src/site/apt/userguide/rng.apt

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  -----------------------------
  The Apache Commons RNG User Guide
  -----------------------------

1. Purpose

  <<<Commons RNG>>> provides generators of "pseudo-randomness", i.e. the
  generators produce deterministic sequences of bytes, currently in chunks
  of 32 (a.k.a. <<<int>>>) or 64 bits (a.k.a. <<<long>>>), depending on the
  implementation.

  The goal was to provide an API that is simple and unencumbered with old
  design decisions.

  The design is clean and its rationale is explained in the code and Javadoc
  (as well as in the extensive discussions on the "Apache Commons" project's
  mailing list).

  The code evolved during several months in order to accommodate the
  requirements gathered from the design issues identified in the
  <<<org.apache.commons.math3.random>>> package and the explicit design
  goal of {{{./why_not_java_random.html}severing ties}} to <<<java.util.Random>>>.

  The library is divided into modules:

  * {{{../commons-rng-client-api/apidocs/org/apache/commons/rng/package-summary.html}Client API}} (requires Java 6)

  This module provides the
  {{{../commons-rng-client-api/apidocs/org/apache/commons/rng/RestorableUniformRandomProvider.html}interface}}
  to be passed as argument to a procedure that needs to access to a sequence of random numbers.

  * {{{../commons-rng-core/apidocs/org/apache/commons/rng/core/package-summary.html}Core}} (requires Java 6)

  This module contains the implementations of several generators of pseudo-random sequences of numbers.
  Code in this module is intended to be internal to this library and no user code should access it
  directly.
  With the advent of {{{http://openjdk.java.net/projects/jigsaw/}Java modularization}}, it is possible
  that future releases of the library will enforce access through the
  {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/RandomSource.html}RandomSource}}
  factory.

  * {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/package-summary.html}Simple}} (requires Java 6)

  This module provides factory methods for creating instances of all the generators implemented
  in the <<<commons-rng-core>>> module.

  * {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/package-summary.html}Sampling}} (requires Java 6)

  This module provides implementations that generate a sequence of numbers according to some
  specified probability distribution, and utilities to sample from a generic collection of items.
  It is an example of usage of the API provided in the <<<commons-rng-client-api>>> module.

  * Examples

  This module provides miscellaneous complete applications that illustrate usage of the library.
  Please note that this module is not part of the library's API; no compatibility should be expected
  in successive releases of "Commons RNG".

  As of version 1.1, the following modules are provided:

   ** <<<examples-jmh>>>: JMH benchmarking (requires Java 8)

   This module uses the {{{http://openjdk.java.net/projects/code-tools/jmh/}JMH micro-benchmark framework}}
   in order to assess the relative performance of the generators (see tables below).

   ** <<<examples-stress>>>: Stress testing (requires Java 8)

   This module implements a wrapper that calls external tools that can assess the quality of
   the generators by submitting their output to a battery of "stress tests" (see tables below).

   ** <<<examples-sampling>>>: Probability density (requires Java 8)

   This module contains the code that generates the data used to produce the probability density
   plots shown in {{{./dist_density_approx.html}this userguide}}.

   ** <<<examples-jpms>>>: JPMS integration (requires Java 9)

   This module implements a dummy application that shows how to use the artefacts (produced
   from the maven modules described above) as Java modules ({{{https://en.wikipedia.org/wiki/Java_Platform_Module_System}JPMS}}).

   ** <<<examples-quadrature>>>: Quadrature (requires Java 8)

   This module contains an application that estimates the number 𝞹 using quasi-Montecarlo integration.

   []

  []


2. Usage overview

  Please refer to the generated documentation (of the appropriate module)
  for details on the API illustrated by the following examples.


  * Random number generator objects are instantiated through factory
    methods defined in <<<RandomSource>>>, an <<<enum>>> that declares
    {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/RandomSource.html#enum.constant.detail}all the available implementations}}.

+--------------------------+
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;

UniformRandomProvider rng = RandomSource.create(RandomSource.MT);
+--------------------------+


  * A generator will return a randomly selected element from a range
    of possible values of some Java (primitive) type.

