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<a name="boost_random.reference"></a><a class="link" href="reference.html" title="Reference">Reference</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts">Concepts</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.generators">Generators</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.distributions">Distributions</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.utilities">Utilities</a></span></dt>
<dt><span class="section"><a href="reference.html#headers">Headers</a></span></dt>
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<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.reference.concepts"></a><a class="link" href="reference.html#boost_random.reference.concepts" title="Concepts">Concepts</a>
</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.uniform_random_number_generator">Uniform
Random Number Generator</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.non_deterministic_uniform_random_number_generator">Non-deterministic
Uniform Random Number Generator</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator">Pseudo-Random
Number Generator</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.quasi_random_number_generator">Quasi-Random
Number Generator</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.seed_sequence">Seed
Sequence</a></span></dt>
<dt><span class="section"><a href="reference.html#boost_random.reference.concepts.random_distribution">Random
Distribution</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.introduction"></a><a class="link" href="reference.html#boost_random.reference.concepts.introduction" title="Introduction">Introduction</a>
</h4></div></div></div>
<p>
Random numbers are required in a number of different problem domains, such
as
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
numerics (simulation, Monte-Carlo integration)
</li>
<li class="listitem">
games (non-deterministic enemy behavior)
</li>
<li class="listitem">
security (key generation)
</li>
<li class="listitem">
testing (random coverage in white-box tests)
</li>
</ul></div>
<p>
The Boost Random Number Generator Library provides a framework for random
number generators with well-defined properties so that the generators can
be used in the demanding numerics and security domains. For a general introduction
to random numbers in numerics, see
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
"Numerical Recipes in C: The art of scientific computing",
William H. Press, Saul A. Teukolsky, William A. Vetterling, Brian P.
Flannery, 2nd ed., 1992, pp. 274-328
</p></blockquote></div>
<p>
Depending on the requirements of the problem domain, different variations
of random number generators are appropriate:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
non-deterministic random number generator
</li>
<li class="listitem">
pseudo-random number generator
</li>
<li class="listitem">
quasi-random number generator
</li>
</ul></div>
<p>
All variations have some properties in common, the concepts (in the STL
sense) is called <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>.
This concept will be defined in a subsequent section.
</p>
<p>
The goals for this library are the following:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
allow easy integration of third-party random-number generators
</li>
<li class="listitem">
provide easy-to-use front-end classes which model popular distributions
</li>
<li class="listitem">
provide maximum efficiency
</li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.uniform_random_number_generator"></a><a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">Uniform
Random Number Generator</a>
</h4></div></div></div>
<p>
A uniform random number generator provides a sequence of random numbers
uniformly distributed on a given range. The range can be compile-time fixed
or available (only) after run-time construction of the object.
</p>
<p>
The <span class="emphasis"><em>tight lower bound</em></span> of some (finite) set S is the
(unique) member l in S, so that for all v in S, l <= v holds. Likewise,
the <span class="emphasis"><em>tight upper bound</em></span> of some (finite) set S is the
(unique) member u in S, so that for all v in S, v <= u holds.
</p>
<p>
In the following table, X denotes a number generator class returning objects
of type T, and v is a const value of X.
</p>
<div class="table">
<a name="boost_random.reference.concepts.uniform_random_number_generator.uniformrandomnumbergenerator_requirements"></a><p class="title"><b>Table 34.1. UniformRandomNumberGenerator requirements</b></p>
<div class="table-contents"><table class="table" summary="UniformRandomNumberGenerator requirements">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
expression
</p>
</th>
<th>
<p>
return type
</p>
</th>
<th>
<p>
pre/post-condition
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">::</span><span class="identifier">result_type</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_specialized</span></code> is <code class="computeroutput"><span class="keyword">true</span></code>, <code class="computeroutput"><span class="identifier">T</span></code>
is <a href="../../../doc/html/LessThanComparable.html" target="_top">LessThanComparable</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">.</span><span class="keyword">operator</span><span class="special">()()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">min</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
tight lower bound on the set of all values returned by <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>.
The return value of this function shall not change during the
lifetime of the object.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">max</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
if <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span></code>, tight upper bound
on the set of all values returned by <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>, otherwise, the smallest representable
number larger than the tight upper bound on the set of all values
returned by <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>. In any case, the return value
of this function shall not change during the lifetime of the
object.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
The member functions <code class="computeroutput"><span class="identifier">min</span></code>,
<code class="computeroutput"><span class="identifier">max</span></code>, and <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>
shall have amortized constant time complexity.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top">
<p>
For integer generators (i.e. integer <code class="computeroutput"><span class="identifier">T</span></code>),
the generated values <code class="computeroutput"><span class="identifier">x</span></code>
fulfill <code class="computeroutput"><span class="identifier">min</span><span class="special">()</span>
<span class="special"><=</span> <span class="identifier">x</span>
<span class="special"><=</span> <span class="identifier">max</span><span class="special">()</span></code>, for non-integer generators (i.e. non-integer
<code class="computeroutput"><span class="identifier">T</span></code>), the generated values
<code class="computeroutput"><span class="identifier">x</span></code> fulfill <code class="computeroutput"><span class="identifier">min</span><span class="special">()</span> <span class="special"><=</span> <span class="identifier">x</span> <span class="special"><</span> <span class="identifier">max</span><span class="special">()</span></code>.
</p>
<p>
Rationale: The range description with min and max serves two purposes.
First, it allows scaling of the values to some canonical range, such
as [0..1). Second, it describes the significant bits of the values, which
may be relevant for further processing.
</p>
<p>
The range is a closed interval [min,max] for integers, because the underlying
type may not be able to represent the half-open interval [min,max+1).
It is a half-open interval [min, max) for non-integers, because this
is much more practical for borderline cases of continuous distributions.
</p>
</td></tr>
</table></div>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top">
<p>
The <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
concept does not require <code class="computeroutput"><span class="keyword">operator</span><span class="special">()(</span><span class="keyword">long</span><span class="special">)</span></code> and thus it does not fulfill the <code class="computeroutput"><span class="identifier">RandomNumberGenerator</span></code> (std:25.2.11
[lib.alg.random.shuffle]) requirements. Use the <code class="computeroutput"><a class="link" href="../boost/random/random_number_generator.html" title="Class template random_number_generator">random_number_generator</a></code>
adapter for that.
</p>
<p>
Rationale: <code class="computeroutput"><span class="keyword">operator</span><span class="special">()(</span><span class="keyword">long</span><span class="special">)</span></code>
is not provided, because mapping the output of some generator with integer
range to a different integer range is not trivial.
</p>
</td></tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.non_deterministic_uniform_random_number_generator"></a><a class="link" href="reference.html#boost_random.reference.concepts.non_deterministic_uniform_random_number_generator" title="Non-deterministic Uniform Random Number Generator">Non-deterministic
Uniform Random Number Generator</a>
</h4></div></div></div>
<p>
A non-deterministic uniform random number generator is a <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
that is based on some stochastic process. Thus, it provides a sequence
of truly-random numbers. Examples for such processes are nuclear decay,
noise of a Zehner diode, tunneling of quantum particles, rolling a die,
drawing from an urn, and tossing a coin. Depending on the environment,
inter-arrival times of network packets or keyboard events may be close
approximations of stochastic processes.
</p>
<p>
The class <code class="computeroutput"><a class="link" href="../boost/random/random_device.html" title="Class random_device">random_device</a></code>
is a model for a non-deterministic random number generator.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
This type of random-number generator is useful for security applications,
where it is important to prevent an outside attacker from guessing the
numbers and thus obtaining your encryption or authentication key. Thus,
models of this concept should be cautious not to leak any information,
to the extent possible by the environment. For example, it might be advisable
to explicitly clear any temporary storage as soon as it is no longer
needed.
</p></td></tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.pseudo_random_number_generator"></a><a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">Pseudo-Random
Number Generator</a>
</h4></div></div></div>
<p>
A pseudo-random number generator is a <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
which provides a deterministic sequence of pseudo-random numbers, based
on some algorithm and internal state. <code class="computeroutput"><a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">Linear
congruential</a></code> and <code class="computeroutput"><a class="link" href="../boost/random/invers_1_3_35_5_6_20_1_1_1.html" title="Class template inversive_congruential_engine">inversive
congruential</a></code> generators are examples of such <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo-random
number generators</a>. Often, these generators are very sensitive to
their parameters. In order to prevent wrong implementations from being
used, an external testsuite should check that the generated sequence and
the validation value provided do indeed match.
</p>
<p>
Donald E. Knuth gives an extensive overview on pseudo-random number generation
in his book "The Art of Computer Programming, Vol. 2, 3rd edition,
Addison-Wesley, 1997". The descriptions for the specific generators
contain additional references.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
Because the state of a pseudo-random number generator is necessarily
finite, the sequence of numbers returned by the generator will loop eventually.
</p></td></tr>
</table></div>
<p>
In addition to the <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
requirements, a pseudo-random number generator has some additional requirements.
In the following table, <code class="computeroutput"><span class="identifier">X</span></code>
denotes a pseudo-random number generator class, <code class="computeroutput"><span class="identifier">u</span></code>
is a value of <code class="computeroutput"><span class="identifier">X</span></code>, <code class="computeroutput"><span class="identifier">i</span></code> is a value of integral type, <code class="computeroutput"><span class="identifier">s</span></code> is a value of a type which models
<a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">SeedSeq</a>,
and <code class="computeroutput"><span class="identifier">j</span></code> a value of type
<code class="computeroutput"><span class="keyword">unsigned</span> <span class="keyword">long</span>
<span class="keyword">long</span></code>.
