ('a', 'z') gen'z'
```
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:
Example1 expression
```
>>> fst $ randomR (('a', 5.0), ('z', 10.0)) $ mkStdGen 26('z',5.22694980853051)
```
In case when a lawful range is desired uniformR should be used instead.
random :: RandomGen g => 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 floating point types, the range is normally the closed interval [0,1].
- For Integer, the range is (arbitrarily) the range of Int.
randomRs :: RandomGen g => (a, a) -> g -> [a]
Plural variant of randomR, producing an infinite list of pseudo-random values instead of returning a new generator.
randoms :: RandomGen g => g -> [a]
Plural variant of random, producing an infinite list of pseudo-random values instead of returning a new generator.

Instances43Random, …

Random IntegerDefined in random-1.3.1 · System.Random
Note - random generates values in the Int range
Random CBoolDefined in random-1.3.1 · System.Random
Random CCharDefined in random-1.3.1 · System.Random
Random CDoubleDefined in random-1.3.1 · System.Random
Note - random produces values in the closed range [0,1].
Random CFloatDefined in random-1.3.1 · System.Random
Note - random produces values in the closed range [0,1].
Random CIntDefined in random-1.3.1 · System.Random
Random CIntMaxDefined in random-1.3.1 · System.Random
Random CIntPtrDefined in random-1.3.1 · System.Random
Random CLLongDefined in random-1.3.1 · System.Random
Random CLongDefined in random-1.3.1 · System.Random
Random CPtrdiffDefined in random-1.3.1 · System.Random
Random CSCharDefined in random-1.3.1 · System.Random
Random CShortDefined in random-1.3.1 · System.Random
Random CSigAtomicDefined in random-1.3.1 · System.Random
Random CSizeDefined in random-1.3.1 · System.Random
Random CUCharDefined in random-1.3.1 · System.Random
Random CUIntDefined in random-1.3.1 · System.Random
Random CUIntMaxDefined in random-1.3.1 · System.Random
Random CUIntPtrDefined in random-1.3.1 · System.Random
Random CULLongDefined in random-1.3.1 · System.Random
Random CULongDefined in random-1.3.1 · System.Random
Random CUShortDefined in random-1.3.1 · System.Random
Random CWcharDefined in random-1.3.1 · System.Random
Random Int16Defined in random-1.3.1 · System.Random
Random Int32Defined in random-1.3.1 · System.Random
Random Int64Defined in random-1.3.1 · System.Random
Random Int8Defined in random-1.3.1 · System.Random
Random BoolDefined in random-1.3.1 · System.Random
Random CharDefined in random-1.3.1 · System.Random
Random DoubleDefined in random-1.3.1 · System.Random
Note - random produces values in the closed range [0,1].
Random FloatDefined in random-1.3.1 · System.Random
Note - random produces values in the closed range [0,1].
Random IntDefined in random-1.3.1 · System.Random
Random WordDefined in random-1.3.1 · System.Random
Random Word16Defined in random-1.3.1 · System.Random
Random Word32Defined in random-1.3.1 · System.Random
Random Word64Defined in random-1.3.1 · System.Random
Random Word8Defined in random-1.3.1 · System.Random
(Random a, Random b) => Random (a, b)Defined in random-1.3.1 · System.Random
Note - randomR treats a and b types independently
(Random a, Random b, Random c) => Random (a, b, c)Defined in random-1.3.1 · System.Random
Note - randomR treats a, b and c types independently
(Random a, Random b, Random c, Random d) => Random (a, b, c, d)Defined in random-1.3.1 · System.Random
Note - randomR treats a, b, c and d types independently
(Random a, Random b, Random c, Random d, Random e) => Random (a, b, c, d, e)Defined in random-1.3.1 · System.Random
Note - randomR treats a, b, c, d and e types independently
(Random a, Random b, Random c, Random d, Random e, Random f) => Random (a, b, c, d, e, f)Defined in random-1.3.1 · System.Random
Note - randomR treats a, b, c, d, e and f types independently