+--------------------------+
boolean isOn = rng.nextBoolean(); // "true" or "false".
+--------------------------+
+--------------------------+
int n = rng.nextInt(); // Integer.MIN_VALUE <= n <= Integer.MAX_VALUE.
int m = rng.nextInt(max); // 0 <= m < max.
+--------------------------+
+--------------------------+
long n = rng.nextLong(); // Long.MIN_VALUE <= n <= Long.MAX_VALUE.
long m = rng.nextLong(max); // 0 <= m < max.
+--------------------------+
+--------------------------+
float x = rng.nextFloat(); // 0 <= x < 1.
+--------------------------+
+--------------------------+
double x = rng.nextDouble(); // 0 <= x < 1.
+--------------------------+


  * A generator will fill a given <<<byte>>> array with random values.

+--------------------------+
byte[] a = new byte[47];
// The elements of "a" are replaced with random values from the interval [-128, 127].
rng.nextBytes(a);
+--------------------------+
+--------------------------+
byte[] a = new byte[47];
// Replace 3 elements of the array (at indices 15, 16 and 17) with random values.
rng.nextBytes(a, 15, 3);
+--------------------------+


  * In order to generate reproducible sequences, generators must be instantiated with a user-defined seed.

+--------------------------+
UniformRandomProvider rng = RandomSource.create(RandomSource.SPLIT_MIX_64, 5776);
+--------------------------+

    If no seed is passed, a random seed is generated implicitly.

    Convenience methods are provided for explicitly generating random seeds of the various types.

+--------------------------+
int seed = RandomSource.createInt();
+--------------------------+
+--------------------------+
long seed = RandomSource.createLong();
+--------------------------+
+--------------------------+
int[] seed = RandomSource.createIntArray(128); // Length of returned array is 128.
+--------------------------+
+--------------------------+
long[] seed = RandomSource.createLongArray(128); // Length of returned array is 128.
+--------------------------+


  * Any of the following types can be passed to the <<<create>>> method as the "seed" argument:

    ** <<<int>>> or <<<Integer>>>

    ** <<<long>>> or <<<Long>>>

    ** <<<int[]>>>

    ** <<<long[]>>>

    ** <<<byte[]>>>

    []

+--------------------------+
UniformRandomProvider rng = RandomSource.create(RandomSource.ISAAC, 5776);
+--------------------------+
+--------------------------+
UniformRandomProvider rng = RandomSource.create(RandomSource.ISAAC, new int[] { 6, 7, 7, 5, 6, 1, 0, 2 });
+--------------------------+
+--------------------------+
UniformRandomProvider rng = RandomSource.create(RandomSource.ISAAC, new long[] { 0x638a3fd83bc0e851L, 0x9730fd12c75ae247L });
+--------------------------+

    Note however that, upon initialization, the underlying generation algorithm

    ** may not use all the information contents of the seed,

    ** may use a procedure (using the given seed as input) for further filling its internal state
       (in order to avoid a too uniform initial state).

    []

    In both cases, the behaviour is not standard but should not change between releases of the library
    (bugs notwithstanding).

    Each RNG implementation has a single "native" seed; when the seed argument passed
    to the <<<create>>> method is not of the native type, it is automatically converted.
    The conversion preserves the information contents but is otherwise not specified (i.e.
    different releases of the library may use different conversion procedures).

    Hence, if reproducibility of the generated sequences across successive releases of the
    library is necessary, users should ensure that they use native seeds.

+--------------------------+
long seed = 9246234616L;
if (!RandomSource.TWO_CMRES.isNativeSeed(seed)) {
    throw new IllegalArgumentException("Seed is not native");
}
+--------------------------+

    For each available implementation, the native seed type is specified in the
    {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/RandomSource.html#enum.constant.detail}Javadoc}}.


  * Whenever a random source implementation is parameterized, the custom arguments
    are passed after the seed.

+--------------------------+
int seed = 96912062;
int first = 7; // Subcycle identifier.
int second = 4; // Subcycle identifier.
UniformRandomProvider rng = RandomSource.create(RandomSource.TWO_CMRES_SELECT, seed, first, second);
+--------------------------+

    In the above example, valid "subcycle identifiers" are in the interval [0, 13].


  * The current state of a generator can be
    {{{../commons-rng-client-api/apidocs/org/apache/commons/rng/RestorableUniformRandomProvider.html#saveState--}saved}}
    and
    {{{../commons-rng-client-api/apidocs/org/apache/commons/rng/RestorableUniformRandomProvider.html#restoreState-org.apache.commons.rng.RandomProviderState-}restored}}
    later on.

