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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/System-Random-MWC.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">mwc-random-0.12.0.1: Fast, high quality pseudo random number generation</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>portable</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Maintainer</th><td>bos@serpentine.com</td></tr><tr><th>Safe Haskell</th><td>Safe-Infered</td></tr></table><p class="caption">System.Random.MWC</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Gen: Pseudo-Random Number Generators
</a><ul><li><a href="#g:2">Type helpers
</a></li></ul></li><li><a href="#g:3">Variates: uniformly distributed values
</a></li><li><a href="#g:4">Seed: state management
</a></li><li><a href="#g:5">References
</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Pseudo-random number generation. This module contains code for
generating high quality random numbers that follow a uniform
distribution.
</p><p>For non-uniform distributions, see the
<code><a href="System-Random-MWC.html#t:Distributions">Distributions</a></code> module.
</p><p>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.
</p><p>The generator state is stored in the <code><a href="System-Random-MWC.html#t:Gen">Gen</a></code> data type. It can be
created in several ways:
</p><ol><li> Using the <code><a href="System-Random-MWC.html#v:withSystemRandom">withSystemRandom</a></code> call, which creates a random state.
</li><li> Supply your own seed to <code><a href="System-Random-MWC.html#v:initialize">initialize</a></code> function.
</li><li> Finally, <code><a href="System-Random-MWC.html#v:create">create</a></code> makes a generator from a fixed seed.
Generators created in this way aren't really random.
</li></ol><p>For repeatability, the state of the generator can be snapshotted
and replayed using the <code><a href="System-Random-MWC.html#v:save">save</a></code> and <code><a href="System-Random-MWC.html#v:restore">restore</a></code> functions.
</p><p>The simplest use is to generate a vector of uniformly distributed values:
</p><pre>
vs <a href="- withSystemRandom . asGenST $ \gen -">- withSystemRandom . asGenST $ \gen -</a> uniformVector gen 100
</pre><p>These values can be of any type which is an instance of the class
<code><a href="System-Random-MWC.html#t:Variate">Variate</a></code>.
</p><p>To generate random values on demand, first <code><a href="System-Random-MWC.html#v:create">create</a></code> a random number
generator.
</p><pre>
gen <- create
</pre><p>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 <code><a href="System-Random-MWC.html#v:uniform">uniform</a></code> or <code><a href="System-Random-MWC.html#v:uniformR">uniformR</a></code>:
</p><pre>
v <- uniform gen
</pre><pre>
v <- uniformR (1, 52) gen
</pre></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">data</span> <a href="#t:Gen">Gen</a> s</li><li class="src short"><a href="#v:create">create</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => m (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m))</li><li class="src short"><a href="#v:initialize">initialize</a> :: (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m, <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Generic.html#t:Vector">Vector</a> v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a>) => v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a> -> m (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m))</li><li class="src short"><a href="#v:withSystemRandom">withSystemRandom</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m a) -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a> a</li><li class="src short"><span class="keyword">type</span> <a href="#t:GenIO">GenIO</a> = <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a>)</li><li class="src short"><span class="keyword">type</span> <a href="#t:GenST">GenST</a> s = <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> (<a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a> s))</li><li class="src short"><a href="#v:asGenIO">asGenIO</a> :: (<a href="System-Random-MWC.html#t:GenIO">GenIO</a> -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a> a) -> <a href="System-Random-MWC.html#t:GenIO">GenIO</a> -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a> a</li><li class="src short"><a href="#v:asGenST">asGenST</a> :: (<a href="System-Random-MWC.html#t:GenST">GenST</a> s -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a> s a) -> <a href="System-Random-MWC.html#t:GenST">GenST</a> s -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a> s a</li><li class="src short"><span class="keyword">class</span> <a href="#t:Variate">Variate</a> a <span class="keyword">where</span><ul class="subs"><li><a href="#v:uniform">uniform</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m a</li><li><a href="#v:uniformR">uniformR</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => (a, a) -> <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m a</li></ul></li><li class="src short"><a href="#v:uniformVector">uniformVector</a> :: (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m, <a href="System-Random-MWC.html#t:Variate">Variate</a> a, <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Generic.html#t:Vector">Vector</a> v a) => <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int">Int</a> -> m (v a)</li><li class="src short"><span class="keyword">data</span> <a href="#t:Seed">Seed</a> </li><li class="src short"><a href="#v:fromSeed">fromSeed</a> :: <a href="System-Random-MWC.html#t:Seed">Seed</a> -> <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Unboxed.html#t:Vector">Vector</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a></li><li class="src short"><a href="#v:toSeed">toSeed</a> :: <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Generic.html#t:Vector">Vector</a> v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a> => v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a> -> <a href="System-Random-MWC.html#t:Seed">Seed</a></li><li class="src short"><a href="#v:save">save</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m <a href="System-Random-MWC.html#t:Seed">Seed</a></li><li class="src short"><a href="#v:restore">restore</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => <a href="System-Random-MWC.html#t:Seed">Seed</a> -> m (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m))</li></ul></div><div id="interface"><h1 id="g:1">Gen: Pseudo-Random Number Generators
</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Gen" class="def">Gen</a> s <a href="src/System-Random-MWC.html#Gen" class="link">Source</a></p><div class="doc"><p>State of the pseudo-random number generator.
