haskell / random / 429

{-# LANGUAGE BangPatterns #-}

{-# LANGUAGE CPP #-}

{-# LANGUAGE DefaultSignatures #-}

{-# LANGUAGE MagicHash #-}

{-# LANGUAGE Trustworthy #-}

-- |

-- Module      :  System.Random

-- Copyright   :  (c) The University of Glasgow 2001

-- License     :  BSD-style (see the file LICENSE in the 'random' repository)

-- Maintainer  :  libraries@haskell.org

-- Stability   :  stable

--

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

module System.Random (

  -- * Introduction

  -- $introduction

  -- * Usage

  -- $usagepure

  -- * Pure number generator interface

  -- $interfaces

  RandomGen (

    split,

    genWord8,

    genWord16,

    genWord32,

    genWord64,

    genWord32R,

    genWord64R,

    unsafeUniformFillMutableByteArray

  ),

  SplitGen (splitGen),

  uniform,

  uniformR,

  Random (..),

  Uniform,

  UniformRange,

  Finite,

  -- ** Seed

  module System.Random.Seed,

  -- * Generators for sequences of pseudo-random bytes

  -- ** Lists

  uniforms,

  uniformRs,

  uniformList,

  uniformListR,

  uniformShuffleList,

  -- ** Bytes

  uniformByteArray,

  uniformByteString,

  uniformShortByteString,

  uniformFillMutableByteArray,

  -- *** Deprecated

  genByteString,

  genShortByteString,

  -- ** Standard pseudo-random number generator

  StdGen,

  mkStdGen,

  mkStdGen64,

  initStdGen,

  -- ** Global standard pseudo-random number generator

  -- $globalstdgen

  getStdRandom,

  getStdGen,

  setStdGen,

  newStdGen,

  randomIO,

  randomRIO,

  -- * Compatibility and reproducibility

  -- ** Backwards compatibility and deprecations

  genRange,

  next,

  -- $deprecations

  -- ** Reproducibility

  -- $reproducibility

  -- * Notes for pseudo-random number generator implementors

  -- ** How to implement 'RandomGen'

  -- $implementrandomgen

  -- * References

  -- $references

) where

import Control.Arrow

import Control.Monad.IO.Class

import Control.Monad.ST (ST)

import Control.Monad.State.Strict

import Data.Array.Byte (ByteArray (..), MutableByteArray (..))

import Data.ByteString (ByteString)

import Data.ByteString.Short.Internal (ShortByteString (..))

import Data.IORef

import Data.Int

import Data.Word

import Foreign.C.Types

import GHC.Exts

import System.Random.Array (getSizeOfMutableByteArray, shortByteStringToByteString, shuffleListST)

import System.Random.GFinite (Finite)

import System.Random.Internal hiding (uniformShortByteString)

import System.Random.Seed

import qualified System.Random.SplitMix as SM

-- $introduction

--

-- 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

--     <https://hackage.haskell.org/package/splitmix splitmix> package.

--     Programmers may, of course, supply their own instances of 'RandomGen'.

-- $usagepure

--

-- 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 = fst . uniformListR n (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 = uniformListRM n (1, 6)

--     pureGen = mkStdGen 137

-- in

--     runStateGen_ pureGen (rollsM 10) :: [Word]

-- :}

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

-------------------------------------------------------------------------------

-- Pseudo-random number generator interfaces

-------------------------------------------------------------------------------

-- $interfaces

--

-- 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.

--

-- ['System.Random.Stateful.StatefulGen': monadic pseudo-random number generators]

--     See "System.Random.Stateful" module

-- | Generates a value uniformly distributed over all possible values of that

-- type.

--

-- This is a pure version of 'System.Random.Stateful.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})

--

-- @since 1.2.0

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

{-# INLINE uniform #-}

-- | 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 'System.Random.Stateful.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})

--

-- @since 1.2.0

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

{-# INLINE uniformR #-}

-- | 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]

--

-- @since 1.3.0

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

{-# INLINE uniforms #-}

-- | 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]

--

-- @since 1.3.0

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

{-# INLINE uniformRs #-}

-- | 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})

--

-- @since 1.3.0

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

{-# INLINE uniformList #-}

-- | 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})

--

-- @since 1.3.0

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

{-# INLINE uniformListR #-}

-- | Shuffle elements of a list in a uniformly random order.