</p>
<div class="table">
<a name="boost_random.reference.concepts.pseudo_random_number_generator.pseudorandomnumbergenerator_requirements"></a><p class="title"><b>Table 34.2. PseudoRandomNumberGenerator requirements</b></p>
<div class="table-contents"><table class="table" summary="PseudoRandomNumberGenerator requirements">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
expression
</p>
</th>
<th>
<p>
return type
</p>
</th>
<th>
<p>
pre/post-condition
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
creates a generator with a default seed.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
creates a generator seeding it with the integer <code class="computeroutput"><span class="identifier">i</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
creates a generator setting its initial state from the <a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">SeedSeq</a>
<code class="computeroutput"><span class="identifier">s</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">.</span><span class="identifier">seed</span><span class="special">(...)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
sets the current state to be identical to the state that would
be created by the corresponding constructor.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">.</span><span class="identifier">discard</span><span class="special">(</span><span class="identifier">j</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
Advances the generator by <code class="computeroutput"><span class="identifier">j</span></code>
steps as if by <code class="computeroutput"><span class="identifier">j</span></code>
calls to <code class="computeroutput"><span class="identifier">u</span><span class="special">()</span></code>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
Classes which model a pseudo-random number generator shall also model
<a href="../../../doc/html/EqualityComparable.html" target="_top">EqualityComparable</a>,
i.e. implement <code class="computeroutput"><span class="keyword">operator</span><span class="special">==</span></code>.
Two pseudo-random number generators are defined to be <span class="emphasis"><em>equivalent</em></span>
if they both return an identical sequence of numbers starting from a given
state.
</p>
<p>
Classes which model a pseudo-random number generator shall also model the
Streamable concept, i.e. implement <code class="computeroutput"><span class="keyword">operator</span><span class="special"><<</span></code> and <code class="computeroutput"><span class="keyword">operator</span><span class="special">>></span></code>. <code class="computeroutput"><span class="keyword">operator</span><span class="special"><<</span></code> writes all current state of the
pseudo-random number generator to the given <code class="computeroutput"><span class="identifier">ostream</span></code>
so that <code class="computeroutput"><span class="keyword">operator</span><span class="special">>></span></code>
can restore the state at a later time. The state shall be written in a
platform-independent manner, but it is assumed that the <code class="computeroutput"><span class="identifier">locales</span></code>
used for writing and reading be the same. The pseudo-random number generator
with the restored state and the original at the just-written state shall
be equivalent.
</p>
<p>
Classes which model a pseudo-random number generator should also model
the <a href="../../../doc/html/CopyConstructible.html" target="_top">CopyConstructible</a>
and <a href="../../../doc/html/Assignable.html" target="_top">Assignable</a> concepts.
However, note that the sequences of the original and the copy are strongly
correlated (in fact, they are identical), which may make them unsuitable
for some problem domains. Thus, copying pseudo-random number generators
is discouraged; they should always be passed by (non-const) reference.
</p>
<p>
The classes <code class="computeroutput"><a class="link" href="../boost/random/rand48.html" title="Class rand48">rand48</a></code>,
<code class="computeroutput"><a class="link" href="../boost/random/minstd_rand.html" title="Type definition minstd_rand">minstd_rand</a></code>, and
<code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code> are models
for a pseudo-random number generator.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
This type of random-number generator is useful for numerics, games and
testing. The non-zero arguments constructor(s) and the <code class="computeroutput"><span class="identifier">seed</span><span class="special">()</span></code>
member function(s) allow for a user-provided state to be installed in
the generator. This is useful for debugging Monte-Carlo algorithms and
analyzing particular test scenarios. The Streamable concept allows to
save/restore the state of the generator, for example to re-run a test
suite at a later time.
</p></td></tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.quasi_random_number_generator"></a><a class="link" href="reference.html#boost_random.reference.concepts.quasi_random_number_generator" title="Quasi-Random Number Generator">Quasi-Random
Number Generator</a>
</h4></div></div></div>
<p>
A quasi-random number generator is a <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
which provides a deterministic sequence of quasi-random numbers, based
on some algorithm and internal state. <code class="computeroutput"><a class="link" href="../boost/random/niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">Niederreiter
base 2</a></code> generator is an example of such a <a class="link" href="reference.html#boost_random.reference.concepts.quasi_random_number_generator" title="Quasi-Random Number Generator">quasi-random
number generator</a>. The "quasi" modifier is used to denote
more clearly that the values produced by such a generator are neither random
nor pseudo-random, but they form a low discrepancy sequence. The intuitive
idea is that a low discrepancy sequence is more evenly distributed than
a pseudo random sequence would be. For example, if we generate a low discrepancy
sequence of 2D points on a square, this square would be covered more evenly,
and the number of points falling to any part of the square would be proportional
to the number of points in the whole square. Such sequences share some
properties of random variables and in certain applications such as the
quasi-Monte Carlo method their lower discrepancy is an important advantage.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
The quasi-Monte Carlo method uses a low-discrepancy sequence such as
the Niederreiter base 2 sequence, the Sobol sequence, or the Faure sequence
among the others. The advantage of using low-discrepancy sequences is
a probabilistically faster rate of convergence. Quasi-Monte Carlo has
a rate of convergence O(log(N)<sup>s</sup>/N), whereas the rate of convergence for
the Monte Carlo method, which uses a pseudo-random sequence, is O(N<sup>-0.5</sup>).
</p></td></tr>
</table></div>
<p>
Harold Niederreiter gives an extensive overview on random number generation
and quasi-Monte Carlo methods in his book "Random number generation
and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics,
1992".
</p>
<p>
In addition to the <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
requirements, a quasi-random number generator has some additional requirements.
In the following table, <code class="computeroutput"><span class="identifier">X</span></code>
denotes a quasi-random number generator class, <code class="computeroutput"><span class="identifier">u</span></code>
is a value of <code class="computeroutput"><span class="identifier">X</span></code>, <code class="computeroutput"><span class="identifier">v</span></code> is a const value of <code class="computeroutput"><span class="identifier">X</span></code>,
and <code class="computeroutput"><span class="identifier">j</span></code> a value of type
<code class="computeroutput"><span class="keyword">unsigned</span> <span class="keyword">long</span>
<span class="keyword">long</span></code>.
</p>
<div class="table">
<a name="boost_random.reference.concepts.quasi_random_number_generator.quasirandomnumbergenerator_requirements"></a><p class="title"><b>Table 34.3. QuasiRandomNumberGenerator requirements</b></p>
<div class="table-contents"><table class="table" summary="QuasiRandomNumberGenerator requirements">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
expression
</p>
</th>
<th>
<p>
return type
</p>
</th>
<th>
<p>
pre/post-condition
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
creates an <code class="computeroutput"><span class="identifier">s</span></code>-dimensional
generator with a default seed. Dimension <code class="computeroutput"><span class="identifier">s</span></code>
is an integer no less than 1.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">dimension</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
std::size_t
</p>
</td>
<td>
<p>
the dimension of quasi-random domain.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">.</span><span class="identifier">seed</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
seeds the generator with the integer <code class="computeroutput"><span class="identifier">i</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">.</span><span class="identifier">discard</span><span class="special">(</span><span class="identifier">j</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
Advances the generator by <code class="computeroutput"><span class="identifier">j</span></code>
steps as if by <code class="computeroutput"><span class="identifier">j</span></code>
calls to <code class="computeroutput"><span class="identifier">u</span><span class="special">()</span></code>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
The <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>
returns a successive element of an <code class="computeroutput"><span class="identifier">s</span></code>-dimensional
(<code class="computeroutput"><span class="identifier">s</span></code> = <code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">dimension</span><span class="special">()</span></code>) vector at each invocation. When all
elements are exhausted, <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code> begins anew with the starting element
of a subsequent <code class="computeroutput"><span class="identifier">s</span></code>-dimensional
vector.
</p></td></tr>
</table></div>
<p>
Classes which model a quasi-random number generator shall also model <a href="../../../doc/html/EqualityComparable.html" target="_top">EqualityComparable</a>,
i.e. implement <code class="computeroutput"><span class="keyword">operator</span><span class="special">==</span></code>.
Two quasi-random number generators are defined to be <span class="emphasis"><em>equivalent</em></span>
if they both return an identical sequence of numbers starting from a given
state.
</p>
<p>
Classes which model a quasi-random number generator shall also model the
Streamable concept, i.e. implement <code class="computeroutput"><span class="keyword">operator</span><span class="special"><<</span></code> and <code class="computeroutput"><span class="keyword">operator</span><span class="special">>></span></code>. <code class="computeroutput"><span class="keyword">operator</span><span class="special"><<</span></code> writes all current state of the
quasi-random number generator to the given <code class="computeroutput"><span class="identifier">ostream</span></code>
so that <code class="computeroutput"><span class="keyword">operator</span><span class="special">>></span></code>
can restore the state at a later time. The state shall be written in a
platform-independent manner, but it is assumed that the <code class="computeroutput"><span class="identifier">locales</span></code>
used for writing and reading be the same. The quasi-random number generator
with the restored state and the original at the just-written state shall
be equivalent.
</p>
<p>
Classes which model a quasi-random number generator should also model the
<a href="../../../doc/html/CopyConstructible.html" target="_top">CopyConstructible</a>
and <a href="../../../doc/html/Assignable.html" target="_top">Assignable</a> concepts.
However, note that the sequences of the original and the copy are strongly
correlated (in fact, they are identical), which may make them unsuitable
for some problem domains. Thus, copying quasi-random number generators
is discouraged; they should always be passed by (non-const) reference.
