[rand.eng.sub] (original) (raw)

26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.3 Random number engine class templates [rand.eng]

26.6.3.3 Class template subtract_with_carry_engine [rand.eng.sub]

A subtract_with_carry_engine random number engine produces unsigned integer random numbers.

The state xof a subtract_with_carry_engine object xis of size, and consists of a sequence X of r integer values ; all subscripts applied to X are to be taken modulo r.

The state xadditionally consists of an integer c(known as the carry)whose value is either 0 or 1.

The state transitionis performed as follows:

Let .
Set to . Set c to 1 if , otherwise set c to 0.

[ Note

This algorithm corresponds to a modular linear function of the form, where b is of the form and .

— end note

]

The generation algorithmis given by , where y is the value produced as a result of advancing the engine's state as described above.

template<class UIntType, size_t w, size_t s, size_t r> class subtract_with_carry_engine { public: // types using result_type = UIntType;

// engine characteristics
static constexpr size_t word_size = w;
static constexpr size_t short_lag = s;
static constexpr size_t long_lag = r;
static constexpr result_type min() { return 0; }
static constexpr result_type max() { return ; }
static constexpr result_type default_seed = 19780503u;

// constructors and seeding functions
subtract_with_carry_engine() : subtract_with_carry_engine(default_seed) {}
explicit subtract_with_carry_engine(result_type value);
template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);
void seed(result_type value = default_seed);
template<class Sseq> void seed(Sseq& q);

// generating functions
result_type operator()();
void discard(unsigned long long z);

};

The following relations shall hold:0u < s,s < r,0 < w, andw <= numeric_limits<UIntType>::digits.

The textual representationconsists of the values of, in that order, followed by c.

explicit subtract_with_carry_engine(result_type value);

Effects: Sets the values of, in that order, as specified below.

If is then 0, sets c to 1; otherwise sets c to 0.

To set the values , first construct e, a linear_congruential_engine object, as if by the following definition:

linear_congruential_engine<result_type, 40014u,0u,2147483563u> e(value == 0u ? default_seed : value);

Then, to set each , obtain new values from successive invocations of e taken modulo .

Set to .

Complexity:Exactly invocations of e.

template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);