--

-- ====__Examples__

--

-- >>> uniformShuffleList "ELVIS" $ mkStdGen 252

-- ("LIVES",StdGen {unStdGen = SMGen 17676540583805057877 5302934877338729551})

--

-- @since 1.3.0

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

{-# INLINE uniformShuffleList #-}

-- | 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]

--

-- @since 1.2.0

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

{-# INLINE genByteString #-}

{-# DEPRECATED genByteString "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__

--

-- >>> 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]

--

-- @since 1.3.0

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

    (byteArray, g') ->

{-# INLINE uniformByteString #-}

-- | Same as @`uniformByteArray` `False`@, but for `ShortByteString`.

--

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

--

-- ====__Examples__

--

-- >>> 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]

--

-- @since 1.3.0

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

{-# INLINE uniformShortByteString #-}

-- | 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.

--

-- @since 1.3.0

uniformFillMutableByteArray ::

  RandomGen g =>

  -- | Mutable array to fill with random bytes

  MutableByteArray s ->

  -- | 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.

  Int ->

  g ->

  ST s g

{-# INLINE uniformFillMutableByteArray #-}

-- | 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

class Random a where

  -- | 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 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:

  --

  -- >>> 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.

  --

  -- @since 1.0.0

  {-# INLINE randomR #-}

  randomR :: RandomGen g => (a, a) -> g -> (a, g)

  default randomR :: (RandomGen g, UniformRange a) => (a, a) -> g -> (a, g)

  -- | The same as 'randomR', but using a default range determined by the type:

  --

  -- * For bounded types (instances of 'Bounded', such as 'Char'),

  --   the range is normally the whole type.

  --

  -- * For floating point types, the range is normally the closed interval @[0,1]@.

  --

  -- * For 'Integer', the range is (arbitrarily) the range of 'Int'.

  --

  -- @since 1.0.0

  {-# INLINE random #-}

  random :: RandomGen g => g -> (a, g)

  default random :: (RandomGen g, Uniform a) => g -> (a, g)

  -- | Plural variant of 'randomR', producing an infinite list of

  -- pseudo-random values instead of returning a new generator.

  --

  -- @since 1.0.0

  {-# INLINE randomRs #-}

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

  -- | Plural variant of 'random', producing an infinite list of

  -- pseudo-random values instead of returning a new generator.

  --

  -- @since 1.0.0

  {-# INLINE randoms #-}

  randoms :: RandomGen g => g -> [a]

-- | Produce an infinite list-equivalent of pseudo-random values.

--

-- ====__Examples__

--

-- >>> import System.Random

-- >>> let pureGen = mkStdGen 137

-- >>> (take 4 . buildRandoms (:) random $ pureGen) :: [Int]

-- [7879794327570578227,6883935014316540929,-1519291874655152001,2353271688382626589]

{-# INLINE buildRandoms #-}

buildRandoms ::

  RandomGen g =>

  -- | E.g. @(:)@ but subject to fusion

  (a -> as -> as) ->

  -- | E.g. 'random'

  (g -> (a, g)) ->

  -- | A 'RandomGen' instance

  g ->

  as

  where

    -- The seq fixes part of #4218 and also makes fused Core simpler:

    -- https://gitlab.haskell.org/ghc/ghc/-/issues/4218

-- | /Note/ - `random` generates values in the `Int` range

instance Random Integer where

  {-# INLINE random #-}

instance Random Int8

instance Random Int16

instance Random Int32

instance Random Int64

instance Random Int

instance Random Word

instance Random Word8

instance Random Word16

instance Random Word32

instance Random Word64

#if __GLASGOW_HASKELL__ >= 802

instance Random CBool

#endif

instance Random CChar

instance Random CSChar

instance Random CUChar

instance Random CShort

instance Random CUShort

instance Random CInt

instance Random CUInt

instance Random CLong

instance Random CULong

instance Random CPtrdiff

instance Random CSize

instance Random CWchar

instance Random CSigAtomic

instance Random CLLong

instance Random CULLong

instance Random CIntPtr

instance Random CUIntPtr

instance Random CIntMax

instance Random CUIntMax

-- | /Note/ - `random` produces values in the closed range @[0,1]@.

instance Random CFloat where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-- | /Note/ - `random` produces values in the closed range @[0,1]@.

instance Random CDouble where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

instance Random Char

instance Random Bool

-- | /Note/ - `random` produces values in the closed range @[0,1]@.

instance Random Double where

  {-# INLINE randomR #-}

  -- We return 1 - uniformDouble01M here for backwards compatibility with

  -- v1.2.0. Just return the result of uniformDouble01M in the next major

  -- version.

