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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> |
| <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#headers">Headers</a></span></dt> |
| </dl></div> |
| <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> |
| <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.number_generator">Number |
| Generator</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.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" 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" 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, these concepts (in the STL |
| sense) are called <a class="link" href="reference.html#boost_random.reference.concepts.number_generator" title="Number Generator">NumberGenerator</a> |
| and <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>. |
| Each 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" type="disc"> |
| <li class="listitem"> |
| allow easy integration of third-party random-number generators |
| </li> |
| <li class="listitem"> |
| define a validation interface for the generators |
| </li> |
| <li class="listitem"> |
| provide easy-to-use front-end classes which model popular distributions |
| </li> |
| <li class="listitem"> |
| provide maximum efficiency |
| </li> |
| <li class="listitem"> |
| allow control on quantization effects in front-end processing (not |
| yet done) |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_random.reference.concepts.number_generator"></a><a class="link" href="reference.html#boost_random.reference.concepts.number_generator" title="Number Generator">Number |
| Generator</a> |
| </h4></div></div></div> |
| <p> |
| A number generator is a <span class="emphasis"><em>function object</em></span> (std:20.3 |
| [lib.function.objects]) that takes zero arguments. Each call to <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code> |
| returns a number. In the following table, X denotes a number generator |
| class returning objects of type T, and u is a value of X. |
| </p> |
| <div class="table"> |
| <a name="boost_random.reference.concepts.number_generator.numbergenerator_requirements"></a><p class="title"><b>Table 16.1. NumberGenerator requirements</b></p> |
| <div class="table-contents"><table class="table" summary="NumberGenerator 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> |
| </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 NumberGenerator requirements do not impose any restrictions on the |
| characteristics of the returned numbers. |
| </p></td></tr> |
| </table></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 is a <a class="link" href="reference.html#boost_random.reference.concepts.number_generator" title="Number Generator">NumberGenerator</a> |
| that 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 16.2. 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">has_fixed_range</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="keyword">bool</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| compile-time constant; if <code class="computeroutput"><span class="keyword">true</span></code>, |
| the range on which the random numbers are uniformly distributed |
| is known at compile-time and members <code class="computeroutput"><span class="identifier">min_value</span></code> |
| and <code class="computeroutput"><span class="identifier">max_value</span></code> |
| exist. Note: This flag may also be <code class="computeroutput"><span class="keyword">false</span></code> |
| due to compiler limitations |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">X</span><span class="special">::</span><span class="identifier">min_value</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">T</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| compile-time constant; <code class="computeroutput"><span class="identifier">min_value</span></code> |
| is only defined if <code class="computeroutput"><span class="identifier">has_fixed_range</span></code> |
| is <code class="computeroutput"><span class="keyword">true</span></code>. If it exists, |
| it is equal to <code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">min</span><span class="special">()</span></code>. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">X</span><span class="special">::</span><span class="identifier">max_value</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">T</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| compile-time constant; <code class="computeroutput"><span class="identifier">max_value</span></code> |
| is only defined if <code class="computeroutput"><span class="identifier">has_fixed_range</span></code> |
| is <code class="computeroutput"><span class="keyword">true</span></code>. If it exists, |
| it is equal to <code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">max</span><span class="special">()</span></code> |
| </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_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_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.html" title="Class template linear_congruential">Linear |
| congruential</a></code> and <code class="computeroutput"><a class="link" href="../boost/random/inversive_congruential.html" title="Class template inversive_congruential">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 returning objects of type |
| <code class="computeroutput"><span class="identifier">T</span></code>, <code class="computeroutput"><span class="identifier">x</span></code> |
| is a value of <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>, |
| and <code class="computeroutput"><span class="identifier">v</span></code> is a const value |
| of <code class="computeroutput"><span class="identifier">X</span></code>. |
| </p> |
| <div class="table"> |
| <a name="boost_random.reference.concepts.pseudo_random_number_generator.pseudorandomnumbergenerator_requirements"></a><p class="title"><b>Table 16.3. 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 in some implementation-defined state. Note: |
| Several generators thusly created may possibly produce dependent |
| or identical sequences of random numbers. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="keyword">explicit</span> <span class="identifier">X</span><span class="special">(...)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| <td> |
| <p> |
| creates a generator with user-provided state; the implementation |
| shall specify the constructor argument(s) |
| </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 according to the argument(s); at least |
| functions with the same signature as the non-default constructor(s) |
| shall be provided. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">X</span><span class="special">::</span><span class="identifier">validation</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="keyword">bool</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| compares the pre-computed and hardcoded 10001th element in the |
