-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Fast, high quality pseudo random number generation
--
-- This package contains code for generating high quality random numbers
-- that follow either a uniform or normal distribution. The generated
-- numbers are suitable for use in statistical applications.
--
-- 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.
--
-- Compared to the mersenne-random package, this package has a more
-- convenient API, is faster, and supports more statistical
-- distributions.
@package mwc-random
@version 0.12.0.1
-- | 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 <a>Distributions</a> 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 <a>Gen</a> data type. It can be
-- created in several ways:
--
-- <ol>
-- <li>Using the <a>withSystemRandom</a> call, which creates a random
-- state.</li>
-- <li>Supply your own seed to <a>initialize</a> function.</li>
-- <li>Finally, <a>create</a> makes a generator from a fixed seed.
-- Generators created in this way aren't really random.</li>
-- </ol>
--
-- For repeatability, the state of the generator can be snapshotted and
-- replayed using the <a>save</a> and <a>restore</a> functions.
--
-- The simplest use is to generate a vector of uniformly distributed
-- values:
--
-- <pre>
-- vs <a>- withSystemRandom . asGenST $ \gen -</a> uniformVector gen 100
-- </pre>
--
-- These values can be of any type which is an instance of the class
-- <a>Variate</a>.
--
-- To generate random values on demand, first <a>create</a> a random
-- number generator.
--
-- <pre>
-- gen <- create
-- </pre>
--
-- Hold onto this generator and use it wherever random values are
-- required (creating a new generator is expensive compared to generating
-- a random number, so you don't want to throw them away). Get a random
-- value using <a>uniform</a> or <a>uniformR</a>:
--
-- <pre>
-- v <- uniform gen
-- </pre>
--
-- <pre>
-- v <- uniformR (1, 52) gen
-- </pre>
module System.Random.MWC
-- | State of the pseudo-random number generator.
data Gen s
-- | Create a generator for variates using a fixed seed.
create :: PrimMonad m => m (Gen (PrimState m))
-- | 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:
--
-- <pre>
-- initialize (singleton 42)
-- </pre>
--
-- <pre>
-- initialize (toList [4, 8, 15, 16, 23, 42])
-- </pre>
--
-- If a seed contains fewer than 256 elements, it is first used verbatim,
-- then its elements are <a>xor</a>ed 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. <tt>gen' == gen</tt>
-- in the following example:
--
-- <pre>
-- gen' <- <a>initialize</a> . <a>fromSeed</a> =<< <a>save</a>
-- </pre>
initialize :: (PrimMonad m, Vector v Word32) => v Word32 -> m (Gen (PrimState m))
-- | Seed a PRNG with data from the system's fast source of pseudo-random
-- numbers ("<tt>/dev/urandom</tt>" on Unix-like systems), then run the
-- given action.
--
-- This is a somewhat expensive function, and is intended to be called
-- only occasionally (e.g. once per thread). You should use the
-- <a>Gen</a> it creates to generate many random numbers.
--
-- <i>Note</i>: 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.
withSystemRandom :: PrimMonad m => (Gen (PrimState m) -> m a) -> IO a
-- | A shorter name for PRNG state in the <a>IO</a> monad.
type GenIO = Gen (PrimState IO)
-- | A shorter name for PRNG state in the <a>ST</a> monad.
type GenST s = Gen (PrimState (ST s))
-- | Constrain the type of an action to run in the <a>IO</a> monad.
asGenIO :: (GenIO -> IO a) -> (GenIO -> IO a)
-- | Constrain the type of an action to run in the <a>ST</a> monad.
asGenST :: (GenST s -> ST s a) -> (GenST s -> ST s a)
-- | 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.
--
-- <i>Note</i>: Marsaglia's PRNG is not known to be cryptographically
-- secure, so you should not use it for cryptographic operations.
class Variate a
uniform :: (Variate a, PrimMonad m) => Gen (PrimState m) -> m a
uniformR :: (Variate a, PrimMonad m) => (a, a) -> Gen (PrimState m) -> m a
-- | Generate a vector of pseudo-random variates. This is not necessarily
-- faster than invoking <a>uniform</a> repeatedly in a loop, but it may
-- be more convenient to use in some situations.
uniformVector :: (PrimMonad m, Variate a, Vector v a) => Gen (PrimState m) -> Int -> m (v a)
-- | An immutable snapshot of the state of a <a>Gen</a>.
data Seed
-- | Convert seed into vector.