  {-# INLINE random #-}

-- | /Note/ - `random` produces values in the closed range @[0,1]@.

instance Random Float where

  {-# INLINE randomR #-}

  -- We return 1 - uniformFloat01M here for backwards compatibility with

  -- v1.2.0. Just return the result of uniformFloat01M in the next major

  -- version.

  {-# INLINE random #-}

-- | 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

initStdGen :: MonadIO m => m StdGen

-- | /Note/ - `randomR` treats @a@ and @b@ types independently

instance (Random a, Random b) => Random (a, b) where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-- | /Note/ - `randomR` treats @a@, @b@ and @c@ types independently

instance (Random a, Random b, Random c) => Random (a, b, c) where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-- | /Note/ - `randomR` treats @a@, @b@, @c@ and @d@ types independently

instance (Random a, Random b, Random c, Random d) => Random (a, b, c, d) where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-- | /Note/ - `randomR` treats @a@, @b@, @c@, @d@ and @e@ types independently

instance (Random a, Random b, Random c, Random d, Random e) => Random (a, b, c, d, e) where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-- | /Note/ - `randomR` treats @a@, @b@, @c@, @d@, @e@ and @f@ types independently

instance

  (Random a, Random b, Random c, Random d, Random e, Random f) =>

  Random (a, b, c, d, e, f)

  where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-- | /Note/ - `randomR` treats @a@, @b@, @c@, @d@, @e@, @f@ and @g@ types independently

instance

  (Random a, Random b, Random c, Random d, Random e, Random f, Random g) =>

  Random (a, b, c, d, e, f, g)

  where

  {-# INLINE randomR #-}

  {-# INLINE random #-}

-------------------------------------------------------------------------------

-- Global pseudo-random number generator

-------------------------------------------------------------------------------

-- $globalstdgen

--

-- 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

-- 'System.Random.Stateful.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

-- 'System.Random.Stateful.runStateGen' from stateful interface does not only

-- give us deterministic behaviour without requiring 'IO', but it is also more

-- efficient.

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

-- 'System.Random.Stateful.globalStdGen'

--

-- @since 1.0.0

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

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

-- 'System.Random.Stateful.globalStdGen'

--

-- @since 1.0.0

getStdGen :: MonadIO m => m StdGen

-- | Applies 'split' to the current global pseudo-random generator

-- 'System.Random.Stateful.globalStdGen', updates it with one of the results,

-- and returns the other.

--

-- @since 1.0.0

newStdGen :: MonadIO m => m StdGen

-- | 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 'System.Random.Stateful.applyAtomicGen' instead, possibly with the

-- 'System.Random.Stateful.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]

--

-- @since 1.0.0

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

  where

-- | A variant of 'System.Random.Stateful.randomRM' that uses the global

-- pseudo-random number generator 'System.Random.Stateful.globalStdGen'

--

-- >>> randomRIO (2020, 2100) :: IO Int

-- 2028

--

-- 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

-- 'System.Random.Stateful.uniformRM' instead, possibly with the

-- 'System.Random.Stateful.globalStdGen' if relying on the global state is

-- acceptable.

--

-- >>> import System.Random.Stateful

-- >>> uniformRM (2020, 2100) globalStdGen :: IO Int

-- 2044

--

-- @since 1.0.0

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

-- | A variant of 'System.Random.Stateful.randomM' that uses the global

-- pseudo-random number generator 'System.Random.Stateful.globalStdGen'.

--

-- >>> import Data.Int

-- >>> randomIO :: IO Int32

-- 114794456

--

-- This function is equivalent to @'getStdRandom' 'random'@ and is included in

-- this interface for historical reasons and backwards compatibility. It is

-- recommended to use 'System.Random.Stateful.uniformM' instead, possibly with

-- the 'System.Random.Stateful.globalStdGen' if relying on the global state is

-- acceptable.

--

-- >>> import System.Random.Stateful

-- >>> uniformM globalStdGen :: IO Int32

-- -1768545016

--

-- @since 1.0.0

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

-------------------------------------------------------------------------------

-- Notes

-------------------------------------------------------------------------------

-- $implementrandomgen

--

-- 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](https://en.wikipedia.org/wiki/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

-- <https://dl.acm.org/doi/abs/10.1145/62959.62969 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"

-- :}

-- $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 '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