boost-react-native-bundle

<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Reference</title> <link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> <link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset"> <link rel="up" href="../boost_random.html" title="Chapter 24. Boost.Random"> <link rel="prev" href="tutorial.html" title="Tutorial"> <link rel="next" href="../boost/random/additive_combine_engine.html" title="Class template additive_combine_engine"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td> <td align="center"><a href="../../../index.html">Home</a></td> <td align="center"><a href="../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="tutorial.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../boost_random.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../boost/random/additive_combine_engine.html"><img src="../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section"> <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="boost_random.reference"></a><a class="link" href="reference.html" title="Reference">Reference</a> </h2></div></div></div> <div class="toc"><dl class="toc"> <dt><a href="reference.html#boost_random.reference.concepts">Concepts</a></dt> <dt><a href="reference.html#boost_random.reference.generators">Generators</a></dt> <dt><a href="reference.html#boost_random.reference.distributions">Distributions</a></dt> <dt><a href="reference.html#headers">Headers</a></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 class="toc"> <dt><a href="reference.html#boost_random.reference.concepts.introduction">Introduction</a></dt> <dt><a href="reference.html#boost_random.reference.concepts.uniform_random_number_generator">Uniform Random Number Generator</a></dt> <dt><a href="reference.html#boost_random.reference.concepts.non_deterministic_uniform_random_number_generator">Non-deterministic Uniform Random Number Generator</a></dt> <dt><a href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator">Pseudo-Random Number Generator</a></dt> <dt><a href="reference.html#boost_random.reference.concepts.seed_sequence">Seed Sequence</a></dt> <dt><a href="reference.html#boost_random.reference.concepts.random_distribution">Random Distribution</a></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> Random numbers are required in a number of different problem domains, such as <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> <li class="listitem"> numerics (simulation, Monte-Carlo integration) </li> <li class="listitem"> games (non-deterministic enemy behavior) </li> <li class="listitem"> security (key generation) </li> <li class="listitem"> testing (random coverage in white-box tests) </li> </ul></div> 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 <div class="blockquote"><blockquote class="blockquote"> "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 </blockquote></div> Depending on the requirements of the problem domain, different variations of random number generators are appropriate: <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> <li class="listitem"> non-deterministic random number generator </li> <li class="listitem"> pseudo-random number generator </li> <li class="listitem"> quasi-random number generator </li> </ul></div> All variations have some properties in common, the concepts (in the STL sense) is called <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a>. This concept will be defined in a subsequent section. The goals for this library are the following: <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> <li class="listitem"> allow easy integration of third-party random-number generators </li> <li class="listitem"> provide easy-to-use front-end classes which model popular distributions </li> <li class="listitem"> provide maximum efficiency </li> </ul></div> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="boost_random.reference.concepts.uniform_random_number_generator"></a><a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">Uniform Random Number Generator</a> </h4></div></div></div> A uniform random number generator provides a sequence of random numbers uniformly distributed on a given range. The range can be compile-time fixed or available (only) after run-time construction of the object. The tight lower bound of some (finite) set S is the (unique) member l in S, so that for all v in S, l <= v holds. Likewise, the tight upper bound of some (finite) set S is the (unique) member u in S, so that for all v in S, v <= u holds. In the following table, X denotes a number generator class returning objects of type T, and v is a const value of X. <div class="table"> <a name="boost_random.reference.concepts.uniform_random_number_generator.uniformrandomnumbergenerator_requirements"></a>Table 24.1. UniformRandomNumberGenerator requirements <div class="table-contents"><table class="table" summary="UniformRandomNumberGenerator requirements"> <colgroup> <col> <col> <col> </colgroup> <thead><tr> <th> expression </th> <th> return type </th> <th> pre/post-condition </th> </tr></thead> <tbody> <tr> <td> <code class="computeroutput">X::result_type</code> </td> <td> <code class="computeroutput">T</code> </td> <td> <code class="computeroutput">std::numeric_limits<T>::is_specialized</code> is <code class="computeroutput">true</code>, <code class="computeroutput">T</code> is <a href="../../../doc/html/LessThanComparable.html" target="_top">LessThanComparable</a> </td> </tr> <tr> <td> <code