+--------------------------+
import org.apache.commons.rng.RestorableUniformRandomProvider;
import org.apache.commons.rng.RandomProviderState;

RestorableUniformRandomProvider rng = RandomSource.create(RandomSource.WELL_512_A);
RandomProviderState state = rng.saveState();
double x = rng.nextDouble();
rng.restoreState(state);
double y = rng.nextDouble(); // x == y.
+--------------------------+


  * The <<<UniformRandomProvider>>> objects returned from the <<<create>>> methods do not
    implement the <<<java.io.Serializable>>> interface.

    However, users can easily set up a custom serialization scheme if the random source
    is known at both ends of the communication channel.
    This would be useful namely to save the state to persistent storage, and restore it
    such that the sequence will continue from where it left off.

+--------------------------+
import org.apache.commons.rng.RestorableUniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;
import org.apache.commons.rng.core.RandomProviderDefaultState;

RandomSource source = RandomSource.MT_64; // Known source identifier.

RestorableUniformRandomProvider rngOrig = RandomSource.create(source); // Original RNG instance.

// Save and serialize state.
RandomProviderState stateOrig = rngOrig.saveState(rngOrig);
ByteArrayOutputStream bos = new ByteArrayOutputStream();
ObjectOutputStream oos = new ObjectOutputStream(bos);
oos.writeObject(((RandomProviderDefaultState) stateOrig).getState());

// Deserialize state.
ByteArrayInputStream bis = new ByteArrayInputStream(bos.toByteArray());
ObjectInputStream ois = new ObjectInputStream(bis);
RandomProviderState stateNew = new RandomProviderDefaultState((byte[]) ois.readObject());

RestorableUniformRandomProvider rngNew = RandomSource.create(source); // New RNG instance from the same "source".

// Restore original state on the new instance.
rngNew.restoreState(stateNew);
+--------------------------+


  * Generation of {{{./dist_density_approx.html}random deviates}} for various
    {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/package-summary.html}distributions}}.

+--------------------------+
import org.apache.commons.rng.sampling.distribution.ContinuousSampler;
import org.apache.commons.rng.sampling.distribution.GaussianSampler;
import org.apache.commons.rng.sampling.distribution.MarsagliaNormalizedGaussianSampler;

ContinuousSampler sampler = new GaussianSampler(new MarsagliaNormalizedGaussianSampler(RandomSource.create(RandomSource.MT_64)),
                                                45.6, 2.3);
double random = sampler.sample();
+--------------------------+

+--------------------------+
import org.apache.commons.rng.sampling.distribution.DiscreteSampler;
import org.apache.commons.rng.sampling.distribution.RejectionInversionZipfSampler;

DiscreteSampler sampler = new RejectionInversionZipfSampler(RandomSource.create(RandomSource.ISAAC),
                                                            5, 1.2);
int random = sampler.sample();
+--------------------------+

  * {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/PermutationSampler.html}Permutation}},
    {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/CollectionSampler.html}sampling from a <<<Collection>>>}}
    and shuffling utilities.

+--------------------------+
import org.apache.commons.rng.sampling.PermutationSampler;

PermutationSampler sampler = new PermutationSampler(RandomSource.create(RandomSource.KISS),
                                                    6, 3);

// 3 elements from a shuffling of the (0, 1, 2, 3, 4, 5) tuplet.
int[] random = sampler.sample();
+--------------------------+

+--------------------------+
import java.util.ArrayList;
import org.apache.commons.rng.sampling.CollectionSampler;

ArrayList<String> list = new ArrayList<String>();
list.add("Apache");
list.add("Commons");
list.add("RNG");

CollectionSampler<String> sampler = new CollectionSampler<String>(RandomSource.create(RandomSource.MWC_256),
                                                                  list, 1);
String word = sampler.sample().get(0);
+--------------------------+

  []


3. Library layout

  The API for client code consists of classes and interfaces defined in package
  {{{../commons-rng-client-api/apidocs/org/apache/commons/rng/package-summary.html}org.apache.commons.rng}}.

  * Interface <<<UniformRandomProvider>>> provides access to a sequence of
    random values uniformly distributed within some range.

  * Interfaces <<<RestorableUniformRandomProvider>>> and <<<RandomProviderState>>>
    provide the "save/restore" API.