(Random a, Random b, Random c, Random d, Random e, Random f, Random g) => Random (a, b, c, d, e, f, g)Defined in random-1.3.1 · System.Random
Note - randomR treats a, b, c, d, e, f and g types independently

classclass Uniform a where

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

Instances42Uniform, …

Uniform CBoolDefined in random-1.3.1 · System.Random.Internal
Uniform CCharDefined in random-1.3.1 · System.Random.Internal
Uniform CIntDefined in random-1.3.1 · System.Random.Internal
Uniform CIntMaxDefined in random-1.3.1 · System.Random.Internal
Uniform CIntPtrDefined in random-1.3.1 · System.Random.Internal
Uniform CLLongDefined in random-1.3.1 · System.Random.Internal
Uniform CLongDefined in random-1.3.1 · System.Random.Internal
Uniform CPtrdiffDefined in random-1.3.1 · System.Random.Internal
Uniform CSCharDefined in random-1.3.1 · System.Random.Internal
Uniform CShortDefined in random-1.3.1 · System.Random.Internal
Uniform CSigAtomicDefined in random-1.3.1 · System.Random.Internal
Uniform CSizeDefined in random-1.3.1 · System.Random.Internal
Uniform CUCharDefined in random-1.3.1 · System.Random.Internal
Uniform CUIntDefined in random-1.3.1 · System.Random.Internal
Uniform CUIntMaxDefined in random-1.3.1 · System.Random.Internal
Uniform CUIntPtrDefined in random-1.3.1 · System.Random.Internal
Uniform CULLongDefined in random-1.3.1 · System.Random.Internal
Uniform CULongDefined in random-1.3.1 · System.Random.Internal
Uniform CUShortDefined in random-1.3.1 · System.Random.Internal
Uniform CWcharDefined in random-1.3.1 · System.Random.Internal
Uniform Int16Defined in random-1.3.1 · System.Random.Internal
Uniform Int32Defined in random-1.3.1 · System.Random.Internal
Uniform Int64Defined in random-1.3.1 · System.Random.Internal
Uniform Int8Defined in random-1.3.1 · System.Random.Internal
Uniform BoolDefined in random-1.3.1 · System.Random.Internal
Uniform CharDefined in random-1.3.1 · System.Random.Internal
Uniform IntDefined in random-1.3.1 · System.Random.Internal
Uniform WordDefined in random-1.3.1 · System.Random.Internal
Uniform Word16Defined in random-1.3.1 · System.Random.Internal
Uniform Word32Defined in random-1.3.1 · System.Random.Internal
Uniform Word64Defined in random-1.3.1 · System.Random.Internal
Uniform Word8Defined in random-1.3.1 · System.Random.Internal
Uniform ()Defined in random-1.3.1 · System.Random.Internal
SeedGen g => Uniform (Seed g)Defined in random-1.3.1 · System.Random.Seed · orphan
(Finite a, Uniform a) => Uniform (Maybe a)Defined in random-1.3.1 · System.Random.Internal
(Finite a, Uniform a, Finite b, Uniform b) => Uniform (Either a b)Defined in random-1.3.1 · System.Random.Internal
(Uniform a, Uniform b) => Uniform (a, b)Defined in random-1.3.1 · System.Random.Internal
(Uniform a, Uniform b, Uniform c) => Uniform (a, b, c)Defined in random-1.3.1 · System.Random.Internal
(Uniform a, Uniform b, Uniform c, Uniform d) => Uniform (a, b, c, d)Defined in random-1.3.1 · System.Random.Internal
(Uniform a, Uniform b, Uniform c, Uniform d, Uniform e) => Uniform (a, b, c, d, e)Defined in random-1.3.1 · System.Random.Internal
(Uniform a, Uniform b, Uniform c, Uniform d, Uniform e, Uniform f) => Uniform (a, b, c, d, e, f)Defined in random-1.3.1 · System.Random.Internal
(Uniform a, Uniform b, Uniform c, Uniform d, Uniform e, Uniform f, Uniform g) => Uniform (a, b, c, d, e, f, g)Defined in random-1.3.1 · System.Random.Internal

classclass UniformRange a where

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

Instances45UniformRange, …

UniformRange IntegerDefined in random-1.3.1 · System.Random.Internal
UniformRange NaturalDefined in random-1.3.1 · System.Random.Internal
UniformRange CBoolDefined in random-1.3.1 · System.Random.Internal
UniformRange CCharDefined in random-1.3.1 · System.Random.Internal
