26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.5 Random number engine adaptor class templates [rand.adapt]

26.6.5.1 In general [rand.adapt.general]

Each type instantiated from a class template specified in this subclause [rand.adapt] meets the requirements of a random number engine adaptor type.

Except where specified otherwise, the complexity of each function specified in this subclause [rand.adapt] is constant.

Except where specified otherwise, no function described in this subclause [rand.adapt] throws an exception.

Every function described in this subclause [rand.adapt] that has a function parameter q of type Sseq& for a template type parameter named Sseq that is different from type seed_seq throws what and when the invocation of q.generate throws.

Descriptions are provided in this subclause [rand.adapt] only for adaptor operations that are not described in subclause [rand.req.adapt] or for operations where there is additional semantic information.

In particular, declarations for copy constructors, for copy assignment operators, for streaming operators, and for equality and inequality operators are not shown in the synopses.

Each template specified in this subclause [rand.adapt] requires one or more relationships, involving the value(s) of its non-type template parameter(s), to hold.

A program instantiating any of these templates is ill-formed if any such required relationship fails to hold.

26.6.5.2 Class template discard_block_engine [rand.adapt.disc]

A discard_block_engine random number engine adaptor produces random numbers selected from those produced by some base engine e.

The state x

_{i}

of a discard_block_engine engine adaptor object x consists of the state e

_{i}

of its base engine e and an additional integer n.

The size of the state is the size of e's state plus 1.

The transition algorithm discards all but

r > 0

values from each block of

p \geq r

values delivered by e.

The state transition is performed as follows: If

n \geq r

, advance the state of e from e

_{i}

to e

_{i + p - r}

and set n to 0.

In any case, then increment n and advance e's then-current state e

_{j}

to e

_{j + 1}

The generation algorithm yields the value returned by the last invocation of e() while advancing e's state as described above.

template<class Engine, size_t p, size_t r> class discard_block_engine { public: // types using result_type = typename Engine::result_type; // engine characteristics static constexpr size_t block_size = p; static constexpr size_t used_block = r; static constexpr result_type min() { return Engine::min(); } static constexpr result_type max() { return Engine::max(); } // constructors and seeding functions discard_block_engine(); explicit discard_block_engine(const Engine& e); explicit discard_block_engine(Engine&& e); explicit discard_block_engine(result_type s); template<class Sseq> explicit discard_block_engine(Sseq& q); void seed(); void seed(result_type s); template<class Sseq> void seed(Sseq& q); // generating functions result_type operator()(); void discard(unsigned long long z); // property functions const Engine& base() const noexcept { return e; }; private: Engine e; // exposition only int n; // exposition only };

The following relations shall hold: 0 < r and r <= p.

The textual representation consists of the textual representation of e followed by the value of n.

In addition to its behavior pursuant to subclause [rand.req.adapt], each constructor that is not a copy constructor sets n to 0.

26.6.5.3 Class template independent_bits_engine [rand.adapt.ibits]

An independent_bits_engine random number engine adaptor combines random numbers that are produced by some base engine e, so as to produce random numbers with a specified number of bits w.

The state x

_{i}

of an independent_bits_engine engine adaptor object x consists of the state e

_{i}

of its base engine e; the size of the state is the size of e's state.

The transition and generation algorithms are described in terms of the following integral constants:

(2.1)
Let $R = e.max() - e.min() + 1$ and $m = ⌊ log_{2} R ⌋$ .
(2.2)
With n as determined below, let $w_{0} = ⌊ w / n ⌋$ , $n_{0} = n - w mod n$ , $y_{0} = 2^{w_{0}} ⌊ R / 2^{w_{0}} ⌋$ , and $y_{1} = 2^{w_{0} + 1} ⌊ R / 2^{w_{0} + 1} ⌋$ .
(2.3)
Let $n = ⌈ w / m ⌉$ if and only if the relation $R - y_{0} \leq ⌊ y_{0} / n ⌋$ holds as a result.

Otherwise let $n = 1 + ⌈ w / m ⌉$ .

[Note 1:

The relation

w = n_{0} w_{0} + (n - n_{0}) (w_{0} + 1)

always holds.