  []


  The API for instantiating generators is defined in package
  {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/package-summary.html}org.apache.commons.rng.simple}}.

  * Enum <<<RandomSource>>> determines which algorithm to use for generating the
    sequence of random values.

  []

  The <<<org.apache.commons.rng.simple.internal>>> package contains classes
  for supporting initialization (a.k.a. "seeding") of the generators.
  They must not be used directly in applications, as all the necessary utilities
  are accessible through methods defined in <<<RandomSource>>>.

  * <<<ProviderBuilder>>>: contains methods for instantiating the concrete
    RNG implementations based on the source identifier; it also takes care
    of calling the appropriate classes for seed type conversion.

  * <<<SeedFactory>>>: contains factory methods for generating random seeds.

  * <<<SeedConverter>>>: interface for classes that transform between
    supported seed types.

  * Various classes that implement <<<SeedConverter>>> in order to transform
    from caller's seed to "native" seed.

  []


  The {{{../commons-rng-core/apidocs/org/apache/commons/rng/core/package-summary.html}org.apache.commons.rng.core}}
  package contains the implementation of the algorithms for the generation of
  pseudo-random sequences.
  Applications should not directly import or use classes defined in this package:
  all generators can be instantiated through the <<<RandomSource>>> factory.

  * Class <<<RandomProviderDefaultState>>> implements the <<<RandomProviderState>>>
    interface to enable "save/restore" for all <<<RestorableUniformRandomProvider>>>
    instances created through the <<<RandomSource>>> factory methods.

  * <<<BaseProvider>>>: base class for all concrete RNG implementations;
    it contains higher-level algorithms <<<nextInt(int n)>>> and <<<nextLong(long n)>>>
    common to all implementations.

  * <<<org.apache.commons.rng.core.util>>>

    ** <<<NumberFactory>>>: contains utilities for interpreting and combining
       the output (<<<int>>> or <<<long>>>) of the underlying source of
       randomness into the requested output, i.e. one of the Java primitive
       types supported by <<<UniformRandomProvider>>>.

    []

  * <<<org.apache.commons.rng.core.source32>>>

    ** <<<RandomIntSource>>>: describes an algorithm that generates randomness in
       32-bits chunks (a.k.a Java <<<int>>>).

    ** <<<IntProvider>>>: base class for concrete classes that implement <<<RandomIntSource>>>.

    ** Concrete RNG algorithms that are subclasses of <<<IntProvider>>>.

    []

  * <<<org.apache.commons.rng.core.source64>>>

    ** <<<RandomLongSource>>>: describes an algorithm that generates randomness in
       64-bits chunks (a.k.a Java <<<long>>>).

    ** <<<LongProvider>>>: base class for concrete classes that implement <<<RandomLongSource>>>.

    ** Concrete RNG algorithms that are subclasses of <<<LongProvider>>>.

    []

  []


4. Performance

  This section reports
  {{{../commons-rng-examples/examples-jmh/apidocs/org/apache/commons/rng/jmh/package-summary.html}performance benchmarks}} of the RNG implementations.

  All runs were performed on a platform with the following characteristics:

  * CPU: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz

  * Java version: 1.8.0_121 (build 1.8.0_121-8u121-b13-3-b13)

  * JVM: OpenJDK 64-Bit Server VM (build 25.121-b13, mixed mode)

  []

  The following tables indicate the performance (as measured by
  {{{http://openjdk.java.net/projects/code-tools/jmh/}JMH}}) for generating

  * a sequence of 32-bits integers (a.k.a. Java type <<<int>>>)

  * a sequence of 64-bits integers (a.k.a. Java type <<<long>>>)

  * a sequence of 64-bits floating point numbers (a.k.a. Java type <<<double>>>)

  []


  The first column is the RNG identifier (see {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/RandomSource.html}RandomSource}}).

  In these tables, <lower> is <better>.