UniformRange CDoubleDefined in random-1.3.1 · System.Random.Internal
See Floating point number caveats.
UniformRange CFloatDefined in random-1.3.1 · System.Random.Internal
See Floating point number caveats.
UniformRange CIntDefined in random-1.3.1 · System.Random.Internal
UniformRange CIntMaxDefined in random-1.3.1 · System.Random.Internal
UniformRange CIntPtrDefined in random-1.3.1 · System.Random.Internal
UniformRange CLLongDefined in random-1.3.1 · System.Random.Internal
UniformRange CLongDefined in random-1.3.1 · System.Random.Internal
UniformRange CPtrdiffDefined in random-1.3.1 · System.Random.Internal
UniformRange CSCharDefined in random-1.3.1 · System.Random.Internal
UniformRange CShortDefined in random-1.3.1 · System.Random.Internal
UniformRange CSigAtomicDefined in random-1.3.1 · System.Random.Internal
UniformRange CSizeDefined in random-1.3.1 · System.Random.Internal
UniformRange CUCharDefined in random-1.3.1 · System.Random.Internal
UniformRange CUIntDefined in random-1.3.1 · System.Random.Internal
UniformRange CUIntMaxDefined in random-1.3.1 · System.Random.Internal
UniformRange CUIntPtrDefined in random-1.3.1 · System.Random.Internal
UniformRange CULLongDefined in random-1.3.1 · System.Random.Internal
UniformRange CULongDefined in random-1.3.1 · System.Random.Internal
UniformRange CUShortDefined in random-1.3.1 · System.Random.Internal
UniformRange CWcharDefined in random-1.3.1 · System.Random.Internal
UniformRange Int16Defined in random-1.3.1 · System.Random.Internal
UniformRange Int32Defined in random-1.3.1 · System.Random.Internal
UniformRange Int64Defined in random-1.3.1 · System.Random.Internal
UniformRange Int8Defined in random-1.3.1 · System.Random.Internal
UniformRange BoolDefined in random-1.3.1 · System.Random.Internal
UniformRange CharDefined in random-1.3.1 · System.Random.Internal
UniformRange DoubleDefined in random-1.3.1 · System.Random.Internal
See Floating point number caveats.
UniformRange FloatDefined in random-1.3.1 · System.Random.Internal
See Floating point number caveats.
UniformRange IntDefined in random-1.3.1 · System.Random.Internal
UniformRange WordDefined in random-1.3.1 · System.Random.Internal
UniformRange Word16Defined in random-1.3.1 · System.Random.Internal
UniformRange Word32Defined in random-1.3.1 · System.Random.Internal
UniformRange Word64Defined in random-1.3.1 · System.Random.Internal
UniformRange Word8Defined in random-1.3.1 · System.Random.Internal
UniformRange ()Defined in random-1.3.1 · System.Random.Internal
(UniformRange a, UniformRange b) => UniformRange (a, b)Defined in random-1.3.1 · System.Random.Internal
(UniformRange a, UniformRange b, UniformRange c) => UniformRange (a, b, c)Defined in random-1.3.1 · System.Random.Internal
(UniformRange a, UniformRange b, UniformRange c, UniformRange d) => UniformRange (a, b, c, d)Defined in random-1.3.1 · System.Random.Internal
(UniformRange a, UniformRange b, UniformRange c, UniformRange d, UniformRange e) => UniformRange (a, b, c, d, e)Defined in random-1.3.1 · System.Random.Internal
(UniformRange a, UniformRange b, UniformRange c, UniformRange d, UniformRange e, UniformRange f) => UniformRange (a, b, c, d, e, f)Defined in random-1.3.1 · System.Random.Internal
(UniformRange a, UniformRange b, UniformRange c, UniformRange d, UniformRange e, UniformRange f, UniformRange g) => UniformRange (a, b, c, d, e, f, g)Defined in random-1.3.1 · System.Random.Internal

classclass Finite a where

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.

Example4 expressions

>>> :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)

Instances23Finite, …

Finite VoidDefined in random-1.3.1 · System.Random.GFinite
Finite Int16Defined in random-1.3.1 · System.Random.GFinite
Finite Int32Defined in random-1.3.1 · System.Random.GFinite
Finite Int64Defined in random-1.3.1 · System.Random.GFinite