| generator's random number sequence with x. The generator must |
| have been constructed by its default constructor and seed must |
| not have been called for the validation to be meaningful. |
| </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 seed member function is similar to the assign member function in |
| STL containers. However, the naming did not seem appropriate. |
| </p></td></tr> |
| </table></div> |
| <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 should 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>. If so, <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 may 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/rand48.html" title="Class rand48">rand48</a></code>, <code class="computeroutput"><a class="link" href="../boost/minstd_rand.html" title="Type definition minstd_rand">minstd_rand</a></code>, and <code class="computeroutput"><a class="link" href="../boost/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.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> is a (possibly const) value of <code class="computeroutput"><span class="identifier">X</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_numbergenerator__copyconstructible__and_assignable_"></a><p class="title"><b>Table 16.4. Random distribution requirements (in addition to NumberGenerator, |
| CopyConstructible, and Assignable)</b></p> |
| <div class="table-contents"><table class="table" summary="Random distribution requirements (in addition to NumberGenerator, |
| 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">input_type</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">U</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| <td> |
| <p> |
| compile-time |
| </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 <code class="computeroutput"><span class="identifier">e</span></code> |
| 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 some probability density function |
| <code class="computeroutput"><span class="identifier">p</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> |
| </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">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> |
| <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 16.5. 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/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> |
| 30% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 29% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 100% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 19% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/kreutzer1986.html" title="Type definition kreutzer1986">kreutzer1986</a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| ? |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="number">1368</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> |
| 31% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 78% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 0% |
| </p> |
| </td> |
| <td> |
| <p> |
| good uniform distribution in several dimensions |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 44% |
| </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/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> |
| 44% |
| </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="../boost/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> |
| 26% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 26% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 26% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 26% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 25% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 25% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 25% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 25% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 25% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 2% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 1% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 2% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 1% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 2% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 1% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 2% |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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> |
| 1% |
| </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/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_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.distributions"></a><p class="title"><b>Table 16.6. distributions</b></p> |
| <div class="table-contents"><table class="table" summary="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/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/uniform_int.html" title="Class template uniform_int">uniform_int</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/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/uniform_real.html" title="Class template uniform_real">uniform_real</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> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/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/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/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/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/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/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/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/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/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/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/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="headers"></a>Headers</h3></div></div></div> |
| <div class="toc"><dl> |
| <dt><span class="section"><a href="reference.html#header.boost.nondet_random_hpp">Header <boost/nondet_random.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random_hpp">Header <boost/random.hpp></a></span></dt> |
| <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.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.discard_block_hpp">Header <boost/random/discard_block.hpp></a></span></dt> |