</p>
<p>
The classes <code class="computeroutput"><a class="link" href="../boost/random/niederreiter_base2.html" title="Type definition niederreiter_base2">niederreiter_base2</a></code>,
<code class="computeroutput"><a class="link" href="../boost/random/sobol.html" title="Type definition sobol">sobol</a></code>, <code class="computeroutput"><a class="link" href="../boost/random/faure.html" title="Type definition faure">faure</a></code>
are models for a quasi-random number generator.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.seed_sequence"></a><a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">Seed
Sequence</a>
</h4></div></div></div>
<p>
A SeedSeq represents a sequence of values that can be used to set the initial
state of a <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">PseudoRandomNumberGenerator</a>.
<code class="computeroutput"><span class="identifier">i</span></code> and <code class="computeroutput"><span class="identifier">j</span></code>
are RandomAccessIterators whose <code class="computeroutput"><span class="identifier">value_type</span></code>
is an unsigned integer type with at least 32 bits.
</p>
<div class="table">
<a name="boost_random.reference.concepts.seed_sequence.seedseq_requirements"></a><p class="title"><b>Table 34.4. SeedSeq requirements</b></p>
<div class="table-contents"><table class="table" summary="SeedSeq requirements">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
expression
</p>
</th>
<th>
<p>
return type
</p>
</th>
<th>
<p>
pre/post-condition
</p>
</th>
<th>
<p>
complexity
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">s</span><span class="special">.</span><span class="identifier">generate</span><span class="special">(</span><span class="identifier">i</span><span class="special">,</span>
<span class="identifier">j</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
void
</p>
</td>
<td>
<p>
stores 32-bit values to all the elements in the iterator range
defined by <code class="computeroutput"><span class="identifier">i</span></code>
and <code class="computeroutput"><span class="identifier">j</span></code>
</p>
</td>
<td>
<p>
O(j - i)
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><p>
The class <code class="computeroutput"><a class="link" href="../boost/random/seed_seq.html" title="Class seed_seq">seed_seq</a></code>
and every <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>
provided by the library are models of <a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">SeedSeq</a>.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_random.reference.concepts.random_distribution"></a><a class="link" href="reference.html#boost_random.reference.concepts.random_distribution" title="Random Distribution">Random
Distribution</a>
</h4></div></div></div>
<p>
A random distribution produces random numbers distributed according to
some distribution, given uniformly distributed random values as input.
In the following table, <code class="computeroutput"><span class="identifier">X</span></code>
denotes a random distribution class returning objects of type <code class="computeroutput"><span class="identifier">T</span></code>, <code class="computeroutput"><span class="identifier">u</span></code>
is a value of <code class="computeroutput"><span class="identifier">X</span></code>, <code class="computeroutput"><span class="identifier">x</span></code> and <code class="computeroutput"><span class="identifier">y</span></code>
are (possibly const) values of <code class="computeroutput"><span class="identifier">X</span></code>,
<code class="computeroutput"><span class="identifier">P</span></code> is the <code class="computeroutput"><span class="identifier">param_type</span></code> of the distribution, <code class="computeroutput"><span class="identifier">p</span></code> is a value of <code class="computeroutput"><span class="identifier">P</span></code>,
and <code class="computeroutput"><span class="identifier">e</span></code> is an lvalue of an
arbitrary type that meets the requirements of a <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>,
returning values of type <code class="computeroutput"><span class="identifier">U</span></code>.
</p>
<div class="table">
<a name="boost_random.reference.concepts.random_distribution.random_distribution_requirements__in_addition_to_copyconstructible__and_assignable_"></a><p class="title"><b>Table 34.5. Random distribution requirements (in addition to CopyConstructible,
and Assignable)</b></p>
<div class="table-contents"><table class="table" summary="Random distribution requirements (in addition to CopyConstructible,
and Assignable)">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
expression
</p>
</th>
<th>
<p>
return type
</p>
</th>
<th>
<p>
pre/post-condition
</p>
</th>
<th>
<p>
complexity
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">::</span><span class="identifier">result_type</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
compile-time
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">::</span><span class="identifier">param_type</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">P</span></code>
</p>
</td>
<td>
<p>
A type that stores the parameters of the distribution, but not
any of the state used to generate random variates. <code class="computeroutput"><span class="identifier">param_type</span></code> provides the same
set of constructors and accessors as the distribution.
</p>
</td>
<td>
<p>
compile-time
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span><span class="special">(</span><span class="identifier">p</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">X</span></code>
</p>
</td>
<td>
<p>
Initializes a distribution from its parameters
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">.</span><span class="identifier">reset</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
subsequent uses of <code class="computeroutput"><span class="identifier">u</span></code>
do not depend on values produced by any engine prior to invoking
<code class="computeroutput"><span class="identifier">reset</span></code>.
</p>
</td>
<td>
<p>
constant
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">(</span><span class="identifier">e</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
the sequence of numbers returned by successive invocations with
the same object <code class="computeroutput"><span class="identifier">e</span></code>
is randomly distributed with the probability density function
of the distribution
</p>
</td>
<td>
<p>
amortized constant number of invocations of <code class="computeroutput"><span class="identifier">e</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">u</span><span class="special">(</span><span class="identifier">e</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
Equivalent to X(p)(e), but may use a different (and presumably
more efficient) implementation
</p>
</td>
<td>
<p>
amortized constant number of invocations of <code class="computeroutput"><span class="identifier">e</span></code>
+ O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span><span class="special">.</span><span class="identifier">param</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">P</span></code>
</p>
</td>
<td>
<p>
Returns the parameters of the distribution
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span><span class="special">.</span><span class="identifier">param</span><span class="special">(</span><span class="identifier">p</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
void
</p>
</td>
<td>
<p>
Sets the parameters of the distribution
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span><span class="special">.</span><span class="identifier">min</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
returns the minimum value of the distribution
</p>
</td>
<td>
<p>
constant
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span><span class="special">.</span><span class="identifier">max</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
returns the maximum value of the distribution
</p>
</td>
<td>
<p>
constant
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span></code>
</p>
</td>
<td>
<p>
Indicates whether the two distributions will produce identical
sequences of random variates if given equal generators
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">x</span> <span class="special">!=</span>
<span class="identifier">y</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">bool</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">!(</span><span class="identifier">x</span>
<span class="special">==</span> <span class="identifier">y</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">os</span> <span class="special"><<</span>
<span class="identifier">x</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span></code>
</p>
</td>
<td>
<p>
writes a textual representation for the parameters and additional
internal data of the distribution <code class="computeroutput"><span class="identifier">x</span></code>
to <code class="computeroutput"><span class="identifier">os</span></code>. post:
The <code class="computeroutput"><span class="identifier">os</span><span class="special">.</span><span class="identifier">fmtflags</span></code> and fill character
are unchanged.
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">is</span> <span class="special">>></span>
<span class="identifier">u</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span></code>
</p>
</td>
<td>
<p>
restores the parameters and additional internal data of the distribution
<code class="computeroutput"><span class="identifier">u</span></code>. pre: <code class="computeroutput"><span class="identifier">is</span></code> provides a textual representation
that was previously written by <code class="computeroutput"><span class="keyword">operator</span><span class="special"><<</span></code> post: The <code class="computeroutput"><span class="identifier">is</span><span class="special">.</span><span class="identifier">fmtflags</span></code> are unchanged.
</p>
</td>
<td>
<p>
O(size of state)
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
Additional requirements: The sequence of numbers produced by repeated invocations
of <code class="computeroutput"><span class="identifier">x</span><span class="special">(</span><span class="identifier">e</span><span class="special">)</span></code> does
not change whether or not <code class="computeroutput"><span class="identifier">os</span>
<span class="special"><<</span> <span class="identifier">x</span></code>
is invoked between any of the invocations <code class="computeroutput"><span class="identifier">x</span><span class="special">(</span><span class="identifier">e</span><span class="special">)</span></code>.
If a textual representation is written using <code class="computeroutput"><span class="identifier">os</span>
<span class="special"><<</span> <span class="identifier">x</span></code>
and that representation is restored into the same or a different object
<code class="computeroutput"><span class="identifier">y</span></code> of the same type using
<code class="computeroutput"><span class="identifier">is</span> <span class="special">>></span>
<span class="identifier">y</span></code>, repeated invocations of <code class="computeroutput"><span class="identifier">y</span><span class="special">(</span><span class="identifier">e</span><span class="special">)</span></code> produce the same sequence of random numbers
as would repeated invocations of <code class="computeroutput"><span class="identifier">x</span><span class="special">(</span><span class="identifier">e</span><span class="special">)</span></code>.
</p>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.reference.generators"></a><a class="link" href="reference.html#boost_random.reference.generators" title="Generators">Generators</a>
</h3></div></div></div>
<p>
This library provides several <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo-random
number generators</a>. The quality of a <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo
random number generator</a> crucially depends on both the algorithm and
its parameters. This library implements the algorithms as class templates
with template value parameters, hidden in <code class="computeroutput"><span class="keyword">namespace</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span></code>. Any particular choice of parameters
is represented as the appropriately specializing <code class="computeroutput"><span class="keyword">typedef</span></code>
in <code class="computeroutput"><span class="keyword">namespace</span> <span class="identifier">boost</span></code>.
</p>
<p>
The <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">Pseudo-random
number generators</a> offered in this library have been chosen from a
few families with different underlying principle of operation based on their
performance and quality characteristics. None of the generators are capable
of producing sequences which are indistinguishable from random for longer
than approximately the cubic root of their period. Thus, the generators with
a period of 2<sup>32</sup> or less (most of them are linear congruential generators)
are suitable only for a program or simulation which needs only a few hundred
random numbers.