class="computeroutput">u.operator()()</code> </td> <td> <code class="computeroutput">T</code> </td> <td> - </td> </tr> <tr> <td> <code class="computeroutput">v.min()</code> </td> <td> <code class="computeroutput">T</code> </td> <td> tight lower bound on the set of all values returned by <code class="computeroutput">operator()</code>. The return value of this function shall not change during the lifetime of the object. </td> </tr> <tr> <td> <code class="computeroutput">v.max()</code> </td> <td> <code class="computeroutput">T</code> </td> <td> if <code class="computeroutput">std::numeric_limits<T>::is_integer</code>, tight upper bound on the set of all values returned by <code class="computeroutput">operator()</code>, otherwise, the smallest representable number larger than the tight upper bound on the set of all values returned by <code class="computeroutput">operator()</code>. In any case, the return value of this function shall not change during the lifetime of the object. </td> </tr> </tbody> </table></div> </div> The member functions <code class="computeroutput">min</code>, <code class="computeroutput">max</code>, and <code class="computeroutput">operator()</code> shall have amortized constant time complexity. <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"> For integer generators (i.e. integer <code class="computeroutput">T</code>), the generated values <code class="computeroutput">x</code> fulfill <code class="computeroutput">min() <= x <= max()</code>, for non-integer generators (i.e. non-integer <code class="computeroutput">T</code>), the generated values <code class="computeroutput">x</code> fulfill <code class="computeroutput">min() <= x < max()</code>. 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. 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. </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"> 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">operator()(long)</code> and thus it does not fulfill the <code class="computeroutput">RandomNumberGenerator</code> (std:25.2.11 [lib.alg.random.shuffle]) requirements. Use the <code class="computeroutput"><a class="link" href="../boost/random/random_number_generator.html" title="Class template random_number_generator">random_number_generator</a></code> adapter for that. Rationale: <code class="computeroutput">operator()(long)</code> is not provided, because mapping the output of some generator with integer range to a different integer range is not trivial. </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> 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. The class <code class="computeroutput"><a class="link" href="../boost/random/random_device.html" title="Class random_device">random_device</a></code> is a model for a non-deterministic random number generator. <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"> 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. </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> A pseudo-random number generator is a <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a> which provides a deterministic sequence of pseudo-random numbers, based on some algorithm and internal state. <code class="computeroutput"><a class="link" href="../boost/random/linear_congruential_engine.html" title="Class template linear_congruential_engine">Linear congruential</a></code> and <code class="computeroutput"><a class="link" href="../boost/random/inversive_con_idp198671104.html" title="Class template inversive_congruential_engine">inversive congruential</a></code> generators are examples of such <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo-random number generators</a>. Often, these generators are very sensitive to their parameters. In order to prevent wrong implementations from being used, an external testsuite should check that the generated sequence and the validation value provided do indeed match. 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. <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"> Because the state of a pseudo-random number generator is necessarily finite, the sequence of numbers returned by the generator will loop eventually. </td></tr> </table></div> 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">X</code> denotes a pseudo-random number generator class, <code class="computeroutput">u</code> is a value of <code class="computeroutput">X</code>, <code class="computeroutput">i</code> is a value of integral type, <code class="computeroutput">s</code> is a value of a type which models <a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">SeedSeq</a>, and <code class="computeroutput">j</code> a value of type <code class="computeroutput">unsigned long long</code>. <div class="table"> <a name="boost_random.reference.concepts.pseudo_random_number_generator.pseudorandomnumbergenerator_requirements"></a>Table 24.2. PseudoRandomNumberGenerator requirements <div class="table-contents"><table class="table" summary="PseudoRandomNumberGenerator requirements"> <colgroup> <col> <col> <col> </colgroup> <thead><tr> <th> expression </th> <th> return type </th> <th> pre/post-condition </th> </tr></thead> <tbody> <tr> <td> <code class="computeroutput">X()</code> </td> <td> - </td> <td> creates a generator with a default seed. </td> </tr> <tr> <td> <code class="computeroutput">X(i)</code> </td> <td> - </td> <td> creates a generator seeding it with the integer <code class="computeroutput">i</code>. </td> </tr> <tr> <td> <code class="computeroutput">X(s)</code> </td> <td> - </td> <td> creates a generator setting its initial state from the <a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">SeedSeq</a> <code class="computeroutput">s</code>. </td> </tr> <tr> <td> <code class="computeroutput">u.seed(...)