System.Random

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.

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.

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)

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.

>>> data PCGen = PCGen !Word64 !Word64

It produces a full Word32 of randomness per iteration.

>>> import Data.Bits>>> :{let stepGen :: PCGen -> (Word32, PCGen)    stepGen (PCGen state inc) = let      newState = state * 6364136223846793005 + (inc .|. 1)      xorShifted = fromIntegral (((state `shiftR` 18) `xor` state) `shiftR` 27) :: Word32      rot = fromIntegral (state `shiftR` 59) :: Word32      out = (xorShifted `shiftR` (fromIntegral rot)) .|. (xorShifted `shiftL` fromIntegral ((-rot) .&. 31))      in (out, PCGen newState inc):}

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

You can make it an instance of RandomGen as follows:

>>> :{instance RandomGen PCGen where  genWord32 = stepGen  split _ = error "PCG is not splittable":}

How to implement RandomGen for a pseudo-random number generator without a power-of-2 modulus

We do not recommend you implement any new pseudo-random number generators without a power-of-2 modulus.

Pseudo-random number generators without a power-of-2 modulus perform significantly worse than pseudo-random number generators with a power-of-2 modulus with this library. This is because most functionality in this library is based on generating and transforming uniformly pseudo-random machine words, and generating uniformly pseudo-random machine words using a pseudo-random number generator without a power-of-2 modulus is expensive.

The pseudo-random number generator from L’Ecuyer (1988) natively generates an integer value in the range [1, 2147483562]. This is the generator used by this library before it was replaced by SplitMix in version 1.2.

>>> data LegacyGen = LegacyGen !Int32 !Int32>>> :{let legacyNext :: LegacyGen -> (Int, LegacyGen)    legacyNext (LegacyGen s1 s2) = (fromIntegral z', LegacyGen s1'' s2'') where      z' = if z < 1 then z + 2147483562 else z      z = s1'' - s2''      k = s1 `quot` 53668      s1'  = 40014 * (s1 - k * 53668) - k * 12211      s1'' = if s1' < 0 then s1' + 2147483563 else s1'      k' = s2 `quot` 52774      s2' = 40692 * (s2 - k' * 52774) - k' * 3791      s2'' = if s2' < 0 then s2' + 2147483399 else s2':}

You can make it an instance of RandomGen as follows:

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