Finite Int8Defined in random-1.3.1 · System.Random.GFinite
Finite BoolDefined in random-1.3.1 · System.Random.GFinite
Finite CharDefined in random-1.3.1 · System.Random.GFinite
Finite IntDefined in random-1.3.1 · System.Random.GFinite
Finite OrderingDefined in random-1.3.1 · System.Random.GFinite
Finite WordDefined in random-1.3.1 · System.Random.GFinite
Finite Word16Defined in random-1.3.1 · System.Random.GFinite
Finite Word32Defined in random-1.3.1 · System.Random.GFinite
Finite Word64Defined in random-1.3.1 · System.Random.GFinite
Finite Word8Defined in random-1.3.1 · System.Random.GFinite
Finite ()Defined in random-1.3.1 · System.Random.GFinite
Finite a => Finite (Maybe a)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b) => Finite (Either a b)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b) => Finite (a, b)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b, Finite c) => Finite (a, b, c)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b, Finite c, Finite d) => Finite (a, b, c, d)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b, Finite c, Finite d, Finite e) => Finite (a, b, c, d, e)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b, Finite c, Finite d, Finite e, Finite f) => Finite (a, b, c, d, e, f)Defined in random-1.3.1 · System.Random.GFinite
(Finite a, Finite b, Finite c, Finite d, Finite e, Finite f, Finite g) => Finite (a, b, c, d, e, f, g)Defined in random-1.3.1 · System.Random.GFinite

Seed

valuemkSeed :: (SeedGen g, MonadFail m) => ByteArray -> m (Seed g)

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.

valuemkSeedFromByteString :: (SeedGen g, MonadFail m) => ByteString -> m (Seed g)

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

valuenonEmptyFromSeed :: SeedGen g => Seed g -> NonEmpty Word64

Convert a Seed to a list of 64bit words.

valuenonEmptyToSeed :: SeedGen g => NonEmpty Word64 -> Seed g

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

valueseedGenTypeName :: SeedGen g => String

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

valueseedSize :: SeedGen g => Int

Get the expected size of the Seed in number bytes

valueseedSizeProxy :: SeedGen g => proxy g -> Int

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

valueunSeed :: Seed g -> ByteArray

Unwrap the Seed and get the underlying ByteArray

valueunSeedToByteString :: Seed g -> ByteString

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

valuewithSeed :: SeedGen g => Seed g -> (g -> (a, g)) -> (a, Seed g)

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

Example3 expressions

>>> :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])

valuewithSeedFile

:: (SeedGen g, MonadIO m)
=> FilePath
-> Seed g -> m (a, Seed g)
-> m a

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.

valuewithSeedM

:: (SeedGen g, Functor f)
=> Seed g
-> g -> f (a, g)
-> f (a, Seed g)

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.

newtypenewtype Seed g

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.

Instances4Eq, Ord, Show, Uniform

Eq (Seed g)Defined in random-1.3.1 · System.Random.Internal
Ord (Seed g)Defined in random-1.3.1 · System.Random.Internal
Show (Seed g)Defined in random-1.3.1 · System.Random.Internal
SeedGen g => Uniform (Seed g)Defined in random-1.3.1 · System.Random.Seed · orphan

classclass (KnownNat (SeedSize g), 1 <= SeedSize g, Typeable g) => SeedGen g where

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.

Example6 expressions

>>> :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 :| []):}

Example4 expressions

>>> 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:

Example2 expressions

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

Associated types

type family SeedSize g :: Nat
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
```