</p>
<p>
<a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">Pseudo-random
number generators</a> should not be constructed (initialized) frequently
during program execution, for two reasons. First, initialization requires
full initialization of the internal state of the generator. Thus, generators
with a lot of internal state (see below) are costly to initialize. Second,
initialization always requires some value used as a "seed" for
the generated sequence. It is usually difficult to obtain several good seed
values. For example, one method to obtain a seed is to determine the current
time at the highest resolution available, e.g. microseconds or nanoseconds.
When the <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo-random
number generator</a> is initialized again with the then-current time as
the seed, it is likely that this is at a near-constant (non-random) distance
from the time given as the seed for first initialization. The distance could
even be zero if the resolution of the clock is low, thus the generator re-iterates
the same sequence of random numbers. For some applications, this is inappropriate.
</p>
<p>
Note that all <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo-random
number generators</a> described below are <a href="../../../doc/html/CopyConstructible.html" target="_top">CopyConstructible</a>
and <a href="../../../doc/html/Assignable.html" target="_top">Assignable</a>. Copying
or assigning a generator will copy all its internal state, so the original
and the copy will generate the identical sequence of random numbers. Often,
such behavior is not wanted. In particular, beware of the algorithms from
the standard library such as <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">generate</span></code>.
They take a functor argument by value, thereby invoking the copy constructor
when called.
</p>
<p>
The following table gives an overview of some characteristics of the generators.
The cycle length is a rough estimate of the quality of the generator; the
approximate relative speed is a performance measure, higher numbers mean
faster random number generation.
</p>
<div class="table">
<a name="boost_random.reference.generators.generators"></a><p class="title"><b>Table 34.6. generators</b></p>
<div class="table-contents"><table class="table" summary="generators">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
generator
</p>
</th>
<th>
<p>
length of cycle
</p>
</th>
<th>
<p>
approx. memory requirements
</p>
</th>
<th>
<p>
approx. speed compared to fastest
</p>
</th>
<th>
<p>
comment
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/minstd_rand0.html" title="Type definition minstd_rand0">minstd_rand0</a></code>
</p>
</td>
<td>
<p>
2<sup>31</sup>-2
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">int32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
16%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/minstd_rand.html" title="Type definition minstd_rand">minstd_rand</a></code>
</p>
</td>
<td>
<p>
2<sup>31</sup>-2
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">int32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
16%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/rand48.html" title="Class rand48">rand48</a></code>
</p>
</td>
<td>
<p>
2<sup>48</sup>-1
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint64_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
64%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ecuyer1988.html" title="Type definition ecuyer1988">ecuyer1988</a></code>
</p>
</td>
<td>
<p>
approx. 2<sup>61</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">2</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">int32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
7%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/knuth_b.html" title="Type definition knuth_b">knuth_b</a></code>
</p>
</td>
<td>
<p>
2<sup>31</sup>-2
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">257</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
12%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/kreutzer1986.html" title="Type definition kreutzer1986">kreutzer1986</a></code>
</p>
</td>
<td>
<p>
?
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">98</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
37%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/taus88.html" title="Type definition taus88">taus88</a></code>
</p>
</td>
<td>
<p>
~2<sup>88</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">3</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
100%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/hellekalek1995.html" title="Type definition hellekalek1995">hellekalek1995</a></code>
</p>
</td>
<td>
<p>
2<sup>31</sup>-1
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">int32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
2%
</p>
</td>
<td>
<p>
good uniform distribution in several dimensions
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/mt11213b.html" title="Type definition mt11213b">mt11213b</a></code>
</p>
</td>
<td>
<p>
2<sup>11213</sup>-1
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">352</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
100%
</p>
</td>
<td>
<p>
good uniform distribution in up to 350 dimensions
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code>
</p>
</td>
<td>
<p>
2<sup>19937</sup>-1
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">625</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
93%
</p>
</td>
<td>
<p>
good uniform distribution in up to 623 dimensions
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="reference.html#boost.random.mt19937_64">mt19937_64</a></code>
</p>
</td>
<td>
<p>
2<sup>19937</sup>-1
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">312</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint64_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
38%
</p>
</td>
<td>
<p>
good uniform distribution in up to 311 dimensions
</p>
</td>
</tr>
<tr>
<td>
<p>
__mixmax
</p>
</td>
<td>
<p>
~10<sup>294</sup>
</p>
</td>
<td>
<p>
152
</p>
</td>
<td>
<p>
<span class="strikethrough"></span>
</p>
</td>
<td>
<p>
unconditionally guaranteed MC convergence in up to 17 dimensions
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci607.html" title="Type definition lagged_fibonacci607">lagged_fibonacci607</a></code>
</p>
</td>
<td>
<p>
~2<sup>32000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">607</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
59%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci1279.html" title="Type definition lagged_fibonacci1279">lagged_fibonacci1279</a></code>
</p>
</td>
<td>
<p>
~2<sup>67000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">1279</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
59%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci2281.html" title="Type definition lagged_fibonacci2281">lagged_fibonacci2281</a></code>
</p>
</td>
<td>
<p>
~2<sup>120000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">2281</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
61%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci3217.html" title="Type definition lagged_fibonacci3217">lagged_fibonacci3217</a></code>
</p>
</td>
<td>
<p>
~2<sup>170000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">3217</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
62%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci4423.html" title="Type definition lagged_fibonacci4423">lagged_fibonacci4423</a></code>
</p>
</td>
<td>
<p>
~2<sup>230000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">4423</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
59%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci9689.html" title="Type definition lagged_fibonacci9689">lagged_fibonacci9689</a></code>
</p>
</td>
<td>
<p>
~2<sup>510000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">9689</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
61%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci19937.html" title="Type definition lagged_fibonacci19937">lagged_fibonacci19937</a></code>
</p>
</td>
<td>
<p>
~2<sup>1050000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">19937</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
59%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci23209.html" title="Type definition lagged_fibonacci23209">lagged_fibonacci23209</a></code>
</p>
</td>
<td>
<p>
~2<sup>1200000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">23209</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
61%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lagged_fibonacci44497.html" title="Type definition lagged_fibonacci44497">lagged_fibonacci44497</a></code>
</p>
</td>
<td>
<p>
~2<sup>2300000</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">44497</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
59%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux3.html" title="Type definition ranlux3">ranlux3</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">int</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
5%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux4.html" title="Type definition ranlux4">ranlux4</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">int</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
3%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux64_3.html" title="Type definition ranlux64_3">ranlux64_3</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">int64_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
5%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux64_4.html" title="Type definition ranlux64_4">ranlux64_4</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">int64_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
3%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux3_01.html" title="Type definition ranlux3_01">ranlux3_01</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">float</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
5%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux4_01.html" title="Type definition ranlux4_01">ranlux4_01</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">float</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
3%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux64_3_01.html" title="Type definition ranlux64_3_01">ranlux64_3_01</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
5%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/ranlux64_4_01.html" title="Type definition ranlux64_4_01">ranlux64_4_01</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
3%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="reference.html#boost.random.ranlux24">ranlux24</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">24</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint32_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
5%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="reference.html#boost.random.ranlux48">ranlux48</a></code>
</p>
</td>
<td>
<p>
~10<sup>171</sup>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">12</span><span class="special">*</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">uint64_t</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
3%
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
As observable from the table, there is generally a quality/performance/memory
trade-off to be decided upon when choosing a random-number generator. The
multitude of generators provided in this library allows the application programmer
to optimize the trade-off with regard to his application domain. Additionally,
employing several fundamentally different random number generators for a
given application of Monte Carlo simulation will improve the confidence in
the results.
</p>
<p>
If the names of the generators don't ring any bell and you have no idea which
generator to use, it is reasonable to employ <code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code>
for a start: It is fast and has acceptable quality.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
These random number generators are not intended for use in applications
where non-deterministic random numbers are required. See <code class="computeroutput"><a class="link" href="../boost/random/random_device.html" title="Class random_device">random_device</a></code>
for a choice of (hopefully) non-deterministic random number generators.
</p></td></tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.reference.distributions"></a><a class="link" href="reference.html#boost_random.reference.distributions" title="Distributions">Distributions</a>
</h3></div></div></div>
<p>
In addition to the <a class="link" href="reference.html#boost_random.reference.generators" title="Generators">random
number generators</a>, this library provides distribution functions which
map one distribution (often a uniform distribution provided by some generator)
to another.
</p>
<p>
Usually, there are several possible implementations of any given mapping.
Often, there is a choice between using more space, more invocations of the
underlying source of random numbers, or more time-consuming arithmetic such
as trigonometric functions. This interface description does not mandate any
specific implementation. However, implementations which cannot reach certain
values of the specified distribution or otherwise do not converge statistically
to it are not acceptable.
