# 29 Numerics library [numerics]

## 29.6 Random number generation [rand]

### 29.6.1 Requirements [rand.req]

#### 29.6.1.4 Random number engine requirements [rand.req.eng]

A random number engine (commonly shortened to engine) e of type E is a uniform random bit generator that additionally meets the requirements (e.g., for seeding and for input/output) specified in this section.

At any given time, e has a state ei for some integer i0. Upon construction, e has an initial state e0. An engine's state may be established via a constructor, a seed function, assignment, or a suitable operator>>.

E's specification shall define:

1. a)the size of E's state in multiples of the size of result_­type, given as an integral constant expression;

2. b)the transition algorithm TA by which e's state ei is advanced to its successor state ei+1; and

3. c)the generation algorithm GA by which an engine's state is mapped to a value of type result_­type.

A class E that satisfies the requirements of a uniform random bit generator also satisfies the requirements of a random number engine if the expressions shown in Table 104 are valid and have the indicated semantics, and if E also satisfies all other requirements of this section [rand.req.eng]. In that Table and throughout this section:

1. a)T is the type named by E's associated result_­type;

2. b)e is a value of E, v is an lvalue of E, x and y are (possibly const) values of E;

3. c)s is a value of T;

4. d)q is an lvalue satisfying the requirements of a seed sequence;

5. e)z is a value of type unsigned long long;

6. f)os is an lvalue of the type of some class template specialization basic_­ostream<charT, traits>; and

7. g)is is an lvalue of the type of some class template specialization basic_­istream<charT, traits>;

where charT and traits are constrained according to Clause [strings] and Clause [input.output].

Table 104 — Random number engine requirements
 Expression Return type Pre/post-condition Complexity E() Creates an engine with the same initial state as all other default-constructed engines of type E. O(size of state) E(x) Creates an engine that compares equal to x. O(size of state) E(s) Creates an engine with initial state determined by s. O(size of state) E(q)268 Creates an engine with an initial state that depends on a sequence produced by one call to q.generate. same as complexity of q.generate called on a sequence whose length is size of state e.seed() void Postconditions: e == E(). same as E() e.seed(s) void Postconditions: e == E(s). same as E(s) e.seed(q) void Postconditions: e == E(q). same as E(q) e() T Advances e's state ei to ei+1 =TA(ei) and returns GA(ei). per Table 103 e.discard(z) 269 void Advances e's state ei to ei+z by any means equivalent to z consecutive calls e(). no worse than the complexity of z consecutive calls e() x == y bool This operator is an equivalence relation. With Sx and Sy as the infinite sequences of values that would be generated by repeated future calls to x() and y(), respectively, returns true if Sx=Sy; else returns false. O(size of state) x != y bool !(x == y). O(size of state) os << x reference to the type of os With os.fmtflags set to ios_­base​::​dec|ios_­base​::​left and the fill character set to the space character, writes to os the textual representation of x's current state. In the output, adjacent numbers are separated by one or more space characters. Postconditions: The os.fmtflags and fill character are unchanged. O(size of state) is >> v reference to the type of is With is.fmtflags set to ios_­base​::​dec, sets v's state as determined by reading its textual representation from is. If bad input is encountered, ensures that v's state is unchanged by the operation and calls is.setstate(ios​::​failbit) (which may throw ios​::​failure ([iostate.flags])). If a textual representation written via os << x was subsequently read via is >> v, then x == v provided that there have been no intervening invocations of x or of v. Requires: is provides a textual representation that was previously written using an output stream whose imbued locale was the same as that of is, and whose type's template specialization arguments charT and traits were respectively the same as those of is. Postconditions: The is.fmtflags are unchanged. O(size of state)

E shall meet the requirements of CopyConstructible and CopyAssignable types. These operations shall each be of complexity no worse than O(size of state).

This constructor (as well as the subsequent corresponding seed() function) may be particularly useful to applications requiring a large number of independent random sequences.

This operation is common in user code, and can often be implemented in an engine-specific manner so as to provide significant performance improvements over an equivalent naive loop that makes z consecutive calls e().