  ** Generating <<<int>>> values

*--------------------------*----------------+
|| RNG identifier          || Score (normalized to the score of <<<RandomSource.JDK>>>) |
*--------------------------*----------------+
| MWC_256                  |        0.43405 |
*--------------------------*----------------+
| SPLIT_MIX_64             |        0.46945 |
*--------------------------*----------------+
| TWO_CMRES                |        0.53129 |
*--------------------------*----------------+
| XOR_SHIFT_1024_S         |        0.57792 |
*--------------------------*----------------+
| KISS                     |        0.61673 |
*--------------------------*----------------+
| ISAAC                    |        0.61966 |
*--------------------------*----------------+
| MT                       |        0.67974 |
*--------------------------*----------------+
| MT_64                    |        0.68905 |
*--------------------------*----------------+
| WELL_512_A               |        0.83342 |
*--------------------------*----------------+
| WELL_1024_A              |        0.89916 |
*--------------------------*----------------+
| JDK                      |        1.00000 |
*--------------------------*----------------+
| WELL_19937_C             |        1.10156 |
*--------------------------*----------------+
| WELL_19937_A             |        1.10758 |
*--------------------------*----------------+
| WELL_44497_A             |        1.18293 |
*--------------------------*----------------+
| WELL_44497_B             |        1.23908 |
*--------------------------*----------------+


  ** Generating <<<long>>> values

*--------------------------*----------------+
|| RNG identifier          || Score (normalized to the score of <<<RandomSource.JDK>>>) |
*--------------------------*----------------+
| SPLIT_MIX_64             |        0.20866 |
*--------------------------*----------------+
| TWO_CMRES                |        0.24560 |
*--------------------------*----------------+
| XOR_SHIFT_1024_S         |        0.26774 |
*--------------------------*----------------+
| MWC_256                  |        0.31939 |
*--------------------------*----------------+
| MT_64                    |        0.32588 |
*--------------------------*----------------+
| KISS                     |        0.49883 |
*--------------------------*----------------+
| MT                       |        0.53191 |
*--------------------------*----------------+
| ISAAC                    |        0.54878 |
*--------------------------*----------------+
| WELL_1024_A              |        0.64829 |
*--------------------------*----------------+
| WELL_512_A               |        0.66269 |
*--------------------------*----------------+
| WELL_19937_A             |        0.94553 |
*--------------------------*----------------+
| WELL_19937_C             |        0.99949 |
*--------------------------*----------------+
| JDK                      |        1.00000 |
*--------------------------*----------------+
| WELL_44497_A             |        1.03821 |
*--------------------------*----------------+
| WELL_44497_B             |        1.09792 |
*--------------------------*----------------+


  ** Generating <<<double>>> values

*--------------------------*----------------+
|| RNG identifier          || Score (normalized to the score of <<<RandomSource.JDK>>>) |
*--------------------------*----------------+
| SPLIT_MIX_64             |        0.27214 |
*--------------------------*----------------+
| XOR_SHIFT_1024_S         |        0.30975 |
*--------------------------*----------------+
| TWO_CMRES                |        0.31785 |
*--------------------------*----------------+
| MWC_256                  |        0.37810 |
*--------------------------*----------------+
| MT_64                    |        0.38516 |
*--------------------------*----------------+
| KISS                     |        0.51777 |
*--------------------------*----------------+
| ISAAC                    |        0.62528 |
*--------------------------*----------------+
| MT                       |        0.63868 |
*--------------------------*----------------+
| WELL_512_A               |        0.66895 |
*--------------------------*----------------+
| WELL_1024_A              |        0.70950 |
*--------------------------*----------------+
| JDK                      |        1.00000 |
*--------------------------*----------------+
| WELL_19937_A             |        1.06693 |
*--------------------------*----------------+
| WELL_44497_A             |        1.15398 |
*--------------------------*----------------+
| WELL_19937_C             |        1.15598 |
*--------------------------*----------------+
| WELL_44497_B             |        1.19013 |
*--------------------------*----------------+


  ** Sampling from a <N(0,1)> Gaussian distribution ({{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/MarsagliaNormalizedGaussianSampler.html}MarsagliaNormalizedGaussianSampler}} implementation)