</code> </td> <td> <code class="computeroutput">void</code> </td> <td> sets the current state to be identical to the state that would be created by the corresponding constructor. </td> </tr> <tr> <td> <code class="computeroutput">u.discard(j)</code> </td> <td> <code class="computeroutput">void</code> </td> <td> Advances the generator by <code class="computeroutput">j</code> steps as if by <code class="computeroutput">j</code> calls to <code class="computeroutput">u()</code>. </td> </tr> </tbody> </table></div> </div> 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">operator==</code>. Two pseudo-random number generators are defined to be equivalent if they both return an identical sequence of numbers starting from a given state. Classes which model a pseudo-random number generator shall also model the Streamable concept, i.e. implement <code class="computeroutput">operator<<</code> and <code class="computeroutput">operator>></code>. <code class="computeroutput">operator<<</code> writes all current state of the pseudo-random number generator to the given <code class="computeroutput">ostream</code> so that <code class="computeroutput">operator>></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">locales</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. Classes which model a pseudo-random number generator should also model the <a href="../../../doc/html/CopyConstructible.html" target="_top">CopyConstructible</a> and <a href="../../../doc/html/Assignable.html" target="_top">Assignable</a> concepts. However, note that the sequences of the original and the copy are strongly correlated (in fact, they are identical), which may make them unsuitable for some problem domains. Thus, copying pseudo-random number generators is discouraged; they should always be passed by (non-const) reference. The classes <code class="computeroutput"><a class="link" href="../boost/random/rand48.html" title="Class rand48">rand48</a></code>, <code class="computeroutput"><a class="link" href="../boost/random/minstd_rand.html" title="Type definition minstd_rand">minstd_rand</a></code>, and <code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code> are models for a pseudo-random number generator. <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"> This type of random-number generator is useful for numerics, games and testing. The non-zero arguments constructor(s) and the <code class="computeroutput">seed()</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. </td></tr> </table></div> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="boost_random.reference.concepts.seed_sequence"></a><a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">Seed Sequence</a> </h4></div></div></div> A SeedSeq represents a sequence of values that can be used to set the initial state of a <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">PseudoRandomNumberGenerator</a>. <code class="computeroutput">i</code> and <code class="computeroutput">j</code> are RandomAccessIterators whose <code class="computeroutput">value_type</code> is an unsigned integer type with at least 32 bits. <div class="table"> <a name="boost_random.reference.concepts.seed_sequence.seedseq_requirements"></a>Table 24.3. SeedSeq requirements <div class="table-contents"><table class="table" summary="SeedSeq requirements"> <colgroup> <col> <col> <col> <col> </colgroup> <thead><tr> <th> expression </th> <th> return type </th> <th> pre/post-condition </th> <th> complexity </th> </tr></thead> <tbody><tr> <td> <code class="computeroutput">s.generate(i, j)</code> </td> <td> void </td> <td> stores 32-bit values to all the elements in the iterator range defined by <code class="computeroutput">i</code> and <code class="computeroutput">j</code> </td> <td> O(j - i) </td> </tr></tbody> </table></div> </div> The class <code class="computeroutput"><a class="link" href="../boost/random/seed_seq.html" title="Class seed_seq">seed_seq</a></code> and every <a class="link" href="reference.html#boost_random.reference.concepts.uniform_random_number_generator" title="Uniform Random Number Generator">UniformRandomNumberGenerator</a> provided by the library are models of <a class="link" href="reference.html#boost_random.reference.concepts.seed_sequence" title="Seed Sequence">SeedSeq</a>. </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> 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">X</code> denotes a random distribution class returning objects of type <code class="computeroutput">T</code>, <code class="computeroutput">u</code> is a value of <code class="computeroutput">X</code>, <code class="computeroutput">x</code> and <code class="computeroutput">y</code> are (possibly const) values of <code class="computeroutput">X</code>, <code class="computeroutput">P</code> is the <code class="computeroutput">param_type</code> of the distribution, <code class="computeroutput">p</code> is a value of <code class="computeroutput">P</code>, and <code class="computeroutput">e</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">U</code>. <div