</p>
<div class="table">
<a name="boost_random.reference.distributions.uniform_distributions"></a><p class="title"><b>Table 34.7. Uniform Distributions</b></p>
<div class="table-contents"><table class="table" summary="Uniform Distributions">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
distribution
</p>
</th>
<th>
<p>
explanation
</p>
</th>
<th>
<p>
example
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/uniform_smallint.html" title="Class template uniform_smallint">uniform_smallint</a></code>
</p>
</td>
<td>
<p>
discrete uniform distribution on a small set of integers (much
smaller than the range of the underlying generator)
</p>
</td>
<td>
<p>
drawing from an urn
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/uniform_int_distribution.html" title="Class template uniform_int_distribution">uniform_int_distribution</a></code>
</p>
</td>
<td>
<p>
discrete uniform distribution on a set of integers; the underlying
generator may be called several times to gather enough randomness
for the output
</p>
</td>
<td>
<p>
drawing from an urn
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/uniform_01.html" title="Class template uniform_01">uniform_01</a></code>
</p>
</td>
<td>
<p>
continuous uniform distribution on the range [0,1); important basis
for other distributions
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/uniform_real_distribution.html" title="Class template uniform_real_distribution">uniform_real_distribution</a></code>
</p>
</td>
<td>
<p>
continuous uniform distribution on some range [min, max) of real
numbers
</p>
</td>
<td>
<p>
for the range [0, 2pi): randomly dropping a stick and measuring
its angle in radians (assuming the angle is uniformly distributed)
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_random.reference.distributions.bernoulli_distributions"></a><p class="title"><b>Table 34.8. Bernoulli Distributions</b></p>
<div class="table-contents"><table class="table" summary="Bernoulli Distributions">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
distribution
</p>
</th>
<th>
<p>
explanation
</p>
</th>
<th>
<p>
example
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/bernoulli_distribution.html" title="Class template bernoulli_distribution">bernoulli_distribution</a></code>
</p>
</td>
<td>
<p>
Bernoulli experiment: discrete boolean valued distribution with
configurable probability
</p>
</td>
<td>
<p>
tossing a coin (p=0.5)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/binomial_distribution.html" title="Class template binomial_distribution">binomial_distribution</a></code>
</p>
</td>
<td>
<p>
counts outcomes of repeated Bernoulli experiments
</p>
</td>
<td>
<p>
tossing a coin 20 times and counting how many front sides are shown
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/geometric_distribution.html" title="Class template geometric_distribution">geometric_distribution</a></code>
</p>
</td>
<td>
<p>
measures distance between outcomes of repeated Bernoulli experiments
</p>
</td>
<td>
<p>
throwing a die several times and counting the number of tries until
a "6" appears for the first time
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/negati_1_3_35_5_6_28_1_1_1.html" title="Class template negative_binomial_distribution">negative_binomial_distribution</a></code>
</p>
</td>
<td>
<p>
Counts the number of failures of repeated Bernoulli experiments
required to get some constant number of successes.
</p>
</td>
<td>
<p>
flipping a coin and counting the number of heads that show up before
we get 3 tails
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_random.reference.distributions.poisson_distributions"></a><p class="title"><b>Table 34.9. Poisson Distributions</b></p>
<div class="table-contents"><table class="table" summary="Poisson Distributions">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
distribution
</p>
</th>
<th>
<p>
explanation
</p>
</th>
<th>
<p>
example
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/poisson_distribution.html" title="Class template poisson_distribution">poisson_distribution</a></code>
</p>
</td>
<td>
<p>
poisson distribution
</p>
</td>
<td>
<p>
counting the number of alpha particles emitted by radioactive matter
in a fixed period of time
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/exponential_distribution.html" title="Class template exponential_distribution">exponential_distribution</a></code>
</p>
</td>
<td>
<p>
exponential distribution
</p>
</td>
<td>
<p>
measuring the inter-arrival time of alpha particles emitted by
radioactive matter
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/gamma_distribution.html" title="Class template gamma_distribution">gamma_distribution</a></code>
</p>
</td>
<td>
<p>
gamma distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/hypere_1_3_35_5_6_18_1_1_1.html" title="Class template hyperexponential_distribution">hyperexponential_distribution</a></code>
</p>
</td>
<td>
<p>
hyperexponential distribution
</p>
</td>
<td>
<p>
service time of k-parallel servers each with a given service rate
and probability to be chosen
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/weibull_distribution.html" title="Class template weibull_distribution">weibull_distribution</a></code>
</p>
</td>
<td>
<p>
weibull distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/extreme_value_distribution.html" title="Class template extreme_value_distribution">extreme_value_distribution</a></code>
</p>
</td>
<td>
<p>
extreme value distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/beta_distribution.html" title="Class template beta_distribution">beta_distribution</a></code>
</p>
</td>
<td>
<p>
beta distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/laplace_distribution.html" title="Class template laplace_distribution">laplace_distribution</a></code>
</p>
</td>
<td>
<p>
laplace distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_random.reference.distributions.normal_distributions"></a><p class="title"><b>Table 34.10. Normal Distributions</b></p>
<div class="table-contents"><table class="table" summary="Normal Distributions">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
distribution
</p>
</th>
<th>
<p>
explanation
</p>
</th>
<th>
<p>
example
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/normal_distribution.html" title="Class template normal_distribution">normal_distribution</a></code>
</p>
</td>
<td>
<p>
counts outcomes of (infinitely) repeated Bernoulli experiments
</p>
</td>
<td>
<p>
tossing a coin 10000 times and counting how many front sides are
shown
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/lognormal_distribution.html" title="Class template lognormal_distribution">lognormal_distribution</a></code>
</p>
</td>
<td>
<p>
lognormal distribution (sometimes used in simulations)
</p>
</td>
<td>
<p>
measuring the job completion time of an assembly line worker
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/chi_squared_distribution.html" title="Class template chi_squared_distribution">chi_squared_distribution</a></code>
</p>
</td>
<td>
<p>
chi-squared distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/non_ce_1_3_35_5_6_30_1_1_1.html" title="Class template non_central_chi_squared_distribution">non_central_chi_squared_distribution</a></code>
</p>
</td>
<td>
<p>
non-central chi-squared distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/cauchy_distribution.html" title="Class template cauchy_distribution">cauchy_distribution</a></code>
</p>
</td>
<td>
<p>
Cauchy distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/fisher_f_distribution.html" title="Class template fisher_f_distribution">fisher_f_distribution</a></code>
</p>
</td>
<td>
<p>
Fisher F distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/student_t_distribution.html" title="Class template student_t_distribution">student_t_distribution</a></code>
</p>
</td>
<td>
<p>
Student t distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_random.reference.distributions.sampling_distributions"></a><p class="title"><b>Table 34.11. Sampling Distributions</b></p>
<div class="table-contents"><table class="table" summary="Sampling Distributions">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
distribution
</p>
</th>
<th>
<p>
explanation
</p>
</th>
<th>
<p>
example
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/discrete_distribution.html" title="Class template discrete_distribution">discrete_distribution</a></code>
</p>
</td>
<td>
<p>
discrete distribution with specific probabilities
</p>
</td>
<td>
<p>
rolling an unfair die
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/piecew_1_3_35_5_6_32_1_1_1.html" title="Class template piecewise_constant_distribution">piecewise_constant_distribution</a></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/piecew_1_3_35_5_6_33_1_1_1.html" title="Class template piecewise_linear_distribution">piecewise_linear_distribution</a></code>
</p>
</td>
<td>
<p>
-
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_random.reference.distributions.miscellaneous_distributions"></a><p class="title"><b>Table 34.12. Miscellaneous Distributions</b></p>
<div class="table-contents"><table class="table" summary="Miscellaneous Distributions">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
distribution
</p>
</th>
<th>
<p>
explanation
</p>
</th>
<th>
<p>
example
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/triangle_distribution.html" title="Class template triangle_distribution">triangle_distribution</a></code>
</p>
</td>
<td>
<p>
triangle distribution
</p>
</td>
<td>
<p>
-
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/uniform_on_sphere.html" title="Class template uniform_on_sphere">uniform_on_sphere</a></code>
</p>
</td>
<td>
<p>
uniform distribution on a unit sphere of arbitrary dimension
</p>
</td>
<td>
<p>
choosing a random point on Earth (assumed to be a sphere) where
to spend the next vacations
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.reference.utilities"></a><a class="link" href="reference.html#boost_random.reference.utilities" title="Utilities">Utilities</a>
</h3></div></div></div>
<div class="table">
<a name="boost_random.reference.utilities.utilities"></a><p class="title"><b>Table 34.13. Utilities</b></p>
<div class="table-contents"><table class="table" summary="Utilities">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Name
</p>
</th>
<th>
<p>
Description
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/seed_seq.html" title="Class seed_seq">seed_seq</a></code>
</p>
</td>
<td>
<p>
Used to seed <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">Random
Engines</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/random_number_generator.html" title="Class template random_number_generator">random_number_generator</a></code>
</p>
</td>
<td>
<p>
Adapts a <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">PseudoRandomNumberGenerator</a>
to work with std::random_shuffle
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><a class="link" href="../boost/random/generate_canonical.html" title="Function template generate_canonical">generate_canonical</a></code>
</p>
</td>
<td>
<p>
Produces random floating point values with specific precision.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="headers"></a>Headers</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="reference.html#header.boost.random.additive_combine_hpp">Header <boost/random/additive_combine.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.bernoulli_distribution_hpp">Header <boost/random/bernoulli_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.beta_distribution_hpp">Header <boost/random/beta_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.binomial_distribution_hpp">Header <boost/random/binomial_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.cauchy_distribution_hpp">Header <boost/random/cauchy_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.chi_squared_distribution_hpp">Header <boost/random/chi_squared_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.discard_block_hpp">Header <boost/random/discard_block.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.discrete_distribution_hpp">Header <boost/random/discrete_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.exponential_distribution_hpp">Header <boost/random/exponential_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.extreme_value_distribution_hpp">Header <boost/random/extreme_value_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.faure_hpp">Header <boost/random/faure.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.fisher_f_distribution_hpp">Header <boost/random/fisher_f_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.gamma_distribution_hpp">Header <boost/random/gamma_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.generate_canonical_hpp">Header <boost/random/generate_canonical.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.geometric_distribution_hpp">Header <boost/random/geometric_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.hyperexponential_distribution_hpp">Header <boost/random/hyperexponential_distribution.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.independent_bits_hpp">Header <boost/random/independent_bits.hpp></a></span></dt>
<dt><span class="section"><a href="reference.html#header.boost.random.inversive_congruential_hpp">Header <boost/random/inversive_congruential.hpp></a></span></dt>