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| <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.inversive_congruential_hpp">Header <boost/random/inversive_congruential.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.lagged_fibonacci_hpp">Header <boost/random/lagged_fibonacci.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.linear_congruential_hpp">Header <boost/random/linear_congruential.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.linear_feedback_shift_hpp">Header <boost/random/linear_feedback_shift.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.lognormal_distribution_hpp">Header <boost/random/lognormal_distribution.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.mersenne_twister_hpp">Header <boost/random/mersenne_twister.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.normal_distribution_hpp">Header <boost/random/normal_distribution.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.poisson_distribution_hpp">Header <boost/random/poisson_distribution.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.random_number_generator_hpp">Header <boost/random/random_number_generator.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.ranlux_hpp">Header <boost/random/ranlux.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.shuffle_output_hpp">Header <boost/random/shuffle_output.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.subtract_with_carry_hpp">Header <boost/random/subtract_with_carry.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.triangle_distribution_hpp">Header <boost/random/triangle_distribution.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.uniform_01_hpp">Header <boost/random/uniform_01.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.uniform_int_hpp">Header <boost/random/uniform_int.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.uniform_on_sphere_hpp">Header <boost/random/uniform_on_sphere.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.uniform_real_hpp">Header <boost/random/uniform_real.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.uniform_smallint_hpp">Header <boost/random/uniform_smallint.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.variate_generator_hpp">Header <boost/random/variate_generator.hpp></a></span></dt> |
| <dt><span class="section"><a href="reference.html#header.boost.random.xor_combine_hpp">Header <boost/random/xor_combine.hpp></a></span></dt> |
| </dl></div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="header.boost.nondet_random_hpp"></a>Header <<a href="../../../boost/nondet_random.hpp" target="_top">boost/nondet_random.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">class</span> <a class="link" href="../boost/random_device.html" title="Class random_device">random_device</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_hpp"></a>Header <<a href="../../../boost/random.hpp" target="_top">boost/random.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">typedef</span> <a class="link" href="../boost/random/xor_combine.html" title="Class template xor_combine">random::xor_combine</a><span class="special"><</span> <a class="link" href="../boost/random/xor_combine.html" title="Class template xor_combine">random::xor_combine</a><span class="special"><</span> <a class="link" href="../boost/random/linear_feedback_shift.html" title="Class template linear_feedback_shift">random::linear_feedback_shift</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="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_feedback_shift.html" title="Class template linear_feedback_shift">random::linear_feedback_shift</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="number">0</span> <span class="special">></span><span class="special">,</span> <span class="number">0</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_feedback_shift.html" title="Class template linear_feedback_shift">random::linear_feedback_shift</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="number">0</span> <span class="special">></span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">0</span> <span class="special">></span> <a class="link" href="../boost/taus88.html" title="Type definition taus88"><span class="identifier">taus88</span></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.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">typedef</span> <a class="link" href="../boost/random/additive_combine.html" title="Class template additive_combine">random::additive_combine</a><span class="special"><</span> <a class="link" href="../boost/random/linear_congruential.html" title="Class template linear_congruential">random::linear_congruential</a><span class="special"><</span> <span class="identifier">int32_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="number">0</span> <span class="special">></span><span class="special">,</span> <a class="link" href="../boost/random/linear_congruential.html" title="Class template linear_congruential">random::linear_congruential</a><span class="special"><</span> <span class="identifier">int32_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> <span class="number">0</span> <span class="special">></span><span class="special">,</span> <span class="number">2060321752</span> <span class="special">></span> <a class="link" href="../boost/ecuyer1988.html" title="Type definition ecuyer1988"><span class="identifier">ecuyer1988</span></a><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">typename</span> <span class="identifier">MLCG1</span><span class="special">::</span><span class="identifier">result_type</span> val<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/additive_combine.html" title="Class template additive_combine">additive_combine</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">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/bernoulli_distribution.html" title="Class template bernoulli_distribution">bernoulli_distribution</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.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">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/binomial_distribution.html" title="Class template binomial_distribution">binomial_distribution</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.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">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/cauchy_distribution.html" title="Class template cauchy_distribution">cauchy_distribution</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.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="keyword">unsigned</span> <span class="keyword">int</span> p<span class="special">,</span> |
| <span class="keyword">unsigned</span> <span class="keyword">int</span> r<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/discard_block.html" title="Class template discard_block">discard_block</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">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/exponential_distribution.html" title="Class template exponential_distribution">exponential_distribution</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.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">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/gamma_distribution.html" title="Class template gamma_distribution">gamma_distribution</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.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">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/geometric_distribution.html" title="Class template geometric_distribution">geometric_distribution</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.