*--------------------------*----------------+
|| RNG identifier          || Score (normalized to the score of <<<RandomSource.JDK>>>) |
*--------------------------*----------------+
| SPLIT_MIX_64             |        0.46750 |
*--------------------------*----------------+
| XOR_SHIFT_1024_S         |        0.48672 |
*--------------------------*----------------+
| TWO_CMRES                |        0.54703 |
*--------------------------*----------------+
| MWC_256                  |        0.55824 |
*--------------------------*----------------+
| MT_64                    |        0.58233 |
*--------------------------*----------------+
| ISAAC                    |        0.64820 |
*--------------------------*----------------+
| KISS                     |        0.66279 |
*--------------------------*----------------+
| MT                       |        0.68759 |
*--------------------------*----------------+
| WELL_512_A               |        0.77854 |
*--------------------------*----------------+
| WELL_1024_A              |        0.82204 |
*--------------------------*----------------+
| WELL_19937_A             |        0.93504 |
*--------------------------*----------------+
| WELL_19937_C             |        0.98401 |
*--------------------------*----------------+
| WELL_44497_A             |        0.99620 |
*--------------------------*----------------+
| JDK                      |        1.00000 |
*--------------------------*----------------+
| WELL_44497_B             |        1.03380 |
*--------------------------*----------------+

  ** Comparing {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/BoxMullerNormalizedGaussianSampler.html}BoxMullerNormalizedGaussianSampler}}, {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/MarsagliaNormalizedGaussianSampler.html}MarsagliaNormalizedGaussianSampler}}, {{{../commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/ZigguratNormalizedGaussianSampler.html}ZigguratNormalizedGaussianSampler}}.
     Each score is normalized to the score of {{{https://docs.oracle.com/javase/8/docs/api/java/util/Random.html#nextGaussian--}nextGaussian()}} method of <<<java.util.Random>>>.

*--------------------------*----------------+----------------+----------------+
|| RNG identifier          || <<<BoxMullerNormalizedGaussianSampler>>> || <<<MarsagliaNormalizedGaussianSampler>>> || <<<ZigguratNormalizedGaussianSampler>>> |
*--------------------------*----------------+----------------+----------------+
| ISAAC                    |        0.96494 |        0.41090 |        0.26529 |
*--------------------------*----------------+----------------+----------------+
| JDK                      |        1.04037 |        0.65917 |        0.35473 |
*--------------------------*----------------+----------------+----------------+
| KISS                     |        0.93580 |        0.41354 |        0.24676 |
*--------------------------*----------------+----------------+----------------+
| MT                       |        0.95563 |        0.43966 |        0.25891 |
*--------------------------*----------------+----------------+----------------+
| MT_64                    |        0.85963 |        0.37269 |        0.22864 |
*--------------------------*----------------+----------------+----------------+
| MWC_256                  |        0.90648 |        0.34902 |        0.21321 |
*--------------------------*----------------+----------------+----------------+
| SPLIT_MIX_64             |        0.82831 |        0.29894 |        0.18664 |
*--------------------------*----------------+----------------+----------------+
| TWO_CMRES                |        0.84886 |        0.35546 |        0.18992 |
*--------------------------*----------------+----------------+----------------+
| WELL_1024_A              |        1.00718 |        0.52266 |        0.29707 |
*--------------------------*----------------+----------------+----------------+
| WELL_19937_A             |        1.06638 |        0.61714 |        0.32631 |
*--------------------------*----------------+----------------+----------------+
| WELL_19937_C             |        1.09771 |        0.61585 |        0.37650 |
*--------------------------*----------------+----------------+----------------+
| WELL_44497_A             |        1.10244 |        0.62584 |        0.36866 |
*--------------------------*----------------+----------------+----------------+
| WELL_44497_B             |        1.10634 |        0.65012 |        0.38879 |
*--------------------------*----------------+----------------+----------------+
| WELL_512_A               |        0.99513 |        0.50448 |        0.31737 |
*--------------------------*----------------+----------------+----------------+
| XOR_SHIFT_1024_S         |        0.84066 |        0.30669 |        0.19735 |
*--------------------------*----------------+----------------+----------------+


5. Quality

  This section reports results of
  {{{../commons-rng-examples/apidocs/org/apache/commons/rng/examples/stress/package-summary.html}performing "stress tests"}}
  that aim at detecting failures of an implementation to produce sequences of numbers
  that follow a uniform distribution.

  Two different test suites were used:

  * {{{http://www.phy.duke.edu/~rgb/General/dieharder.php}Dieharder}}

  * {{{http://simul.iro.umontreal.ca/testu01/tu01.html}TestU01}}

  []

  The first column is the RNG identifier (see {{{../commons-rng-simple/apidocs/org/apache/commons/rng/simple/RandomSource.html}RandomSource}}).
  The second and third columns contain the number of tests which <Dieharder> and <TestU01>
  respectively reported as below the accepted threshold for considering the sequence as
  uniformly random; hence, in this table, <lower> is <better>.