</p></div></div><div class="top"><p class="src"><a name="v:create" class="def">create</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => m (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m))<a href="src/System-Random-MWC.html#create" class="link">Source</a></p><div class="doc"><p>Create a generator for variates using a fixed seed.
</p></div></div><div class="top"><p class="src"><a name="v:initialize" class="def">initialize</a> :: (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m, <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Generic.html#t:Vector">Vector</a> v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a>) => v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a> -> m (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m))<a href="src/System-Random-MWC.html#initialize" class="link">Source</a></p><div class="doc"><p>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.
</p><p>Examples:
</p><pre> initialize (singleton 42)
</pre><pre> initialize (toList [4, 8, 15, 16, 23, 42])
</pre><p>If a seed contains fewer than 256 elements, it is first used
verbatim, then its elements are <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Bits.html#v:xor">xor</a></code>ed against elements of the
default seed until 256 elements are reached.
</p><p>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. <code>gen' == gen</code> in
the following example:
</p><pre>gen' <- <code><a href="System-Random-MWC.html#v:initialize">initialize</a></code> . <code><a href="System-Random-MWC.html#v:fromSeed">fromSeed</a></code> =<< <code><a href="System-Random-MWC.html#v:save">save</a></code></pre></div></div><div class="top"><p class="src"><a name="v:withSystemRandom" class="def">withSystemRandom</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m a) -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a> a<a href="src/System-Random-MWC.html#withSystemRandom" class="link">Source</a></p><div class="doc"><p>Seed a PRNG with data from the system's fast source of
pseudo-random numbers ("<code>/dev/urandom</code>" on Unix-like systems),
then run the given action.
</p><p>This is a somewhat expensive function, and is intended to be called
only occasionally (e.g. once per thread). You should use the <code><a href="System-Random-MWC.html#t:Gen">Gen</a></code>
it creates to generate many random numbers.
</p><p><em>Note</em>: 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.
</p></div></div><h2 id="g:2">Type helpers
</h2><div class="doc"><p>The functions in this package are deliberately written for
flexibility, and will run in both the <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a></code> and <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a></code> monads.
</p><p>This can defeat the compiler's ability to infer a principal type in
simple (and common) cases. For instance, we would like the
following to work cleanly:
</p><pre> import System.Random.MWC
import Data.Vector.Unboxed
main = do
v <- withSystemRandom $ \gen -> uniformVector gen 20
print (v :: Vector Int)
</pre><p>Unfortunately, the compiler cannot tell what monad <code><a href="System-Random-MWC.html#v:uniformVector">uniformVector</a></code>
should execute in. The "fix" of adding explicit type annotations
is not pretty:
</p><pre> {-# LANGUAGE ScopedTypeVariables #-}
import Control.Monad.ST
main = do
vs <- withSystemRandom $
\(gen::GenST s) -> uniformVector gen 20 :: ST s (Vector Int)
print vs
</pre><p>As a more readable alternative, this library provides <code><a href="System-Random-MWC.html#v:asGenST">asGenST</a></code> and
<code><a href="System-Random-MWC.html#v:asGenIO">asGenIO</a></code> to constrain the types appropriately. We can get rid of
the explicit type annotations as follows:
</p><pre> main = do
vs <- withSystemRandom . asGenST $ \gen -> uniformVector gen 20
print (vs :: Vector Int)
</pre><p>This is almost as compact as the original code that the compiler
rejected.
</p></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:GenIO" class="def">GenIO</a> = <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a>)<a href="src/System-Random-MWC.html#GenIO" class="link">Source</a></p><div class="doc"><p>A shorter name for PRNG state in the <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a></code> monad.
