Safe Haskell | None |
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A random number effect, using a pure mersenne twister under the hood. This algorithm is not suitable for cryptography!

If you need cryptographically secure random numbers,
you MUST use `mkSecureRandomIO`

. Otherwise, `mkRandom`

and
`mkRandomIO`

are much faster.

This effect should be plug-and-play with any application making use of extensible effects.

Patches, even for the smallest of documentation bugs, are always welcome!

- data Random
- mkRandom :: Word64 -> Random
- mkRandomIO :: SetMember Lift (Lift IO) r => Eff r Random
- mkSecureRandomIO :: SetMember Lift (Lift IO) r => Eff r Random
- forRandEff :: Eff r Random -> Eff (State Random :> r) w -> Eff r w
- runRandomState :: Random -> Eff (State Random :> r) w -> Eff r w
- uniformIntDist :: Member (State Random) r => Integer -> Integer -> Eff r Integer
- uniformIntegralDist :: (Member (State Random) r, Integral a) => a -> a -> Eff r a
- uniformRealDist :: Member (State Random) r => Double -> Double -> Eff r Double
- linearRealDist :: Member (State Random) r => Double -> Double -> Eff r Double
- bernoulliDist :: Member (State Random) r => Rational -> Eff r Bool
- binomialDist :: Member (State Random) r => Int -> Rational -> Eff r Int
- negativeBinomialDist :: Member (State Random) r => Rational -> Integer -> Eff r Integer
- geometricDist :: Member (State Random) r => Rational -> Eff r Integer
- poissonDist :: Member (State Random) r => Double -> Eff r Double
- exponentialDist :: Member (State Random) r => Double -> Eff r Double
- gammaDist :: Member (State Random) r => Double -> Double -> Eff r Double
- weibullDist :: Member (State Random) r => Double -> Double -> Eff r Double
- extremeValueDist :: Member (State Random) r => Double -> Double -> Eff r Double
- normalDist :: Member (State Random) r => Double -> Double -> Eff r Double
- lognormalDist :: Member (State Random) r => Double -> Double -> Eff r Double
- chiSquaredDist :: Member (State Random) r => Int -> Eff r Double
- cauchyDist :: Member (State Random) r => Double -> Double -> Eff r Double
- fisherFDist :: Member (State Random) r => Int -> Int -> Eff r Double
- studentTDist :: Member (State Random) r => Double -> Eff r Double
- data DiscreteDistributionHelper
- buildDDH :: [Word64] -> DiscreteDistributionHelper
- discreteDist :: Member (State Random) r => DiscreteDistributionHelper -> Eff r Int
- piecewiseConstantDist :: Member (State Random) r => [Double] -> DiscreteDistributionHelper -> Eff r Double
- piecewiseLinearDist :: Member (State Random) r => [Double] -> DiscreteDistributionHelper -> Eff r Double
- knuthShuffle :: Member (State Random) r => Vector a -> Eff r (Vector a)
- knuthShuffleM :: (PrimMonad m, Applicative m, Typeable1 m, Member (State Random) r, SetMember Lift (Lift m) r) => MVector (PrimState m) a -> Eff r ()
- randomInt :: Member (State Random) r => Eff r Int
- randomInt64 :: Member (State Random) r => Eff r Int64
- randomWord :: Member (State Random) r => Eff r Word
- randomWord64 :: Member (State Random) r => Eff r Word64
- randomDouble :: Member (State Random) r => Eff r Double
- randomBits :: (Member (State Random) r, Bits x) => Eff r x
- randomBitList :: Member (State Random) r => Int -> Eff r [Bool]

# Documentation

A random number generator. Either a fast, insecure mersenne twister or a secure one, depending on which smart constructor is used to construct this type.

# Seeding

mkRandom :: Word64 -> RandomSource

Create a random number generator from a `Word64`

seed.
This uses the insecure (but fast) mersenne twister.

mkRandomIO :: SetMember Lift (Lift IO) r => Eff r RandomSource

Create a new random number generator, using the clocktime as the base for
the seed. This must be called from a computation with a lifted base effect
of `IO`

.

This is just a conveniently seeded mersenne twister.

mkSecureRandomIO :: SetMember Lift (Lift IO) r => Eff r RandomSource

Creates a new random number generator, using the system entropy source
as a seed. The random number generator returned from this function is
cryptographically secure, but not nearly as fast as the one returned
by `mkRandom`

and `mkRandomIO`

.

# Running

forRandEff :: Eff r Random -> Eff (State Random :> r) w -> Eff r wSource

Use a non-random effect as the Random source for running a random effect.

runRandomState :: Random -> Eff (State Random :> r) w -> Eff r wSource

Runs an effectful random computation, returning the computation's result.

# Uniform Distributions

Generates a uniformly distributed random number in the inclusive range [a, b].

Generates a uniformly distributed random number in the inclusive range [a, b].

This function is more flexible than `uniformIntDist`

since it relaxes type constraints, but passing in
constant bounds such as `uniformIntegralDist 0 10`

will warn with -Wall.

Generates a uniformly distributed random number in the range [a, b).

NOTE: This code might not be correct, in that the returned value may not be perfectly uniformly distributed. If you know how to make one of these a better way, PLEASE send me a pull request. I just stole this implementation from the C++11 random header.

