Random Number Generators

A random number generator is an object that produces a sequence of pseudo-random values. A generator that produces values uniformly distributed within a specified range is an engine. An engine can be combined with a distribution, either by passing the engine as an argument to the distribution's operator() or by using a variate_generator, to produce values that are distributed in a manner defined by the distribution.

Most of the random number generators are templates whose parameters customize the generator. The descriptions of generators that take a type as an argument use common template parameter names to describe some of the properties of the type permitted as an actual argument type:

• IntType -- indicates a signed or unsigned integral type
• UIntType -- indicates an unsigned integral type
• RealType -- indicates a floating point type

Engines

An engine is a class or template class whose instances act as a source of random numbers uniformly distributed between a minimum and maximum value. An engine can be a simple engine or a compound engine. Every engine has the following members:

• a default constructor -- creates an engine seeded as if by calling seed().
• [added with C++11] an explicit constructor with argument result_type x0 -- creates an engine seeded as if by calling seed(x0).
• [added with C++11] an explicit constructor with argument Seed_seq& seq -- creates an engine seeded as if by calling seed(seq), where Seed_seq is a seed sequence template parameter.
• typedef numeric-type result_type -- the type returned by the generator's operator().
• result_type min() -- returns the minimum value returned by the generator's operator().
• result_type max() -- returns the maximum value returned by the generator's operator(). When result_type is an integral type this is the maximum value that can actually be returned; when result_type is a floating point type this is the smallest value greater than all values that can be returned.
• void seed() -- the seed function seeds the engine with default seed values.
• [added with C++11] void seed(result_type x0) -- the seed function seeds the engine with seed value x0.
• [added with C++11] void seed(Seed_seq& seq) -- the seed function seeds the engine with seed values from seq, where Seed_seq is a seed sequence template parameter.
• [TR1 engines only] template <class InIt> void seed(InIt& first, InIt last) -- the seed function seeds the engine with values of type unsigned long from the half-open sequence pointed to by [first, last). If the sequence is not long enough to fully initialize the engine the function stores the value last in first and throws an object of type invalid_argument.
• result_type operator()() -- returns values uniformly distributed between min() and max().
• [added with C++11] void discard(unsigned long long count) -- effectively calls operator() count times and discards each value.

In addition, every engine has a state that determines the sequence of values that will be generated by subsequent calls to operator(). The states of two objects of the same type can be compared with operator== and operator!=; if the two states compare equal the objects will generate the same sequence of values. The state of an object can be saved to a stream as a sequence of 32-bit unsigned values with the object's operator<<; the state is not changed by saving it. A saved state can be read into an object of the same type with operator>>.

A simple engine is an engine that produces random numbers directly. This library provides one class whose objects are simple engines. It also provides four class templates which can be instantiated with values that provide parameters for the algorithm they implement, and nine predefined instances of those class templates. Objects of these types are also simple engines.

A compound engine is an engine that obtains random numbers from one or more simple engines and generates a stream of uniformly distributed random numbers from those values. The library provides class templates for two compound engines.

Distributions

A distribution is a class or template class whose instances transform a stream of uniformly distributed random numbers obtained from an engine into a stream of random numbers with a particular distribution. Every distribution has the following members:

• typedef numeric-type input_type [removed with C++11] -- the type that the engine passed to operator() should return.
• typedef numeric-type result_type -- the type returned by the distribution's operator().
• void reset() -- discards any cached values, so that the result of the next call to operator() will not depend on any values obtained from the engine prior to the call.
• template <class Engine> result_type operator()(Engine& eng) -- returns values distributed in accordance with the distribution's definition, using eng as a source of uniformly distributed random values and the stored parameter package.

Beginning with C++11, every distribution also has:

• typedef unspecified-type param_type -- the package of parameters passed to operator() to generate its return value.
• A const param& constructor -- initializes the stored parameter package from its argument
• param_type param() const -- gets the stored parameter package
• void param(const param_type&) -- sets the stored parameter package from its argument
• template <class Engine> result_type operator()(Engine& eng, param_type par0) -- returns values distributed in accordance with the distribution's definition, using eng as a source of uniformly distributed random values and the parameter package par0.

A parameter package is an object that stores all the parameters needed for a distribution. It contains:

• typedef distribution-type distribution_type -- the type of its distribution.
• One or more constructors that take the same parameter lists as for the distribution constructors.
• The same parameter-access functions as the distribution.
• Equality and inequality comparison operators.

Seed Sequences

A seed sequence is a C++11 class or template class whose instances supply the initial, or seed, sequence for initializing a generator. Every seed sequence of type Seed_seq has the following members:

• typedef numeric-type result_type -- an unsigned integer type of at least 32 bits.
• Seed_seq -- creates a default seed sequence.
• Seed_seq(InIt begin, InIt end) -- creates a seed sequence initialized from the parameter sequence [begin, end).
• Seed_seq(initializer_list<result_type> ilist) -- creates a seed sequence initialized from ilist.
• void generate(RanIt begin, RanIt end) -- stores values into the iterator range [begin, end).
• size_t size() -- returns the length of the parameter sequence.
• void param(Seed_seq& dest) -- copies the parameter sequence to dest

Class seed_seq is the prototypical example of a seed sequence.