  For each the two test suites, three runs were performed (using random seeds): Click on one
  of the numbers of the comma-separated list in order to see the text report of the
  corresponding run.
  Note: For <Dieharder>, a failure on the "Diehard Sums Test" can be {{{http://www.phy.duke.edu/~rgb/General/dieharder.php}ignored}}.


*---------------------------------*----------------*---------------------*
|| RNG identifier             || Dieharder     || TestU01 (BigCrush) |
*----------------*----------------*----------------*---------------------*
| JDK         | {{{../txt/userguide/stress/dh/run_1/dh_1}14}}, {{{../txt/userguide/stress/dh/run_2/dh_1}16}}, {{{../txt/userguide/stress/dh/run_3/dh_1}15}} | {{{../txt/userguide/stress/tu/run_1/tu_1}78}}, {{{../txt/userguide/stress/tu/run_2/tu_1}75}}, {{{../txt/userguide/stress/tu/run_3/tu_1}76}} |
*---------------------------------*----------------*----------------*
| MT   | {{{../txt/userguide/stress/dh/run_1/dh_2}0}}, {{{../txt/userguide/stress/dh/run_2/dh_2}0}}, {{{../txt/userguide/stress/dh/run_3/dh_2}0}} | {{{../txt/userguide/stress/tu/run_1/tu_2}2}}, {{{../txt/userguide/stress/tu/run_2/tu_2}2}}, {{{../txt/userguide/stress/tu/run_3/tu_2}2}} |
*---------------------------------*----------------*----------------*
| WELL_512_A          | {{{../txt/userguide/stress/dh/run_1/dh_3}0}}, {{{../txt/userguide/stress/dh/run_2/dh_3}0}}, {{{../txt/userguide/stress/dh/run_3/dh_3}0}} | {{{../txt/userguide/stress/tu/run_1/tu_3}6}}, {{{../txt/userguide/stress/tu/run_2/tu_3}6}}, {{{../txt/userguide/stress/tu/run_3/tu_3}6}} |
*---------------------------------*----------------*----------------*
| WELL_1024_A         | {{{../txt/userguide/stress/dh/run_1/dh_4}0}}, {{{../txt/userguide/stress/dh/run_2/dh_4}0}}, {{{../txt/userguide/stress/dh/run_3/dh_4}1}}| {{{../txt/userguide/stress/tu/run_1/tu_4}4}}, {{{../txt/userguide/stress/tu/run_2/tu_4}6}}, {{{../txt/userguide/stress/tu/run_3/tu_4}5}} |
*---------------------------------*----------------*----------------*
| WELL_19937_A        | {{{../txt/userguide/stress/dh/run_1/dh_5}0}}, {{{../txt/userguide/stress/dh/run_2/dh_5}0}}, {{{../txt/userguide/stress/dh/run_3/dh_5}0}} | {{{../txt/userguide/stress/tu/run_1/tu_5}2}}, {{{../txt/userguide/stress/tu/run_2/tu_5}3}}, {{{../txt/userguide/stress/tu/run_3/tu_5}4}} |
*---------------------------------*----------------*----------------*
| WELL_19937_C        | {{{../txt/userguide/stress/dh/run_1/dh_6}0}}, {{{../txt/userguide/stress/dh/run_2/dh_6}0}}, {{{../txt/userguide/stress/dh/run_3/dh_6}0}} | {{{../txt/userguide/stress/tu/run_1/tu_6}2}}, {{{../txt/userguide/stress/tu/run_2/tu_6}2}}, {{{../txt/userguide/stress/tu/run_3/tu_6}2}} |
*---------------------------------*----------------*----------------*
| WELL_44497_A        | {{{../txt/userguide/stress/dh/run_1/dh_7}0}}, {{{../txt/userguide/stress/dh/run_2/dh_7}0}}, {{{../txt/userguide/stress/dh/run_3/dh_7}0}} | {{{../txt/userguide/stress/tu/run_1/tu_7}3}}, {{{../txt/userguide/stress/tu/run_2/tu_7}3}}, {{{../txt/userguide/stress/tu/run_3/tu_7}2}} |
