# 28 Numerics library [numerics]

## 28.5 Random number generation [rand]

### 28.5.5 Random number engine adaptor class templates [rand.adapt]

#### 28.5.5.3 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 of an independent_bits_engine engine adaptor object x consists of the state e 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:
• Let and .
• With n as determined below, let , , , and .
• Let if and only if the relation holds as a result.
Otherwise let .
[Note 1:
The relation always holds.
— end note]
The transition algorithm is carried out by invoking e() as often as needed to obtain values less than and values less than .
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 += 1) { do u = e() - e.min(); while (); S = ; } for (k = ; k  ≠ n; k += 1) { do u = e() - e.min(); while (); S = ; }
namespace std { 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 ; } // 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); // equality operators friend bool operator==(const independent_bits_engine& x, const independent_bits_engine& y); // generating functions result_type operator()(); void discard(unsigned long long z); // property functions const Engine& base() const noexcept { return e; } // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const independent_bits_engine& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, independent_bits_engine& x); 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.