haskell / random / 146

{-# LANGUAGE CPP #-}

{-# LANGUAGE DefaultSignatures #-}

{-# 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(..)

  , uniform

  , uniformR

  , genByteString

  , Random(..)

  , Uniform

  , UniformRange

  , Finite

  -- ** Standard pseudo-random number generator

  , StdGen

  , mkStdGen

  , initStdGen

  -- ** Global standard pseudo-random number generator

  -- $globalstdgen

  , getStdRandom

  , getStdGen

  , setStdGen

  , newStdGen

  , randomIO

  , randomRIO

  -- * Compatibility and reproducibility

  -- ** Backwards compatibility and deprecations

  -- $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.State.Strict

import Data.ByteString (ByteString)

import Data.Int

import Data.IORef

import Data.Word

import Foreign.C.Types

import GHC.Exts

import System.Random.GFinite (Finite)

import System.Random.Internal

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 = 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]

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

-- 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:

--

-- >>> :set -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:

--

-- >>> :set -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 #-}

-- | 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

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

{-# INLINE genByteString #-}

-- | 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.

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 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.

  {-# 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'.

  {-# 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.

  {-# 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.

  {-# 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

             => (a -> as -> as)  -- ^ E.g. @(:)@ but subject to fusion

             -> (g -> (a,g))     -- ^ E.g. 'random'

             -> g                -- ^ A 'RandomGen' instance

             -> as

  where

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

-- | /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 entropy available on the system (time, ...)

--

-- @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

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

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

-- | /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

-- | /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

-- | /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

-- | /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

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

-- Global pseudo-random number generator

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

-- $globalstdgen

--

-- There is a single, implicit, global pseudo-random number generator of type

-- 'StdGen', held in a global variable maintained by the 'IO' monad. It is

-- initialised automatically in some system-dependent fashion. To get

-- deterministic behaviour, use 'setStdGen'.

--

-- Note that 'mkStdGen' also gives deterministic behaviour without requiring an

-- 'IO' context.

-- |Sets the global pseudo-random number generator.

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

-- |Gets the global pseudo-random number generator.

getStdGen :: MonadIO m => m StdGen

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

-- updates it with one of the results, and returns the other.

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@ gets a pseudo-random integer

between 1 and 6:

>  rollDice :: IO Int

>  rollDice = getStdRandom (randomR (1,6))

-}

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

-- | A variant of 'randomR' that uses the global pseudo-random number

-- generator.

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

-- | A variant of 'random' that uses the global pseudo-random number

-- generator.

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

--

-- 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)

--

-- $references

--

-- 1. 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>

-- $setup

--

-- >>> import Control.Monad (replicateM)

-- >>> import Data.List (unfoldr)