Methods

fromSeed :: Seed g -> g
Convert from a binary representation to a pseudo-random number generator
toSeed :: g -> Seed g
Convert to a binary representation of a pseudo-random number generator
fromSeed64 :: NonEmpty Word64 -> g
Construct pseudo-random number generator from a list of words. Whenever list does not have enough bytes to satisfy the SeedSize requirement, it will be padded with zeros. On the other hand when it has more than necessary, extra bytes will be dropped.
For example if SeedSize is set to 2, then only the lower 16 bits of the first element in the list will be used.
toSeed64 :: g -> NonEmpty Word64
Convert pseudo-random number generator to a list of words
In case when SeedSize is not a multiple of 8, then the upper bits of the last word in the list will be set to zero.

Instances8SeedGen, …

SeedGen StdGenDefined in random-1.3.1 · System.Random.Seed
SeedGen SMGenDefined in random-1.3.1 · System.Random.Seed
SeedGen SMGenDefined in random-1.3.1 · System.Random.Seed
SeedGen g => SeedGen (StateGen g)Defined in random-1.3.1 · System.Random.Seed
SeedGen g => SeedGen (AtomicGen g)Defined in random-1.3.1 · System.Random.Stateful
SeedGen g => SeedGen (IOGen g)Defined in random-1.3.1 · System.Random.Stateful
SeedGen g => SeedGen (STGen g)Defined in random-1.3.1 · System.Random.Stateful
SeedGen g => SeedGen (TGen g)Defined in random-1.3.1 · System.Random.Stateful

familytype family SeedSize g :: Nat

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

Instances8SeedSize, …

type SeedSize StdGen = SeedSize SMGenDefined in random-1.3.1 · System.Random.Seed
type SeedSize SMGen = 16Defined in random-1.3.1 · System.Random.Seed
type SeedSize SMGen = 8Defined in random-1.3.1 · System.Random.Seed
type SeedSize (StateGen g) = SeedSize gDefined in random-1.3.1 · System.Random.Seed
type SeedSize (AtomicGen g) = SeedSize gDefined in random-1.3.1 · System.Random.Stateful
type SeedSize (IOGen g) = SeedSize gDefined in random-1.3.1 · System.Random.Stateful
type SeedSize (STGen g) = SeedSize gDefined in random-1.3.1 · System.Random.Stateful
type SeedSize (TGen g) = SeedSize gDefined in random-1.3.1 · System.Random.Stateful

Generators for sequences of pseudo-random bytes

0 declarations

Lists

valueuniforms :: (Uniform a, RandomGen g) => g -> [a]

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

Example3 expressions

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

valueuniformRs :: (UniformRange a, RandomGen g) => (a, a) -> g -> [a]

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

Example2 expressions

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

valueuniformList :: (Uniform a, RandomGen g) => Int -> g -> ([a], g)

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

See uniformListM for a stateful counterpart.

Examples

Example3 expressions

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

valueuniformListR

:: (UniformRange a, RandomGen g)
=> Int
-> (a, a)
-> g
-> ([a], g)

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

See uniformListM for a stateful counterpart.

Examples

Example2 expressions

>>> 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})

valueuniformShuffleList :: RandomGen g => [a] -> g -> ([a], g)

Shuffle elements of a list in a uniformly random order.

Examples

Example1 expression

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

Bytes

valueuniformByteArray

:: RandomGen g
=> Bool
Should byte array be allocated in pinned or unpinned memory.
-> Int
Number of bytes to generate
-> g
Pure pseudo-random numer generator
-> (ByteArray, g)

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

valueuniformByteString :: RandomGen g => Int -> g -> (ByteString, g)

Generates a ByteString of the specified size using a pure pseudo-random number generator. See uniformByteStringM for the monadic version.

Examples

Example4 expressions

>>> 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]

valueuniformShortByteString :: RandomGen g => Int -> g -> (ShortByteString, g)

Same as uniformByteArray False, but for ShortByteString.

Returns a ShortByteString of length n filled with pseudo-random bytes.

Examples

Example4 expressions

>>> import System.Random>>> import Data.ByteString.Short (unpack)>>> let pureGen = mkStdGen 137>>> unpack . fst $ uniformShortByteString 10 pureGen[51,123,251,37,49,167,90,109,1,4]

valueuniformFillMutableByteArray

:: RandomGen g
=> MutableByteArray s
Mutable array to fill with random bytes
-> Int
Offset into a mutable array from the beginning in number of bytes. Offset will be clamped into the range between 0 and the total size of the mutable array
-> Int
Number of randomly generated bytes to write into the array. This number will be clamped between 0 and the total size of the array without the offset.
-> g
-> ST s g

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.

