Class template niederreiter_base2_engine

boost::random::niederreiter_base2_engine

Synopsis

// In header: <boost/random/niederreiter_base2.hpp>

template<typename UIntType, unsigned w, 
         typename Nb2Table = default_niederreiter_base2_table> 
class niederreiter_base2_engine {
public:
  // types
  typedef UIntType result_type;

  // public member functions
  explicit niederreiter_base2_engine(std::size_t);
  std::size_t dimension() const;
  void seed();
  void seed(UIntType);
  result_type operator()();
  void discard(boost::uintmax_t);

  // public static functions
  static constexpr result_type min();
  static constexpr result_type max();

  // friend functions
  bool operator==(const niederreiter_base2_engine &, 
                  const niederreiter_base2_engine &);
  bool operator!=(const niederreiter_base2_engine &, 
                  const niederreiter_base2_engine &);
  template<typename CharT, typename Traits> 
    std::basic_ostream< CharT, Traits > & 
    operator<<(std::basic_ostream< CharT, Traits > &, 
               const niederreiter_base2_engine &);
  template<typename CharT, typename Traits> 
    std::basic_istream< CharT, Traits > & 
    operator>>(std::basic_istream< CharT, Traits > &, 
               const niederreiter_base2_engine &);
};

Description

Instantiations of class template niederreiter_base2_engine model a quasi-random number generator . The niederreiter_base2_engine uses the algorithm described in

Bratley, Fox, Niederreiter, ACM Trans. Model. Comp. Sim. 2, 195 (1992).

Important

	Important
niederreiter_base2_engine skips trivial zeroes at the start of the sequence. For example, the beginning of the 2-dimensional Niederreiter base 2 sequence in `uniform_01` distribution will look like this: 0.5, 0.5, 0.75, 0.25, 0.25, 0.75, 0.375, 0.375, 0.875, 0.875, ...

niederreiter_base2_engine skips trivial zeroes at the start of the sequence. For example, the beginning of the 2-dimensional Niederreiter base 2 sequence in uniform_01 distribution will look like this:

0.5, 0.5,
0.75, 0.25,
0.25, 0.75,
0.375, 0.375,
0.875, 0.875,
...

In the following documentation X denotes the concrete class of the template niederreiter_base2_engine returning objects of type UIntType, u and v are the values of X.

Some member functions may throw exceptions of type std::range_error. This happens when the quasi-random domain is exhausted and the generator cannot produce any more values. The length of the low discrepancy sequence is given by .

`niederreiter_base2_engine` public member functions

```
explicit niederreiter_base2_engine(std::size_t s);
```
Effects: Constructs the default s-dimensional Niederreiter base 2 quasi-random number generator.

Throws: bad_alloc, invalid_argument, range_error.
```
std::size_t dimension() const;
```
Returns: The dimension of of the quasi-random domain.

Throws: nothing.
```
void seed();
```
Throws: nothing.
Effects: Resets the quasi-random number generator state to the one given by the default construction. Equivalent to u.seed(0).

void seed(UIntType init);

Throws: range_error.

Effects: Effectively sets the quasi-random number generator state to the init-th vector in the s-dimensional quasi-random domain, where s == X::dimension().

X u, v;
for(int i = 0; i < N; ++i)
    for( std::size_t j = 0; j < u.dimension(); ++j )
        u();
v.seed(N);
assert(u() == v());

```
result_type operator()();
```
Returns: Returns a successive element of an s-dimensional (s = X::dimension()) vector at each invocation. When all elements are exhausted, X::operator() begins anew with the starting element of a subsequent s-dimensional vector.

Throws: range_error.

void discard(boost::uintmax_t z);

Effects: Advances *this state as if z consecutive X::operator() invocations were executed.

X u = v;
for(int i = 0; i < N; ++i)
    u();
v.discard(N);
assert(u() == v());

Throws: range_error.

`niederreiter_base2_engine` public static functions

```
static constexpr result_type min();
```
Returns: Tight lower bound on the set of values returned by operator().

Throws: nothing.
```
static constexpr result_type max();
```
Returns: Tight upper bound on the set of values returned by operator().

Throws: nothing.

`niederreiter_base2_engine` friend functions

bool operator==(const niederreiter_base2_engine & x, 
                const niederreiter_base2_engine & y);

Returns true if the two generators will produce identical sequences of outputs.

bool operator!=(const niederreiter_base2_engine & lhs, 
                const niederreiter_base2_engine & rhs);

Returns true if the two generators will produce different sequences of outputs.

template<typename CharT, typename Traits> 
  std::basic_ostream< CharT, Traits > & 
  operator<<(std::basic_ostream< CharT, Traits > & os, 
             const niederreiter_base2_engine & s);

Writes the textual representation of the generator to a std::ostream.

template<typename CharT, typename Traits> 
  std::basic_istream< CharT, Traits > & 
  operator>>(std::basic_istream< CharT, Traits > & is, 
             const niederreiter_base2_engine & s);

Reads the textual representation of the generator from a std::istream.

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