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</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.additive_combine_hpp"></a>Header <<a href="../../../boost/random/additive_combine.hpp" target="_top">boost/random/additive_combine.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> MLCG1<span class="special">,</span> <span class="keyword">typename</span> MLCG2<span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/additive_combine_engine.html" title="Class template additive_combine_engine">additive_combine_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/additive_combine_engine.html" title="Class template additive_combine_engine">additive_combine_engine</a><span class="special"><</span> <a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">linear_congruential_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">40014</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">2147483563</span> <span class="special">></span><span class="special">,</span> <a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">linear_congruential_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">40692</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">2147483399</span> <span class="special">>></span> <a class="link" href="../boost/random/ecuyer1988.html" title="Type definition ecuyer1988"><span class="identifier">ecuyer1988</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.bernoulli_distribution_hpp"></a>Header <<a href="../../../boost/random/bernoulli_distribution.hpp" target="_top">boost/random/bernoulli_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/bernoulli_distribution.html" title="Class template bernoulli_distribution">bernoulli_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.beta_distribution_hpp"></a>Header <<a href="../../../boost/random/beta_distribution.hpp" target="_top">boost/random/beta_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/beta_distribution.html" title="Class template beta_distribution">beta_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.binomial_distribution_hpp"></a>Header <<a href="../../../boost/random/binomial_distribution.hpp" target="_top">boost/random/binomial_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/binomial_distribution.html" title="Class template binomial_distribution">binomial_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.cauchy_distribution_hpp"></a>Header <<a href="../../../boost/random/cauchy_distribution.hpp" target="_top">boost/random/cauchy_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/cauchy_distribution.html" title="Class template cauchy_distribution">cauchy_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.chi_squared_distribution_hpp"></a>Header <<a href="../../../boost/random/chi_squared_distribution.hpp" target="_top">boost/random/chi_squared_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/chi_squared_distribution.html" title="Class template chi_squared_distribution">chi_squared_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.discard_block_hpp"></a>Header <<a href="../../../boost/random/discard_block.hpp" target="_top">boost/random/discard_block.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UniformRandomNumberGenerator<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> p<span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> r<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.discrete_distribution_hpp"></a>Header <<a href="../../../boost/random/discrete_distribution.hpp" target="_top">boost/random/discrete_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">typename</span> WeightType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/discrete_distribution.html" title="Class template discrete_distribution">discrete_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.exponential_distribution_hpp"></a>Header <<a href="../../../boost/random/exponential_distribution.hpp" target="_top">boost/random/exponential_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/exponential_distribution.html" title="Class template exponential_distribution">exponential_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.extreme_value_distribution_hpp"></a>Header <<a href="../../../boost/random/extreme_value_distribution.hpp" target="_top">boost/random/extreme_value_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/extreme_value_distribution.html" title="Class template extreme_value_distribution">extreme_value_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.faure_hpp"></a>Header <<a href="../../../boost/random/faure.hpp" target="_top">boost/random/faure.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType<span class="special">,</span> <span class="keyword">typename</span> SeqSizeT<span class="special">,</span>
<span class="keyword">typename</span> PrimeTable <span class="special">=</span> <span class="identifier">default_faure_prime_table</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/faure_engine.html" title="Class template faure_engine">faure_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/faure_engine.html" title="Class template faure_engine">faure_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uint_least64_t</span><span class="special">,</span> <span class="identifier">default_faure_prime_table</span> <span class="special">></span> <a class="link" href="../boost/random/faure.html" title="Type definition faure"><span class="identifier">faure</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.fisher_f_distribution_hpp"></a>Header <<a href="../../../boost/random/fisher_f_distribution.hpp" target="_top">boost/random/fisher_f_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/fisher_f_distribution.html" title="Class template fisher_f_distribution">fisher_f_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.gamma_distribution_hpp"></a>Header <<a href="../../../boost/random/gamma_distribution.hpp" target="_top">boost/random/gamma_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/gamma_distribution.html" title="Class template gamma_distribution">gamma_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.generate_canonical_hpp"></a>Header <<a href="../../../boost/random/generate_canonical.hpp" target="_top">boost/random/generate_canonical.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> bits<span class="special">,</span> <span class="keyword">typename</span> URNG<span class="special">></span>
<span class="identifier">RealType</span> <a class="link" href="../boost/random/generate_canonical.html" title="Function template generate_canonical"><span class="identifier">generate_canonical</span></a><span class="special">(</span><span class="identifier">URNG</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.geometric_distribution_hpp"></a>Header <<a href="../../../boost/random/geometric_distribution.hpp" target="_top">boost/random/geometric_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/geometric_distribution.html" title="Class template geometric_distribution">geometric_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.hyperexponential_distribution_hpp"></a>Header <<a href="../../../boost/random/hyperexponential_distribution.hpp" target="_top">boost/random/hyperexponential_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealT <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/hypere_1_3_35_5_6_18_1_1_1.html" title="Class template hyperexponential_distribution">hyperexponential_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.independent_bits_hpp"></a>Header <<a href="../../../boost/random/independent_bits.hpp" target="_top">boost/random/independent_bits.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Engine<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> w<span class="special">,</span> <span class="keyword">typename</span> UIntType<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/independent_bits_engine.html" title="Class template independent_bits_engine">independent_bits_engine</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.inversive_congruential_hpp"></a>Header <<a href="../../../boost/random/inversive_congruential.hpp" target="_top">boost/random/inversive_congruential.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType<span class="special">,</span> <span class="identifier">IntType</span> a<span class="special">,</span> <span class="identifier">IntType</span> b<span class="special">,</span> <span class="identifier">IntType</span> p<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/invers_1_3_35_5_6_20_1_1_1.html" title="Class template inversive_congruential_engine">inversive_congruential_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/invers_1_3_35_5_6_20_1_1_1.html" title="Class template inversive_congruential_engine">inversive_congruential_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">9102</span><span class="special">,</span> <span class="number">2147483647</span><span class="special">-</span><span class="number">36884165</span><span class="special">,</span> <span class="number">2147483647</span> <span class="special">></span> <a class="link" href="../boost/random/hellekalek1995.html" title="Type definition hellekalek1995"><span class="identifier">hellekalek1995</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.lagged_fibonacci_hpp"></a>Header <<a href="../../../boost/random/lagged_fibonacci.hpp" target="_top">boost/random/lagged_fibonacci.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType<span class="special">,</span> <span class="keyword">int</span> w<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> p<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> q<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special">;</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="keyword">int</span> w<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> p<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> q<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/lagged_fibonacci_engine.html" title="Class template lagged_fibonacci_engine">lagged_fibonacci_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">607</span><span class="special">,</span> <span class="number">273</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci607.html" title="Type definition lagged_fibonacci607"><span class="identifier">lagged_fibonacci607</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">1279</span><span class="special">,</span> <span class="number">418</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci1279.html" title="Type definition lagged_fibonacci1279"><span class="identifier">lagged_fibonacci1279</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">2281</span><span class="special">,</span> <span class="number">1252</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci2281.html" title="Type definition lagged_fibonacci2281"><span class="identifier">lagged_fibonacci2281</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">3217</span><span class="special">,</span> <span class="number">576</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci3217.html" title="Type definition lagged_fibonacci3217"><span class="identifier">lagged_fibonacci3217</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">4423</span><span class="special">,</span> <span class="number">2098</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci4423.html" title="Type definition lagged_fibonacci4423"><span class="identifier">lagged_fibonacci4423</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">9689</span><span class="special">,</span> <span class="number">5502</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci9689.html" title="Type definition lagged_fibonacci9689"><span class="identifier">lagged_fibonacci9689</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">19937</span><span class="special">,</span> <span class="number">9842</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci19937.html" title="Type definition lagged_fibonacci19937"><span class="identifier">lagged_fibonacci19937</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">23209</span><span class="special">,</span> <span class="number">13470</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci23209.html" title="Type definition lagged_fibonacci23209"><span class="identifier">lagged_fibonacci23209</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01_engine.html" title="Class template lagged_fibonacci_01_engine">lagged_fibonacci_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">44497</span><span class="special">,</span> <span class="number">21034</span> <span class="special">></span> <a class="link" href="../boost/random/lagged_fibonacci44497.html" title="Type definition lagged_fibonacci44497"><span class="identifier">lagged_fibonacci44497</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.laplace_distribution_hpp"></a>Header <<a href="../../../boost/random/laplace_distribution.hpp" target="_top">boost/random/laplace_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/laplace_distribution.html" title="Class template laplace_distribution">laplace_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.linear_congruential_hpp"></a>Header <<a href="../../../boost/random/linear_congruential.hpp" target="_top">boost/random/linear_congruential.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType<span class="special">,</span> <span class="identifier">IntType</span> a<span class="special">,</span> <span class="identifier">IntType</span> c<span class="special">,</span> <span class="identifier">IntType</span> m<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">linear_congruential_engine</a><span class="special">;</span>
