26 Numerics library [numerics]

26.6 Random number generation [rand]

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

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 Numerics library [numerics]

26.6 Random number generation [rand]

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

26.6.5.3 Class template independent_­bits_­engine [rand.adapt.ibits]

26.6.5.3 Class template independent_bits_engine [rand.adapt.ibits]