12 KiB
[rand.req.dist]
29 Numerics library [numerics]
29.5 Random number generation [rand]
29.5.3 Requirements [rand.req]
29.5.3.6 Random number distribution requirements [rand.req.dist]
A random number distribution (commonly shortened to distribution)d of type D is a function object returning values that are distributed according to an associated mathematical probability density functionp(z) or according to an associated discrete probability functionP(zi).
A distribution's specification identifies its associated probability functionp(z) or P(zi).
An associated probability function is typically expressed using certain externally-supplied quantities known as the parameters of the distribution.
Such distribution parameters are identified in this context by writing, for example, p(z | a,b) or P(zi|a,b), to name specific parameters, or by writing, for example, p(z |{p}) or P(zi|{p}), to denote a distribution's parameters p taken as a whole.
A class D meets the requirements of a random number distribution if the expressions shown in Table 128 are valid and have the indicated semantics, and if D and its associated types also meet all other requirements of [rand.req.dist].
In Table 128 and throughout this subclause,
T is the type named by D's associated result_type;
P is the type named by D's associated param_type;
d is a value of D, and x and y are (possibly const) values of D;
glb and lub are values of T respectively corresponding to the greatest lower bound and the least upper bound on the values potentially returned by d's operator(), as determined by the current values of d's parameters;
p is a (possibly const) value of P;
g, g1, and g2 are lvalues of a type meeting the requirements of a uniform random bit generator;
os is an lvalue of the type of some class template specialization basic_ostream<charT, traits>; and
is is an lvalue of the type of some class template specialization basic_istream<charT, traits>;
where charT and traits are constrained according to [strings] and [input.output].
Table 128 — Random number distribution requirements [tab:rand.req.dist]
| ð Expression |
Return type | Pre/post-condition | Complexity |
|---|---|---|---|
| ð D::result_type |
T | T is an arithmetic type. | |
| ð D::param_type |
P | ||
| ð D() |
Creates a distribution whose behavior is indistinguishable from that of any other newly default-constructed distribution of type D. | constant | |
| ð D(p) |
Creates a distribution whose behavior is indistinguishable from that of a distribution newly constructed directly from the values used to construct p. | same as p's construction | |
| ð d.reset() |
void | Subsequent uses of d do not depend on values produced by any engine prior to invoking reset. | constant |
| ð x.param() |
P | Returns a value p such that D(p).param() == p. | no worse than the complexity of D(p) |
| ð d.param(p) |
void | Postconditions: d.param() == p. | no worse than the complexity of D(p) |
| ð d(g) |
T | With p=d.param(), the sequence of numbers returned by successive invocations with the same object g is randomly distributed according to the associated p(z | {p}) or P(zi |
| ð d(g,p) |
T | The sequence of numbers returned by successive invocations with the same objects g and p is randomly distributed according to the associated p(z | {p}) or P(zi |
| ð x.min() |
T | Returns glb. | constant |
| ð x.max() |
T | Returns lub. | constant |
| ð x == y |
bool | This operator is an equivalence relation. Returns true if x.param() == y.param() and S1=S2, where S1 and S2 are the infinite sequences of values that would be generated, respectively, by repeated future calls to x(g1) and y(g2) whenever g1 == g2. Otherwise returns false. |
constant |
| ð x != y |
bool | !(x == y). | same as x == y. |
D shall meet theCpp17CopyConstructible (Table 32) and Cpp17CopyAssignable (Table 34) requirements.
The sequence of numbers produced by repeated invocations of d(g) shall be independent of any invocation ofos << d or of any const member function of D between any of the invocations of d(g).
If a textual representation is written using os << x and that representation is restored into the same or a different object y of the same type using is >> y, repeated invocations of y(g) shall produce the same sequence of numbers as would repeated invocations of x(g).
It is unspecified whether D::param_type is declared as a (nested) class or via a typedef.
In [rand], declarations of D::param_type are in the form of typedefs for convenience of exposition only.
P shall meet theCpp17CopyConstructible (Table 32),Cpp17CopyAssignable (Table 34), andCpp17EqualityComparable (Table 28) requirements.
For each of the constructors of D taking arguments corresponding to parameters of the distribution,P shall have a corresponding constructor subject to the same requirements and taking arguments identical in number, type, and default values.
Moreover, for each of the member functions of D that return values corresponding to parameters of the distribution,P shall have a corresponding member function with the identical name, type, and semantics.
P shall have a declaration of the formusing distribution_type = D;
On hosted implementations, the following expressions are well-formed and have the specified semantics.
os << x
Effects: Writes to os a textual representation for the parameters and the additional internal data of x.
Postconditions: The os.fmtflags and fill character are unchanged.
Result: reference to the type of os.
Returns: os.
is >> d
Preconditions: is provides a textual representation that was previously written using an os whose imbued locale and whose type's template specialization argumentscharT and traits were the same as those of is.
Effects: Restores from is the parameters and additional internal data of the lvalue d.
If bad input is encountered, ensures that d is unchanged by the operation and calls is.setstate(ios_base::failbit) (which may throw ios_base::failure ([iostate.flags])).
Postconditions: The is.fmtflags are unchanged.
Result: reference to the type of is.
Returns: is.