C++ named requirements: RandomNumberDistribution (since C++11)

A RandomNumberDistribution is a function object returning random numbers according to a probability density function p(x) or a discrete probability distribution P(xi).

[edit] Requirements

The type D satisfies RandomNumberDistribution if

D satisfies CopyConstructible
D satisfies CopyAssignable

Given

T, the type named by D::result_type
P, the type named by D::param_type, which

satisfies CopyConstructible
satisfies CopyAssignable
satisfies EqualityComparable
has a constructor taking identical arguments as each of the constructors of D that take arguments corresponding to the distribution parameters
has a member function with the identical name, type, and semantics, as every member function of D that returns a parameter of the distribution
declares a member typedef using distribution_type = D;

d, a value of type D
x and y, (possibly const) values of type D
p, a (possibly const) value of type P
g, g1, g2, lvalues of a type satisfying UniformRandomBitGenerator
os, lvalue of a specialization of std::basic_ostream
is, lvalue of a specialization of std::basic_istream

The following expressions must be valid and have their specified effects

Expression	Type	Notes	Complexity
`D::result_type`	`T`	An arithmetic type	Compile-time
`D::param_type`	`P`	Compile-time
`D()`	Creates a distribution indistinguishable from any other default-constructed `D`	Constant
`D(p)`	Creates a distribution indistinguishable from `D` constructed directly from the values used to construct `p`	Same as `p`'s construction
`d.reset()`	`void`	Resets the internal state of the distribution. The next call to `operator()` on `d` will not depend on values produced by any engine prior to `reset()`	Constant
`x.param()`	`P`	Returns `p` such that D(p).param() == p	No worse than `D(p)`
`d.param(p)`	`void`	Postcondition: d.param() == p	No worse than `D(p)`
`d(g)`	`T`	The sequence of numbers returned by successive invocations of this call with the same `g` are randomly distributed according to the distribution parametrized by `d.param()`	Amortized constant number of invocations of `g`
`d(g,p)`	`T`	The sequence of numbers returned by successive invocations of this call with the same `g` are randomly distributed according to the distribution parametrized by `p`	Amortized constant number of invocations of `g`
`x.min()`	`T`	The greatest lower bound on the values potentially returned by `x`’s `operator()`, as determined by the current values of `x`’s parameters	Constant
`x.max()`	`T`	The least upper bound on the values potentially returned by `x`’s `operator()`, as determined by the current values of `x`’s parameters	Constant
`x == y`	`bool`	Establishes an equivalence relation. Returns `true` if x.param() == y.param() and future infinite sequences of values that would be generated by repeated invocations of x(g1) and y(g2) would be equal as long as g1 == g2	Constant
`x != y`	`bool`	`!(x == y)`	Constant
`os << x`	Reference to the type of `os`	Writes a textual representation of the distribution parameters and internal state to `os`. The formatting flags and fill character of `os` are unchanged
`is >> d`	Reference to the type of `is`	Restores the distribution parameters and internal state with data read from `is`. The formatting flags of `is` are unchanged. The data must have been written using a stream with the same locale, `CharT` and `Traits` stream template parameters, otherwise the behavior is undefined. If bad input is encountered, is.setstate(std::ios::failbit) is called, which may throw std::ios_base::failure . `d` is unchanged in that case

[edit] Notes

The parameters of a distribution object may be changed either permanently, by using d.param(p) or just for the duration of a single operator() call, by using d(g,p).

Calls to const member functions of the distribution and os << d do not affect the sequence of numbers produced by repeated d(g).