class="table"> <a name="boost_random.reference.concepts.random_distribution.random_distribution_requirements__in_addition_to_copyconstructible__and_assignable_"></a>Table 24.4. Random distribution requirements (in addition to CopyConstructible, and Assignable) <div class="table-contents"><table class="table" summary="Random distribution requirements (in addition to CopyConstructible, and Assignable)"> <colgroup> <col> <col> <col> <col> </colgroup> <thead><tr> <th> expression </th> <th> return type </th> <th> pre/post-condition </th> <th> complexity </th> </tr></thead> <tbody> <tr> <td> <code class="computeroutput">X::result_type</code> </td> <td> <code class="computeroutput">T</code> </td> <td> - </td> <td> compile-time </td> </tr> <tr> <td> <code class="computeroutput">X::param_type</code> </td> <td> <code class="computeroutput">P</code> </td> <td> A type that stores the parameters of the distribution, but not any of the state used to generate random variates. <code class="computeroutput">param_type</code> provides the same set of constructors and accessors as the distribution. </td> <td> compile-time </td> </tr> <tr> <td> <code class="computeroutput">X(p)</code> </td> <td> <code class="computeroutput">X</code> </td> <td> Initializes a distribution from its parameters </td> <td> O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">u.reset()</code> </td> <td> <code class="computeroutput">void</code> </td> <td> subsequent uses of <code class="computeroutput">u</code> do not depend on values produced by any engine prior to invoking <code class="computeroutput">reset</code>. </td> <td> constant </td> </tr> <tr> <td> <code class="computeroutput">u(e)</code> </td> <td> <code class="computeroutput">T</code> </td> <td> the sequence of numbers returned by successive invocations with the same object <code class="computeroutput">e</code> is randomly distributed with the probability density function of the distribution </td> <td> amortized constant number of invocations of <code class="computeroutput">e</code> </td> </tr> <tr> <td> <code class="computeroutput">u(e, p)</code> </td> <td> <code class="computeroutput">T</code> </td> <td> Equivalent to X(p)(e), but may use a different (and presumably more efficient) implementation </td> <td> amortized constant number of invocations of <code class="computeroutput">e</code> + O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">x.param()</code> </td> <td> <code class="computeroutput">P</code> </td> <td> Returns the parameters of the distribution </td> <td> O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">x.param(p)</code> </td> <td> void </td> <td> Sets the parameters of the distribution </td> <td> O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">x.min()</code> </td> <td> <code class="computeroutput">T</code> </td> <td> returns the minimum value of the distribution </td> <td> constant </td> </tr> <tr> <td> <code class="computeroutput">x.max()</code> </td> <td> <code class="computeroutput">T</code> </td> <td> returns the maximum value of the distribution </td> <td> constant </td> </tr> <tr> <td> <code class="computeroutput">x == y</code> </td> <td> <code class="computeroutput">bool</code> </td> <td> Indicates whether the two distributions will produce identical sequences of random variates if given equal generators </td> <td> O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">x != y</code> </td> <td> <code class="computeroutput">bool</code> </td> <td> <code class="computeroutput">!(x == y)</code> </td> <td> O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">os << x</code> </td> <td> <code class="computeroutput">std::ostream&</code> </td> <td> writes a textual representation for the parameters and additional internal data of the distribution <code class="computeroutput">x</code> to <code class="computeroutput">os</code>. post: The <code class="computeroutput">os.fmtflags</code> and fill character are unchanged. </td> <td> O(size of state) </td> </tr> <tr> <td> <code class="computeroutput">is >> u</code> </td> <td> <code class="computeroutput">std::istream&</code> </td> <td> restores the parameters and additional internal data of the distribution <code class="computeroutput">u</code>. pre: <code class="computeroutput">is</code> provides a textual representation that was previously written by <code class="computeroutput">operator<<</code> post: The <code class="computeroutput">is.fmtflags</code> are unchanged. </td> <td> O(size of state) </td> </tr> </tbody> </table></div> </div> Additional requirements: The sequence of numbers produced by repeated invocations of <code class="computeroutput">x(e)</code> does not change whether or not <code class="computeroutput">os << x</code> is invoked between any of the invocations <code class="computeroutput">x(e)</code>. If a textual representation is written using <code class="computeroutput">os << x</code> and that representation is restored into the same or a different object <code class="computeroutput">y</code> of the same type using <code class="computeroutput">is >> y</code>, repeated invocations of <code class="computeroutput">y(e)</code> produce the same sequence of random numbers as would repeated invocations of <code class="computeroutput">x(e)</code>. </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> This library provides several <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" ti