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">typedef</span> <a class="link" href="../boost/random/inversive_congruential.html" title="Class template inversive_congruential">random::inversive_congruential</a><span class="special"><</span> <span class="identifier">int32_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> <span class="number">0</span> <span class="special">></span> <a class="link" href="../boost/hellekalek1995.html" title="Type definition hellekalek1995"><span class="identifier">hellekalek1995</span></a><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="identifier">IntType</span> val<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/inversive_congruential.html" title="Class template inversive_congruential">inversive_congruential</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">typedef</span> <a class="link" href="../boost/random/lagged_fibonacci_01.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/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.html" title="Class template lagged_fibonacci_01">random::lagged_fibonacci_01</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/lagged_fibonacci44497.html" title="Type definition lagged_fibonacci44497"><span class="identifier">lagged_fibonacci44497</span></a><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">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="identifier">UIntType</span> val <span class="special">=</span> <span class="number">0</span><span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/lagged_fibonacci.html" title="Class template lagged_fibonacci">lagged_fibonacci</a><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.html" title="Class template lagged_fibonacci_01">lagged_fibonacci_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.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">class</span> <a class="link" href="../boost/rand48.html" title="Class rand48">rand48</a><span class="special">;</span> |
| <span class="keyword">typedef</span> <a class="link" href="../boost/random/linear_congruential.html" title="Class template linear_congruential">random::linear_congruential</a><span class="special"><</span> <span class="identifier">int32_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> <span class="number">1043618065</span> <span class="special">></span> <a class="link" href="../boost/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.html" title="Class template linear_congruential">random::linear_congruential</a><span class="special"><</span> <span class="identifier">int32_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> <span class="number">399268537</span> <span class="special">></span> <a class="link" href="../boost/minstd_rand.html" title="Type definition minstd_rand"><span class="identifier">minstd_rand</span></a><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="identifier">IntType</span> val<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/linear_congruential.html" title="Class template linear_congruential">linear_congruential</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="identifier">UIntType</span> val<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/linear_feedback_shift.html" title="Class template linear_feedback_shift">linear_feedback_shift</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">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/lognormal_distribution.html" title="Class template lognormal_distribution">lognormal_distribution</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.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"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> |
| <span class="keyword">typedef</span> <a class="link" href="../boost/random/mersenne_twister.html" title="Class template mersenne_twister">random::mersenne_twister</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">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">0xa37d3c92</span> <span class="special">></span> <a class="link" href="../boost/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.html" title="Class template mersenne_twister">random::mersenne_twister</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">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">3346425566U</span> <span class="special">></span> <a class="link" href="../boost/mt19937.html" title="Type definition mt19937"><span class="identifier">mt19937</span></a><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> n<span class="special">,</span> <span class="keyword">int</span> m<span class="special">,</span> <span class="keyword">int</span> r<span class="special">,</span> <span class="identifier">UIntType</span> a<span class="special">,</span> <span class="keyword">int</span> u<span class="special">,</span> |
| <span class="keyword">int</span> s<span class="special">,</span> <span class="identifier">UIntType</span> b<span class="special">,</span> <span class="keyword">int</span> t<span class="special">,</span> <span class="identifier">UIntType</span> c<span class="special">,</span> <span class="keyword">int</span> l<span class="special">,</span> <span class="identifier">UIntType</span> val<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/mersenne_twister.html" title="Class template mersenne_twister">mersenne_twister</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">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/normal_distribution.html" title="Class template normal_distribution">normal_distribution</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.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">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/poisson_distribution.html" title="Class template poisson_distribution">poisson_distribution</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.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">template</span><span class="special"><</span><span class="keyword">typename</span> UniformRandomNumberGenerator<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_number_generator.html" title="Class template random_number_generator">random_number_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.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">typedef</span> <a class="link" href="../boost/random/discard_block.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base">random::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/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.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base">random::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/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.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base_01">random::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/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.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux_base_01">random::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/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.