fromSeed :: Seed -> Vector Word32
-- | Convert vector to <a>Seed</a>. It acts similarily to <a>initialize</a>
-- and will accept any vector. If you want to pass seed immediately to
-- restore you better call initialize directly since following law holds:
--
-- <pre>
-- restore (toSeed v) = initialize v
-- </pre>
toSeed :: Vector v Word32 => v Word32 -> Seed
-- | Save the state of a <a>Gen</a>, for later use by <a>restore</a>.
save :: PrimMonad m => Gen (PrimState m) -> m Seed
-- | Create a new <a>Gen</a> that mirrors the state of a saved <a>Seed</a>.
restore :: PrimMonad m => Seed -> m (Gen (PrimState m))
instance Typeable Seed
instance Eq Seed
instance Show Seed
instance (Variate a, Variate b, Variate c, Variate d) => Variate (a, b, c, d)
instance (Variate a, Variate b, Variate c) => Variate (a, b, c)
instance (Variate a, Variate b) => Variate (a, b)
instance Variate Word
instance Variate Int
instance Variate Double
instance Variate Float
instance Variate Bool
instance Variate Word64
instance Variate Word32
instance Variate Word16
instance Variate Word8
instance Variate Int64
instance Variate Int32
instance Variate Int16
instance Variate Int8
-- | Pseudo-random number generation for non-uniform distributions.
module System.Random.MWC.Distributions
-- | Generate a normally distributed random variate with given mean and
-- standard deviation.
normal :: PrimMonad m => Double -> Double -> Gen (PrimState m) -> m Double
-- | Generate a normally distributed random variate with zero mean and unit
-- variance.
--
-- The implementation uses Doornik's modified ziggurat algorithm.
-- Compared to the ziggurat algorithm usually used, this is slower, but
-- generates more independent variates that pass stringent tests of
-- randomness.
standard :: PrimMonad m => Gen (PrimState m) -> m Double
-- | Generate an exponentially distributed random variate.
exponential :: PrimMonad m => Double -> Gen (PrimState m) -> m Double
-- | Random variate generator for gamma distribution.
gamma :: PrimMonad m => Double -> Double -> Gen (PrimState m) -> m Double
-- | Random variate generator for the chi square distribution.
chiSquare :: PrimMonad m => Int -> Gen (PrimState m) -> m Double
-- | Table-driven generation of random variates. This approach can generate
-- random variates in <i>O(1)</i> time for the supported distributions,
-- at a modest cost in initialization time.
module System.Random.MWC.CondensedTable
-- | A lookup table for arbitrary discrete distributions. It allows the
-- generation of random variates in <i>O(1)</i>. Note that probability is
-- quantized in units of <tt>1/2^32</tt>, and all distributions with
-- infinite support (e.g. Poisson) should be truncated.
data CondensedTable v a
-- | A <a>CondensedTable</a> that uses boxed vectors, and is able to hold
-- any type of element.
type CondensedTableV = CondensedTable Vector
-- | A <a>CondensedTable</a> that uses unboxed vectors.
type CondensedTableU = CondensedTable Vector
-- | Generate a random value using a condensed table.
genFromTable :: (PrimMonad m, Vector v a) => CondensedTable v a -> Gen (PrimState m) -> m a
-- | Generate a condensed lookup table from a list of outcomes with given
-- probabilities. The vector should be non-empty and the probabilites
-- should be non-negative and sum to 1. If this is not the case, this
-- algorithm will construct a table for some distribution that may bear
-- no resemblance to what you intended.
tableFromProbabilities :: (Vector v (a, Word32), Vector v (a, Double), Vector v a, Vector v Word32, Show a) => v (a, Double) -> CondensedTable v a
-- | Same as <a>tableFromProbabilities</a> but treats number as weights not
-- probilities. Non-positive weights are discarded, and those remaining
-- are normalized to 1.
tableFromWeights :: (Vector v (a, Word32), Vector v (a, Double), Vector v a, Vector v Word32, Show a) => v (a, Double) -> CondensedTable v a
-- | Generate a condensed lookup table from integer weights. Weights should
-- sum to <tt>2^32</tt>. If they don't, the algorithm will alter the
-- weights so that they do. This approach should work reasonably well for
-- rounding errors.
tableFromIntWeights :: (Vector v (a, Word32), Vector v a, Vector v Word32) => v (a, Word32) -> CondensedTable v a
-- | Create a lookup table for the Poisson distibution. Note that table
-- construction may have significant cost. For λ < 100 it takes as
-- much time to build table as generation of 1000-30000 variates.
tablePoisson :: Double -> CondensedTableU Int
-- | Create a lookup table for the binomial distribution.
tableBinomial :: Int -> Double -> CondensedTableU Int