*---------------------------------*----------------*----------------*
| WELL_44497_B        | {{{../txt/userguide/stress/dh/run_1/dh_8}0}}, {{{../txt/userguide/stress/dh/run_2/dh_8}1}}, {{{../txt/userguide/stress/dh/run_3/dh_8}0}} | {{{../txt/userguide/stress/tu/run_1/tu_8}2}}, {{{../txt/userguide/stress/tu/run_2/tu_8}2}}, {{{../txt/userguide/stress/tu/run_3/tu_8}3}} |
*---------------------------------*----------------*----------------*
| ISAAC       | {{{../txt/userguide/stress/dh/run_1/dh_9}0}}, {{{../txt/userguide/stress/dh/run_2/dh_9}0}}, {{{../txt/userguide/stress/dh/run_3/dh_9}0}} | {{{../txt/userguide/stress/tu/run_1/tu_9}1}}, {{{../txt/userguide/stress/tu/run_2/tu_9}0}}, {{{../txt/userguide/stress/tu/run_3/tu_9}0}} |
*---------------------------------*----------------*----------------*
| MT_64 | {{{../txt/userguide/stress/dh/run_1/dh_10}0}}, {{{../txt/userguide/stress/dh/run_2/dh_10}0}}, {{{../txt/userguide/stress/dh/run_3/dh_10}0}} | {{{../txt/userguide/stress/tu/run_1/tu_10}2}}, {{{../txt/userguide/stress/tu/run_2/tu_10}2}}, {{{../txt/userguide/stress/tu/run_3/tu_10}3}} |
*---------------------------------*----------------*----------------*
| SPLIT_MIX_64        | {{{../txt/userguide/stress/dh/run_1/dh_11}0}}, {{{../txt/userguide/stress/dh/run_2/dh_11}0}}, {{{../txt/userguide/stress/dh/run_3/dh_11}0}} | {{{../txt/userguide/stress/tu/run_1/tu_11}0}}, {{{../txt/userguide/stress/tu/run_2/tu_11}0}}, {{{../txt/userguide/stress/tu/run_3/tu_11}0}} |
*---------------------------------*----------------*----------------*
| XOR_SHIFT_1024_S  | {{{../txt/userguide/stress/dh/run_1/dh_12}0}}, {{{../txt/userguide/stress/dh/run_2/dh_12}0}}, {{{../txt/userguide/stress/dh/run_3/dh_12}0}} | {{{../txt/userguide/stress/tu/run_1/tu_12}0}}, {{{../txt/userguide/stress/tu/run_2/tu_12}0}}, {{{../txt/userguide/stress/tu/run_3/tu_12}0}} |
*---------------------------------*----------------*----------------*
| TWO_CMRES          | {{{../txt/userguide/stress/dh/run_1/dh_13}0}}, {{{../txt/userguide/stress/dh/run_2/dh_13}1}}, {{{../txt/userguide/stress/dh/run_3/dh_13}0}} | {{{../txt/userguide/stress/tu/run_1/tu_13}0}}, {{{../txt/userguide/stress/tu/run_2/tu_13}0}}, {{{../txt/userguide/stress/tu/run_3/tu_13}0}} |
*---------------------------------*----------------*----------------*
| MWC_256          | {{{../txt/userguide/stress/dh/run_1/dh_14}0}}, {{{../txt/userguide/stress/dh/run_2/dh_14}0}}, {{{../txt/userguide/stress/dh/run_3/dh_14}0}} | {{{../txt/userguide/stress/tu/run_1/tu_14}0}}, {{{../txt/userguide/stress/tu/run_2/tu_14}0}}, {{{../txt/userguide/stress/tu/run_3/tu_14}0}} |
*---------------------------------*----------------*----------------*
| KISS          | {{{../txt/userguide/stress/dh/run_1/dh_15}0}}, {{{../txt/userguide/stress/dh/run_2/dh_15}0}}, {{{../txt/userguide/stress/dh/run_3/dh_15}0}} | {{{../txt/userguide/stress/tu/run_1/tu_15}0}}, {{{../txt/userguide/stress/tu/run_2/tu_15}1}}, {{{../txt/userguide/stress/tu/run_3/tu_15}0}} |
*---------------------------------*----------------*----------------*


6. Dependencies

  Apache Commons RNG requires JDK 1.6+ and has no runtime dependencies.