24 Numerics library [numerics]

24.7 Random number generation [rand]

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

24.7.4.3 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:

a)
Let $R = e.max() - e.min() + 1$ and $m = ⌊ log_{2} R ⌋$ .
b)
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 $y_{1} = 2^{w_{0} + 1} ⌊ R / 2^{w_{0} + 1} ⌋$ .
c)
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

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.

24 Numerics library [numerics]

24.7 Random number generation [rand]

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

24.7.4.3 Class template independent_­bits_­engine [rand.adapt.ibits]

24.7.4.3 Class template independent_bits_engine [rand.adapt.ibits]