— end note]

The transition algorithm is carried out by invoking e() as often as needed to obtain

n_{0}

values less than

y_{0} + e.min()

and

n - n_{0}

values less than

y_{1} + e.min()

The generation algorithm uses the values produced while advancing the state as described above to yield a quantity S obtained as if by the following algorithm: S = 0; for (k = 0;

k \neq n_{0}

; k += 1) { do u = e() - e.min(); while (

u \geq y_{0}

); S =

2^{w_{0}} \cdot S + u mod 2^{w_{0}}

; } for (k =

n_{0}

;

k \neq n

; k += 1) { do u = e() - e.min(); while (

u \geq y_{1}

); S =

2^{w_{0} + 1} \cdot S + u mod 2^{w_{0} + 1}

; }

template<class Engine, size_t w, class UIntType> class independent_bits_engine { public: // types using result_type = UIntType; // engine characteristics static constexpr result_type min() { return 0; } static constexpr result_type max() { return

2^{w} - 1

; } // constructors and seeding functions independent_bits_engine(); explicit independent_bits_engine(const Engine& e); explicit independent_bits_engine(Engine&& e); explicit independent_bits_engine(result_type s); template<class Sseq> explicit independent_bits_engine(Sseq& q); void seed(); void seed(result_type s); template<class Sseq> void seed(Sseq& q); // generating functions result_type operator()(); void discard(unsigned long long z); // property functions const Engine& base() const noexcept { return e; }; private: Engine e; // exposition only };

The following relations shall hold: 0 < w and w <= numeric_limits<result_type>::digits.

The textual representation consists of the textual representation of e.

26.6.5.4 Class template shuffle_order_engine [rand.adapt.shuf]

A shuffle_order_engine random number engine adaptor produces the same random numbers that are produced by some base engine e, but delivers them in a different sequence.

The state x

_{i}

of a shuffle_order_engine engine adaptor object x consists of the state e

_{i}

of its base engine e, an additional value Y of the type delivered by e, and an additional sequence V of k values also of the type delivered by e.

The size of the state is the size of e's state plus

k + 1

The transition algorithm permutes the values produced by e.

The state transition is performed as follows:

(2.1)
Calculate an integer $j = ⌊ \frac{k \cdot (Y - e_{min})}{e_{max} - e_{min} + 1} ⌋$ .
(2.2)
Set Y to $V_{j}$ and then set $V_{j}$ to e().

The generation algorithm yields the last value of Y produced while advancing e's state as described above.

template<class Engine, size_t k> class shuffle_order_engine { public: // types using result_type = typename Engine::result_type; // engine characteristics static constexpr size_t table_size = k; static constexpr result_type min() { return Engine::min(); } static constexpr result_type max() { return Engine::max(); } // constructors and seeding functions shuffle_order_engine(); explicit shuffle_order_engine(const Engine& e); explicit shuffle_order_engine(Engine&& e); explicit shuffle_order_engine(result_type s); template<class Sseq> explicit shuffle_order_engine(Sseq& q); void seed(); void seed(result_type s); template<class Sseq> void seed(Sseq& q); // generating functions result_type operator()(); void discard(unsigned long long z); // property functions const Engine& base() const noexcept { return e; }; private: Engine e; // exposition only result_type V[k]; // exposition only result_type Y; // exposition only };

The following relation shall hold: 0 < k.

The textual representation consists of the textual representation of e, followed by the k values of V, followed by the value of Y.

In addition to its behavior pursuant to subclause [rand.req.adapt], each constructor that is not a copy constructor initializes

V[0], \dots, V[k-1]

and Y, in that order, with values returned by successive invocations of e().

26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.5 Random number engine adaptor class templates [rand.adapt]

26.6.5.1 In general [rand.adapt.general]

26.6.5.2 Class template discard_­block_­engine [rand.adapt.disc]

26.6.5.3 Class template independent_­bits_­engine [rand.adapt.ibits]

26.6.5.4 Class template shuffle_­order_­engine [rand.adapt.shuf]

26.6.5.2 Class template discard_block_engine [rand.adapt.disc]

26.6.5.3 Class template independent_bits_engine [rand.adapt.ibits]

26.6.5.4 Class template shuffle_order_engine [rand.adapt.shuf]