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base_01">random::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/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.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base_01">random::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/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/discard_block.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base">random::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/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.html" title="Class template discard_block">random::discard_block</a><span class="special"><</span> <a class="link" href="reference.html#boost.random.ranlux64_base">random::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/ranlux64_4.html" title="Type definition ranlux64_4"><span class="identifier">ranlux64_4</span></a><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.html" title="Class template subtract_with_carry">subtract_with_carry</a><span class="special"><</span> <span class="keyword">int</span><span class="special">,</span><span class="special">(</span><span class="number">1</span><span class="special"><<</span> <span class="number">24</span><span class="special">)</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span><span class="special">,</span> <span class="number">0</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/subtract_with_carry_01.html" title="Class template subtract_with_carry_01">subtract_with_carry_01</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/subtract_with_carry_01.html" title="Class template subtract_with_carry_01">subtract_with_carry_01</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/subtract_with_carry.html" title="Class template subtract_with_carry">random::subtract_with_carry</a><span class="special"><</span> <span class="identifier">int64_t</span><span class="special">,</span><span class="special">(</span><span class="identifier">int64_t</span><span class="special">(</span><span class="number">1</span><span class="special">)</span><span class="special"><<</span> <span class="number">48</span><span class="special">)</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">24</span><span class="special">,</span> <span class="number">0</span> <span class="special">></span> <a name="boost.random.ranlux64_base"></a><span class="identifier">ranlux64_base</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.shuffle_output_hpp"></a>Header <<a href="../../../boost/random/shuffle_output.hpp" target="_top">boost/random/shuffle_output.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">typedef</span> <a class="link" href="../boost/random/shuffle_output.html" title="Class template shuffle_output">random::shuffle_output</a><span class="special"><</span> <a class="link" href="../boost/random/linear_congruential.html" title="Class template linear_congruential">random::linear_congruential</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="number">0</span> <span class="special">></span><span class="special">,</span> <span class="number">97</span><span class="special">,</span> <span class="number">139726</span> <span class="special">></span> <a class="link" href="../boost/kreutzer1986.html" title="Type definition kreutzer1986"><span class="identifier">kreutzer1986</span></a><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="keyword">int</span> k<span class="special">,</span> |
| <span class="keyword">typename</span> <span class="identifier">UniformRandomNumberGenerator</span><span class="special">::</span><span class="identifier">result_type</span> val <span class="special">=</span> <span class="number">0</span><span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/shuffle_output.html" title="Class template shuffle_output">shuffle_output</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> IntType<span class="special">,</span> <span class="identifier">IntType</span> m<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> s<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> r<span class="special">,</span> |
| <span class="identifier">IntType</span> val<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/subtract_with_carry.html" title="Class template subtract_with_carry">subtract_with_carry</a><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> s<span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span> r<span class="special">,</span> |
| <span class="keyword">int</span> val <span class="special">=</span> <span class="number">0</span><span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="../boost/random/subtract_with_carry_01.html" title="Class template subtract_with_carry_01">subtract_with_carry_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.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">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/triangle_distribution.html" title="Class template triangle_distribution">triangle_distribution</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.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">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/uniform_01.html" title="Class template uniform_01">uniform_01</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.uniform_int_hpp"></a>Header <<a href="../../../boost/random/uniform_int.hpp" target="_top">boost/random/uniform_int.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> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/uniform_int.html" title="Class template uniform_int">uniform_int</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.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">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/uniform_on_sphere.html" title="Class template uniform_on_sphere">uniform_on_sphere</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.uniform_real_hpp"></a>Header <<a href="../../../boost/random/uniform_real.hpp" target="_top">boost/random/uniform_real.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> RealType <span class="special">=</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">class</span> <a class="link" href="../boost/uniform_real.html" title="Class template uniform_real">uniform_real</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.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">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/uniform_smallint.html" title="Class template uniform_smallint">uniform_smallint</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.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.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.html" title="Class template xor_combine">xor_combine</a><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="special">}</span></pre> |
| </div> |
| </div> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2000 -2005 Jens Maurer, 2009 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>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
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