</p></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:GenST" class="def">GenST</a> s = <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> (<a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a> s))<a href="src/System-Random-MWC.html#GenST" class="link">Source</a></p><div class="doc"><p>A shorter name for PRNG state in the <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a></code> monad.
</p></div></div><div class="top"><p class="src"><a name="v:asGenIO" class="def">asGenIO</a> :: (<a href="System-Random-MWC.html#t:GenIO">GenIO</a> -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a> a) -> <a href="System-Random-MWC.html#t:GenIO">GenIO</a> -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a> a<a href="src/System-Random-MWC.html#asGenIO" class="link">Source</a></p><div class="doc"><p>Constrain the type of an action to run in the <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/System-IO.html#t:IO">IO</a></code> monad.
</p></div></div><div class="top"><p class="src"><a name="v:asGenST" class="def">asGenST</a> :: (<a href="System-Random-MWC.html#t:GenST">GenST</a> s -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a> s a) -> <a href="System-Random-MWC.html#t:GenST">GenST</a> s -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a> s a<a href="src/System-Random-MWC.html#asGenST" class="link">Source</a></p><div class="doc"><p>Constrain the type of an action to run in the <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Control-Monad-ST-Safe.html#t:ST">ST</a></code> monad.
</p></div></div><h1 id="g:3">Variates: uniformly distributed values
</h1><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Variate" class="def">Variate</a> a <span class="keyword">where</span><a href="src/System-Random-MWC.html#Variate" class="link">Source</a></p><div class="doc"><p>The class of types for which we can generate uniformly
distributed random variates.
</p><p>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.
</p><p><em>Note</em>: Marsaglia's PRNG is not known to be cryptographically
secure, so you should not use it for cryptographic operations.
</p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:uniform" class="def">uniform</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m a<a href="src/System-Random-MWC.html#uniform" class="link">Source</a></p><div class="doc"><p>Generate a single uniformly distributed random variate. The
range of values produced varies by type:
</p><ul><li> For fixed-width integral types, the type's entire range is
used.
</li><li> 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 <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Prelude.html#v:log">log</a></code> function).
</li></ul><p>To generate a <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Prelude.html#t:Float">Float</a></code> variate with a range of [0,1), subtract
2**(-33). To do the same with <code><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Prelude.html#t:Double">Double</a></code> variates, subtract
2**(-53).
</p></div><p class="src"><a name="v:uniformR" class="def">uniformR</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => (a, a) -> <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m a<a href="src/System-Random-MWC.html#uniformR" class="link">Source</a></p><div class="doc"><p>Generate single uniformly distributed random variable in a
given range.
</p><ul><li> For integral types inclusive range is used.
</li><li> For floating point numbers range (a,b] is used if one ignores
rounding errors.
</li></ul></div></div><div class="subs instances"><p id="control.i:Variate" class="caption collapser" onclick="toggleSection('i:Variate')">Instances</p><div id="section.i:Variate" class="show"><table><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Bool.html#t:Bool">Bool</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Prelude.html#t:Double">Double</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Prelude.html#t:Float">Float</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int">Int</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int8">Int8</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int16">Int16</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int32">Int32</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int64">Int64</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word">Word</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word8">Word8</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word16">Word16</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="System-Random-MWC.html#t:Variate">Variate</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word64">Word64</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="System-Random-MWC.html#t:Variate">Variate</a> a, <a href="System-Random-MWC.html#t:Variate">Variate</a> b) => <a href="System-Random-MWC.html#t:Variate">Variate</a> (a, b)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="System-Random-MWC.html#t:Variate">Variate</a> a, <a href="System-Random-MWC.html#t:Variate">Variate</a> b, <a href="System-Random-MWC.html#t:Variate">Variate</a> c) => <a href="System-Random-MWC.html#t:Variate">Variate</a> (a, b, c)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="System-Random-MWC.html#t:Variate">Variate</a> a, <a href="System-Random-MWC.html#t:Variate">Variate</a> b, <a href="System-Random-MWC.html#t:Variate">Variate</a> c, <a href="System-Random-MWC.html#t:Variate">Variate</a> d) => <a href="System-Random-MWC.html#t:Variate">Variate</a> (a, b, c, d)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:uniformVector" class="def">uniformVector</a> :: (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m, <a href="System-Random-MWC.html#t:Variate">Variate</a> a, <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Generic.html#t:Vector">Vector</a> v a) => <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Int.html#t:Int">Int</a> -> m (v a)<a href="src/System-Random-MWC.html#uniformVector" class="link">Source</a></p><div class="doc"><p>Generate a vector of pseudo-random variates. This is not
necessarily faster than invoking <code><a href="System-Random-MWC.html#v:uniform">uniform</a></code> repeatedly in a loop,
but it may be more convenient to use in some situations.
