mwc-random-0.11.0.0: Fast, high quality pseudo random number generation

Portabilityportable
Stabilityexperimental
Maintainerbos@serpentine.com

System.Random.MWC

Contents

Description

Pseudo-random number generation. This module contains code for generating high quality random numbers that follow a uniform distribution.

For non-uniform distributions, see the System.Random.MWC.Distributions module.

The uniform PRNG uses Marsaglia's MWC256 (also known as MWC8222) multiply-with-carry generator, which has a period of 2^8222 and fares well in tests of randomness. It is also extremely fast, between 2 and 3 times faster than the Mersenne Twister.

The generator state is stored in the Gen data type. It can be created in several ways:

  1. Using the withSystemRandom call, which creates a random state.
  2. Supply your own seed to initialize function.
  3. Finally, create makes a generator from a fixed seed. Generators created in this way aren't really random.

For repeatability, the state of the generator can be snapshotted and replayed using the save and restore functions.

The simplest use is to generate a vector of uniformly distributed values: 

   vs <- withSystemRandom (uniformVector 100)

These values can be of any type which is an instance of the class Variate.

To generate random values on demand, first create a random number generator. 

   gen <- create

Keep this generator and use it wherever random values are required. Get a random value using uniform or uniformR: 

   v <- uniform gen

   v <- uniformR (1, 52) gen

Synopsis

Gen: Pseudo-Random Number Generators

data Gen s Source

State of the pseudo-random number generator.

type GenIO = Gen (PrimState IO)Source

A shorter name for PRNG state in the IO monad.

type GenST s = Gen (PrimState (ST s))Source

A shorter name for PRNG state in the ST monad.

create :: PrimMonad m => m (Gen (PrimState m))Source

Create a generator for variates using a fixed seed.

initialize :: (PrimMonad m, Vector v Word32) => v Word32 -> m (Gen (PrimState m))Source

Create a generator for variates using the given seed, of which up to 256 elements will be used. For arrays of less than 256 elements, part of the default seed will be used to finish initializing the generator's state.

Examples: 

 initialize (singleton 42)

 initialize (toList [4, 8, 15, 16, 23, 42])

If a seed contains fewer than 256 elements, it is first used verbatim, then its elements are xored against elements of the default seed until 256 elements are reached.

If a seed contains exactly 258 elements, then the last two elements are used to set the generator's initial state. This allows for complete generator reproducibility, so that e.g. gen' == gen in the following example: 

gen' <- initialize . fromSeed =<< save

withSystemRandom :: PrimMonad m => (Gen (PrimState m) -> m a) -> IO aSource

Seed a PRNG with data from the system's fast source of pseudo-random numbers ("/dev/urandom" on Unix-like systems), then run the given action.

This is a heavyweight function, intended to be called only occasionally (e.g. once per thread). You should use the Gen it creates to generate many random numbers.

Note: on Windows, this code does not yet use the native Cryptographic API as a source of random numbers (it uses the system clock instead). As a result, the sequences it generates may not be highly independent.

Variates: uniformly distributed values

class Variate a whereSource

The class of types for which we can generate uniformly distributed random variates.

The uniform PRNG uses Marsaglia's MWC256 (also known as MWC8222) multiply-with-carry generator, which has a period of 2^8222 and fares well in tests of randomness. It is also extremely fast, between 2 and 3 times faster than the Mersenne Twister.

Note: Marsaglia's PRNG is not known to be cryptographically secure, so you should not use it for cryptographic operations.

Methods

uniform :: PrimMonad m => Gen (PrimState m) -> m aSource

Generate a single uniformly distributed random variate. The range of values produced varies by type:

  • For fixed-width integral types, the type's entire range is used.
  • For floating point numbers, the range (0,1] is used. Zero is explicitly excluded, to allow variates to be used in statistical calculations that require non-zero values (e.g. uses of the log function).

To generate a Float variate with a range of [0,1), subtract 2**(-33). To do the same with Double variates, subtract 2**(-53).

uniformR :: PrimMonad m => (a, a) -> Gen (PrimState m) -> m aSource

Generate single uniformly distributed random variable in a given range.

  • For integral types inclusive range is used.
  • For floating point numbers range (a,b] is used if one ignores rounding errors.

Instances

uniformVector :: (PrimMonad m, Variate a, Vector v a) => Gen (PrimState m) -> Int -> m (v a)Source

Generate a vector of pseudo-random variates. This is not necessarily faster than invoking uniform repeatedly in a loop, but it may be more convenient to use in some situations.

Seed: state management

data Seed Source

An immutable snapshot of the state of a Gen.

Instances

fromSeed :: Seed -> Vector Word32Source

Convert seed into vector.

toSeed :: Vector v Word32 => v Word32 -> SeedSource

Convert vector to Seed. It acts similarily to initialize and will accept any vector. If you want to pass seed immediately to restore you better call initialize directly since following law holds: 

 restore (toSeed v) = initialize v

save :: PrimMonad m => Gen (PrimState m) -> m SeedSource

Save the state of a Gen, for later use by restore.

restore :: PrimMonad m => Seed -> m (Gen (PrimState m))Source

Create a new Gen that mirrors the state of a saved Seed.

References