<span class="keyword">class</span> <a class="link" href="../boost/random/rand48.html" title="Class rand48">rand48</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">linear_congruential_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">16807</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">2147483647</span> <span class="special">></span> <a class="link" href="../boost/random/minstd_rand0.html" title="Type definition minstd_rand0"><span class="identifier">minstd_rand0</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">linear_congruential_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">48271</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">2147483647</span> <span class="special">></span> <a class="link" href="../boost/random/minstd_rand.html" title="Type definition minstd_rand"><span class="identifier">minstd_rand</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.linear_feedback_shift_hpp"></a>Header <<a href="../../../boost/random/linear_feedback_shift.hpp" target="_top">boost/random/linear_feedback_shift.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="keyword">int</span> w<span class="special">,</span> <span class="keyword">int</span> k<span class="special">,</span> <span class="keyword">int</span> q<span class="special">,</span> <span class="keyword">int</span> s<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/linear_1_3_35_5_6_24_1_1_1.html" title="Class template linear_feedback_shift_engine">linear_feedback_shift_engine</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.lognormal_distribution_hpp"></a>Header <<a href="../../../boost/random/lognormal_distribution.hpp" target="_top">boost/random/lognormal_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/lognormal_distribution.html" title="Class template lognormal_distribution">lognormal_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.mersenne_twister_hpp"></a>Header <<a href="../../../boost/random/mersenne_twister.hpp" target="_top">boost/random/mersenne_twister.hpp</a>></h4></div></div></div>
<pre class="synopsis">
<a class="link" href="../BOOST_RAND_1_3_35_5_6_26_2.html" title="Macro BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD">BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD</a></pre>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> w<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> n<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> m<span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> r<span class="special">,</span> <span class="identifier">UIntType</span> a<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> u<span class="special">,</span> <span class="identifier">UIntType</span> d<span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> s<span class="special">,</span> <span class="identifier">UIntType</span> b<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> t<span class="special">,</span> <span class="identifier">UIntType</span> c<span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> l<span class="special">,</span> <span class="identifier">UIntType</span> f<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/mersenne_twister_engine.html" title="Class template mersenne_twister_engine">mersenne_twister_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/mersenne_twister_engine.html" title="Class template mersenne_twister_engine">mersenne_twister_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">32</span><span class="special">,</span> <span class="number">351</span><span class="special">,</span> <span class="number">175</span><span class="special">,</span> <span class="number">19</span><span class="special">,</span> <span class="number">0xccab8ee7</span><span class="special">,</span> <span class="number">11</span><span class="special">,</span> <span class="number">0xffffffff</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">0x31b6ab00</span><span class="special">,</span> <span class="number">15</span><span class="special">,</span> <span class="number">0xffe50000</span><span class="special">,</span> <span class="number">17</span><span class="special">,</span> <span class="number">1812433253</span> <span class="special">></span> <a class="link" href="../boost/random/mt11213b.html" title="Type definition mt11213b"><span class="identifier">mt11213b</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/mersenne_twister_engine.html" title="Class template mersenne_twister_engine">mersenne_twister_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">32</span><span class="special">,</span> <span class="number">624</span><span class="special">,</span> <span class="number">397</span><span class="special">,</span> <span class="number">31</span><span class="special">,</span> <span class="number">0x9908b0df</span><span class="special">,</span> <span class="number">11</span><span class="special">,</span> <span class="number">0xffffffff</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">0x9d2c5680</span><span class="special">,</span> <span class="number">15</span><span class="special">,</span> <span class="number">0xefc60000</span><span class="special">,</span> <span class="number">18</span><span class="special">,</span> <span class="number">1812433253</span> <span class="special">></span> <a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937"><span class="identifier">mt19937</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/mersenne_twister_engine.html" title="Class template mersenne_twister_engine">mersenne_twister_engine</a><span class="special"><</span> <span class="identifier">uint64_t</span><span class="special">,</span> <span class="number">64</span><span class="special">,</span> <span class="number">312</span><span class="special">,</span> <span class="number">156</span><span class="special">,</span> <span class="number">31</span><span class="special">,</span> <span class="number">0xb5026f5aa96619e9ull</span><span class="special">,</span> <span class="number">29</span><span class="special">,</span> <span class="number">0x5555555555555555ull</span><span class="special">,</span> <span class="number">17</span><span class="special">,</span> <span class="number">0x71d67fffeda60000ull</span><span class="special">,</span> <span class="number">37</span><span class="special">,</span> <span class="number">0xfff7eee000000000ull</span><span class="special">,</span> <span class="number">43</span><span class="special">,</span> <span class="number">6364136223846793005ull</span> <span class="special">></span> <a name="boost.random.mt19937_64"></a><span class="identifier">mt19937_64</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.mixmax_hpp"></a>Header <<a href="../../../boost/random/mixmax.hpp" target="_top">boost/random/mixmax.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">int</span> Ndim<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> SPECIALMUL<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int64_t</span> SPECIAL<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/mixmax_engine.html" title="Class template mixmax_engine">mixmax_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/mixmax_engine.html" title="Class template mixmax_engine">mixmax_engine</a><span class="special"><</span> <span class="number">17</span><span class="special">,</span> <span class="number">36</span><span class="special">,</span> <span class="number">0</span> <span class="special">></span> <a class="link" href="../boost/random/mixmax.html" title="Type definition mixmax"><span class="identifier">mixmax</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.negative_binomial_distribution_hpp"></a>Header <<a href="../../../boost/random/negative_binomial_distribution.hpp" target="_top">boost/random/negative_binomial_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/negati_1_3_35_5_6_28_1_1_1.html" title="Class template negative_binomial_distribution">negative_binomial_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.niederreiter_base2_hpp"></a>Header <<a href="../../../boost/random/niederreiter_base2.hpp" target="_top">boost/random/niederreiter_base2.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="keyword">unsigned</span> w<span class="special">,</span>
<span class="keyword">typename</span> Nb2Table <span class="special">=</span> <span class="identifier">default_niederreiter_base2_table</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a><span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uint_least64_t</span><span class="special">,</span> <span class="number">64u</span><span class="special">,</span> <span class="identifier">default_niederreiter_base2_table</span> <span class="special">></span> <a class="link" href="../boost/random/niederreiter_base2.html" title="Type definition niederreiter_base2"><span class="identifier">niederreiter_base2</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.non_central_chi_squared_distribution_hpp"></a>Header <<a href="../../../boost/random/non_central_chi_squared_distribution.hpp" target="_top">boost/random/non_central_chi_squared_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/non_ce_1_3_35_5_6_30_1_1_1.html" title="Class template non_central_chi_squared_distribution">non_central_chi_squared_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.normal_distribution_hpp"></a>Header <<a href="../../../boost/random/normal_distribution.hpp" target="_top">boost/random/normal_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/normal_distribution.html" title="Class template normal_distribution">normal_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.piecewise_constant_distribution_hpp"></a>Header <<a href="../../../boost/random/piecewise_constant_distribution.hpp" target="_top">boost/random/piecewise_constant_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> <span class="keyword">typename</span> WeightType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/piecew_1_3_35_5_6_32_1_1_1.html" title="Class template piecewise_constant_distribution">piecewise_constant_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.piecewise_linear_distribution_hpp"></a>Header <<a href="../../../boost/random/piecewise_linear_distribution.hpp" target="_top">boost/random/piecewise_linear_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/piecew_1_3_35_5_6_33_1_1_1.html" title="Class template piecewise_linear_distribution">piecewise_linear_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.poisson_distribution_hpp"></a>Header <<a href="../../../boost/random/poisson_distribution.hpp" target="_top">boost/random/poisson_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/poisson_distribution.html" title="Class template poisson_distribution">poisson_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.random_device_hpp"></a>Header <<a href="../../../boost/random/random_device.hpp" target="_top">boost/random/random_device.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">class</span> <a class="link" href="../boost/random/random_device.html" title="Class random_device">random_device</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.random_number_generator_hpp"></a>Header <<a href="../../../boost/random/random_number_generator.hpp" target="_top">boost/random/random_number_generator.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> URNG<span class="special">,</span> <span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">long</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/random_number_generator.html" title="Class template random_number_generator">random_number_generator</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.ranlux_hpp"></a>Header <<a href="../../../boost/random/ranlux.hpp" target="_top">boost/random/ranlux.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/subtract_with_carry_engine.html" title="Class template subtract_with_carry_engine">subtract_with_carry_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">24</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a name="boost.random.ranlux_base"></a><span class="identifier">ranlux_base</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/subtra_1_3_35_5_6_42_1_1_1.html" title="Class template subtract_with_carry_01_engine">subtract_with_carry_01_engine</a><span class="special"><</span> <span class="keyword">float</span><span class="special">,</span> <span class="number">24</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a name="boost.random.ranlux_base_01"></a><span class="identifier">ranlux_base_01</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/subtra_1_3_35_5_6_42_1_1_1.html" title="Class template subtract_with_carry_01_engine">subtract_with_carry_01_engine</a><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a name="boost.random.ranlux64_base_01"></a><span class="identifier">ranlux64_base_01</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base">ranlux_base</a><span class="special">,</span> <span class="number">223</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux3.html" title="Type definition ranlux3"><span class="identifier">ranlux3</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base">ranlux_base</a><span class="special">,</span> <span class="number">389</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux4.html" title="Type definition ranlux4"><span class="identifier">ranlux4</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base_01">ranlux_base_01</a><span class="special">,</span> <span class="number">223</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux3_01.html" title="Type definition ranlux3_01"><span class="identifier">ranlux3_01</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base_01">ranlux_base_01</a><span class="special">,</span> <span class="number">389</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux4_01.html" title="Type definition ranlux4_01"><span class="identifier">ranlux4_01</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base_01">ranlux64_base_01</a><span class="special">,</span> <span class="number">223</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux64_3_01.html" title="Type definition ranlux64_3_01"><span class="identifier">ranlux64_3_01</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base_01">ranlux64_base_01</a><span class="special">,</span> <span class="number">389</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux64_4_01.html" title="Type definition ranlux64_4_01"><span class="identifier">ranlux64_4_01</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/subtract_with_carry_engine.html" title="Class template subtract_with_carry_engine">subtract_with_carry_engine</a><span class="special"><</span> <span class="identifier">uint64_t</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a name="boost.random.ranlux64_base"></a><span