# 29 Numerics library [numerics]

## 29.6 Random number generation [rand]

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 xi of an independent_­bits_­engine engine adaptor object x consists of the state ei 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. a)Let R=e.max() - e.min() + 1 and m=log2R.

2. b)With n as determined below, let w0=w/n, n0=nwmodn, y0=2w0R/2w0, and y1=2w0+1R/2w0+1.

3. c)Let n=w/m if and only if the relation Ry0y0/n holds as a result. Otherwise let n=1+w/m.

[Note: The relation w=n0w0+(nn0)(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 nn0 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+umod2w0;
}
for (k = n0; k≠n; k += 1)  {
do u = e() - e.min(); while (u≥y1);
S = 2w0+1⋅S+umod2w0+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 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()();