# Linear Distributions

linearRealDist :: Member (State Random) r => Double -> Double -> Eff r DoubleSource

Generates a linearly-distributed random number in the range `[a, b)`

;
`a`

with a probability of 0.
This code is not guaranteed to be correct.

# Bernoulli Distributions

:: Member (State Random) r | |

=> Rational | k: The fraction of results which should be true. |

-> Eff r Bool |

Produces random boolean values, according to a discrete probability.

k must be in the range [0, 1].

The value obtained is the number of successes in a sequence of t yes/no experiments, each of which succeeds with probability p.

t must be >= 0 p must be in the range [0, 1].

The value represents the number of failures in a series of independent yes/no trials (each succeeds with probability p), before exactly k successes occur.

p must be in the range (0, 1] k must be >= 0

Warning: NOT IMPLEMENTED!

The value represents the number of yes/no trials (each succeeding with probability p) which are necessary to obtain a single success.

`geometricDist`

p is equivalent to negativeBinomialDist 1 p

p must be in the range (0, 1]

Warning: NOT IMPLEMENTED!

# Poisson Distributions

The value obtained is the probability of exactly i occurrences of a random event if the expected, mean number of its occurrence under the same conditions (on the same time/space interval) is μ.

Warning: NOT IMPLEMENTED!

The value obtained is the time/distance until the next random event if random events occur at constant rate λ per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.

This is the continuous counterpart of `geometricDist`

.

:: Member (State Random) r | |

=> Double | α. The shape parameter. |

-> Double | β. The scale parameter. |

-> Eff r Double |

For floating-point α, the value obtained is the sum of independent exponentially distributed random variables, each of which has a mean of β.

:: Member (State Random) r | |

=> Double | α. The shape parameter. |

-> Double | β. The scale parameter. |

-> Eff r Double |

Generates random numbers as sampled from a Weibull distribution. It was originally identified to describe particle size distribution.

:: Member (State Random) r | |

=> Double | α. The shape parameter. |

-> Double | β. The scale parameter. |

-> Eff r Double |

???

Warning: NOT IMPLEMENTED!

# Normal Distributions

Generates random numbers as sampled from the normal distribution.

Generates a log-normally distributed random number. This is based off of sampling the normal distribution, and then following the instructions at http://en.wikipedia.org/wiki/Log-normal_distribution#Generating_log-normally_distributed_random_variates.

Produces random numbers according to a chi-squared distribution.

:: Member (State Random) r | |

=> Double | Central point |

-> Double | Scale parameter (full width half maximum) |

-> Eff r Double |

Produced random numbers according to a Cauchy (or Lorentz) distribution.

Produces random numbers according to an F-distribution.

m and n are the degrees of freedom.

This distribution is used when estimating the mean of an unknown normally distributed value given n+1 independent measurements, each with additive errors of unknown standard deviation, as in physical measurements. Or, alternatively, when estimating the unknown mean of a normal distribution with unknown standard deviation, given n+1 samples.

# Sampling Distributions

data DiscreteDistributionHelper Source

Contains a sorted list of cumulative probabilities, so we can do a sample by generating a uniformly distributed random number in the range [0, 1), and binary searching the vector for where to put it.

buildDDH :: [Word64] -> DiscreteDistributionHelperSource

Performs O(n) work building a table which we can later use
sample with `discreteDist`

.

discreteDist :: Member (State Random) r => DiscreteDistributionHelper -> Eff r IntSource

Given a pre-build `DiscreteDistributionHelper`

(use `buildDDH`

),
produces random integers on the interval [0, n), where the
probability of each individual integer i is defined as w_i/S,
that is the weight of the ith integer divided by the sum of all
n weights.

i.e. This function produces an integer with probability equal to
the weight given in its index into the parameter to `buildDDH`

.

:: Member (State Random) r | |

=> [Double] | Intervals |

-> DiscreteDistributionHelper | Weights |

-> Eff r Double |

This function produces random floating-point numbers, which are uniformly distributed within each of the several subintervals [b_i, b_(i+1)), each with its own weight w_i. The set of interval boundaries and the set of weights are the parameters of this distribution.

For example, ```
piecewiseConstantDist [ 0, 1, 10, 15 ]
(buildDDH [ 1, 0, 1 ])
```

will produce values between 0 and 1 half the time, and values
between 10 and 15 the other half of the time.

:: Member (State Random) r | |

=> [Double] | Intervals |

-> DiscreteDistributionHelper | Weights |

-> Eff r Double |

This function produces random floating-point numbers, which are distributed with linearly-increasing probability within each of the several subintervals [b_i, b_(i+1)), each with its own weight w_i. The set of interval boundaries and the set of weights are the parameters of this distribution.

For example, `piecewiseLinearDist [ 0, 1, 10, 15 ] (buildDDH [ 1, 0, 1 ])` will produce values between 0 and 1 half the time, and values between 10 and 15 the other half of the time.

# Shuffling

knuthShuffle :: Member (State Random) r => Vector a -> Eff r (Vector a)Source

Shuffle an immutable vector.

knuthShuffleM :: (PrimMonad m, Applicative m, Typeable1 m, Member (State Random) r, SetMember Lift (Lift m) r) => MVector (PrimState m) a -> Eff r ()Source

Shuffle a mutable vector.

# Raw Generators

randomBits :: (Member (State Random) r, Bits x) => Eff r xSource

Yields a set of random from the internal generator,
using `randomWord64`

internally.