</p></div></div><h1 id="g:4">Seed: state management
</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Seed" class="def">Seed</a> <a href="src/System-Random-MWC.html#Seed" class="link">Source</a></p><div class="doc"><p>An immutable snapshot of the state of a <code><a href="System-Random-MWC.html#t:Gen">Gen</a></code>.
</p></div><div class="subs instances"><p id="control.i:Seed" class="caption collapser" onclick="toggleSection('i:Seed')">Instances</p><div id="section.i:Seed" class="show"><table><tr><td class="src"><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Eq.html#t:Eq">Eq</a> <a href="System-Random-MWC.html#t:Seed">Seed</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Text-Show.html#t:Show">Show</a> <a href="System-Random-MWC.html#t:Seed">Seed</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> <a href="System-Random-MWC.html#t:Seed">Seed</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:fromSeed" class="def">fromSeed</a> :: <a href="System-Random-MWC.html#t:Seed">Seed</a> -> <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Unboxed.html#t:Vector">Vector</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a><a href="src/System-Random-MWC.html#fromSeed" class="link">Source</a></p><div class="doc"><p>Convert seed into vector.
</p></div></div><div class="top"><p class="src"><a name="v:toSeed" class="def">toSeed</a> :: <a href="/usr/share/doc/ghc/html/libraries/vector-0.9.1/Data-Vector-Generic.html#t:Vector">Vector</a> v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a> => v <a href="/usr/share/doc/ghc/html/libraries/base-4.5.0.0/Data-Word.html#t:Word32">Word32</a> -> <a href="System-Random-MWC.html#t:Seed">Seed</a><a href="src/System-Random-MWC.html#toSeed" class="link">Source</a></p><div class="doc"><p>Convert vector to <code><a href="System-Random-MWC.html#t:Seed">Seed</a></code>. It acts similarily to <code><a href="System-Random-MWC.html#v:initialize">initialize</a></code> and
will accept any vector. If you want to pass seed immediately to
restore you better call initialize directly since following law holds:
</p><pre> restore (toSeed v) = initialize v
</pre></div></div><div class="top"><p class="src"><a name="v:save" class="def">save</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => <a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m) -> m <a href="System-Random-MWC.html#t:Seed">Seed</a><a href="src/System-Random-MWC.html#save" class="link">Source</a></p><div class="doc"><p>Save the state of a <code><a href="System-Random-MWC.html#t:Gen">Gen</a></code>, for later use by <code><a href="System-Random-MWC.html#v:restore">restore</a></code>.
</p></div></div><div class="top"><p class="src"><a name="v:restore" class="def">restore</a> :: <a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimMonad">PrimMonad</a> m => <a href="System-Random-MWC.html#t:Seed">Seed</a> -> m (<a href="System-Random-MWC.html#t:Gen">Gen</a> (<a href="/usr/share/doc/ghc/html/libraries/primitive-0.4.1/Control-Monad-Primitive.html#t:PrimState">PrimState</a> m))<a href="src/System-Random-MWC.html#restore" class="link">Source</a></p><div class="doc"><p>Create a new <code><a href="System-Random-MWC.html#t:Gen">Gen</a></code> that mirrors the state of a saved <code><a href="System-Random-MWC.html#t:Seed">Seed</a></code>.
</p></div></div><h1 id="g:5">References
</h1><div class="doc"><ul><li> Marsaglia, G. (2003) Seeds for random number generators.
<em>Communications of the ACM</em> 46(5):90–93.
<a href="http://doi.acm.org/10.1145/769800.769827">http://doi.acm.org/10.1145/769800.769827</a>
</li><li> Thomas, D.B.; Leong, P.G.W.; Luk, W.; Villasenor, J.D.
(2007). Gaussian random number generators.
<em>ACM Computing Surveys</em> 39(4).
<a href="http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/grng_acmcs07.pdf">http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/grng_acmcs07.pdf</a>
</li></ul></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.10.0</p></div></body></html>
