26 Numerics library [numerics]

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:

1. (2.1)

   Let R = e.max() - e.min() + 1 and m = ⌊ log₂ R ⌋ .

2. (2.2)

   With n as determined below, let w₀ = ⌊ w / n ⌋ , n₀ = n - w mod n , y₀ = 2^w₀ ⌊ R / 2^w₀ ⌋ , and y₁ = 2^{w₀ + 1} ⌊ R / 2^{w₀ + 1} ⌋ .

3. (2.3)

   Let n = ⌈ w / m ⌉ if and only if the relation R - y₀ ≤ ⌊ y₀ / n ⌋ holds as a result. Otherwise let n = 1 + ⌈ w / m ⌉ .

[ Note: The relation w = n₀ w₀ + (n - n₀)(w₀ + 1) always holds.  — end note ]

The transition algorithm is carried out by invoking e() as often as needed to obtain n₀ values less than y₀ + e.min() and n - n₀ values less than y₁ + 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 ≠ n0; k += 1)  {
 do u = e() - e.min(); while ( u ≥ y0 );
 S =  2w0 · S + u mod 2w0 ;
}
for (k = n0; k ≠ n; k += 1)  {
 do u = e() - e.min(); while ( u ≥ y1 );
 S =  2w0 + 1 · S + u mod 2w0 + 1 ;
}

template<class Engine, size_t w, class UIntType>
class independent_bits_engine{
public:
 // types
 typedef UIntType result_type;

 // engine characteristics
 static constexpr result_type min() { return 0; }
 static constexpr result_type max() { return 2w - 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.