Deprecated

valuegenByteString :: RandomGen g => Int -> g -> (ByteString, g)

Deprecated. In favor of uniformByteString

Generates a ByteString of the specified size using a pure pseudo-random number generator. See uniformByteStringM for the monadic version.

Examples

Example5 expressions

>>> 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]

methodgenShortByteString :: Int -> g -> (ShortByteString, g)

Deprecated. In favor of uniformShortByteString

Same as uniformByteArray False, but for ShortByteString.

genShortByteString n g returns a ShortByteString of length n filled with pseudo-random bytes.

Note - This function will be removed from the type class in the next major release as it is no longer needed because of unsafeUniformFillMutableByteArray.

Standard pseudo-random number generator

newtypenewtype StdGen

The standard pseudo-random number generator.

Instances7Eq, Show, NFData, RandomGen, SplitGen, SeedGen, …

Eq StdGenDefined in random-1.3.1 · System.Random.Internal
Show StdGenDefined in random-1.3.1 · System.Random.Internal
NFData StdGenDefined in random-1.3.1 · System.Random.Internal
RandomGen StdGenDefined in random-1.3.1 · System.Random.Internal
SplitGen StdGenDefined in random-1.3.1 · System.Random.Internal
SeedGen StdGenDefined in random-1.3.1 · System.Random.Seed
type SeedSize StdGen = SeedSize SMGenDefined in random-1.3.1 · System.Random.Seed

valuemkStdGen :: Int -> StdGen

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

valuemkStdGen64 :: Word64 -> StdGen

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

valueinitStdGen :: MonadIO m => m StdGen

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

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.

valuegetStdRandom :: MonadIO m => (StdGen -> (a, StdGen)) -> m a

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:

Example2 expressions

>>> 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.

Example3 expressions

>>> 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]

valuegetStdGen :: MonadIO m => m StdGen

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

valuesetStdGen :: MonadIO m => StdGen -> m ()

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

valuenewStdGen :: MonadIO m => m StdGen

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

valuerandomIO :: (Random a, MonadIO m) => m a

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

Example2 expressions

>>> 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.

Example2 expressions

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

valuerandomRIO :: (Random a, MonadIO m) => (a, a) -> m a

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

Example1 expression

>>> 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.

Example2 expressions

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

Compatibility and reproducibility

0 declarations

Backwards compatibility and deprecations

methodgenRange :: g -> (Int, Int)

Deprecated. No longer used

Yields the range of values returned by next.

It is required that:

If (a, b) = genRange g, then a < b.
genRange must not examine its argument so the value it returns is determined only by the instance of RandomGen.

The default definition spans the full range of Int.

methodnext :: g -> (Int, g)

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.

Version 1.2 mostly maintains backwards compatibility with version 1.1. This has a few consequences users should be aware of:

The type class Random is only provided for backwards compatibility. New code should use Uniform and UniformRange instead.
The methods next and genRange in RandomGen are deprecated and only provided for backwards compatibility. New instances of RandomGen should implement word-based methods instead. See below for more information about how to write a RandomGen instance.
This library provides instances for Random for 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 the random implementation for unbounded types actually generates a value based on some fixed range.
For Integer, random generates a value in the Int range. For Float and Double, random generates a floating point value in the range [0, 1).
This library does not provide Uniform instances 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

0 declarations

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^n bits of randomness for some n, implement genWord8, genWord16, genWord32 and genWord64. See below for more details.
If the pseudo-random number generator does not have a power-of-2 modulus, implement next and genRange. See below for more details.
If the pseudo-random number generator is splittable, implement split. If there is no suitable implementation, split should 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.

Example1 expression

>>> data PCGen = PCGen !Word64 !Word64

It produces a full Word32 of randomness per iteration.

Example2 expressions

>>> 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):}

Example1 expression

>>> fst $ stepGen $ snd $ stepGen (PCGen 17 29)3288430965

You can make it an instance of RandomGen as follows:

Example1 expression

>>> :{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.

Example2 expressions

>>> 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:

Example1 expression

>>> :{instance RandomGen LegacyGen where  next = legacyNext  genRange _ = (1, 2147483562)  split _ = error "Not implemented":}

References

0 declarations

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