class="identifier">ranlux64_base</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base">ranlux64_base</a><span class="special">,</span> <span class="number">223</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux64_3.html" title="Type definition ranlux64_3"><span class="identifier">ranlux64_3</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base">ranlux64_base</a><span class="special">,</span> <span class="number">389</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a class="link" href="../boost/random/ranlux64_4.html" title="Type definition ranlux64_4"><span class="identifier">ranlux64_4</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/subtract_with_carry_engine.html" title="Class template subtract_with_carry_engine">subtract_with_carry_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">24</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span> <span class="special">></span> <a name="boost.random.ranlux24_base"></a><span class="identifier">ranlux24_base</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/subtract_with_carry_engine.html" title="Class template subtract_with_carry_engine">subtract_with_carry_engine</a><span class="special"><</span> <span class="identifier">uint64_t</span><span class="special">,</span> <span class="number">48</span><span class="special">,</span> <span class="number">5</span><span class="special">,</span> <span class="number">12</span> <span class="special">></span> <a name="boost.random.ranlux48_base"></a><span class="identifier">ranlux48_base</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux24_base">ranlux24_base</a><span class="special">,</span> <span class="number">223</span><span class="special">,</span> <span class="number">23</span> <span class="special">></span> <a name="boost.random.ranlux24"></a><span class="identifier">ranlux24</span><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/discard_block_engine.html" title="Class template discard_block_engine">discard_block_engine</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux48_base">ranlux48_base</a><span class="special">,</span> <span class="number">389</span><span class="special">,</span> <span class="number">11</span> <span class="special">></span> <a name="boost.random.ranlux48"></a><span class="identifier">ranlux48</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.seed_seq_hpp"></a>Header <<a href="../../../boost/random/seed_seq.hpp" target="_top">boost/random/seed_seq.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">class</span> <a class="link" href="../boost/random/seed_seq.html" title="Class seed_seq">seed_seq</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.shuffle_order_hpp"></a>Header <<a href="../../../boost/random/shuffle_order.hpp" target="_top">boost/random/shuffle_order.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UniformRandomNumberGenerator<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> k<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/shuffle_order_engine.html" title="Class template shuffle_order_engine">shuffle_order_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/shuffle_order_engine.html" title="Class template shuffle_order_engine">shuffle_order_engine</a><span class="special"><</span> <a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">linear_congruential_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">1366</span><span class="special">,</span> <span class="number">150889</span><span class="special">,</span> <span class="number">714025</span> <span class="special">></span><span class="special">,</span> <span class="number">97</span> <span class="special">></span> <a class="link" href="../boost/random/kreutzer1986.html" title="Type definition kreutzer1986"><span class="identifier">kreutzer1986</span></a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/shuffle_order_engine.html" title="Class template shuffle_order_engine">shuffle_order_engine</a><span class="special"><</span> <a class="link" href="../boost/random/minstd_rand0.html" title="Type definition minstd_rand0">minstd_rand0</a><span class="special">,</span> <span class="number">256</span> <span class="special">></span> <a class="link" href="../boost/random/knuth_b.html" title="Type definition knuth_b"><span class="identifier">knuth_b</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.sobol_hpp"></a>Header <<a href="../../../boost/random/sobol.hpp" target="_top">boost/random/sobol.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="keyword">unsigned</span> w<span class="special">,</span>
<span class="keyword">typename</span> SobolTables <span class="special">=</span> <span class="identifier">default_sobol_table</span><span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/sobol_engine.html" title="Class template sobol_engine">sobol_engine</a><span class="special">;</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/sobol_engine.html" title="Class template sobol_engine">sobol_engine</a><span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uint_least64_t</span><span class="special">,</span> <span class="number">64u</span><span class="special">,</span> <span class="identifier">default_sobol_table</span> <span class="special">></span> <a class="link" href="../boost/random/sobol.html" title="Type definition sobol"><span class="identifier">sobol</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.student_t_distribution_hpp"></a>Header <<a href="../../../boost/random/student_t_distribution.hpp" target="_top">boost/random/student_t_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/student_t_distribution.html" title="Class template student_t_distribution">student_t_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.subtract_with_carry_hpp"></a>Header <<a href="../../../boost/random/subtract_with_carry.hpp" target="_top">boost/random/subtract_with_carry.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> w<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> s<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> r<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/subtra_1_3_35_5_6_42_1_1_1.html" title="Class template subtract_with_carry_01_engine">subtract_with_carry_01_engine</a><span class="special">;</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> w<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> s<span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> r<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/subtract_with_carry_engine.html" title="Class template subtract_with_carry_engine">subtract_with_carry_engine</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.taus88_hpp"></a>Header <<a href="../../../boost/random/taus88.hpp" target="_top">boost/random/taus88.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">typedef</span> <a class="link" href="../boost/random/xor_combine_engine.html" title="Class template xor_combine_engine">xor_combine_engine</a><span class="special"><</span> <a class="link" href="../boost/random/xor_combine_engine.html" title="Class template xor_combine_engine">xor_combine_engine</a><span class="special"><</span> <a class="link" href="../boost/random/linear_1_3_35_5_6_24_1_1_1.html" title="Class template linear_feedback_shift_engine">linear_feedback_shift_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">32</span><span class="special">,</span> <span class="number">31</span><span class="special">,</span> <span class="number">13</span><span class="special">,</span> <span class="number">12</span> <span class="special">></span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <a class="link" href="../boost/random/linear_1_3_35_5_6_24_1_1_1.html" title="Class template linear_feedback_shift_engine">linear_feedback_shift_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">32</span><span class="special">,</span> <span class="number">29</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">4</span> <span class="special">></span><span class="special">,</span> <span class="number">0</span> <span class="special">></span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <a class="link" href="../boost/random/linear_1_3_35_5_6_24_1_1_1.html" title="Class template linear_feedback_shift_engine">linear_feedback_shift_engine</a><span class="special"><</span> <span class="identifier">uint32_t</span><span class="special">,</span> <span class="number">32</span><span class="special">,</span> <span class="number">28</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="number">17</span> <span class="special">></span><span class="special">,</span> <span class="number">0</span> <span class="special">></span> <a class="link" href="../boost/random/taus88.html" title="Type definition taus88"><span class="identifier">taus88</span></a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.traits_hpp"></a>Header <<a href="../../../boost/random/traits.hpp" target="_top">boost/random/traits.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">traits</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span> <span class="keyword">struct</span> <a class="link" href="../boost/random/traits/is_integral.html" title="Struct template is_integral">is_integral</a><span class="special">;</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span> <span class="keyword">struct</span> <a class="link" href="../boost/random/traits/is_signed.html" title="Struct template is_signed">is_signed</a><span class="special">;</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span> <span class="keyword">struct</span> <a class="link" href="../boost/random/traits/make_unsigned.html" title="Struct template make_unsigned">make_unsigned</a><span class="special">;</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span> <span class="keyword">struct</span> <a class="link" href="../boost/random/traits/make_unsigned_or_unbounded.html" title="Struct template make_unsigned_or_unbounded">make_unsigned_or_unbounded</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.triangle_distribution_hpp"></a>Header <<a href="../../../boost/random/triangle_distribution.hpp" target="_top">boost/random/triangle_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/triangle_distribution.html" title="Class template triangle_distribution">triangle_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.uniform_01_hpp"></a>Header <<a href="../../../boost/random/uniform_01.hpp" target="_top">boost/random/uniform_01.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/uniform_01.html" title="Class template uniform_01">uniform_01</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.uniform_int_distribution_hpp"></a>Header <<a href="../../../boost/random/uniform_int_distribution.hpp" target="_top">boost/random/uniform_int_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/uniform_int_distribution.html" title="Class template uniform_int_distribution">uniform_int_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.uniform_on_sphere_hpp"></a>Header <<a href="../../../boost/random/uniform_on_sphere.hpp" target="_top">boost/random/uniform_on_sphere.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">typename</span> Cont <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">></span> <span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/uniform_on_sphere.html" title="Class template uniform_on_sphere">uniform_on_sphere</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.uniform_real_distribution_hpp"></a>Header <<a href="../../../boost/random/uniform_real_distribution.hpp" target="_top">boost/random/uniform_real_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/uniform_real_distribution.html" title="Class template uniform_real_distribution">uniform_real_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.uniform_smallint_hpp"></a>Header <<a href="../../../boost/random/uniform_smallint.hpp" target="_top">boost/random/uniform_smallint.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/uniform_smallint.html" title="Class template uniform_smallint">uniform_smallint</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.variate_generator_hpp"></a>Header <<a href="../../../boost/random/variate_generator.hpp" target="_top">boost/random/variate_generator.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Engine<span class="special">,</span> <span class="keyword">typename</span> Distribution<span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/variate_generator.html" title="Class template variate_generator">variate_generator</a><span class="special">;</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.weibull_distribution_hpp"></a>Header <<a href="../../../boost/random/weibull_distribution.hpp" target="_top">boost/random/weibull_distribution.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/random/weibull_distribution.html" title="Class template weibull_distribution">weibull_distribution</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="header.boost.random.xor_combine_hpp"></a>Header <<a href="../../../boost/random/xor_combine.hpp" target="_top">boost/random/xor_combine.hpp</a>></h4></div></div></div>
<pre class="synopsis"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">random</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> URNG1<span class="special">,</span> <span class="keyword">int</span> s1<span class="special">,</span> <span class="keyword">typename</span> URNG2<span class="special">,</span> <span class="keyword">int</span> s2<span class="special">></span>
<span class="keyword">class</span> <a class="link" href="../boost/random/xor_combine_engine.html" title="Class template xor_combine_engine">xor_combine_engine</a><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span></pre>
</div>
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<td align="right"><div class="copyright-footer">Copyright © 2000-2005 Jens Maurer<br>Copyright © 2009, 2010 Steven Watanabe<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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